diff --git a/.gitattributes b/.gitattributes
index bb8a2680ea742680ec16c434879f5a20fb2bdd38..722488bca9ec175937846abe85e8bbdbdbabbe1e 100644
--- a/.gitattributes
+++ b/.gitattributes
@@ -154,3 +154,7 @@ etE2T4oBgHgl3EQfGgZ8/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -tex
 9tAyT4oBgHgl3EQfqPjX/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
 n9E5T4oBgHgl3EQfjw-t/content/2301.05658v1.pdf filter=lfs diff=lfs merge=lfs -text
 o9FMT4oBgHgl3EQf7jFB/content/2301.12464v1.pdf filter=lfs diff=lfs merge=lfs -text
+W9FQT4oBgHgl3EQfcjYS/content/2301.13327v1.pdf filter=lfs diff=lfs merge=lfs -text
+H9AyT4oBgHgl3EQfrvmy/content/2301.00567v1.pdf filter=lfs diff=lfs merge=lfs -text
+OtFKT4oBgHgl3EQffy6V/content/2301.11831v1.pdf filter=lfs diff=lfs merge=lfs -text
+QNE0T4oBgHgl3EQfkQEN/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text
diff --git a/3dFRT4oBgHgl3EQfoTds/content/tmp_files/2301.13608v1.pdf.txt b/3dFRT4oBgHgl3EQfoTds/content/tmp_files/2301.13608v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3c182c157178179a772a2440c1434fb1fbda0395
--- /dev/null
+++ b/3dFRT4oBgHgl3EQfoTds/content/tmp_files/2301.13608v1.pdf.txt
@@ -0,0 +1,1120 @@
+arXiv:2301.13608v1  [quant-ph]  25 Jan 2023
+Orbit quantization in a retarded harmonic oscillator
+Alvaro G. Lopez1
+1Nonlinear Dynamics, Chaos and Complex Systems Group,
+Departamento de F´ısica, Universidad Rey Juan Carlos,
+Tulip´an s/n, 28933 M´ostoles, Madrid, Spain
+(Dated: February 1, 2023)
+Abstract
+We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential
+with state-dependent time-delayed feedback. In the limit of small time-delays, we show that the
+oscillator is equivalent to a Li´enard system. This allows us to analytically predict the value of the
+first Hopf bifurcation, unleashing a self-oscillatory motion. We compute bifurcation diagrams for
+several model parameter values and analyse multistable domains in detail. Using the Lyapunov
+energy function, two well-resolved energy levels represented by two coexisting stable limit cycles
+are discerned. Further exploration of the parameter space reveals the existence of a superposition
+limit cycle, encompassing two degenerate coexisting limit cycles at the fundamental energy level.
+When the system is driven very far from equilibrium, a multiscale strange attractor displaying
+intrinsic and robust intermittency is uncovered.
+1
+
+I.
+INTRODUCTION
+The importance of time-delayed feedback has been extensively confirmed across many
+disciplines in science, ranging from mechanical physical systems [1], to chemical complex
+reactions [2], or complex biological systems, as for example cardiac oscillations [3], the prop-
+agation of impulses through the nervous system [4] or the modelling of the cell cycle [5]. Time
+delays are also inescapable to understand climate phenomena, such as El Ni˜no-Southern Os-
+cillation [6]. In epidemiology and population dynamics retardations can be crucial as well
+[7], just as much as they are in the modelling of economic cycles [8] or transmission lines
+[9]. Indeed, whenever the forces between two physical interacting bodies are mediated by a
+medium or a field, or whenever large causal chains in a network of connections are reduced
+in a model, time-delays must be present. Consequently, the existence of retardations in
+differential equations describing the evolution of dynamical systems should be taken more
+as the rule, than as the exception.
+However, this contrasts with the standard practice, where ordinary differential equations
+are much preferred for their simplicity, both from an analytical and a numerical point of view.
+Furthermore, not much attention has been dedicated to study dynamical systems where the
+the time retardation is state-dependent [10–13], specially in the field of fundamental physics.
+Recent findings in the study of extended electrodynamic bodies using the retarded Li´enard-
+Wiechert potential have shown that these particles can experience nonlinear oscillations due
+to self-forces, with a frequency similar to the “zitterbewegung” frequency [13, 14].
+The
+crucial importance of time-delay in atomic physics had initially been stressed by C. K. Raju
+[15]. Later on, the expression “Atiyah’s hypothesis” was coined, after Sir Michael Atiyah
+claimed the necessity of functional differential equations to faithfully represent the dynamics
+of microscopic bodies, in a lecture entitled “The nature of space”, which was the first annual
+Einstein Public Lecture, delivered in 2005 [16].
+By the same year, Yves Couder and his collaborators demonstrated empirically the po-
+tential of hydrodynamic quantum analogs consisting of silicone oil droplets bouncing on a
+vibrating bath to describe quantum phenomena [17, 18]. These pilot-wave mechanical sys-
+tems present striking similarities with the quantum mechanics of electromagnetically charged
+bodies, such as orbit quantization [19], diffraction and interference phenomena through slits
+[20], tunneling over barriers [21], or the entanglement of particles [22]. In mathematical
+2
+
+models where the fluid is not explicitly represented [23], these features translate into a time-
+delayed feedback arising from the self-affection of the particle through the fluid medium.
+Just as it occurs in electrodynamics, perturbations produced in the past by the particle can
+affect it at the present time, introducing memory effects that can trigger its self-propulsion
+[23].
+In the present work we demonstrate that the phase space orbits of a harmonic oscillator
+with state-dependent time-delayed feedback are quantized and organized conforming a two-
+level system. We also report new compelling dynamical phenomena, as for example the
+superposition of quantized orbits and the existence of robust intermittency. The paper is
+organized as follows. In Sec. 2 we introduce the mathematical model of our oscillator and
+explain its origin.
+Then, in Sec.
+3 we analytically bridge state-dependent time-delayed
+oscillators and Li´enard systems, proving that the periodic motion corresponds to a self-
+oscillation [24]. In the following section we show that there exist quantized orbits, which
+are well-resolved in the energy landscape given by the harmonic external potential. Secs. 4
+and 5 are dedicated to introduce two new phenomena, which might be crucial to understand
+other aspects of microscopic physics, such as the superposition of orbits and the passage
+of particles over external potential barriers. Finally, in the conclusions, we summarize the
+main results of the present work and the future perspectives, as usual.
+II.
+MODEL
+We use an apparently simple model consisting in a harmonic oscillator with linear damp-
+ing, according to Stokes’s law of dissipation [25], an external quadratic potential V (x) repre-
+senting Hooke’s law and another quadratic potential with state-dependent time-delay Q(xτ),
+where xτ ≡ x(t − τ(x)). Following traditional studies in classical electrodynamics, we bor-
+row the concept of retarded potential [26] hereafter to denote this self-excited contribution.
+Therefore, we can write our dynamical equation of motion in the form
+m¨x + µ ˙x + dV
+dx + dQ
+dxτ
+= 0,
+(1)
+where m is the mass of the oscillator and µ represents the rate of dissipation.
+This model is a simplified version of an oscillator recently encountered in the study of the
+dynamics of extended electromagnetic bodies, for which the presence of self-forces produces
+3
+
+self-oscillations through a Hopf bifurcation [13, 14].
+Thus, if desired, we can physically
+interpret to some extent this new time-delay term as the result of some complicated mass
+self-interactions in a mass-spring system, arising from the mass’ structure. A similar, though
+more sophisticated, model has been previously used in the literature to study the effect of
+state-dependence of the delay on the phenomenon of vibrational resonance [11]. In summary,
+we can mathematically express the external potential as V (x) = kx2/2 and the same holds
+for Q(xτ) = αx2
+τ/2, yielding the differential equation
+m¨x(t) + µ ˙x(t) + kx(t) + αx(t − τ(x)) = 0.
+(2)
+For convenience and without loss of generality, we shall consider m = 1, k = 1 and µ = 0.1
+hereafter. We are intending to describe the dynamics of our oscillator in the phase space
+representation, as it is traditionally done in the study of nonlinear dynamical systems,
+specially regarding mechanical and electronic oscillators. However, we notice that, rigorously
+speaking, the true phase space of our dynamical systems is infinite-dimensional, since history
+functions have to be provided to integrate the Eq. (2), instead of mere initial conditions [27].
+In the phase space (x, y) we can write the differential equation as follows
+˙x = y
+(3)
+˙y = −0.1y − x − αxτ.
+(4)
+One of the crucial issues of the present work is the nature of the function τ(x). Some
+constraints on this function to ensure that the system is well-behaved must be provided.
+For example, we want the trajectories to remain bounded in the external well for x → ±∞,
+so that the state-dependent delay decays to zero asymptotically. It is also reasonable to
+demand that the delay function τ(x) remains bounded all over its domain, guaranteeing
+that the feedback coming from the past history of the dynamics does not extend to minus
+infinity. In this manner, we bound the memory of this non-Markovian system to a finite
+domain of its temporal past. Finally, symmetry with respect to spatial reflections (x → −x)
+is also present in the original model [13]. Moreover, as we show ahead, we can exploit the
+degeneracy introduced by this symmetry to obtain intriguing new dynamical phenomena. A
+simple function that has been used in previous works is the Gaussian distribution [11], which
+accounts for these three requirements. In conclusion, we assume that τ(x) = τ0e−x2/2σ2, and
+fix σ = 1/
+√
+2 unless otherwise stated. The parameter τ0 represents the maximum value of
+4
+
+the time-delay feedback, attained at the centre of the potential well. It consitutes one of the
+two key parameters investigated in the present study.
+All things considered, we have a time-delayed nonlinear oscillator with two independent
+parameters α and τ0. Interestingly, we note that the system’s nonlinearity comes entirely
+from the retardation, since both potentials have been assumed harmonic. Even though this
+system has been designed following previous findings in electrodynamics, we would like to
+stress all the simplifications performed. Firstly, the delay in the functional differential equa-
+tion appearing in Ref. [13] depends both on the speed and the acceleration of the particle.
+Secondly, such differential equation is of the advanced type [13], since the acceleration and
+the speed appearing in the Li´enard-Wiechert potentials are retarded themselves. Unfortu-
+nately, numerical schemes to integrate advanced differential equations with state-dependent
+delays are lacking. This has motivated the authors to develop the present approximated
+model. Finally, some speed-dependent nonlinearities appearing in the dissipation term and
+also in the restoring force term have been neglected.
+They are related to the Lorentz’s
+gamma factor, which is required to comply with the principle of relativity in classical elec-
+trodynamics. Consequently, the present model remains somewhat abstract. It is not our
+purpose to rigorously fit it to any specific physical system. We just use it to illustrate some
+physical phenomena that are frequently believed to belong exclusively to the atomic realm
+of physics.
+III.
+RELATED LI´ENARD SYSTEM
+Given the fact that there is dissipation in the system, in the absence of retardation
+(α = 0 or τ0 = 0), it can be immediately proved using the Lyapunov energy function
+E(x, y) = (x2 + y2)/2 that the rest state at the equilibrium x = 0 is the only global stable
+fixed point of the system, which asymptotically attracts all the initial conditions in the phase
+space [28]. We recall that this function only comprises the conservative part of the energetic
+content of our dynamical system. However, when the retarded potential is activated for
+α > 0, as we increase τ0 bellow a critical value, a Hopf bifurcation appears destabilizing
+such an equilibrium point. A fundamental energy level appears with non-zero energy fluctu-
+ations, in which the system performs limit cycle oscillations. Therefore, the orbit becomes
+quantized as a consequence of the time-delayed feedback. The system becomes unstable and
+5
+
+locally active [29], performing a periodic self-oscillatory motion around the minimum of the
+square well potential. Of course, this is only possible at the expense of an energy input in
+the system, which must come from external field sources [13, 24]. Therefore, the present
+dynamical system must be regarded as as a non-equilibrium open physical system, whose
+nonlinear periodic motion can be interpreted as a cyclic thermodynamic engine [30]. Due
+to the existence of energy losses, these dynamical systems are frequently named dissipative
+structures. This contrasts to conservative dynamical systems, which are generally equipped
+with a symplectic structure [31].
+We now prove that the dynamics of the system is a self-oscillation, triggered by the well-
+known Hopf bifurcation. To compute the value of τ0 at the bifurcation point, we approximate
+this system to a Li´enard system. Expanding in Taylor series the retarded potential to second
+order yields
+x(t − τ(x)) = x(t) − τ(x) ˙x(t) + 1
+2τ 2(x)¨x(t) + O(τ 3).
+(5)
+When the time-delay is small, we can neglect the third and higher order terms, substitute
+the two leading order contributions in the Eq. 2, and obtain
+¨x + f(x) ˙x + g(x) = 0,
+(6)
+where the functions f(x) = (µ − ατ(x))/(1 + ατ 2(x)/2) and g(x) = (k + α)/(1 + ατ 2(x)/2)
+have been defined. Thus, as we can see, small retardations have two fundamental physical
+consequences. Firstly, an antidamping correction to the drag force appears to first order.
+Secondly, the inertia of the mass becomes dependent on the dynamical state through its
+evolution along the trajectory. To demonstrate that this Li´enard system with f(x) and
+g(x) as defined, fulfils the conditions required to produce the Hopf bifurcation, we appeal to
+Li´enard’s theorem. Given the importance of this theorem, we first enunciate it, so that the
+reader is aware of all the technical details [32]. For this purpose it is convenient to introduce
+the primitive function F(x) =
+� x
+0 f(s)ds, since it is alluded in the theorem, which reads
+Theorem 1 (Li´enard, 1928) Under the assumptions that the functions F(x), g(x) ∈
+C1(R) are odd, xg(x) > 0 for x ̸= 0, F(0) = 0, F ′(0) < 0 and F has one single root
+for x = a, beyond which it increases monotonically to infinity, it follows that there exists
+only one limit cycle and that it is stable.
+For a proof of the theorem we refer the reader to Ref. [33]. It is immediate to confirm
+that all the requirements for the existence of the Hopf bifurcation are accomplished. Indeed,
+6
+
+the function F fulfils F(0) = 0, has a root at a ∈ R+, and for x ≥ a we find that it
+increases monotonically towards infinity (see Fig. 1(a)). This follows from an analytical
+estimation of F(x), which can be provided by neglecting the postive term τ 2(x) ≪ 2/α in
+the denominator of f(x), yielding the function F(x) = µx −
+√
+2πατ0 erf(x/
+√
+2), with erf(x)
+the error function. It is also confirmed by the numerical solution of the integral, which has
+been computed using the trapezoidal rule. Recall, this rule works by approximating the
+region under the graph of a function as a trapezoid and calculating its area. The condition
+xg(x) > 0 is trivially verified, while the condition F ′(0) > 0 can be used to find out the value
+of the Hopf bifurcation, since F ′(0) = (µ − ατ0)/(1 + ατ 2
+0 /2), which entails that τ0 > µ/α.
+For the parameter values here considered and α = 1/2, we can approximate the value of
+the point where the Hopf bifurcation takes place to τ0 = 1/5. This analytical results holds
+nicely, as depicted in Fig. 1(b).
+In the following section we show that, as we push the
+system even further from thermodynamic equilibrium [30] by increasing the effects of the
+time-delay feedback, the oscillator undergoes further bifurcation phenomena producing a
+second quantized excited orbit, at a higher energy level.
+IV.
+ENERGY LEVELS: MULTISTABILITY
+Once we have demonstrated that the time retardation can destabilize the rest state,
+generating a fundamental energy level with zero-point fluctuations, it is worth asking if by
+posing the system even further from equilibrium, i.e. by increasing the delay feedback, orbits
+with larger amplitude representing excited energy levels can appear. For this purpose we
+have computed the bifurcation diagrams of the related maxima map of the system. As it is
+well-known, this map can be constructed by computing the local maxima of the temporal
+series. Together with its related minima map, this is the simplest general way to discretize
+the dynamics of delayed differential equations.
+We insist again that, strictly speaking,
+the phase space of retarded differential equations is infinite-dimensional.
+An alternative
+possibility is to build an embedding from the temporal series and to construct a Poincar´e
+section out of it. However, this technique it computationally more intensive and does not
+produce better insights into the dynamics of the system.
+To compute the bifurcation diagrams we have to integrate the Eq. (2). This requires
+to consider history functions [27].
+Since in the absence of time retardation the system
+7
+
+Figure 1: Hopf bifurcation. The conditions for Li´enard’s theorem are shown. (a) The function
+F for τ0 = 1 and α = 1/2. It clearly verifies F(0) = 0, F ′(0) < 0, has a single root for a ≈ 10 and
+increases monotonically without bounds thereafter. An analytical approximation using the error
+function. (b) The bifurcation diagram, with the maximum value of x along the orbit resulting
+from the numerical solution of the retarded differential (red curve), showing a Hopf bifurcation for
+the value τ0c = 0.195, very close to the analytical prediction of the related Li´enard system, which
+corresponds to τ0c = 0.2. The rest state becomes unstable beyond the critical bifurcation point,
+entailing the zero-point fluctuations of the fundamental energy level.
+is harmonic, we consider that the most natural choice of history functions are periodic
+solutions, Therefore, we take the functions x(t) = A sin(ωt + ϕ) for t < 0. Moreover, this
+choice can be used later to ascertain relevant dynamical aspects of the system under finite-
+time external periodic drivings, which can be physically interpreted as brief pulses exerted
+on the oscillator. As it is expected, external perturbations acting on the system can produce
+transitions between the energy levels.
+Because our aim is to figure out if there exists multistable parameter regimes, repre-
+sented by two or more coexisting stable limit cycles, we throw ten different initial conditions
+randomly chosen in the range A ∈ [0, 3], ω ∈ [−π, π] and ϕ ∈ [0, π]. We compute the trajec-
+tories in the temporal interval t ∈ [0, 2000] using a residual order integrator implemented in
+MATLAB. Transients as long as seven-tenths or even larger of the whole temporal series are
+8
+
+3
+Numerical
+Stable
+ Analytical approximation
+1
+2
+F
+mac
+Hopf
+0
+0
+Toc
+Unstable
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0
+10
+20
+To
+(a)
+(b)1.5 F
+1.0
+0.5
+0.0
+0.5
+0
+5
+10
+15
+20
+253
+2.5
+20.4
+0.51.5
+1
+0.5
+0
+-0.5
+0
+0.1
+0.2
+0.3Figure 2: Bifurcation diagrams (α > 0). The bifurcation diagrams of the maxima map of x are
+represented for increasing values of the maximum delay τ0. A total number of ten initial randomly
+chosen histories have been used, and depicted using two different colors to represent the asymptotic
+sets, clearly distinguishing multistable regions (green background). (a) For α = 0.5 several Hopf
+bifurcations (arrows), interrupted by an amplitude death region (AD), end in a quasiperiodic
+route to chaos.
+Multistability (MS) starts at the critical value τ0c = 6.1, when a high energy
+limit cycle (green) is born, coexisting with the fundamental energy level, which involves periodic,
+quasiperiodic or chaotic attractors (blue). (b) For α = 0.9 similar results are observed, except for
+the disappearance of the amplitude death region, and the fact that the mustilstable regions appear
+and disappear through several crises.
+discarded, since time-delayed systems usually display long transient phenomena [34]. Finally,
+we obtain the maxima map and represent these points for 1200 varying parameter values of
+the maximum time-delay in the range τ0 ∈ [0, 11]. Recalling that several conditions can lead
+to the same asymptotic limit cycle, we have coloured the bifurcations diagrams in two colors,
+to clearly distinguish the two energy levels, whenever they exist. As we can see in Fig. 2(a),
+and as detailed in the previous section, for α = 1/2, as the time-delay is increased from
+zero, a first Hopf bifurcation reveals at τ0 = 1/5. Then, if we increase further the maximum
+delay τ0, the fundamental orbit first enlarges reaching a maximum amplitude of xmax = 6.0
+for τ0 close to 2.0, then shrinks again and, finally, it disappears. This is the well-studied
+9
+
+AD
+MS
+6
+MS
+8
+6
+4
+mac
+4
+Cmac
+2
+2
+α= 0.5
+0
+α = 0.9
+0
+2
+4
+6
+8
+10
+0
+2
+4
+6
+8
+10
+To
+To
+(a)
+(b)10
+8
+6: 2. .:
+8
+104
+2
+0
+2
+0
+2
+4
+6AD
+MS
+6
+Cmac
+2
+0
+4
+6
+8
+10
+2
+To6
+58
+104
+3
+2
+0
+0
+2
+4
+6phenomena of amplitude death (AD), frequently displayed by time-delayed differential equa-
+tions [35]. However, for values beyond τ0 = 5.25 a Hopf bifurcation shows anew, which is
+now followed by a secondary Hopf bifurcation, giving rise to quasiperiodic motion. For an
+approximate critical value of the maximum time-delay τ0c = 6.1, a new periodic limit cycle
+of higher amplitude is born, rendering a multistable (MS) two-level system. The second
+quantized excited state shall persist all along the bifurcation diagram and remains periodic,
+although its amplitude shrinks as the retardation increases. Then, the fundamental energy
+level experiences further bifurcations through a quasiperiodic route to chaos [36], ending in a
+chaotic strange attractor (see Figs. 3(a) and (b)). The chaotic attractor experiences a crisis
+at approximately τ0 = 9.0, yielding two coexisting periodic limit cycles, which are depicted
+in Fig. 3(c). For α = 0.9 similar results are observed in Fig. 2(b), except for the fact that the
+amplitude death region is missing, and also the multistable regions appear and disappear
+intermittently along the bifurcation diagram through several crises. Some new interesting
+dynamical features are also discerned, as for example the coexistence of two quasiperiodic
+attractors for τ0 = 9.5. Naturally, whenever a strange attractor disappears through a cri-
+sis, transient chaos phenomena [37] can be observed, where a trajectory can spend large
+transients in the fundamental level, and then spiral away towards the first excited level.
+We now investigate if the two energy levels are well-resolved across the different energy
+shells. For this purpose, and also for aesthetic purposes, we have used a value of α = 0.9
+and τ0 = 5.87 to illustrate this two-level system. For these parameter values, we can find
+two stable symmetric degenerate coexisting orbits at the fundamental level, as shown in
+Fig. 4(a). This degeneracy is a consequence of the fact that the Eq. (2) is invariant under
+spatial reflections, and the splitting of these two orbits constitutes a typical phenomenon
+of symmetry breaking at the fundamental energy level. We recall that symmetry breaking
+is an ordinary phenomenon frequently observed in nonlinear self-excited systems [29]. In
+Fig. 4(b) we have plotted the harmonic external potential in red. We have used the Lyapunov
+energy function E(x, y) = (x2 + y2)/2 to compute the energy of the particle along the
+limit cycles [33], and numerically integrated its average value along these periodic orbits,
+using the trapezoidal rule once more. The average energy has been plotted in the energy
+diagram in dashed lines, together with the energy fluctuations that the stable quantized
+orbits experience along their periodic motions. As we can clearly appreciate, despite the
+fact that the fluctuations are substantial and the oscillator performs excursions out of shell
+10
+
+Figure 3: Multistability. Three phase space portraits along a quasiperiodic route to chaos in the
+multistable region for α = 0.5 (see first bifurcation diagram in Fig. 2). (a) Two doubly-degenerate
+quasiperiodic attractors coexist with a higher amplitude periodic limit cycle surrounding them.
+(b) The quasiperiodic attractors have merged into a single chaotic attractor as the delay increases,
+while the most exterior limit cycle has enlarged. (c) The chaotic orbit disappears through a crisis
+for even higher time-delays, yielding two coexisting periodic limit cycles of different amplitude.
+with respect the average energy, the two levels are well differentiated and they do not overlap
+in the energy diagram. Consequently, it can be safely stated that the present system displays
+quantized stable orbits at two independent energies, which can be denoted as E1 = 0.4 and
+E2 = 26.
+To conclude this section, we have also studied the basins of attraction of the system for
+this particular situation, to ascertain if there exists sensitivity to external perturbations.
+This is of crucial importance, for if an external perturbation is effected on this system,
+we may wonder which of the possible asymptotic limit cycles is attained in the end. Or,
+equivalently, we may ask about the ultimate energy of the oscillator when it is perturbed from
+the outside. In Fig. 5 we show the basins of attraction in the history subspace of periodic
+functions. We have used a resolution of 300 × 300, fixed an amplitude of A = 0.43, and
+computed trajectories until they get close enough to one of the three attractors. Depending
+on which attractor is approached, each initial history is plotted in the parameter space with
+a different color. As we can see, the basins are fractalized, what introduces unpredictability
+at all the scales of precision [38]. However, this basin does not posses the Wada property
+[27]. In general, unless infinite experimental accuracy is accessible, the best that we can say
+11
+
+4
+3
+22
+3
+41
+0
+-1
+-2
+-3
+-4
+-4
+-3
+-2
+-1
+0
+12
+1.5
+11
+1.5
+20.5
+0
+-0.5
+-1
+-1.5
+-2
+-2
+-1.5
+-1
+-0.5
+0
+0.54
+3
+21
+2
+31
+0
+-1
+-2
+-3
+-3
+-2 
+-1
+0Figure 4: Energy levels. A two-level system for α = 0.9 and τ0 = 5.87. The fundamental level E1
+is doubly degenerate, with two coexisting symmetric (under reflection) limit cycles, E1,+ and E1,−.
+(a) Limit cycles representing the quantization of orbits, with two different average energies, one
+corresponding to the fundamental level, and the other to the first and last excited level. (b) The
+harmonic potential is represented in red, while the average energy of the limit cycles is represented
+with dashed lines. In gray we can see the detour of the orbit through different energy shells. The
+fluctuations are considerable, although the two levels are well resolved.
+is that there exists some probability that the system might end in one of the two energy
+levels.
+This probability can be roughly approximated by merging the two basins of the
+respective orbits at the fundamental level, and by computing the size of the resulting basins
+of attraction in the parameter space. The fraction of volume of each basin in relation to the
+total volume in the parameter space in the region at investigation allows to introduce the
+concept of basin stability [39]. In addition, the asymptotic uncertainty can be further studied
+through the concept of basin entropy, which offers a more concise probabilistic account of
+the hidden structure of the basins [40].
+12
+
+10
+30
+E2
+E2
+6
+25
+2
+20
+E1,
+E1,+
+E
+y
+15
+-2
+10
+-6
+5
+E1
+E1,+
+-10
+0
+-6
+-4
+4
+6
+-5
+0
+5
+(b)
+aFigure 5: Unpredictability. The basins of attraction in the history space of the three stable
+attractive orbits for α = 0.9 and τ0 = 5.87.
+The two energy levels are clearly mixed in the
+phase space of initial histories, rendering the basins their fractal nature. Thus, arbitrarily small
+perturbations in the initial histories can lead to different asymptotic energy levels. (a) The basin
+of attraction for A = 0.43 and varying frequency in the phase space of the periodic histories. (b)
+A blow-up of the basins, evincing the sensitivity of the system to initial conditions, which entails
+unpredictability at all scales of precision.
+V.
+LIMIT CYCLE SUPERPOSITION
+The present section is dedicated to describe a new dynamical phenomenon that we have
+encountered for α < 0, which reminds of phenomena typically appearing in microscopic
+physics. In fact, the Eq. (2) with α < 0 resembles more exactly the electrodynamic self-
+oscillator encountered in previous works [13]. Specifically, we refer to the existence of states
+of superposition of orbits. In the present case, this corresponds to a quasiperiodic limit cycle
+encompassing two smaller symmetric degenerate limit cycles. This phenomenon can only be
+detected when the effects of the retarded potential are comparable to the magnitude of the
+external potential. Here we have selected a value of α = −0.9 to illustrate the phenomenon,
+which in absolute value is rather close to the value k = 1.
+In the first place we plot the bifurcation diagram. It has been computed following exactly
+the same recipe described in the previous section. As the reader can see in Fig. 6, for α < 0
+we cannot find a corresponding Li´enard system that experiences a Hopf bifurcation for
+13
+
+2.2
+1.8
+1.6
+1.4
+1.2
+1.4
+1.6
+1.8
+2
+2.2
+2.4
+1.2
+2.64.5
+4
+3.5
+3
+2.5
+1.5
+1
+0.5
+.5
+5Figure 6: Bifurcation diagram (α < 0). The bifurcation diagrams of the maxima map of x
+are represented for increasing values of the maximum delay τ0 and α = −0.9. A total number
+of ten initial randomly chosen histories have been used and depicted using two different colors to
+represent the asymptotic sets. A first Hopf bifurcation (arrow) appears now for τ0 = 2.4, followed
+by a Pitchfork bifurcation (green and blue branches). We can distinguish a region where limit cycle
+superposition (LCS) is detected (red background). For τ0 > 9.2 a strange attractor with robust
+intermittency (RI) appears.
+small values of the maximum time-delay τ0. This occurs because the change in the sign of α
+precludes the antidamping effect produced in the first derivative of x appearing in Eq. (6).
+However, as τ0 is further increased, again a Hopf bifurcation reveals at the approximate
+maximum delay critical value τ0c = 2.4. Thus, now, the instability occurs when the system
+is posed quite far from the original equilibrium. It must be the result of high-order terms
+in the Taylor expansion of the delayed potential, involving the jerk, the jounce and other
+derivatives of higher order. Later on, at the critical value τ0c = 2.7, a Pitchfork bifurcation
+ensues, which then transits to the chaotic regime, as we keep increasing the retardation.
+As far as we have computed, a period three orbit coexisting with the two period one orbits
+suddenly appears. As we zoom in the bifurcation diagram, we can see that these period-3
+orbits then experience a period doubling bifurcation. Nevertheless, the cascade cannot be
+clearly distinguished, since it includes very complicated dynamics with truly large chaotic
+14
+
+3
+LCS
+RI
+2
+Cmac
+0
+-1
+0
+2
+4
+6
+8
+10
+To3
+2.5
+28
+101.5
+1
+0.5
+0
+-0.5
+-1
+-1.5
+0
+2
+4
+6transients, involving heterogeneous alternating motions.
+For higher values of the maximum time-delay, around τ0 = 8.5, we can find a window
+of parameter values in the bifurcation diagram where a limit cycle superposition can be
+found. We describe this new phenomenon in detail. In this region, we have numerically
+detected at least five different coexisting limit cycles, by scrutinizing the history parameter
+space. Two of them are symmetric and have lower amplitude. They could describe a first
+fundamental level, but this time unresolved from the second, which is the one concerned
+now. For simplicity, we omit them from our analysis. Then, another two limit cycles of
+larger amplitude have also been found, which consist in two complicated period-6 stable
+symmetric degenerate orbits. By varying initial histories in the parameter space (A, ω, ϕ),
+one can find many past histories leading to any these two limit cycles, just as shown in Fig. 5
+for E1,±. But, to our surprise, we have also found a superposition limit cycle travelling along
+both limit cycles (see Figs. 7(a)). This orbit spends some time going close to one of the
+degenerate stable periodic orbits, and then switches to the other one, alternating between
+them in a regular fashion.
+The new limit set corresponds to an apparently quasiperiodic stable attractor, and it can
+also be accessed from many parameter values (A, ω, ϕ) in the parameter space chosen as
+initial histories. Since this superposition limit cycle resembles to its encompassed orbits, it
+can be numerically shown that its average energy is, although slightly below, close to the
+average energy of the other two period-6 orbits. The small difference arises because the
+superposition limit set visits regions of the phase space with lower energy (closer to the
+origin of the square well), which are not covered by the periodic trajectories. Thus, as far as
+we are concerned, we describe here for the first time a stable limit cycle that can be partly
+constructed from two smaller stable orbits, by nearly taking their union in the phase space.
+This would be impossible in a finite-dimensional dynamical system represented by some
+set of ordinary differential equations, as they are frequently used to describe conventional
+mechanical conservative systems: two orbits cannot cross in the phase space of a finite-
+dimensional continuous system.
+Of course, if we interpret the true phase space of our
+retarded oscillator as infinite-dimensional, neither they do cross here.
+To conclude our analysis, because the superposition state takes after the two encom-
+passed smaller cycles, we have computed the power spectra (see Figs. 7(b) and (c)) of the
+temporal series of the quantized periodic orbits and their superposition orbit, to ascertain
+15
+
+Figure 7: Limit cycle superposition. We can see two symmetric degenerate periodic limit cycles
+at the fundamental (red and blue orbits) level for τ0 = 8.5 and α = −0.9. Another limit cycle
+(green orbit) encompassing the previous two orbits can be appreciated. (b) Power spectra of the
+periodic orbits. (c) Power spectra of the superposition limit cycle encompassing the periodic orbits,
+where the lower frequencies (arrows) are different, rendering this attractor its quasiperiodic nature.
+the periodicity of the later. As expected, the power spectra of both orbits take after one
+another, since their average energy is similar. However, we can see that differences appear
+in the lower frequency domain of the spectrum, which render the superposition limit cycle
+quasiperiodic or, in the worst case, of a very high period, as compared to the other orbits.
+Nevertheless, without taking advantage of spectral analysis, it is really striking to see how
+this quasiperiodic orbit resembles to the underlying periodic limit cycles.
+VI.
+ROBUST INTERMITTENCY
+We now investigate an interesting dynamical phenomenon that is encountered in our
+retarded oscillator for α = −0.9 when the maximum time-delay is substantially increased
+(see Fig. 8(a)). This phenomenon consists in a multiscale strange attractor that appears
+to be robust [41] and which also exhibits intrinsic intermittency in a double sense.
+To
+understand it properly, we first show some complicated symmetric degenerate limit cycles
+16
+
+0.45
+0.4
+0.35.4
+0.50.3
+Powe
+0.2
+0.15
+0.1
+0.05
+0.1
+0.2
+0.3
+Frequency (Hz)1.5
+1
+0.5
+0
+-0.5
+-1
+-1.5
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.50.5
+0.40.4
+0.5Power
+0.3
+0.2
+0.1
+0.1
+0.2
+0.3
+Frequency (Hz)Figure 8: Multiscale limit cycles. (a) Two degenerate symmetric limit quiasiperiodic attractors
+for α = −0.9 and τ0 = 3.35. The trajectories are reminiscent of a saddle-focus projected on the
+2D phase space. (b) The magnitude of the continuous wavelet transform is represented (colorbar),
+using the analytic Morse wavelet with the symmetry parameter equal to 3 and a time-bandwidth
+product equal to 60.
+We can already appreciate in the temporal evolution of the spectrum a
+complex on-off periodic oscillatory behaviour. The inset shows the total power spectra, with a
+bimodal distribution displaying a rich frequency content.
+with two intrinsic scales. By intrinsic we mean a property that results from the structure
+of the limit cycles, and not as a consequence of some crises at a bifurcation point.
+As
+shown in Fig. 8(a), for τ0 = 3.35, this attracting orbits spiral out of the rest state and
+then are reinjected back to the limit cycle, drifting slowly towards the equilibrium point
+without oscillating at all.
+They clearly evoke a saddle-focus structure, as appearing in
+Shilnikov’s bifurcation [42], specially when embedded in a higher dimensional subspace of the
+full infinite-dimensional true phase space (see below). Their frequency spectrum is very rich,
+having two maxima and many frequencies at different scales. Interestingly, by implementing
+a continuous wavelet transform method, we can capture dynamical phenomena that is not
+displayed by conventional stationary spectral analysis. As it can be appreciated in Fig. 8(b),
+this time-multiscale method uses several time-windows, showing how the frequency spectrum
+evolves in time, and evincing the alternation in the system between oscillatory dynamics
+and low-speed silent drifts. This dynamics is somewhat reminiscent of relaxation oscillators,
+17
+
+0.20.3
+0.35
+0.40.15
+Power
+0.1
+0.05
+0.05
+0.1
+0.15
+0.2
+0.25
+Frequency (Hz)1.5
+0.50.5
+1
+1.50
+-0.5
+-1
+-1.5
+-1.5
+-1
+-0.5
+0Magnitude Scalogram
+0.7
+8
+4
+0.6
+2
+0.5
+1
+Frequency (Hz)
+0.5
+Magnitude
+0.4
+0.25
+0.125
+0.3
+0.0625
+0.2
+0.03125
+0.015625
+0.1
+0.0078125
+0
+2
+4
+6
+8
+10
+Time (mins)Figure 9: Intrinsic intermittency. (a) The two degenerate symmetric limit quiasiperiodic at-
+tractors have merged into a chaotic strange attractor in the 2D phase space. This attractor possess
+two dynamical and well differentiated scales. (b) The continuous wavelet transform is represented
+(colorbar), using again the analytic Morse wavelet with the symmetry parameter equal to 3 and
+a time-bandwidth product equal to 60. We can newly appreciate in the temporal evolution of
+the spectrum a complex behaviour that switches between two oscillatory motions with different
+amplitude. (c) The time series of x and its derivative y in the phase space. A sequence of bursts
+is clearly appreciated. Note how the trajectories can be reinserted into the attractor through two
+different arms, making the phenomenon doubly intermittent.
+although these limit cycles are way more sophisticated in the present case [43].
+For higher parameter values, as for example for τ0 = 9.5, these two complex limit cycles
+have merged into a strange chaotic attractor, as shown in Fig. 9(a). Now we find that the
+system alternates between two different states of chaotic oscillation, one with low amplitude
+18
+
+Magnitude Scalogram
+2
+1.2
+1
+0.5
+0.25
+(zH)
+0.125
+0.8
+Magnitude
+Frequency (
+0.0625
+0.6
+0.03125
+0.015625
+0.4
+0.0078125
+0.00390625
+0.2
+0.00195312
+0
+10
+20
+30
+40
+Time (mins)1.5
+1
+0.5
+0
+-0.5
+-1
+-1.5
+-2
+2
+-1.5
+-1
+-0.5
+0
+0.5
+1
+1.5
+2Figure 10: Robustness. (a) The largest Lyapunov exponent has been computed by using embed-
+ding techniques across different values of the time-delay for α = −0.9. A value of 0.05 has been
+chosen as a threshold to determine if the motion is chaotic. We see that its positive value rarely
+goes below the threshold, what entails great robustness of the attractor to parameter perturba-
+tions. (b) The attractor embedded in D = 3 dimensions, reconstructed with an embedding delay
+τ = 10. We see how it unfolds in this higher-dimensional space, so that the saddle-focus hidden
+structure is more clearly appreciated. Its projected shadow manifestly resembles the attractor in
+2D phase space.
+and another with a higher amplitude (Fig. 9(c)).
+In this sense, we can affirm that the
+system displays intermittent behaviour, switching between these two nonperiodic modes of
+oscillation. Comparing this dynamics with the dynamics along the underlying multiscale
+limit cycles previously described, we can say that the low-speed drift towards the original
+equilibrium of the system without retardation, have now become an oscillation of small
+amplitude around it.
+Note also how the system is reinjected into the domain through
+two possible routes: the lower branch and the higher branch of the residual multiscale
+attractors, rendering a second form of intermittency. Importantly, this doubly intermittent
+behavior is intrinsic to the complex heterogeneous nature of the attractor. Simply put, it
+does not require a fine-tuning of the parameter τ0, as opposed to conventional intermittency
+phenomena, which occurs close to bifurcation critical points [44]. Moreover, it can be shown
+that this chaotic attractor does not disappear as we move across the parameter space τ0.
+Thus it is robust under parameter perturbations.
+19
+
+2
+1.5
+0.5
+-0.5
+.1
+-1.5
+-2
+2.5
+-3
+2
+1
+0
+2
+1
+0
+2
+-2Fascinated by this dynamical behavior and by the fact that the attractor seems to be
+robust, in the sense that no periodic windows appear as we zoom in the bifurcation diagram
+around some value of τ0, we have computed the largest Lyapunov exponent (LLE) across a
+continuous interval of parameter values of the maximum time-delay τ0. Since MATLAB’s
+integrator does not allow to compute the LLE dynamically, we have taken advantage of
+embedology and used the entire time series. We follow a method exposed by Rosenstein et
+al. to efficiently compute the LLE from experimental time series [45]. These computations
+have been carried out using an embedding dimension of D = 3, and embedding time-delay
+for the series of τ = 10. The mean period T to compute the LLE considered can be obtained
+from spectral analysis (see Ref. [45]). We have used a value of T = 35, which is an upper
+bound obtained for many parameter values of the attractor. The time of integration has
+been considered t ∈ [0, 3000] and the maximum number of iteration for the algorithm was
+set to 1500, keeping our conservative attitude (see again Ref. [45]). The 3D embedding is
+depicted in Fig. 10(b).
+In Fig. 10(a) we can see the value of the maximum Lyapunov exponent for α = −0.9,
+starting with a periodic orbit at τ0 = 9.1, where the value of the Lyapunov exponents is very
+small or negative, as it should be for a periodic stable motion. When the chaotic attractor
+is born, a sudden jump to positive high values of the exponent is computed. We have set
+a threshold of λmax = 0.05 as the limiting value below which we cannot safely affirm that
+a sensitivity to initial histories occurs. This value is a conservative choice consistent with
+the temporal series of the periodic window, before the chaotic dynamics is triggered. As
+shown in Fig. 10(a), we have performed magnifications at several scales whenever downward
+peak fluctuations in the LLE exponent are present. The threshold limit is rarely exceeded.
+Furthermore, whenever the exponent drops bellow the value of 0.05, we have systematically
+computed bifurcation diagrams to see if the chaotic behavior vanishes. However, we have
+not found any periodic windows, and if periodic orbits exist, they coexist with the chaotic
+attractor. Thus we can conclude that the chaotic attractor is very robust in the present
+dynamical system, even though an analytical proof of robustness can not be easily provided
+in this case, as in previous works [41]. Since the intermittency arises as a consequence of the
+complicated nature of the attractor, which is robust, it is reasonable to say that, in addition
+to being intrinsic, it is robust, as well.
+20
+
+VII.
+CONCLUSIONS
+In the present work we have developed a very simple retarded oscillator with state-
+dependent delays, uncovering crucial dynamical behaviour that is frequently believed to be
+impossible in classical physics. Firstly, we have shown that orbits can be quantized in the
+phase space, producing one or more energy levels. We believe that the fact that these levels
+are produced in a finite number, as compared to having an infinite spectra of energy levels,
+is due to the fact that our delayed differential equations are not of the advanced type, as
+encountered in electrodynamics [46]. Secondly, we have found sensitivity to initial condi-
+tions in the history space, what introduces unpredictability in a simple fashion, making the
+concept of randomness redundant, in principle [47]. Are the apparent random fluctuations
+of fundamental physical systems just a byproduct of the complicated, even heterogeneous
+and high-dimensional [48], chaotic dynamics introduced by the dynamics of fields and the
+subsequent retardation effects in functional differential equations? [46]. Finally, we have
+uncovered a robust intermittency in the absence of multistable external wells, simply caused
+by the inherent multiscale nature of our chaotic system. Of course, this is possible because
+retardation introduces more dimensions in the dynamical system, ultimately approaching
+its center or slow manifold. In this respect, a deep connection between Lorenz-like chaotic
+dynamical systems and walking droplets has been recently proved [49].
+Interestingly, other related phenomena commonly attributed to the microscopic realm,
+such as tunneling through external potential barriers (or in multistable external potentials)
+can be easily demonstrated with our retarded potential by introducing an external Duffing
+potential in replacement of the harmonic well used here [50]. A similar situation occurs when
+studying the flow of electrons through potential barriers, where this paradoxical phenomenon
+becomes explained when interpreted in terms of the quantum potential, which appears in
+the Hamilton-Jacobi equation of the quantum system, and which is frequently disregarded
+when interpreting physical phenomena [51]. For a connection between retarded potentials
+and the quantum potential we refer the reader to previous works [13]. In other words, we
+are suggesting that the switch between different wells leading to an intermittent behavior
+can be interpreted in terms of the robust intermittency phenomenon. This dynamics is due
+to the nonlinear resonances that allow the particle to jump back and forth over the potential
+barrier [50].
+21
+
+Another important phenomena that might be studied with our oscillator is the existence
+of entangled states, which can be explained in terms of synchronization of oscillations [13].
+These states have already been predicted in previous works in classical electrodynamics to
+arise as a consequence of delay-coupling τi(xi, xj) and synchronization between systems of
+self-oscillating bodies. Synchronization phenomena has already found to actually produce
+entanglement in theoretical models of bouncing silicone oil droplets [22], although not with
+dynamical setups closing the locality loophole so far. Synchronization is more complicated
+for fluids, because the dissipation is higher at the scale of macroscopic fluid dynamics.
+Specially when compared to electrodynamic fields, where light travels mostly unimpeded
+when particles communicate through the electrovacuum. This can entail loopholes produced
+by the long-range correlations in the background fields [52].
+Importantly, time-delays are frequently considered constant, so that their dynamical na-
+ture is disregarded.
+Fortunately, thanks to the development of numerical methods and
+computational techniques, an increasing number of works in the literature of dynamical
+systems is being dedicated to the dynamical evolution of time-delays [53]. We have shown
+that the state-dependence of delays can produce very complicated behavior, entailing non-
+linear oscillations through the ubiquitous Hopf bifurcation, and producing counterintuitive
+new complex dynamical chaotic behavior. The connection between state-dependent time-
+delayed differential equations and Li´enard systems had been barely suggested [24]. A much
+deeper exploration has been provided here. It was certainly lacking in the literature, and
+opens forefront possibilities to study new physical nonlinear phenomena.
+In summary, we have provided new evidence in support of Raju-Atiyah’s hypothesis,
+claiming that physical phenomena in the microscopic physical realm can be understood by
+using functional differential equations to study dynamical phenomena produced by time
+retardation in non-Markovian systems. Importantly, we highlight that the dissipation and
+the time-delay, which both constitute genuine radiative phenomena, introduce an arrow of
+time in physical systems [54]. Thus perhaps the time-reversal symmetry of conservative field
+theories might be broken when oscillating and radiating solitons are formed in these fields
+[55]. Partly, the abusive neglect of delayed feedback in physics stems from the tradition of
+Newtonian mechanics, where action at a distance is artificially introduced to simplify forces
+of interaction.
+Certainly, this approximation has rendered many accurate and valuable
+results, allowing a great progress in the knowledge of many macroscopic physical systems,
+22
+
+which would have been impossible otherwise. Quite the opposite, the principle of causality
+in classical field theories produces memory effects that are always present whenever physical
+entities communicate through a background field with themselves, and among each other.
+VIII.
+ACKNOWLEDGMENT
+The author would like to thank Mattia Coccolo for valuable comments on the elaboration
+of the present manuscript, the discussion of some of its ideas and the computation of the
+basins of attraction.
+[1] Airy, G. B. (1830). On certain conditions under which perpetual motion is possible. Trans.
+Cambridge Phil. Soc. 3, 369-372.
+[2] Schell, M., Ross, J. (1986). Effects of time delay in rate processes. J. Chem. Phys. 85, 6489-
+6503.
+[3] Mackey, M. C., Glass, L. (1977). Oscillation and chaos in physiological control systems. Science
+197, 287-289.
+[4] Hansen, M., Protachevicz, P. R., Iarosz, K. C., Caldas, I. L., Batista, A. M., Macau, E. E. N.
+(2022). The effect of time delay for synchronisation suppression in neuronal networks. Chaos,
+Solitons & Fractals 164, 112690.
+[5] Ferrell Jr, J. E., Tsai, T. Y. C., Yang, Q. (2011). Modeling the cell cycle: Why do certain
+circuits oscillate? Cell 144, 874-885.
+[6] Boutle, I., Taylor, R. H., R¨omer, R. A. (2007). El Ni˜no and the delayed action oscillator. Am.
+J. Phys. 75, 15-24.
+[7] Salpeter, E. E., Salpeter, S. R. (1998). Mathematical model for the epidemiology of tuberculo-
+sis, with estimates of the reproductive number and infection-delay function. Am. J. Epidemiol.
+147, 398–406.
+[8] Kalecki, M. (1935). A macrodynamic theory of business cycles. Econometrica 3, 327-344.
+[9] Kolmanovskii, V. B., Nosov, V. R. (1986). Stability of functional differential equations (Vol.
+180). Elsevier.
+23
+
+[10] Insperger, T., St´ep´an, G. Turi, J. (2007). State-dependent delay in regenerative turning pro-
+cesses. Nonlinear Dyn. 47, 275–283.
+[11] Jeevarathinam, C., Rajasekar, S. (2015). Vibrational resonance in the Duffing oscillator with
+state-dependent time-delay. IJARPS 2, 1-8.
+[12] Mart´ınez-Llin`as, J., Porte, X., Soriano, M. et al. (2015). Dynamical properties induced by
+state-dependent delays in photonic systems. Nat. Commun. 6, 7425
+[13] L´opez, A. G. (2020). On an electrodynamic origin of quantum fluctuations. Nonlinear Dyn.
+102, 621-634.
+[14] L´opez, A. G. (2021). Stability analysis of the uniform motion of electrodynamic bodies. Phys.
+Scr. 96, 015506.
+[15] Raju, C. K. (2004). The electrodynamic 2-body problem and the origin of quantum mechanics.
+Found. Phys. 34, 937-963.
+[16] Johnson, G. W., Walker, M. E. (2006). Sir Michael Atiyah’s Einstein Lecture: “The Nature
+of Space”. Notices of the AMS 53, 674-678.
+[17] Couder, Y., Proti`ere, S., Fort, E., Boudaoud, A. (2005). Dynamical phenomena: walking and
+orbiting droplets. Nature 437, 208.
+[18] Proti`ere, S., Boudaoud, A., Couder, Y. (2006). Particle-wave association on a fluid interface.
+J. Fluid Mech. 544, 85-108.
+[19] Fort, E., Eddi, A., Boudaoud, A., Moukhtar, J., Couder, Y. (2010). Path-memory induced
+quantization of classical orbits. Proc. Natl. Acad. Sci. 107, 17515-17520.
+[20] Pucci, G., Harris, D., Faria, L., Bush, J. (2018). Walking droplets interacting with single and
+double slits. J. Fluid Mech. 835, 1136-1156.
+[21] Eddi, A., Fort, E., Moisy, F., Couder, Y. (2009). Unpredictable tunneling of a classical wave-
+particle association. Phys. Rev. Lett. 102, 240401.
+[22] Papatryfonos, K., Vervoort, L., Nachbin, A., Matthieu, L., Bush, J. W. M. (2022). Bell test
+in a classical pilot-wave system. arXiv:2208.08940 [physics.flu-dyn]
+[23] Turton S. E., Couchman, M. M. P., Bush, J. W. M. (2018). A review of theoretical modeling
+of walking droplets: toward a generalized pilot-wave framework. Chaos 28, 096111.
+[24] Jenkins, A. (2013). Self-oscillation. Phys. Rep. 525, 167-222.
+[25] Stokes, G. G. (1851). On the effect of internal friction of fluids on the motion of pendulums.
+Trans. Cambridge Philos. Soc. 9, 8–106.
+24
+
+[26] Li´enard, A. (1898). Champ ´electrique et magn´etique produit par une charge concentr´ee en un
+point et anim´ee d’un mouvement quelconque. L’´eclairage electrique 16, 5-14.
+[27] Daza, A., Wagemakers, A., Sanju´an, M.A.F. (2017). Wada property in systems with delay.
+Commun. Nonlinear Sci. Numer. Simulat. 43, 220-226.
+[28] Alligood, K. T., Sauer, T. D., Yorke, J. A. (1996). Chaos: An Introduction to Dynamical
+Systems. Springer, New York.
+[29] Mainzer, K., Chua, L. O. (2013). Local Activity Principle: the Cause of Complexity and
+Symmetry Breaking. Imperial College Press, London.
+[30] L´opez, ´A. G., Benito, F., Sabuco, J., Delgado-Bonal, A. (2022). The thermodynamic efficiency
+of the Lorenz system. arXiv:2202.07653 [cond-mat.stat-mech]
+[31] Abraham, R., Marsden, J. E. (1987). Foundations of Mechanics (Second Ed.). Addison-Wesley
+Publishing Company, Inc., Redwood City, CA.
+[32] Li´enard, A. (1928). Etude des oscillations entretenues. Revue g´en´erale de l’´electricit´e 23,
+901–912.
+[33] Perko, L. (1991). Differential Equations and Dynamical Systems (Third ed.). New York,
+Springer. pp. 254–257.
+[34] Lakshmanan, M., Senthilkumar, D. V. (2011). Dynamics of nonlinear time-delay systems.
+Springer Science & Business Media. pp. 37-41.
+[35] Ramana Reddy, D. V., Sen, A., Johnston, G. L. (1998). Time delay induced death in coupled
+limit cycle oscillators. Phys. Rev. Lett. 80, 5109.
+[36] Elhadj, Z. Sprott, J. C. (2008). A minimal 2-D quadradtic map with quasi-periodic route to
+chaos. Int. J. Bif. Chaos 18, 1567-1577.
+[37] Lai, Y. -C. and T´el, T. (2011). Transient Chaos: Complex Dynamics on Finite-Time Scales.
+Springer, New York.
+[38] Aguirre, J., Viana, R. L., and Sanju´an, M. A. F. (2009). Fractal structures in nonlinear
+dynamics. Rev. Mod. Phys. 81, 333-386.
+[39] Menck, P., Heitzig, J., Marwan, N. et al. (2013). How basin stability complements the linear-
+stability paradigm. Nature Phys. 9, 89–92.
+[40] Daza, A., Wagemakers, A., Georgeot, B. et al. (2016). Basin entropy: a new tool to analyze
+uncertainty in dynamical systems. Sci. Rep. 6, 31416.
+[41] Banerjee, S., Yorke, J. A., Grebogi, C. (1998). Robust chaos. Phys. Rev. Lett. 80, 3049.
+25
+
+[42] Shilnikov, L. P. (1967). The existence of a denumerable set of periodic motions in four-
+dimensional space in an extended neighborhood of a saddle-focus. Soviet Math. Dokl. 8, 54–58.
+[43] Van der Pol, B. (1920). A theory of the amplitude of free and forced triode vibrations. Radio
+Review 1, 701-710.
+[44] Pomeau, Y., Manneville, P. (1980). Intermittent transition to turbulence in dissipative dy-
+namical systems. Commun. Math. Phys. 74, 189–197.
+[45] Rosenstein, M. T., Collins, J. J., De Luca, C. J. (1993). A practical method for calculating
+largest Lyapunov exponents from small data sets. Phys. D: Nonlinear Phenom. 65, 117-134.
+[46] L´opez, ´A. G. (2022). The electrodynamic origin of the wave-particle duality. In: Banerjee, S.,
+Saha, A. (eds) Nonlinear Dynamics and Applications. Springer Proceedings in Complexity.
+Springer, Cham.
+[47] Sprott, J. C. (2007). A simple chaotic delay differential equation. Phys. Lett. A 366, 397-402.
+[48] Saiki, Y., Takahasi, H., Yorke, J. A. (2021). Piecewise linear maps with heterogeneous chaos.
+Nonlinearity 34, 5744.
+[49] Valani, R. N. (2022). Lorenz-like systems emerging from an integro-differential trajectory
+equation of a one-dimensional wave–particle entity. Chaos 32, 023129.
+[50] Coccolo, M., Zhu, B., Sanju´an, M.A.F. et al. (2018). Bogdanov–Takens resonance in time-
+delayed systems. Nonlinear Dyn. 91, 1939–1947.
+[51] Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of “hidden”
+variables. I. Phys. Rev. 85, 166-179.
+[52] Morgan, P. (2006). Bell inequalities for random fields. Phys. A: Math. Gen. 39, 7441.
+[53] M¨uller, D., Otto, A., Radons, G. (2018). Laminar chaos. Phys. Rev. Lett. 120, 084102.
+[54] Mackey, M. C. (1992). Time’s arrow: the origins of thermodynamic behaviour. Springer, New
+York. pp. 101-102.
+[55] Fodor, G., Forg´acs, P., Grandcl´ement, P, R´acz, I. (2006). Oscillons and quasibreathers in the
+φ4 Klein-Gordon model. Phys. Rev. D 74, 124003.
+26
+
diff --git a/3dFRT4oBgHgl3EQfoTds/content/tmp_files/load_file.txt b/3dFRT4oBgHgl3EQfoTds/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5e2e9a7ff0076db50c98451d7d1b4cd0467f24b0
--- /dev/null
+++ b/3dFRT4oBgHgl3EQfoTds/content/tmp_files/load_file.txt
@@ -0,0 +1,1002 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf,len=1001
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='13608v1  [quant-ph]  25 Jan 2023  Orbit quantization in a retarded harmonic oscillator  Alvaro G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Lopez1  1Nonlinear Dynamics, Chaos and Complex Systems Group,  Departamento de F´ısica, Universidad Rey Juan Carlos,  Tulip´an s/n, 28933 M´ostoles, Madrid, Spain  (Dated: February 1, 2023)  Abstract  We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential  with state-dependent time-delayed feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In the limit of small time-delays, we show that the  oscillator is equivalent to a Li´enard system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This allows us to analytically predict the value of the  first Hopf bifurcation, unleashing a self-oscillatory motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We compute bifurcation diagrams for  several model parameter values and analyse multistable domains in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Using the Lyapunov  energy function, two well-resolved energy levels represented by two coexisting stable limit cycles  are discerned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Further exploration of the parameter space reveals the existence of a superposition  limit cycle, encompassing two degenerate coexisting limit cycles at the fundamental energy level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  When the system is driven very far from equilibrium, a multiscale strange attractor displaying  intrinsic and robust intermittency is uncovered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  1  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  INTRODUCTION  The importance of time-delayed feedback has been extensively confirmed across many  disciplines in science, ranging from mechanical physical systems [1], to chemical complex  reactions [2], or complex biological systems, as for example cardiac oscillations [3], the prop-  agation of impulses through the nervous system [4] or the modelling of the cell cycle [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Time  delays are also inescapable to understand climate phenomena, such as El Ni˜no-Southern Os-  cillation [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In epidemiology and population dynamics retardations can be crucial as well  [7], just as much as they are in the modelling of economic cycles [8] or transmission lines  [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Indeed, whenever the forces between two physical interacting bodies are mediated by a  medium or a field, or whenever large causal chains in a network of connections are reduced  in a model, time-delays must be present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Consequently, the existence of retardations in  differential equations describing the evolution of dynamical systems should be taken more  as the rule, than as the exception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  However, this contrasts with the standard practice, where ordinary differential equations  are much preferred for their simplicity, both from an analytical and a numerical point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Furthermore, not much attention has been dedicated to study dynamical systems where the  the time retardation is state-dependent [10–13], specially in the field of fundamental physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Recent findings in the study of extended electrodynamic bodies using the retarded Li´enard-  Wiechert potential have shown that these particles can experience nonlinear oscillations due  to self-forces, with a frequency similar to the “zitterbewegung” frequency [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  The  crucial importance of time-delay in atomic physics had initially been stressed by C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Raju  [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Later on, the expression “Atiyah’s hypothesis” was coined, after Sir Michael Atiyah  claimed the necessity of functional differential equations to faithfully represent the dynamics  of microscopic bodies, in a lecture entitled “The nature of space”, which was the first annual  Einstein Public Lecture, delivered in 2005 [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  By the same year, Yves Couder and his collaborators demonstrated empirically the po-  tential of hydrodynamic quantum analogs consisting of silicone oil droplets bouncing on a  vibrating bath to describe quantum phenomena [17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' These pilot-wave mechanical sys-  tems present striking similarities with the quantum mechanics of electromagnetically charged  bodies, such as orbit quantization [19], diffraction and interference phenomena through slits  [20], tunneling over barriers [21], or the entanglement of particles [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In mathematical  2  models where the fluid is not explicitly represented [23], these features translate into a time-  delayed feedback arising from the self-affection of the particle through the fluid medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Just as it occurs in electrodynamics, perturbations produced in the past by the particle can  affect it at the present time, introducing memory effects that can trigger its self-propulsion  [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  In the present work we demonstrate that the phase space orbits of a harmonic oscillator  with state-dependent time-delayed feedback are quantized and organized conforming a two-  level system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We also report new compelling dynamical phenomena, as for example the  superposition of quantized orbits and the existence of robust intermittency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The paper is  organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 2 we introduce the mathematical model of our oscillator and  explain its origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Then, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  3 we analytically bridge state-dependent time-delayed  oscillators and Li´enard systems, proving that the periodic motion corresponds to a self-  oscillation [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In the following section we show that there exist quantized orbits, which  are well-resolved in the energy landscape given by the harmonic external potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 4  and 5 are dedicated to introduce two new phenomena, which might be crucial to understand  other aspects of microscopic physics, such as the superposition of orbits and the passage  of particles over external potential barriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Finally, in the conclusions, we summarize the  main results of the present work and the future perspectives, as usual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  MODEL  We use an apparently simple model consisting in a harmonic oscillator with linear damp-  ing, according to Stokes’s law of dissipation [25], an external quadratic potential V (x) repre-  senting Hooke’s law and another quadratic potential with state-dependent time-delay Q(xτ),  where xτ ≡ x(t − τ(x)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Following traditional studies in classical electrodynamics, we bor-  row the concept of retarded potential [26] hereafter to denote this self-excited contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Therefore, we can write our dynamical equation of motion in the form  m¨x + µ ˙x + dV  dx + dQ  dxτ  = 0,  (1)  where m is the mass of the oscillator and µ represents the rate of dissipation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  This model is a simplified version of an oscillator recently encountered in the study of the  dynamics of extended electromagnetic bodies, for which the presence of self-forces produces  3  self-oscillations through a Hopf bifurcation [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Thus, if desired, we can physically  interpret to some extent this new time-delay term as the result of some complicated mass  self-interactions in a mass-spring system, arising from the mass’ structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A similar, though  more sophisticated, model has been previously used in the literature to study the effect of  state-dependence of the delay on the phenomenon of vibrational resonance [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In summary,  we can mathematically express the external potential as V (x) = kx2/2 and the same holds  for Q(xτ) = αx2  τ/2, yielding the differential equation  m¨x(t) + µ ˙x(t) + kx(t) + αx(t − τ(x)) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  (2)  For convenience and without loss of generality, we shall consider m = 1, k = 1 and µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  hereafter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We are intending to describe the dynamics of our oscillator in the phase space  representation, as it is traditionally done in the study of nonlinear dynamical systems,  specially regarding mechanical and electronic oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' However, we notice that, rigorously  speaking, the true phase space of our dynamical systems is infinite-dimensional, since history  functions have to be provided to integrate the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2), instead of mere initial conditions [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  In the phase space (x, y) we can write the differential equation as follows  ˙x = y  (3)  ˙y = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1y − x − αxτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  (4)  One of the crucial issues of the present work is the nature of the function τ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Some  constraints on this function to ensure that the system is well-behaved must be provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  For example, we want the trajectories to remain bounded in the external well for x → ±∞,  so that the state-dependent delay decays to zero asymptotically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' It is also reasonable to  demand that the delay function τ(x) remains bounded all over its domain, guaranteeing  that the feedback coming from the past history of the dynamics does not extend to minus  infinity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In this manner, we bound the memory of this non-Markovian system to a finite  domain of its temporal past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Finally, symmetry with respect to spatial reflections (x → −x)  is also present in the original model [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Moreover, as we show ahead, we can exploit the  degeneracy introduced by this symmetry to obtain intriguing new dynamical phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A  simple function that has been used in previous works is the Gaussian distribution [11], which  accounts for these three requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In conclusion, we assume that τ(x) = τ0e−x2/2σ2, and  fix σ = 1/  √  2 unless otherwise stated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The parameter τ0 represents the maximum value of  4  the time-delay feedback, attained at the centre of the potential well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' It consitutes one of the  two key parameters investigated in the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  All things considered, we have a time-delayed nonlinear oscillator with two independent  parameters α and τ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Interestingly, we note that the system’s nonlinearity comes entirely  from the retardation, since both potentials have been assumed harmonic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Even though this  system has been designed following previous findings in electrodynamics, we would like to  stress all the simplifications performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Firstly, the delay in the functional differential equa-  tion appearing in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' [13] depends both on the speed and the acceleration of the particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Secondly, such differential equation is of the advanced type [13], since the acceleration and  the speed appearing in the Li´enard-Wiechert potentials are retarded themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Unfortu-  nately, numerical schemes to integrate advanced differential equations with state-dependent  delays are lacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This has motivated the authors to develop the present approximated  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Finally, some speed-dependent nonlinearities appearing in the dissipation term and  also in the restoring force term have been neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  They are related to the Lorentz’s  gamma factor, which is required to comply with the principle of relativity in classical elec-  trodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Consequently, the present model remains somewhat abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' It is not our  purpose to rigorously fit it to any specific physical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We just use it to illustrate some  physical phenomena that are frequently believed to belong exclusively to the atomic realm  of physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  RELATED LI´ENARD SYSTEM  Given the fact that there is dissipation in the system, in the absence of retardation  (α = 0 or τ0 = 0), it can be immediately proved using the Lyapunov energy function  E(x, y) = (x2 + y2)/2 that the rest state at the equilibrium x = 0 is the only global stable  fixed point of the system, which asymptotically attracts all the initial conditions in the phase  space [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We recall that this function only comprises the conservative part of the energetic  content of our dynamical system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' However, when the retarded potential is activated for  α > 0, as we increase τ0 bellow a critical value, a Hopf bifurcation appears destabilizing  such an equilibrium point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A fundamental energy level appears with non-zero energy fluctu-  ations, in which the system performs limit cycle oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Therefore, the orbit becomes  quantized as a consequence of the time-delayed feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The system becomes unstable and  5  locally active [29], performing a periodic self-oscillatory motion around the minimum of the  square well potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Of course, this is only possible at the expense of an energy input in  the system, which must come from external field sources [13, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Therefore, the present  dynamical system must be regarded as as a non-equilibrium open physical system, whose  nonlinear periodic motion can be interpreted as a cyclic thermodynamic engine [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Due  to the existence of energy losses, these dynamical systems are frequently named dissipative  structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This contrasts to conservative dynamical systems, which are generally equipped  with a symplectic structure [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  We now prove that the dynamics of the system is a self-oscillation, triggered by the well-  known Hopf bifurcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' To compute the value of τ0 at the bifurcation point, we approximate  this system to a Li´enard system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Expanding in Taylor series the retarded potential to second  order yields  x(t − τ(x)) = x(t) − τ(x) ˙x(t) + 1  2τ 2(x)¨x(t) + O(τ 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  (5)  When the time-delay is small, we can neglect the third and higher order terms, substitute  the two leading order contributions in the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 2, and obtain  ¨x + f(x) ˙x + g(x) = 0,  (6)  where the functions f(x) = (µ − ατ(x))/(1 + ατ 2(x)/2) and g(x) = (k + α)/(1 + ατ 2(x)/2)  have been defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Thus, as we can see, small retardations have two fundamental physical  consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Firstly, an antidamping correction to the drag force appears to first order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Secondly, the inertia of the mass becomes dependent on the dynamical state through its  evolution along the trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' To demonstrate that this Li´enard system with f(x) and  g(x) as defined, fulfils the conditions required to produce the Hopf bifurcation, we appeal to  Li´enard’s theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Given the importance of this theorem, we first enunciate it, so that the  reader is aware of all the technical details [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' For this purpose it is convenient to introduce  the primitive function F(x) =  � x  0 f(s)ds, since it is alluded in the theorem, which reads  Theorem 1 (Li´enard, 1928) Under the assumptions that the functions F(x), g(x) ∈  C1(R) are odd, xg(x) > 0 for x ̸= 0, F(0) = 0, F ′(0) < 0 and F has one single root  for x = a, beyond which it increases monotonically to infinity, it follows that there exists  only one limit cycle and that it is stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  For a proof of the theorem we refer the reader to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' It is immediate to confirm  that all the requirements for the existence of the Hopf bifurcation are accomplished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Indeed,  6  the function F fulfils F(0) = 0, has a root at a ∈ R+, and for x ≥ a we find that it  increases monotonically towards infinity (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 1(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This follows from an analytical  estimation of F(x), which can be provided by neglecting the postive term τ 2(x) ≪ 2/α in  the denominator of f(x), yielding the function F(x) = µx −  √  2πατ0 erf(x/  √  2), with erf(x)  the error function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' It is also confirmed by the numerical solution of the integral, which has  been computed using the trapezoidal rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Recall, this rule works by approximating the  region under the graph of a function as a trapezoid and calculating its area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The condition  xg(x) > 0 is trivially verified, while the condition F ′(0) > 0 can be used to find out the value  of the Hopf bifurcation, since F ′(0) = (µ − ατ0)/(1 + ατ 2  0 /2), which entails that τ0 > µ/α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  For the parameter values here considered and α = 1/2, we can approximate the value of  the point where the Hopf bifurcation takes place to τ0 = 1/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This analytical results holds  nicely, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  In the following section we show that, as we push the  system even further from thermodynamic equilibrium [30] by increasing the effects of the  time-delay feedback, the oscillator undergoes further bifurcation phenomena producing a  second quantized excited orbit, at a higher energy level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  ENERGY LEVELS: MULTISTABILITY  Once we have demonstrated that the time retardation can destabilize the rest state,  generating a fundamental energy level with zero-point fluctuations, it is worth asking if by  posing the system even further from equilibrium, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' by increasing the delay feedback, orbits  with larger amplitude representing excited energy levels can appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' For this purpose we  have computed the bifurcation diagrams of the related maxima map of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As it is  well-known, this map can be constructed by computing the local maxima of the temporal  series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Together with its related minima map, this is the simplest general way to discretize  the dynamics of delayed differential equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  We insist again that, strictly speaking,  the phase space of retarded differential equations is infinite-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  An alternative  possibility is to build an embedding from the temporal series and to construct a Poincar´e  section out of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' However, this technique it computationally more intensive and does not  produce better insights into the dynamics of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  To compute the bifurcation diagrams we have to integrate the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This requires  to consider history functions [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Since in the absence of time retardation the system  7  Figure 1: Hopf bifurcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The conditions for Li´enard’s theorem are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (a) The function  F for τ0 = 1 and α = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' It clearly verifies F(0) = 0, F ′(0) < 0, has a single root for a ≈ 10 and  increases monotonically without bounds thereafter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' An analytical approximation using the error  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (b) The bifurcation diagram, with the maximum value of x along the orbit resulting  from the numerical solution of the retarded differential (red curve), showing a Hopf bifurcation for  the value τ0c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='195, very close to the analytical prediction of the related Li´enard system, which  corresponds to τ0c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The rest state becomes unstable beyond the critical bifurcation point,  entailing the zero-point fluctuations of the fundamental energy level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  is harmonic, we consider that the most natural choice of history functions are periodic  solutions, Therefore, we take the functions x(t) = A sin(ωt + ϕ) for t < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Moreover, this  choice can be used later to ascertain relevant dynamical aspects of the system under finite-  time external periodic drivings, which can be physically interpreted as brief pulses exerted  on the oscillator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As it is expected, external perturbations acting on the system can produce  transitions between the energy levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Because our aim is to figure out if there exists multistable parameter regimes, repre-  sented by two or more coexisting stable limit cycles, we throw ten different initial conditions  randomly chosen in the range A ∈ [0, 3], ω ∈ [−π, π] and ϕ ∈ [0, π].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We compute the trajec-  tories in the temporal interval t ∈ [0, 2000] using a residual order integrator implemented in  MATLAB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Transients as long as seven-tenths or even larger of the whole temporal series are  8  3  Numerical  Stable  Analytical approximation  1  2  F  mac  Hopf  0  0  Toc  Unstable  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  10  20  To  (a)  (b)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5 F  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  5  10  15  20  253  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='3Figure 2: Bifurcation diagrams (α > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The bifurcation diagrams of the maxima map of x are  represented for increasing values of the maximum delay τ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A total number of ten initial randomly  chosen histories have been used, and depicted using two different colors to represent the asymptotic  sets, clearly distinguishing multistable regions (green background).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (a) For α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5 several Hopf  bifurcations (arrows), interrupted by an amplitude death region (AD), end in a quasiperiodic  route to chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Multistability (MS) starts at the critical value τ0c = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1, when a high energy  limit cycle (green) is born, coexisting with the fundamental energy level, which involves periodic,  quasiperiodic or chaotic attractors (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (b) For α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9 similar results are observed, except for  the disappearance of the amplitude death region, and the fact that the mustilstable regions appear  and disappear through several crises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  discarded, since time-delayed systems usually display long transient phenomena [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Finally,  we obtain the maxima map and represent these points for 1200 varying parameter values of  the maximum time-delay in the range τ0 ∈ [0, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Recalling that several conditions can lead  to the same asymptotic limit cycle, we have coloured the bifurcations diagrams in two colors,  to clearly distinguish the two energy levels, whenever they exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As we can see in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 2(a),  and as detailed in the previous section, for α = 1/2, as the time-delay is increased from  zero, a first Hopf bifurcation reveals at τ0 = 1/5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Then, if we increase further the maximum  delay τ0, the fundamental orbit first enlarges reaching a maximum amplitude of xmax = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='0  for τ0 close to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='0, then shrinks again and, finally, it disappears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This is the well-studied  9  AD  MS  6  MS  8  6  4  mac  4  Cmac  2  2  α= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9  0  2  4  6  8  10  0  2  4  6  8  10  To  To  (a)  (b)10  8  6: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' :  8  104  2  0  2  0  2  4  6AD  MS  6  Cmac  2  0  4  6  8  10  2  To6  58  104  3  2  0  0  2  4  6phenomena of amplitude death (AD), frequently displayed by time-delayed differential equa-  tions [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' However, for values beyond τ0 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='25 a Hopf bifurcation shows anew, which is  now followed by a secondary Hopf bifurcation, giving rise to quasiperiodic motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' For an  approximate critical value of the maximum time-delay τ0c = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1, a new periodic limit cycle  of higher amplitude is born, rendering a multistable (MS) two-level system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The second  quantized excited state shall persist all along the bifurcation diagram and remains periodic,  although its amplitude shrinks as the retardation increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Then, the fundamental energy  level experiences further bifurcations through a quasiperiodic route to chaos [36], ending in a  chaotic strange attractor (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 3(a) and (b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The chaotic attractor experiences a crisis  at approximately τ0 = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='0, yielding two coexisting periodic limit cycles, which are depicted  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 3(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' For α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9 similar results are observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 2(b), except for the fact that the  amplitude death region is missing, and also the multistable regions appear and disappear  intermittently along the bifurcation diagram through several crises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Some new interesting  dynamical features are also discerned, as for example the coexistence of two quasiperiodic  attractors for τ0 = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Naturally, whenever a strange attractor disappears through a cri-  sis, transient chaos phenomena [37] can be observed, where a trajectory can spend large  transients in the fundamental level, and then spiral away towards the first excited level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  We now investigate if the two energy levels are well-resolved across the different energy  shells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' For this purpose, and also for aesthetic purposes, we have used a value of α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9  and τ0 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='87 to illustrate this two-level system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' For these parameter values, we can find  two stable symmetric degenerate coexisting orbits at the fundamental level, as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 4(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This degeneracy is a consequence of the fact that the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2) is invariant under  spatial reflections, and the splitting of these two orbits constitutes a typical phenomenon  of symmetry breaking at the fundamental energy level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We recall that symmetry breaking  is an ordinary phenomenon frequently observed in nonlinear self-excited systems [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 4(b) we have plotted the harmonic external potential in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We have used the Lyapunov  energy function E(x, y) = (x2 + y2)/2 to compute the energy of the particle along the  limit cycles [33], and numerically integrated its average value along these periodic orbits,  using the trapezoidal rule once more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The average energy has been plotted in the energy  diagram in dashed lines, together with the energy fluctuations that the stable quantized  orbits experience along their periodic motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As we can clearly appreciate, despite the  fact that the fluctuations are substantial and the oscillator performs excursions out of shell  10  Figure 3: Multistability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Three phase space portraits along a quasiperiodic route to chaos in the  multistable region for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5 (see first bifurcation diagram in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (a) Two doubly-degenerate  quasiperiodic attractors coexist with a higher amplitude periodic limit cycle surrounding them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  (b) The quasiperiodic attractors have merged into a single chaotic attractor as the delay increases,  while the most exterior limit cycle has enlarged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (c) The chaotic orbit disappears through a crisis  for even higher time-delays, yielding two coexisting periodic limit cycles of different amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  with respect the average energy, the two levels are well differentiated and they do not overlap  in the energy diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Consequently, it can be safely stated that the present system displays  quantized stable orbits at two independent energies, which can be denoted as E1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4 and  E2 = 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  To conclude this section, we have also studied the basins of attraction of the system for  this particular situation, to ascertain if there exists sensitivity to external perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  This is of crucial importance, for if an external perturbation is effected on this system,  we may wonder which of the possible asymptotic limit cycles is attained in the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Or,  equivalently, we may ask about the ultimate energy of the oscillator when it is perturbed from  the outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 5 we show the basins of attraction in the history subspace of periodic  functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We have used a resolution of 300 × 300, fixed an amplitude of A = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='43, and  computed trajectories until they get close enough to one of the three attractors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Depending  on which attractor is approached, each initial history is plotted in the parameter space with  a different color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As we can see, the basins are fractalized, what introduces unpredictability  at all the scales of precision [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' However, this basin does not posses the Wada property  [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In general, unless infinite experimental accuracy is accessible, the best that we can say  11  4  3  22  3  41  0  1  2  3  4  4  3  2  1  0  12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  2  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='54  3  21  2  31  0  1  2  3  3  2  1  0Figure 4: Energy levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A two-level system for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9 and τ0 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The fundamental level E1  is doubly degenerate, with two coexisting symmetric (under reflection) limit cycles, E1,+ and E1,−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  (a) Limit cycles representing the quantization of orbits, with two different average energies, one  corresponding to the fundamental level, and the other to the first and last excited level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (b) The  harmonic potential is represented in red, while the average energy of the limit cycles is represented  with dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In gray we can see the detour of the orbit through different energy shells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The  fluctuations are considerable, although the two levels are well resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  is that there exists some probability that the system might end in one of the two energy  levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  This probability can be roughly approximated by merging the two basins of the  respective orbits at the fundamental level, and by computing the size of the resulting basins  of attraction in the parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The fraction of volume of each basin in relation to the  total volume in the parameter space in the region at investigation allows to introduce the  concept of basin stability [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In addition, the asymptotic uncertainty can be further studied  through the concept of basin entropy, which offers a more concise probabilistic account of  the hidden structure of the basins [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  12  10  30  E2  E2  6  25  2  20  E1,  E1,+  E  y  15  2  10  6  5  E1  E1,+  10  0  6  4  4  6  5  0  5  (b)  aFigure 5: Unpredictability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The basins of attraction in the history space of the three stable  attractive orbits for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9 and τ0 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  The two energy levels are clearly mixed in the  phase space of initial histories, rendering the basins their fractal nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Thus, arbitrarily small  perturbations in the initial histories can lead to different asymptotic energy levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (a) The basin  of attraction for A = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='43 and varying frequency in the phase space of the periodic histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (b)  A blow-up of the basins, evincing the sensitivity of the system to initial conditions, which entails  unpredictability at all scales of precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  LIMIT CYCLE SUPERPOSITION  The present section is dedicated to describe a new dynamical phenomenon that we have  encountered for α < 0, which reminds of phenomena typically appearing in microscopic  physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In fact, the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2) with α < 0 resembles more exactly the electrodynamic self-  oscillator encountered in previous works [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Specifically, we refer to the existence of states  of superposition of orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In the present case, this corresponds to a quasiperiodic limit cycle  encompassing two smaller symmetric degenerate limit cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This phenomenon can only be  detected when the effects of the retarded potential are comparable to the magnitude of the  external potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Here we have selected a value of α = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9 to illustrate the phenomenon,  which in absolute value is rather close to the value k = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  In the first place we plot the bifurcation diagram.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' It has been computed following exactly  the same recipe described in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As the reader can see in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 6, for α < 0  we cannot find a corresponding Li´enard system that experiences a Hopf bifurcation for  13  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='8  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  5Figure 6: Bifurcation diagram (α < 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The bifurcation diagrams of the maxima map of x  are represented for increasing values of the maximum delay τ0 and α = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A total number  of ten initial randomly chosen histories have been used and depicted using two different colors to  represent the asymptotic sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A first Hopf bifurcation (arrow) appears now for τ0 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4, followed  by a Pitchfork bifurcation (green and blue branches).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We can distinguish a region where limit cycle  superposition (LCS) is detected (red background).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' For τ0 > 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2 a strange attractor with robust  intermittency (RI) appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  small values of the maximum time-delay τ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This occurs because the change in the sign of α  precludes the antidamping effect produced in the first derivative of x appearing in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  However, as τ0 is further increased, again a Hopf bifurcation reveals at the approximate  maximum delay critical value τ0c = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Thus, now, the instability occurs when the system  is posed quite far from the original equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' It must be the result of high-order terms  in the Taylor expansion of the delayed potential, involving the jerk, the jounce and other  derivatives of higher order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Later on, at the critical value τ0c = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='7, a Pitchfork bifurcation  ensues, which then transits to the chaotic regime, as we keep increasing the retardation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  As far as we have computed, a period three orbit coexisting with the two period one orbits  suddenly appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As we zoom in the bifurcation diagram, we can see that these period-3  orbits then experience a period doubling bifurcation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Nevertheless, the cascade cannot be  clearly distinguished, since it includes very complicated dynamics with truly large chaotic  14  3  LCS  RI  2  Cmac  0  1  0  2  4  6  8  10  To3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  28  101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  2  4  6transients, involving heterogeneous alternating motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  For higher values of the maximum time-delay, around τ0 = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5, we can find a window  of parameter values in the bifurcation diagram where a limit cycle superposition can be  found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We describe this new phenomenon in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In this region, we have numerically  detected at least five different coexisting limit cycles, by scrutinizing the history parameter  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Two of them are symmetric and have lower amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' They could describe a first  fundamental level, but this time unresolved from the second, which is the one concerned  now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' For simplicity, we omit them from our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Then, another two limit cycles of  larger amplitude have also been found, which consist in two complicated period-6 stable  symmetric degenerate orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' By varying initial histories in the parameter space (A, ω, ϕ),  one can find many past histories leading to any these two limit cycles, just as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 5  for E1,±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' But, to our surprise, we have also found a superposition limit cycle travelling along  both limit cycles (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 7(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This orbit spends some time going close to one of the  degenerate stable periodic orbits, and then switches to the other one, alternating between  them in a regular fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  The new limit set corresponds to an apparently quasiperiodic stable attractor, and it can  also be accessed from many parameter values (A, ω, ϕ) in the parameter space chosen as  initial histories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Since this superposition limit cycle resembles to its encompassed orbits, it  can be numerically shown that its average energy is, although slightly below, close to the  average energy of the other two period-6 orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The small difference arises because the  superposition limit set visits regions of the phase space with lower energy (closer to the  origin of the square well), which are not covered by the periodic trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Thus, as far as  we are concerned, we describe here for the first time a stable limit cycle that can be partly  constructed from two smaller stable orbits, by nearly taking their union in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  This would be impossible in a finite-dimensional dynamical system represented by some  set of ordinary differential equations, as they are frequently used to describe conventional  mechanical conservative systems: two orbits cannot cross in the phase space of a finite-  dimensional continuous system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Of course, if we interpret the true phase space of our  retarded oscillator as infinite-dimensional, neither they do cross here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  To conclude our analysis, because the superposition state takes after the two encom-  passed smaller cycles, we have computed the power spectra (see Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 7(b) and (c)) of the  temporal series of the quantized periodic orbits and their superposition orbit, to ascertain  15  Figure 7: Limit cycle superposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We can see two symmetric degenerate periodic limit cycles  at the fundamental (red and blue orbits) level for τ0 = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5 and α = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Another limit cycle  (green orbit) encompassing the previous two orbits can be appreciated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (b) Power spectra of the  periodic orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (c) Power spectra of the superposition limit cycle encompassing the periodic orbits,  where the lower frequencies (arrows) are different, rendering this attractor its quasiperiodic nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  the periodicity of the later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As expected, the power spectra of both orbits take after one  another, since their average energy is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' However, we can see that differences appear  in the lower frequency domain of the spectrum, which render the superposition limit cycle  quasiperiodic or, in the worst case, of a very high period, as compared to the other orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Nevertheless, without taking advantage of spectral analysis, it is really striking to see how  this quasiperiodic orbit resembles to the underlying periodic limit cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  ROBUST INTERMITTENCY  We now investigate an interesting dynamical phenomenon that is encountered in our  retarded oscillator for α = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9 when the maximum time-delay is substantially increased  (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 8(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This phenomenon consists in a multiscale strange attractor that appears  to be robust [41] and which also exhibits intrinsic intermittency in a double sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  To  understand it properly, we first show some complicated symmetric degenerate limit cycles  16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='3  Powe  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='3  Frequency (Hz)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5Power  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='3  Frequency (Hz)Figure 8: Multiscale limit cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (a) Two degenerate symmetric limit quiasiperiodic attractors  for α = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9 and τ0 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The trajectories are reminiscent of a saddle-focus projected on the  2D phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (b) The magnitude of the continuous wavelet transform is represented (colorbar),  using the analytic Morse wavelet with the symmetry parameter equal to 3 and a time-bandwidth  product equal to 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  We can already appreciate in the temporal evolution of the spectrum a  complex on-off periodic oscillatory behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The inset shows the total power spectra, with a  bimodal distribution displaying a rich frequency content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  with two intrinsic scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' By intrinsic we mean a property that results from the structure  of the limit cycles, and not as a consequence of some crises at a bifurcation point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  As  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 8(a), for τ0 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='35, this attracting orbits spiral out of the rest state and  then are reinjected back to the limit cycle, drifting slowly towards the equilibrium point  without oscillating at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  They clearly evoke a saddle-focus structure, as appearing in  Shilnikov’s bifurcation [42], specially when embedded in a higher dimensional subspace of the  full infinite-dimensional true phase space (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Their frequency spectrum is very rich,  having two maxima and many frequencies at different scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Interestingly, by implementing  a continuous wavelet transform method, we can capture dynamical phenomena that is not  displayed by conventional stationary spectral analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As it can be appreciated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 8(b),  this time-multiscale method uses several time-windows, showing how the frequency spectrum  evolves in time, and evincing the alternation in the system between oscillatory dynamics  and low-speed silent drifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This dynamics is somewhat reminiscent of relaxation oscillators,  17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='15  Power  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='25  Frequency (Hz)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0Magnitude Scalogram  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='7  8  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='6  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  Frequency (Hz)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  Magnitude  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='0625  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='03125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='015625  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='0078125  0  2  4  6  8  10  Time (mins)Figure 9: Intrinsic intermittency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (a) The two degenerate symmetric limit quiasiperiodic at-  tractors have merged into a chaotic strange attractor in the 2D phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This attractor possess  two dynamical and well differentiated scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (b) The continuous wavelet transform is represented  (colorbar), using again the analytic Morse wavelet with the symmetry parameter equal to 3 and  a time-bandwidth product equal to 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We can newly appreciate in the temporal evolution of  the spectrum a complex behaviour that switches between two oscillatory motions with different  amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (c) The time series of x and its derivative y in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A sequence of bursts  is clearly appreciated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Note how the trajectories can be reinserted into the attractor through two  different arms, making the phenomenon doubly intermittent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  although these limit cycles are way more sophisticated in the present case [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  For higher parameter values, as for example for τ0 = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5, these two complex limit cycles  have merged into a strange chaotic attractor, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 9(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Now we find that the  system alternates between two different states of chaotic oscillation, one with low amplitude  18  Magnitude Scalogram  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='25  (zH)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='8  Magnitude  Frequency (  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='0625  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='03125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='015625  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='0078125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='00390625  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='00195312  0  10  20  30  40  Time (mins)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  2  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  2Figure 10: Robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (a) The largest Lyapunov exponent has been computed by using embed-  ding techniques across different values of the time-delay for α = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='05 has been  chosen as a threshold to determine if the motion is chaotic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We see that its positive value rarely  goes below the threshold, what entails great robustness of the attractor to parameter perturba-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (b) The attractor embedded in D = 3 dimensions, reconstructed with an embedding delay  τ = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We see how it unfolds in this higher-dimensional space, so that the saddle-focus hidden  structure is more clearly appreciated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Its projected shadow manifestly resembles the attractor in  2D phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  and another with a higher amplitude (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 9(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  In this sense, we can affirm that the  system displays intermittent behaviour, switching between these two nonperiodic modes of  oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Comparing this dynamics with the dynamics along the underlying multiscale  limit cycles previously described, we can say that the low-speed drift towards the original  equilibrium of the system without retardation, have now become an oscillation of small  amplitude around it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Note also how the system is reinjected into the domain through  two possible routes: the lower branch and the higher branch of the residual multiscale  attractors, rendering a second form of intermittency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Importantly, this doubly intermittent  behavior is intrinsic to the complex heterogeneous nature of the attractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Simply put, it  does not require a fine-tuning of the parameter τ0, as opposed to conventional intermittency  phenomena, which occurs close to bifurcation critical points [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Moreover, it can be shown  that this chaotic attractor does not disappear as we move across the parameter space τ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Thus it is robust under parameter perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  19  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='5  3  2  1  0  2  1  0  2  2Fascinated by this dynamical behavior and by the fact that the attractor seems to be  robust, in the sense that no periodic windows appear as we zoom in the bifurcation diagram  around some value of τ0, we have computed the largest Lyapunov exponent (LLE) across a  continuous interval of parameter values of the maximum time-delay τ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Since MATLAB’s  integrator does not allow to compute the LLE dynamically, we have taken advantage of  embedology and used the entire time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We follow a method exposed by Rosenstein et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' to efficiently compute the LLE from experimental time series [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' These computations  have been carried out using an embedding dimension of D = 3, and embedding time-delay  for the series of τ = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The mean period T to compute the LLE considered can be obtained  from spectral analysis (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' [45]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We have used a value of T = 35, which is an upper  bound obtained for many parameter values of the attractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The time of integration has  been considered t ∈ [0, 3000] and the maximum number of iteration for the algorithm was  set to 1500, keeping our conservative attitude (see again Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' [45]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The 3D embedding is  depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 10(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 10(a) we can see the value of the maximum Lyapunov exponent for α = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='9,  starting with a periodic orbit at τ0 = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='1, where the value of the Lyapunov exponents is very  small or negative, as it should be for a periodic stable motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' When the chaotic attractor  is born, a sudden jump to positive high values of the exponent is computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We have set  a threshold of λmax = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='05 as the limiting value below which we cannot safely affirm that  a sensitivity to initial histories occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This value is a conservative choice consistent with  the temporal series of the periodic window, before the chaotic dynamics is triggered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' As  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 10(a), we have performed magnifications at several scales whenever downward  peak fluctuations in the LLE exponent are present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The threshold limit is rarely exceeded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Furthermore, whenever the exponent drops bellow the value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='05, we have systematically  computed bifurcation diagrams to see if the chaotic behavior vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' However, we have  not found any periodic windows, and if periodic orbits exist, they coexist with the chaotic  attractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Thus we can conclude that the chaotic attractor is very robust in the present  dynamical system, even though an analytical proof of robustness can not be easily provided  in this case, as in previous works [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Since the intermittency arises as a consequence of the  complicated nature of the attractor, which is robust, it is reasonable to say that, in addition  to being intrinsic, it is robust, as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  20  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  CONCLUSIONS  In the present work we have developed a very simple retarded oscillator with state-  dependent delays, uncovering crucial dynamical behaviour that is frequently believed to be  impossible in classical physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Firstly, we have shown that orbits can be quantized in the  phase space, producing one or more energy levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We believe that the fact that these levels  are produced in a finite number, as compared to having an infinite spectra of energy levels,  is due to the fact that our delayed differential equations are not of the advanced type, as  encountered in electrodynamics [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Secondly, we have found sensitivity to initial condi-  tions in the history space, what introduces unpredictability in a simple fashion, making the  concept of randomness redundant, in principle [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Are the apparent random fluctuations  of fundamental physical systems just a byproduct of the complicated, even heterogeneous  and high-dimensional [48], chaotic dynamics introduced by the dynamics of fields and the  subsequent retardation effects in functional differential equations?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Finally, we have  uncovered a robust intermittency in the absence of multistable external wells, simply caused  by the inherent multiscale nature of our chaotic system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Of course, this is possible because  retardation introduces more dimensions in the dynamical system, ultimately approaching  its center or slow manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In this respect, a deep connection between Lorenz-like chaotic  dynamical systems and walking droplets has been recently proved [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Interestingly, other related phenomena commonly attributed to the microscopic realm,  such as tunneling through external potential barriers (or in multistable external potentials)  can be easily demonstrated with our retarded potential by introducing an external Duffing  potential in replacement of the harmonic well used here [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A similar situation occurs when  studying the flow of electrons through potential barriers, where this paradoxical phenomenon  becomes explained when interpreted in terms of the quantum potential, which appears in  the Hamilton-Jacobi equation of the quantum system, and which is frequently disregarded  when interpreting physical phenomena [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' For a connection between retarded potentials  and the quantum potential we refer the reader to previous works [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In other words, we  are suggesting that the switch between different wells leading to an intermittent behavior  can be interpreted in terms of the robust intermittency phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This dynamics is due  to the nonlinear resonances that allow the particle to jump back and forth over the potential  barrier [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  21  Another important phenomena that might be studied with our oscillator is the existence  of entangled states, which can be explained in terms of synchronization of oscillations [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  These states have already been predicted in previous works in classical electrodynamics to  arise as a consequence of delay-coupling τi(xi, xj) and synchronization between systems of  self-oscillating bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Synchronization phenomena has already found to actually produce  entanglement in theoretical models of bouncing silicone oil droplets [22], although not with  dynamical setups closing the locality loophole so far.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Synchronization is more complicated  for fluids, because the dissipation is higher at the scale of macroscopic fluid dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Specially when compared to electrodynamic fields, where light travels mostly unimpeded  when particles communicate through the electrovacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' This can entail loopholes produced  by the long-range correlations in the background fields [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Importantly, time-delays are frequently considered constant, so that their dynamical na-  ture is disregarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Fortunately, thanks to the development of numerical methods and  computational techniques, an increasing number of works in the literature of dynamical  systems is being dedicated to the dynamical evolution of time-delays [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' We have shown  that the state-dependence of delays can produce very complicated behavior, entailing non-  linear oscillations through the ubiquitous Hopf bifurcation, and producing counterintuitive  new complex dynamical chaotic behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The connection between state-dependent time-  delayed differential equations and Li´enard systems had been barely suggested [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A much  deeper exploration has been provided here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' It was certainly lacking in the literature, and  opens forefront possibilities to study new physical nonlinear phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  In summary, we have provided new evidence in support of Raju-Atiyah’s hypothesis,  claiming that physical phenomena in the microscopic physical realm can be understood by  using functional differential equations to study dynamical phenomena produced by time  retardation in non-Markovian systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Importantly, we highlight that the dissipation and  the time-delay, which both constitute genuine radiative phenomena, introduce an arrow of  time in physical systems [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Thus perhaps the time-reversal symmetry of conservative field  theories might be broken when oscillating and radiating solitons are formed in these fields  [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Partly, the abusive neglect of delayed feedback in physics stems from the tradition of  Newtonian mechanics, where action at a distance is artificially introduced to simplify forces  of interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Certainly, this approximation has rendered many accurate and valuable  results, allowing a great progress in the knowledge of many macroscopic physical systems,  22  which would have been impossible otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Quite the opposite, the principle of causality  in classical field theories produces memory effects that are always present whenever physical  entities communicate through a background field with themselves, and among each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  ACKNOWLEDGMENT  The author would like to thank Mattia Coccolo for valuable comments on the elaboration  of the present manuscript, the discussion of some of its ideas and the computation of the  basins of attraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [1] Airy, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1830).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' On certain conditions under which perpetual motion is possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Cambridge Phil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 3, 369-372.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [2] Schell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Ross, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Effects of time delay in rate processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 85, 6489-  6503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [3] Mackey, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Glass, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Oscillation and chaos in physiological control systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Science  197, 287-289.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [4] Hansen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Protachevicz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Iarosz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Caldas, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Batista, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Macau, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The effect of time delay for synchronisation suppression in neuronal networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Chaos,  Solitons & Fractals 164, 112690.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [5] Ferrell Jr, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Tsai, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Yang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Modeling the cell cycle: Why do certain  circuits oscillate?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Cell 144, 874-885.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [6] Boutle, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Taylor, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', R¨omer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' El Ni˜no and the delayed action oscillator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 75, 15-24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [7] Salpeter, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Salpeter, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Mathematical model for the epidemiology of tuberculo-  sis, with estimates of the reproductive number and infection-delay function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Epidemiol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  147, 398–406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [8] Kalecki, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1935).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A macrodynamic theory of business cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Econometrica 3, 327-344.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [9] Kolmanovskii, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Nosov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Stability of functional differential equations (Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  180).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Elsevier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  23  [10] Insperger, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', St´ep´an, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Turi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' State-dependent delay in regenerative turning pro-  cesses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Nonlinear Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 47, 275–283.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [11] Jeevarathinam, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Rajasekar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Vibrational resonance in the Duffing oscillator with  state-dependent time-delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' IJARPS 2, 1-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [12] Mart´ınez-Llin`as, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Porte, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Soriano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Dynamical properties induced by  state-dependent delays in photonic systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 6, 7425  [13] L´opez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' On an electrodynamic origin of quantum fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Nonlinear Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  102, 621-634.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [14] L´opez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Stability analysis of the uniform motion of electrodynamic bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Scr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 96, 015506.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [15] Raju, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The electrodynamic 2-body problem and the origin of quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 34, 937-963.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [16] Johnson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Walker, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Sir Michael Atiyah’s Einstein Lecture: “The Nature  of Space”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Notices of the AMS 53, 674-678.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [17] Couder, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Proti`ere, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Fort, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Boudaoud, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Dynamical phenomena: walking and  orbiting droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Nature 437, 208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [18] Proti`ere, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Boudaoud, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Couder, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Particle-wave association on a fluid interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 544, 85-108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [19] Fort, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Eddi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Boudaoud, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Moukhtar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Couder, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Path-memory induced  quantization of classical orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 107, 17515-17520.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [20] Pucci, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Harris, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Faria, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Bush, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Walking droplets interacting with single and  double slits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 835, 1136-1156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [21] Eddi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Fort, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Moisy, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Couder, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Unpredictable tunneling of a classical wave-  particle association.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 102, 240401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [22] Papatryfonos, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Vervoort, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Nachbin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Matthieu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Bush, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Bell test  in a classical pilot-wave system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='08940 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='flu-dyn]  [23] Turton S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Couchman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Bush, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A review of theoretical modeling  of walking droplets: toward a generalized pilot-wave framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Chaos 28, 096111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [24] Jenkins, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Self-oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 525, 167-222.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [25] Stokes, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1851).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' On the effect of internal friction of fluids on the motion of pendulums.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Cambridge Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 9, 8–106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  24  [26] Li´enard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1898).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Champ ´electrique et magn´etique produit par une charge concentr´ee en un  point et anim´ee d’un mouvement quelconque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' L’´eclairage electrique 16, 5-14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [27] Daza, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Wagemakers, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Sanju´an, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Wada property in systems with delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Nonlinear Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Numer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Simulat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 43, 220-226.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [28] Alligood, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Sauer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Yorke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Chaos: An Introduction to Dynamical  Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Springer, New York.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [29] Mainzer, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Chua, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Local Activity Principle: the Cause of Complexity and  Symmetry Breaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Imperial College Press, London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [30] L´opez, ´A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Benito, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Sabuco, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Delgado-Bonal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The thermodynamic efficiency  of the Lorenz system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='07653 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='stat-mech]  [31] Abraham, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Marsden, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Foundations of Mechanics (Second Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Addison-Wesley  Publishing Company, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Redwood City, CA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [32] Li´enard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1928).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Etude des oscillations entretenues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Revue g´en´erale de l’´electricit´e 23,  901–912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [33] Perko, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Differential Equations and Dynamical Systems (Third ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' New York,  Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 254–257.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [34] Lakshmanan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Senthilkumar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Dynamics of nonlinear time-delay systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Springer Science & Business Media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 37-41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [35] Ramana Reddy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Sen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Johnston, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Time delay induced death in coupled  limit cycle oscillators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 80, 5109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [36] Elhadj, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Sprott, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A minimal 2-D quadradtic map with quasi-periodic route to  chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Bif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Chaos 18, 1567-1577.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [37] Lai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' -C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' and T´el, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Transient Chaos: Complex Dynamics on Finite-Time Scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Springer, New York.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [38] Aguirre, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Viana, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', and Sanju´an, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Fractal structures in nonlinear  dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 81, 333-386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [39] Menck, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Heitzig, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Marwan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' How basin stability complements the linear-  stability paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Nature Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 9, 89–92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [40] Daza, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Wagemakers, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Georgeot, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Basin entropy: a new tool to analyze  uncertainty in dynamical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 6, 31416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [41] Banerjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Yorke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Grebogi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Robust chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 80, 3049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  25  [42] Shilnikov, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1967).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The existence of a denumerable set of periodic motions in four-  dimensional space in an extended neighborhood of a saddle-focus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Soviet Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Dokl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 8, 54–58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [43] Van der Pol, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1920).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A theory of the amplitude of free and forced triode vibrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Radio  Review 1, 701-710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [44] Pomeau, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Manneville, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Intermittent transition to turbulence in dissipative dy-  namical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 74, 189–197.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [45] Rosenstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Collins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', De Luca, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A practical method for calculating  largest Lyapunov exponents from small data sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' D: Nonlinear Phenom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 65, 117-134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [46] L´opez, ´A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' The electrodynamic origin of the wave-particle duality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' In: Banerjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=',  Saha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (eds) Nonlinear Dynamics and Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Springer Proceedings in Complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Springer, Cham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [47] Sprott, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A simple chaotic delay differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A 366, 397-402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [48] Saiki, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Takahasi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Yorke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Piecewise linear maps with heterogeneous chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  Nonlinearity 34, 5744.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [49] Valani, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Lorenz-like systems emerging from an integro-differential trajectory  equation of a one-dimensional wave–particle entity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Chaos 32, 023129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [50] Coccolo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Zhu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Sanju´an, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Bogdanov–Takens resonance in time-  delayed systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Nonlinear Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 91, 1939–1947.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [51] Bohm, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1952).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A suggested interpretation of the quantum theory in terms of “hidden”  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 85, 166-179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [52] Morgan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Bell inequalities for random fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' A: Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 39, 7441.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [53] M¨uller, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Otto, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Radons, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Laminar chaos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 120, 084102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [54] Mackey, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Time’s arrow: the origins of thermodynamic behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Springer, New  York.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' 101-102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  [55] Fodor, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Forg´acs, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=', Grandcl´ement, P, R´acz, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Oscillons and quasibreathers in the  φ4 Klein-Gordon model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content=' D 74, 124003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
+page_content='  26' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3dFRT4oBgHgl3EQfoTds/content/2301.13608v1.pdf'}
diff --git a/4dE4T4oBgHgl3EQf0w2N/content/tmp_files/2301.05285v1.pdf.txt b/4dE4T4oBgHgl3EQf0w2N/content/tmp_files/2301.05285v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0e2aa96577d42dea544fbc50d3ae0ef0405fbde9
--- /dev/null
+++ b/4dE4T4oBgHgl3EQf0w2N/content/tmp_files/2301.05285v1.pdf.txt
@@ -0,0 +1,1002 @@
+Laser Inter-Satellite Link Setup Delay:
+Quantification, Impact, and Tolerable Value
+Dhiraj Bhattacharjee1, Aizaz U. Chaudhry1, Halim Yanikomeroglu1, Peng Hu2, and Guillaume Lamontagne3
+1Department of Systems and Computer Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada
+2National Research Council Canada (NRC), 1200 Montreal Road, Ottawa, ON K1A 0R6, Canada
+3MDA, Sainte-Anne-de-Bellevue, QC H9X 3R2, Canada
+1{dhirajbhattacharjee, auhchaud, halim}@sce.carleton.ca, 2peng.hu@nrc-cnrc.gc.ca, 3guillaume.lamontagne@mda.space
+Abstract—Dynamic laser inter-satellite links (LISLs) provide
+the flexibility of connecting a pair of satellites as required (dynam-
+ically) while static LISLs need to be active continuously between
+the energy-constrained satellites. However, due to the LISL estab-
+lishment time (termed herein as LISL setup delay) being in the
+order of seconds, realizing dynamic LISLs is currently unfeasible.
+Towards the realization of dynamic LISLs, we first study the
+quantification of LISL setup delay; then we calculate the end-
+to-end latency of a free-space optical satellite network (FSOSN)
+with the LISL setup delay; subsequently, we analyze the impact
+of LISL setup delay on the end-to-end latency of the FSOSN.
+We also provide design guidelines for the laser communication
+terminal manufacturers in the form of maximum tolerable value
+of LISL setup delay for which the FSOSN based on Starlink’s
+Phase I satellite constellation will be meaningful to use for low-
+latency long-distance inter-continental data communications.
+Index Terms—dynamic laser inter-satellite links, free-space
+optical satellite networks, laser inter-satellite link setup delay,
+Starlink.
+I. INTRODUCTION
+In recent advancements of wireless communication of 6G era,
+satellite networks have been seen as an integral part along with
+terrestrial networks for global broadband coverage specially
+for enabling broadband Internet in rural and remote areas [1],
+low-latency long-distance inter-continental data communications
+[2], and IoT based monitoring and remote surveillance [3]. From
+3GPP definition, satellite payloads could either be transparent
+or regenerative [4]. In transparent scenario, inter-continental
+communication has to go up (ground station to satellite) and
+down (satellite to ground station) frequently to reach from
+source to destination. With regenerative payload, communication
+between satellites over inter-satellite links (ISLs) could be a
+better option in such long-distance communication. Compared
+to RF-based ISLs, laser ISLs (LISLs) have the advantage of
+higher bandwidth, smaller antenna size, higher directivity, less
+power consumption, less chance of interception and interference,
+etc [5]. Exploiting these LISLs in low Earth orbit (LEO) or very
+low Earth orbit (VLEO) satellite mega constellations, free-space
+optical satellite networks (FSOSNs) can be realized in space [6].
+On the basis of an LISL’s active duration, LISLs can be
+classified into two types: static LISLs and dynamic LISLs. Static
+LISLs are those LISLs which are kept active all the time, e.g.,
+SpaceX’s Starlink will have four static LISLs per satellite which
+will be operating all the time [7]. In contrast, dynamic LISLs
+can be established dynamically between satellites (which are
+within the LISL range) at any time on demand depending upon
+data communication requirements. To realize such dynamic
+LISLs instantaneously, we need to have very precise and
+efficient pointing, acquisition, and tracking (PAT) system [8].
+Before two satellites start communicating via LISLs,
+transmitting satellite needs to position its laser beam within
+the field of view of receiver satellite (pointing). Then the
+receiver satellite needs to align itself towards the arriving beam
+(acquisition). Finally, transmitter and receiver continue this
+process as the communication goes on (tracking) [9]. Now, we
+define LISL setup delay as the time taken by the PAT system to
+establish the LISL, i.e., the sum of pointing time and acquisition
+time. This delay will be introduced to the end-to-end latency
+from a source ground station to destination ground station when
+the path over an FSOSN changes. Note that when the path
+changes, it could lead to one or multiple new LISLs. However,
+LISL setup delay will be introduced only once as multiple
+LISLs can be established simultaneously during a time slot.
+Satellites are driven by onboard battery and solar power, and
+satellite battery power is a very precious resource, which should
+be used intelligently. On that regard, static LISLs are always
+active whether they are being used or not. This will drain the
+satellite battery and satellites could be dead more often and they
+need to be de-orbited and new satellites have to be launched.
+This in turn will increase the maintenance expenditure. On the
+other hand, dynamic LISLs will be an energy efficient approach
+where LISLs are only established as required. With dynamic
+LISLs, two neighbour satellites could connect whenever they
+are within LISL range and this will provide more routing
+options. These links between neighbour satellites could be
+inter-orbital plane, crossing orbital plane, inter-shell, and even
+inter-constellation (e.g., between Starlink and OneWeb). Also, as
+the LEO/VLEO satellites are mobile, communications between
+satellites and ground stations will always be through dynamic
+laser links. Furthermore, in an operating satellite constellation, if
+one or many satellites fail, dynamic LISLs will instantaneously
+reroute the traffic by avoiding the dead satellite(s).
+LISL setup delay for current laser communication terminals
+(LCTs) varies from few seconds to tens of seconds [10]. This
+prevents us from realizing dynamic LISLs in next-generation
+FSOSNs (NG-FSOSNs) in late 2020s. In next-next-generation
+FSOSNs (NNG-FSOSNs) (in 2030s), due to advancement in
+satellite PAT technology, LISL setup delay could be reduced to
+the order of a few milliseconds and dynamic LISLs could become
+a reality. In this context, we study the quantification of LISL setup
+delay in the FSOSN based on Starlink’s Phase I constellation [7].
+We calculate the end-to-end latency of this FSOSN using different
+values of the LISL setup delay in different inter-continental
+connection scenarios and different LISL ranges for satellites.
+We investigate the impact of LISL setup delay on overall
+latency and provide design guidelines for LCT manufacturers
+to leverage full potential of NNG-FSOSNs via dynamic LISLs.
+To the best of our knowledge, there exists no study on LISL
+arXiv:2301.05285v1  [cs.NI]  12 Jan 2023
+
+setup delay that examines its quantification, and its impact on
+end-to-end latency along with its maximum tolerable values.
+The authors of [11] state that for terrestrial distances
+larger than 3000 km, FSOSNs could provide a better latency
+performance as compared to the optical fiber terrestrial network
+(OFTN). In high-frequency trading of stocks, even 1 ms
+improvement in latency could generate $100 million of revenue
+per year [12]. Thus, in such long distance-communication,
+FSOSNs could be a better solution compared to the OFTN.
+With this objective, we come up with maximum tolerable values
+of LISL setup delay for which latency performance of the
+FSOSN based on Starlink’s Phase I constellation will be better
+than the OFTN. This maximum value of LISL setup delay
+can be a design guideline for LCT manufacturers to leverage
+advantages of dynamic LISLs in NNG-FSOSNs.
+The paper organization is as follows. We discuss related
+work on network latency of satellite networks and examine
+LISL setup delays of current LCT manufacturers in Section
+II. In Section III, we elaborate on how we quantify LISL setup
+delay, calculate end-to-end latency, and define performance
+metrics. We present our results in Section IV, discuss insights
+and design guidelines in Section V, and conclude our discussion
+with some possible future extensions in Section VI.
+II. RELATED WORK
+Currently, Mynaric’s LCT CONDOR needs 30 seconds to
+establish an LISL between two satellites for the first time. Once
+the orbital parameters are exchanged between satellites, it takes 2
+seconds to setup an LISL for every next time [10]. Tesat [13] and
+General Atomics [14] have LCTs for LEO/VLEO constellations
+which have LISL setup delay in the range of tens of seconds.
+In any communications network, the end-to-end latency from
+source to destination typically has four components: propagation
+delay, transmission delay, queuing delay, and processing delay
+[15]. Based on this latency model, authors of [2] compared the
+latency performance of FSOSNs and OFTNs. As stated earlier
+that latency-wise, FSOSNs can be a better alternative to OFTN for
+longer communication distances [11]. On that regard, authors of
+[12] and [16] have come up with a concept of crossover distance
+to determine that for a certain terrestrial distance, which one will
+provide a better latency performance among FSOSN and OFTN.
+Authors of [17] have suggested ground stations as relays as a
+substitute of ISLs where satellites have transparent payload. With
+this network architecture, they proved that constellations like Star-
+link can provide better latency performance compared to OFTN.
+In addition to that, idle user terminals can also be used which will
+provide further improvement in latency performance. However,
+[18] shows that exploiting ISLs can reduce variation in latency
+performance as well as reduce the effects of weather impairments.
+To analyze network delay, authors of [19] have modeled each
+satellite node as M/M/1 queue in a multihop scenario where
+each satellite can receive packets from ground station as well as
+other satellite node. Authors of [20] highlighted the importance
+of temporary LISLs (defined as LISLs which are established
+temporarily with satellites that are within LISL range) in order
+to achieve better latency performance compared to static LISLs
+in FSOSNs. They showed that with temporary LISLs, there exist
+more number of LISLs which will provide better routing options.
+They also reported that temporary LISLs are more useful at lower
+LISL ranges. Authors of [12] and [20] mentioned about LISL
+setup delay in FSOSNs. With that respect, in FSOSNs, along
+with the other four end-to-end latency components discussed
+earlier, we introduce LISL setup delay to the latency model.
+III. METHODOLOGY
+To quantify LISL setup delay, calculate end-to-end latency
+from source to destination with the LISL setup delay, investigate
+the impact of LISL setup delay on overall latency, and present
+design guidelines for LCT as a form of maximum tolerable value
+of LISL setup delay, we simulate Starlink’s Phase I Version 2 con-
+stellation in AGI’s Systems Tool Kit (STK) platform [21]. This
+constellation has a total of 1584 satellites consisting 24 orbital
+planes with each of them having 66 satellites [7]. The orbits are
+at an inclination of 53° with respect to the equator and satellites
+are at an altitude of 550 km. With these constellation parameters,
+we generate this constellation’s satellites in STK with a certain
+LISL range (i.e., the range over which a satellite in an FSOSN
+can establish an LISL with any other satellite within this range)
+along with ground stations at New York, London, Istanbul, and
+Hanoi. Next we extract the data from STK (e.g., vertices, edges,
+length of edges, etc) at every second for one hour simulation
+period to Python platform. Then we apply Dijkstra’s shortest
+path algorithm [22] to find shortest path at every time slot (equal
+to one second in duration) for the source to destination pairs:
+New York–London, New York–Istanbul, and New York–Hanoi.
+In our investigation, we consider 4 different values of LISL
+range: 1500 km, 1700 km, 2500 km, and 5016 km. The minimum
+range to have communication with nearest neighbor at the imme-
+diate left and right orbital planes is 1500 km in Starlink’s Phase
+I Version 2 constellation. At this range, a satellite can connect to
+two satellites in front and two at rear in the same orbital plane
+making total 6 connections. At 1700 km range, a satellite can
+connect to three immediate neighbors on the left, three immediate
+neighbors on the right, and four intra-orbital plane neighbors
+making a total of 10 possible connections. The maximum possible
+LISL range for Starlink’s Phase 1 constellation can be calculated
+as 5016 km [6]. The 2500 km LISL range is taken as an
+intermediate value between 1700 km and 5016 km.
+A. Quantification of LISL Setup Delay
+We define LISL setup delay indicator (a binary variable)
+as follows: if the shortest paths of (i − 1)th time slot and
+ith time slot are exactly same, no LISL setup delay is to be
+included in the end-to-end latency, and the LISL setup delay
+indicator, αi is 0. If shortest path changes from (i−1)th to
+ith time slot, αi is 1. Considering ηs as LISL setup delay, we
+denote end-to-end latency without and with LISL setup delay
+as ηLE(withoutηs) and ηLE(withηs), respectively. In Table
+I, we show shortest paths (satellite naming convention follows
+[6]) and corresponding values of ηLE(without ηs), αi, and
+ηLE(withηs) for first 6 time slots over the FSOSN for New
+York to Istanbul inter-continental connection at an LISL range
+of 1500 km. From Table I, we can see that shortest path could
+change from time to time. This is due to the fact that as LEO
+satellites are moving at high orbital speeds, either a shortest path
+at one time instance may even not exist in the next time instance
+(due to one or multiple satellites moving out of range) or there
+may become available a new shortest path. ηLE(withoutηs) has
+
+Table I. ηLE(without ηs), αi, ηs, and ηLE(with ηs) of the shortest paths at first 6 time slots
+over the FSOSN for New York–Istanbul inter-continental connection.
+ηLE
+ηLE
+Time
+Shortest
+(without
+αi
+ηs
+(with
+Slot
+Path
+ηs)
+(ms)
+ηs)
+(ms)
+(ms)
+1
+GS at New York, satellite x10919, x11115, x11312, x11509, x11609, x11611, x12166, GS at Istanbul
+38.09
+0
+0
+38.09
+2
+GS at New York, satellite x11503, x11505, x11507, x11509, x11609, x11611, x12166, GS at Istanbul
+38.08
+1
+100
+138.08
+3
+GS at New York, satellite x11503,x11505, x11507, x11509, x11609, x11611, x12166, GS at Istanbul
+38.07
+0
+0
+38.07
+4
+GS at New York, satellite x11503,x11505, x11507, x11509, x11609, x11611, x12166, GS at Istanbul
+38.06
+0
+0
+38.06
+5
+GS at New York, satellite x11503,x11505, x11507, x11509, x11609, x11611, x12166, GS at Istanbul
+38.05
+0
+0
+38.05
+6
+GS at New York, satellite x11503, x11505, x11507, x11508, x11608, x11903, x12166, GS at Istanbul
+38.00
+1
+100
+138.00
+two major components: propagation delay and node delay (sum
+of processing and queuing delay is node delay). We calculate
+propagation delay as sum of lengths of all the laser links in
+the shortest path divided by speed of light in vacuum and we
+consider node delay as 1 ms [23]. From Table I, it is evident that
+shortest paths are not same for 1st and 2nd time slots, so α2 =1.
+Considering ηs =100 ms, ηLE(withηs) will be 38.08+100, i.e.,
+138.08 ms at time slot 2. The shortest path remains unchanged
+from time slot 3 to 5, i.e., α3 =α4 =α5 =0 and corresponding
+ηLE(withηs) values remain same as ηLE(withoutηs). Then
+again at time slot 6, shortest path changes which makes α6 =1.
+B. Path Change Rate
+We simulate for 3600 time slots, one time slot being equal
+to 1 second in duration and we define the path change rate,
+λ as the average number of instances the shortest path from
+source to destination changes (represented in percentage) and
+mathematically it can be calculated as
+λ=
+1
+3600
+3600
+�
+i=1
+αi ×100%.
+(1)
+C. End-to-End Latency
+Averaging ηLE(with ηs) and ηLE(without ηs) over 3600
+time slots, we get average end-to-end latency with and without
+ηs as ηLE(withηs) and ηLE(withoutηs), respectively. They
+are related to λ and ηs as follows:
+ηLE(withηs)=ηLE(withoutηs)+ λ
+100 ηs.
+(2)
+D. Impact of ηs
+To measure the impact of LISL setup delay, ηs on average end-
+to-end latency, we define β as percentage of delay introduced due
+to ηs in average end-to-end latency and calculate it as follows:
+β = ηLE(withηs)−ηLE(withoutηs)
+ηLE(withηs)
+×100%.
+(3)
+E. Tolerable Value of ηs
+For an inter-continental connection, it is meaningful to use
+the FSOSN only when ηLE(withηs) is lesser than end-to-end
+latency of the OFTN, ηLE,OF T N. Using (2), the following can
+be written,
+ηLE(withoutηs)+ λ
+100 ηs ≤ηLE,OF T N.
+(4)
+Now we define the maximum tolerable value of LISL setup
+delay, ηs,max as the maximum value of ηs so that the average
+Figure 1. Path change rate.
+end-to-end latency of the FSOSN is lesser or equal to that of
+the OFTN and calculate it from (4) as follows:
+ηs,max = ηLE,OF T N −ηLE(withoutηs)
+λ/100
+.
+(5)
+To calculate ηLE,OF T N, first we determine the distance
+from the source ground station to the destination ground
+station along the surface of the Earth using Haversine formula
+[24] from latitudes and longitudes of source and destination
+ground stations. Later we find ηLE,OF T N as that distance
+divided by speed of light in the optical fiber (having refractive
+index=1.4675), i.e., 204,287,876 m/s.
+IV. RESULTS
+We consider three inter-continental connections: New York to
+London (low inter-continental distance connection with terrestrial
+distance=5593 km), New York to Istanbul (mid inter-continental
+distance connection with terrestrial distance=8079 km), and
+New York to Hanoi (high inter-continental distance connection
+with terrestrial distance=13164 km). For the metrics λ, ηLE,
+and β, we show bar plots for the four LISL ranges. To clearly
+show both high and low values in the same figure, we use log
+scale in the y-axis in Figs. 1 to 3.
+A. Path Change Rate
+In Fig. 1, we plot λ with LISL range varying along x-axis for
+the three inter-continental connections. For any inter-continental
+connection, we can observe that λ reduces as LISL range
+increases. Also note that for a particular LISL range, the more
+the inter-continental distance, the higher the value of λ.
+B. End-to-End Latency
+Fig. 2 shows end-to-end latency for the three inter-continental
+connections averaged over one hour of simulation period
+without considering ηs and with four ηs values. As LISL range
+increases along x-axis, both ηLE(withoutηs) (black bars) and
+ηLE(withηs) (other bars) decrease. For a certain LISL range, the
+
+102
+New York to London
+New York to Istanbul
+37.5 39.1
+New York to Hanoi
+33.9
+17.5
+14.4
+12.3
+(%)
+9.8
+9.6
+101
+8.7
+8.0
+6.8
+5.8
+100
+1500
+1700
+2500
+5016
+LISL Range (km)(a) New York to London.
+(b) New York to Istanbul.
+(c) New York to Hanoi.
+Figure 2. Average end-to-end latency performance.
+more the value of ηs, the more the overall latency. For example, in
+Fig. 2a with LISL range of 1700 km, ηLE(withηs) is 123.9 ms
+for ηs=1 sec and it reduces to 35.7 ms when ηs is considered to
+be 100 ms. Also, for a certain LISL range with a certain ηs value,
+the more the inter-continental distance, the more the end-to-end
+latency for both the cases: ηLE(withoutηs) and ηLE(withηs).
+It is interesting to note that with the increase of LISL range,
+ηLE(with ηs) reduces faster compared to ηLE(without ηs).
+For example, considering Fig. 2a, ηLE(withoutηs) drops from
+25.9 ms to 24.6 ms when LISL range increases from 1700
+km to 2500 km. If we take the ratio and term the ratio as
+reduction ratio, for this case it will be 25.9
+24.6 =1.053. Similarly,
+for ηLE(with ηs), the reduction ratio will be 123.9
+92.1 = 1.345
+which is greater than that of ηLE(withoutηs).
+C. Impact of ηs
+In Fig. 3, we show the variation of β with LISL range for
+four ηs values in the three inter-continental connections. As we
+see, β reduces as LISL range increases for a certain ηs value.
+Also, at a certain LISL range, β reduces as ηs reduces. For
+example, in Fig. 3b with LISL range of 2500 km, β is 71%
+for ηs=1 sec. However, when ηs reduces to 100 ms, β reduces
+to 19.7%. In addition, for a certain LISL range with a particular
+ηs value, β reduces as inter-continental distance increases. For
+example, assuming 1700 km of LISL range and ηs as 1 sec, β
+reduces from 77% to 73.1% when inter-continental connection
+changes from New York–Istanbul to New York–Hanoi.
+D. Tolerable Value of ηs
+In Fig. 4, we plot ηLE(withηs) and ηLE,OF T N against ηs.
+Note that, ηLE(withηs) is a straight line with a constant slope
+and as LISL range increases, the slope reduces. The significance
+of this figure is where ηLE(withηs) for a certain LISL range
+cuts ηLE,OF T N, the x-coordinate value of the intersection point
+is ηs,max as beyond that point, ηLE(with ηs) will be greater
+than ηLE,OF T N. To show the intersection points clearly, we
+only present ηs values on the x-axis varying from 1 ms to
+100 ms where we mention the coordinates of the intersection
+points. If we substitute ηLE,OF T N =39.55 ms (from Fig. 4b),
+ηLE(without ηs) = 37.9 ms (from Fig. 2b), and λ = 37.5%
+(from Fig. 1) for New York to Istanbul inter-continental
+connection with 1500 km LISL range in (5), we get ηs,max
+as 4.4 ms which matches with Fig. 4b. Also, we should observe
+from Fig. 4 that, as LISL range increases, ηs,max also increases.
+Interesting point to note in Fig. 4c is that it only shows two
+intersection points because ηLE(withηs) for 1500 km and 1700
+km LISL range straight lines (black and blue lines) never intersect
+with ηLE,OF T N for ηs >1 ms values. For 1500 km LISL range,
+ηLE(withoutηs)=66.5 ms (from Fig. 2c) and ηLE,OF T N=64.44
+ms (from Fig. 4c). Putting these values in (5), we get negative
+ηs,max value which does not exist. Similarly, for 1700 km LISL
+range, ηLE(withoutηs)≈ηLE,OF T N which makes ηs,max ≈0.
+V. INSIGHTS AND DESIGN GUIDELINES
+A. Insights
+1) Path Change Rate
+• As LISL range increases, there will be lesser hops, i.e., lesser
+number of satellites for the signal to reach from source to
+destination. For example, in New York to Istanbul inter-
+continental connection, average number of hops drops from
+7 to 6 when LISL range increases from 1500 km to 1700 km.
+The lesser the number of hops, the lesser is the chance of a
+new shortest path. This in turn reduces λ. Also, when the LISL
+range increases, two satellites remain in communication range
+for a longer time span. One of the reasons for the shortest
+path to change is satellites going out of LISL range, and a
+shortest path tends to change lesser with longer LISL range.
+Due to these two reasons, λ reduces as LISL range increases.
+• For a certain LISL range, the longer the inter-continental
+distance, the higher the average number of hops which leads
+to more chances of a new shortest path, and this increases
+the path change rate, λ.
+2) End-to-End Latency
+• Increase in LISL range reduces the number of hops which
+reduces total node delays. This decreases ηLE(withoutηs)
+with the increase in LISL range. Now, as both λ and
+ηLE(withoutηs) decrease with the increase of LISL range,
+from (2), it is clear that ηLE(withηs) also decreases.
+• From (2), we can see that if ηs reduces, ηLE(with ηs)
+reduces for a certain LISL range.
+• For a certain LISL range with a certain ηs value, when
+inter-continental distance increases, λ increases. From (2), we
+can say that ηLE(withηs) will increase with the increase of
+λ. For longer inter-continental connections, propagation delay
+as well as node delay (due to more number of hops) is more
+which increases ηLE(withoutηs) for longer inter-continental
+connections.
+• We consider that at LISL range la and lb (lb > la), path
+change rates are λa and λb, respectively. Also, the average
+end-to-end latencies without ηs are ηLEa(without ηs)
+
+103
+Without ns
+With ns=1 sec
+With ns=100 ms
+365.1
+Withns=10 ms
+With ns=1 ms
+(sw) 3u
+123.9
+102
+92.1
+81.6
+60.5
+35.7
+30.0
+31.4
+29.2
+26.8.
+25.3.
+26.6
+27.0
+25.9
+25.9
+24.6
+23.9.
+24.7
+23.3
+23.4
+101
+1500
+2500
+1700
+5016
+LiSL Range (km)103
+Without ns
+With ns=l sec
+With ns=100 ms
+413.0
+With ns=10 ms
+With ns=1 ms
+160.2
+(sw) 
+122.8
+113.0
+102
+75.4
+49.3
+44.3
+41.6
+38.2
+41.4
+36.5
+37.9
+38.3
+37.1
+36.9
+34.2.
+35.6
+35.7
+33.4
+33.5
+101
+1500
+1700
+2500
+5016
+LISL Range (km)Without ns
+With ns=1 sec
+With ns=100 ms
+103
+With ns=10 ms
+With ns=1 ms
+457.8
+(ms)
+239.6
+205.3
+nLE
+153.1
+105.7
+102
+82.0
+70.4
+75.3
+66.2
+66.3
+66.5
+62.3
+66.9
+64.4
+64.6
+60.9
+57.6 56.8
+61.0
+56.7
+101
+1500
+1700
+2500
+5016
+LiSL Range (km)(a) New York to London.
+(b) New York to Istanbul.
+(c) New York to Hanoi.
+Figure 3. Impact of ηs on end-to-end latency.
+(a) New York to London.
+(b) New York to Istanbul.
+(c) New York to Hanoi.
+Figure 4. Maximum tolerable value of ηs.
+and ηLEb(without ηs), respectively. From Figs. 1 and 2
+values we observe that λa
+λb > ηLEa(withoutηs)
+ηLEb(withoutηs) . For example,
+considering New York to Istanbul inter-continental connection,
+assuming la=1500 km and lb=1700 km, λa
+λb = 37.5
+12.3 = 3.049
+and ηLEa(withoutηs)
+ηLEb(withoutηs) = 37.9
+36.9 =1.027. Now, we can write the
+following:
+λa
+λb
+> ηLEa(withoutηs)
+ηLEb(withoutηs) ,
+(6)
+λa ηs/100
+ηLEa(withoutηs) >
+λb ηs/100
+ηLEb(withoutηs),
+(7)
+1+
+λa ηs/100
+ηLEa(withoutηs) >1+
+λb ηs/100
+ηLEb(withoutηs),
+(8)
+ηLEa(withoutηs)+ λa
+100 ηs
+ηLEa(withoutηs)
+> ηLEb(withoutηs)+ λb
+100 ηs
+ηLEb(withoutηs)
+.
+(9)
+Assuming
+average
+end-to-end
+latency
+with
+ηs
+as
+ηLEa(withηs) and ηLEb(withηs) for LISL range la and lb,
+respectively and using (2) we can rewrite (9) as follows:
+ηLEa(withηs)
+ηLEb(withηs) > ηLEa(withoutηs)
+ηLEb(withoutηs) .
+(10)
+3) Impact of ηs
+• We have seen that ηLE(with ηs) reduces faster compared
+to ηLE(withoutηs) as LISL range increases. Thus, the ratio
+ηLE(withoutηs)
+ηLE(withηs)
+increases as LISL range increases. From (3),
+as we can see that β is proportional to
+�
+1− ηLE(withoutηs)
+ηLE(withηs)
+�
+,
+β reduces with the increase of LISL range.
+• ηLE(withηs) reduces when ηs reduces but ηLE(withoutηs)
+remains the same which causes the ratio ηLE(withoutηs)
+ηLE(withηs)
+to
+increase. As β is proportional to
+�
+1 − ηLE(withoutηs)
+ηLE(withηs)
+�
+, it
+decreases when ηs reduces.
+• Let us consider that for inter-continental distance dx and dy
+(dy >dx), path change rates are λx and λy, respectively. Also,
+average end-to-end latencies without ηs are ηLEx(withoutηs)
+and ηLEy(without ηs), respectively. From Figs. 1 and 2
+values, we also observe that λx
+λy > ηLEx(withoutηs)
+ηLEy (withoutηs) (note that
+in this discussion, we are varying inter-continental distance, not
+LISL range). For example, at 1700 km LISL range, for New
+York to Istanbul and New York to Hanoi inter-continental con-
+nection, λx, λy, ηLEx(without ηs), and ηLEy(without ηs)
+are 12.3%, 17.5%, 36.9 ms, and 64.4 ms, respectively from
+which we get λx
+λy =0.703 and ηLEx(withoutηs)
+ηLEy (withoutηs) =0.573. Using
+the approach in (6) – (10), we can come to the conclusion that
+ηLEx(withoutηs)
+ηLEx(withηs)
+<
+ηLEy (withoutηs)
+ηLEy (withηs)
+where ηLEx(withηs) and
+ηLEy(withηs) are average end-to-end latencies considering ηs
+for inter-continental distance dx and dy, i.e., ηLE(withoutηs)
+ηLE(withηs)
+in-
+creases as inter-continental distance increases which reduces β.
+4) Tolerable Value of ηs
+• (2) represents an equation of a straight line with slope
+proportional to λ considering ηLE(withηs) as y variable and
+ηs as the x variable. As LISL range increases, λ decreases
+which makes the slope of the straight lines to reduce. In
+addition to λ, ηLE(without ηs) also reduces with the
+
+110
+FSOSN with LiSL Range=1500km
+FSOSN with LISL Range=1700km
+100
+FSOSN with LISL Range=2500km
+FSOSN with LISL Range=5016km
+90
+OFTN
+(ms)
+80
+37u
+70
+(24.58,64.44)
+(80.63,64.44)
+60
+50
+20
+40
+60
+80
+100
+ns (ms)92.7
+102
+79.1
+73.3
+71.4
+56.0
+27.5
+21.5
+20.0
+11.3
+101
+(%)
+3.7
+B
+2.7
+2.4
+1.3
+100
+0.4
+0.3
+0.2
+1500
+1700
+2500
+5016
+LISL Range (km)Ns=l sec
+ns=100 ms
+ns=10 ms
+ns=1 ms
+90.8
+102
+77.0
+71.0
+70.4
+49.8
+25.0
+19.7
+19.2
+101
+9.0
+(%)
+3.2
+B
+2.4
+2.3
+1.0
+100
+0.3
+0.2
+0.2
+1500
+1700
+2500
+5016
+LiSL Range (km)85.5
+102
+73.1
+70.3
+63.0
+37.0
+21.4
+19.2
+14.5
+101
+5.6
+2.6
+2.3
+β
+1.7
+100
+0.6
+0.3
+0.2
+0.17
+1500
+2500
+5016
+1700
+LISL Range (km)60
+FSOSN with LISL Range=1500km
+55
+FSOSN with LISLRange=1700km
+FSOSN with LISL Range=2500km
+50
+FSOSN with LISL Range=5016km
+OFTN
+45
+(ms)
+40
+37
+35
+(2.30,27.38)
+30
+(15.10,27.38)
+(40.88,27.38)
+(70.34,27.38)
+25
+20
+10
+20
+30
+40
+50
+60
+70
+80
+ns (ms)80
+FSOSN with LISL Range=1500km
+FSOSN with LISL Range=1700km
+70
+FSOSN withLISL Range=2500km
+FSOSN with LISL Range=5016km
+OFTN
+60
+(sw) u
+50
+(4.40,39.55)
+(21.54,39.55)
+(45.40,39.55)
+40
+(76.87,39.55)
+30
+20
+40
+60
+80
+100
+Ns (ms)increase of LISL range, and from (5) we can say that ηs,max
+increases with increase in LISL range.
+B. Design Guidelines
+The values we get from (5) are exactly same as we
+get from intersection points shown in Fig. 4. Given that
+ηLE,OF T N, ηLE(withoutηs), and λ are known for a particular
+inter-continental connection for a certain LISL range, (5) can
+be used to design LCTs in order to exploit full potential of
+NNG-FSOSNs. For example:
+• For New York to London inter-continental connection with
+1500 km of LISL range, ηLE,OF T N, ηLE(withoutηs), and λ
+are 27.38 ms, 26.6 ms, and 33.9%, respectively. Putting these
+values in (5), we get ηs,max as 2.3 ms (same as in Fig. 4a).
+• With 1700 km LISL range for New York to Istanbul
+inter-continental connection, putting ηLE,OF T N=39.55 ms,
+ηLE(without ηs)=36.9 ms, and λ=12.3% in (5), we get
+ηs,max=21.54 ms, i.e., exactly as shown in Fig. 4b.
+• Considering New York to Hanoi inter-continental connection
+with 5016 km of LISL range, values of ηLE,OF T N,
+ηLE(withoutηs), and λ are 64.44 ms, 56.7 ms, and 9.6%,
+respectively. Using these values in (5), we get ηs,max equal
+to 80.63 ms (same as in Fig. 4c).
+VI. CONCLUSION AND FUTURE WORK
+Dynamic LISLs are essential to leverage the full potential
+of NNG-FSOSNs due to their on-demand flexibility. However,
+whenever a new LISL is established, LISL setup delay is added to
+the end-to-end latency. To model the end-to-end latency including
+LISL setup delay, we study the quantification of LISL setup delay,
+and calculate the end-to-end latencies for low, medium, and high
+inter-continental distance connections for different LISL setup
+delay values. We find that the end-to-end latency depends on path
+change rate which reduces as LISL range increases but increases
+as inter-continental distance increases. We also highlight the
+impact of LISL setup delay on total end-to-end latency which
+clearly indicates that LISL setup delay cannot be ignored. We
+observe that the impact of LISL setup delay reduces as LISL
+range or inter-continental distance increases. We also deduce
+the formula to find maximum tolerable value of LISL setup
+delay which represents design guidelines for LCT manufacturers
+so that FSOSNs can have better latency performance compared
+to OFTN. We see that for some LISL range, there does not
+exist any such value of ηs,max. An interesting takeaway point is
+that higher LISL range has two major benefits. Firstly, highest
+possible LISL range has the best latency performance. Secondly,
+it has the highest value of ηs,max which can be attainable.
+However, with high LISL range, the penalty is more satellite
+transmission power and energy consumption.
+It is evident that due to change of shortest path with time
+slots, LISL setup delay is introduced which negatively impacts
+the latency of an FSOSN using dynamic LISLs. In order to
+minimize end-to-end latency, we need to minimize the path
+change rate so that LISL setup delay is introduced less often.
+In future, we plan to develop algorithms to minimize the path
+change rate for a better latency performance.
+ACKNOWLEDGMENT
+This work was supported by the High Throughput and Secure
+Networks Challenge Program at the National Research Council
+of Canada. The authors would also like to acknowledge Dr.
+Pablo Madoery for his technical help and feedback.
+REFERENCES
+[1] T. Ahmmed, A. Alidadi, Z. Zhang, A. U. Chaudhry, and H. Yanikomeroglu,
+“The Digital Divide in Canada and the Role of LEO Satellites in Bridging the
+Gap,” IEEE Communications Magazine, vol. 60(6), pp. 24–30, Jun. 2022.
+[2] A. U. Chaudhry and H. Yanikomeroglu, “Optical Wireless Satellite
+Networks versus Optical Fiber Terrestrial Networks: The Latency
+Perspective–Invited Paper,” in Proc. 30th Biennial Symposium on
+Communications, Saskatoon, Canada, 2021, pp. 1–6.
+[3] D. Bhattacharjee, T. Acharya, and S. Chakravarty, “Energy Efficient Data
+Gathering in IoT Networks With Heterogeneous Traffic for Remote Area
+Surveillance Applications: A Cross Layer Approach,” IEEE Transactions
+on Green Communications and Networking, vol. 5(3), pp. 1165–1178,
+Sep. 2021.
+[4] 3GPP, “Technical Specification Group Radio Access Network, Study on
+New Radio (NR) to Support Non-Terrestrial Networks (NTN),” Oct. 2020,
+TR 38.811, v15.4.0, Release 15.
+[5] A. U. Chaudhry and H. Yanikomeroglu, “Free Space Optics for
+Next-Generation Satellite Networks,” IEEE Consumer Electronics
+Magazine, vol. 10(6), pp. 21–31, Nov. 2021.
+[6] A. U. Chaudhry and H. Yanikomeroglu, “Laser Intersatellite Links in
+a Starlink Constellation: A Classification and Analysis,” IEEE Vehicular
+Technology Magazine, vol. 16(2), pp. 48–56, Jun. 2021.
+[7] SpaceX FCC update, 2018, “SpaceX Non-Geostationary Satellite
+System,
+Attachment
+A,
+Technical
+Information
+to
+Supplement
+Schedule
+S,”
+[Online].
+Available:
+https://licensing.fcc.gov/myibfs/
+download.do?attachment key=1569860, accessed on Oct. 2, 2022.
+[8] H. Kaushal, V. Jain, and S. Kar, “Acquisition, Tracking, and Pointing,”
+in Free Space Optical Communication.
+New Delhi: Springer-Verlag,
+2017, pp. 119–137.
+[9] Y. Kaymak, R. Rojas-Cessa, J. Feng, N. Ansari, M. Zhou, and T. Zhang,
+“A Survey on Acquisition, Tracking, and Pointing Mechanisms for Mobile
+Free-Space Optical Communications,” IEEE Communications Surveys
+& Tutorials, vol. 20(2), pp. 1104–1123, 2018.
+[10] C. Carrizo, M. Knapek, J. Horwath, D. D. Gonzalez, and P. Cornwell,
+“Optical Inter-Satellite Link Terminals for Next Generation Satellite
+Constellations,” in Proc. Society of Photo-Optical Instrumentation
+Engineers (SPIE), vol. 11272, 2020, pp. 1–11.
+[11] M. Handley, “Delay is Not an Option: Low Latency Routing in Space,”
+in Proc. 17th ACM Workshop on Hot Topics in Networks, Redmond, WA,
+USA, 2018, pp. 85–91.
+[12] A. U. Chaudhry and H. Yanikomeroglu, “When to Crossover from Earth to
+Space for Lower Latency Data Communications?” IEEE Transactions on
+Aerospace and Electronic Systems, vol. 58(5), pp. 3962–3978, Mar. 2022.
+[13] TESAT,
+“Laser
+products.”
+[Online].
+Available:
+https://www.tesat.de/products#laser, accessed on Oct. 2, 2022.
+[14] General Atomics, “General Atomics Partners with Space Development
+Agency to Demonstrate Optical Intersatellite Link,” Jun. 2020, [Online].
+Available:
+https://www.ga.com/general-atomics-partners-with-space-
+development-agency-to-demonstrate-optical-intersatellite-link, accessed
+on Oct. 2, 2022.
+[15] J. F. Kurose and K. W. Ross, Computer Networks: A Top Down Approach
+Featuring the Internet, Boston: Addison-Wesley, 2010.
+[16] A. U. Chaudhry and H. Yanikomeroglu, “On Crossover Distance for Optical
+Wireless Satellite Networks and Optical Fiber Terrestrial Networks,” in Proc.
+2022 IEEE Future Networks World Forum, Montreal, Canada, 2022, pp. 1–6.
+[17] M. Handley, “Using Ground Relays for Low-Latency Wide-Area Routing
+in Megaconstellations,” in Proc. 18th ACM Workshop on Hot Topics in
+Networks, New York, NY, USA, 2019, pp. 125–132.
+[18] Y. Hauri, D. Bhattacherjee, M. Grossmann, and A. Singla, ““Internet from
+Space” without Inter-Satellite Links?” in Proc. 19th ACM Workshop on
+Hot Topics in Networks, New York, NY, USA, 2020, pp. 205–211.
+[19] B. Soret, S. Ravikanti, and P. Popovski, “Latency and Timeliness
+in Multi-Hop Satellite Networks,” in Proc. 2020 IEEE International
+Conference on Communications (ICC), Dublin, Ireland, pp. 1–6.
+[20] A. U. Chaudhry and H. Yanikomeroglu, “Temporary Laser Inter-Satellite
+Links in Free-Space Optical Satellite Networks,” IEEE Open Journal
+of the Communications Society, vol. 3, pp. 1413–1427, Aug. 2022.
+[21] AGI,
+“Systems
+Tool
+Kit
+(STK),”
+[Online].
+Available:
+https://www.agi.com/products/stk, accessed on Oct. 2, 2022.
+[22] E. W. Dijkstra, “A Note on Two Problems in Connexion with Graphs,”
+Numerische Mathematik, vol. 1, pp. 269–271, Dec. 1959.
+
+[23] R. Hermenier, C. Kissling, and A. Donner, “A Delay Model for Satellite
+Constellation Networks with Inter-Satellite Links,” in Proc. 2009
+International Workshop on Satellite and Space Communications, Siena,
+Italy, 2009, pp. 3–7.
+[24] C. C. Robusto, “The Cosine-Haversine Formula,” The American
+Mathematical Monthly, vol. 64(1), pp. 38–40, Jan. 1957.
+
diff --git a/4dE4T4oBgHgl3EQf0w2N/content/tmp_files/load_file.txt b/4dE4T4oBgHgl3EQf0w2N/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a2501d67b3f4083dd7bc8ce98cf4ebfcc844c7ef
--- /dev/null
+++ b/4dE4T4oBgHgl3EQf0w2N/content/tmp_files/load_file.txt
@@ -0,0 +1,638 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf,len=637
+page_content='Laser Inter-Satellite Link Setup Delay:  Quantification, Impact, and Tolerable Value  Dhiraj Bhattacharjee1, Aizaz U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Chaudhry1, Halim Yanikomeroglu1, Peng Hu2, and Guillaume Lamontagne3  1Department of Systems and Computer Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada  2National Research Council Canada (NRC), 1200 Montreal Road, Ottawa, ON K1A 0R6, Canada  3MDA, Sainte-Anne-de-Bellevue, QC H9X 3R2, Canada  1{dhirajbhattacharjee, auhchaud, halim}@sce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='carleton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='ca, 2peng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='hu@nrc-cnrc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='gc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='ca, 3guillaume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='lamontagne@mda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='space  Abstract—Dynamic laser inter-satellite links (LISLs) provide  the flexibility of connecting a pair of satellites as required (dynam-  ically) while static LISLs need to be active continuously between  the energy-constrained satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' However, due to the LISL estab-  lishment time (termed herein as LISL setup delay) being in the  order of seconds, realizing dynamic LISLs is currently unfeasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Towards the realization of dynamic LISLs, we first study the  quantification of LISL setup delay;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' then we calculate the end-  to-end latency of a free-space optical satellite network (FSOSN)  with the LISL setup delay;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' subsequently, we analyze the impact  of LISL setup delay on the end-to-end latency of the FSOSN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  We also provide design guidelines for the laser communication  terminal manufacturers in the form of maximum tolerable value  of LISL setup delay for which the FSOSN based on Starlink’s  Phase I satellite constellation will be meaningful to use for low-  latency long-distance inter-continental data communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Index Terms—dynamic laser inter-satellite links, free-space  optical satellite networks, laser inter-satellite link setup delay,  Starlink.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' INTRODUCTION  In recent advancements of wireless communication of 6G era,  satellite networks have been seen as an integral part along with  terrestrial networks for global broadband coverage specially  for enabling broadband Internet in rural and remote areas [1],  low-latency long-distance inter-continental data communications  [2], and IoT based monitoring and remote surveillance [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' From  3GPP definition, satellite payloads could either be transparent  or regenerative [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In transparent scenario, inter-continental  communication has to go up (ground station to satellite) and  down (satellite to ground station) frequently to reach from  source to destination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' With regenerative payload, communication  between satellites over inter-satellite links (ISLs) could be a  better option in such long-distance communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Compared  to RF-based ISLs, laser ISLs (LISLs) have the advantage of  higher bandwidth, smaller antenna size, higher directivity, less  power consumption, less chance of interception and interference,  etc [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Exploiting these LISLs in low Earth orbit (LEO) or very  low Earth orbit (VLEO) satellite mega constellations, free-space  optical satellite networks (FSOSNs) can be realized in space [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  On the basis of an LISL’s active duration, LISLs can be  classified into two types: static LISLs and dynamic LISLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Static  LISLs are those LISLs which are kept active all the time, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=',  SpaceX’s Starlink will have four static LISLs per satellite which  will be operating all the time [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In contrast, dynamic LISLs  can be established dynamically between satellites (which are  within the LISL range) at any time on demand depending upon  data communication requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' To realize such dynamic  LISLs instantaneously, we need to have very precise and  efficient pointing, acquisition, and tracking (PAT) system [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Before two satellites start communicating via LISLs,  transmitting satellite needs to position its laser beam within  the field of view of receiver satellite (pointing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Then the  receiver satellite needs to align itself towards the arriving beam  (acquisition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Finally, transmitter and receiver continue this  process as the communication goes on (tracking) [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Now, we  define LISL setup delay as the time taken by the PAT system to  establish the LISL, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=', the sum of pointing time and acquisition  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' This delay will be introduced to the end-to-end latency  from a source ground station to destination ground station when  the path over an FSOSN changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Note that when the path  changes, it could lead to one or multiple new LISLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' However,  LISL setup delay will be introduced only once as multiple  LISLs can be established simultaneously during a time slot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Satellites are driven by onboard battery and solar power, and  satellite battery power is a very precious resource, which should  be used intelligently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' On that regard, static LISLs are always  active whether they are being used or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' This will drain the  satellite battery and satellites could be dead more often and they  need to be de-orbited and new satellites have to be launched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  This in turn will increase the maintenance expenditure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' On the  other hand, dynamic LISLs will be an energy efficient approach  where LISLs are only established as required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' With dynamic  LISLs, two neighbour satellites could connect whenever they  are within LISL range and this will provide more routing  options.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' These links between neighbour satellites could be  inter-orbital plane, crossing orbital plane, inter-shell, and even  inter-constellation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=', between Starlink and OneWeb).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Also, as  the LEO/VLEO satellites are mobile, communications between  satellites and ground stations will always be through dynamic  laser links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Furthermore, in an operating satellite constellation, if  one or many satellites fail, dynamic LISLs will instantaneously  reroute the traffic by avoiding the dead satellite(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  LISL setup delay for current laser communication terminals  (LCTs) varies from few seconds to tens of seconds [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' This  prevents us from realizing dynamic LISLs in next-generation  FSOSNs (NG-FSOSNs) in late 2020s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In next-next-generation  FSOSNs (NNG-FSOSNs) (in 2030s), due to advancement in  satellite PAT technology, LISL setup delay could be reduced to  the order of a few milliseconds and dynamic LISLs could become  a reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In this context, we study the quantification of LISL setup  delay in the FSOSN based on Starlink’s Phase I constellation [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  We calculate the end-to-end latency of this FSOSN using different  values of the LISL setup delay in different inter-continental  connection scenarios and different LISL ranges for satellites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  We investigate the impact of LISL setup delay on overall  latency and provide design guidelines for LCT manufacturers  to leverage full potential of NNG-FSOSNs via dynamic LISLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  To the best of our knowledge, there exists no study on LISL  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='05285v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='NI]  12 Jan 2023  setup delay that examines its quantification, and its impact on  end-to-end latency along with its maximum tolerable values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  The authors of [11] state that for terrestrial distances  larger than 3000 km, FSOSNs could provide a better latency  performance as compared to the optical fiber terrestrial network  (OFTN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In high-frequency trading of stocks, even 1 ms  improvement in latency could generate $100 million of revenue  per year [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Thus, in such long distance-communication,  FSOSNs could be a better solution compared to the OFTN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  With this objective, we come up with maximum tolerable values  of LISL setup delay for which latency performance of the  FSOSN based on Starlink’s Phase I constellation will be better  than the OFTN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' This maximum value of LISL setup delay  can be a design guideline for LCT manufacturers to leverage  advantages of dynamic LISLs in NNG-FSOSNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  The paper organization is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' We discuss related  work on network latency of satellite networks and examine  LISL setup delays of current LCT manufacturers in Section  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In Section III, we elaborate on how we quantify LISL setup  delay, calculate end-to-end latency, and define performance  metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' We present our results in Section IV, discuss insights  and design guidelines in Section V, and conclude our discussion  with some possible future extensions in Section VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' RELATED WORK  Currently, Mynaric’s LCT CONDOR needs 30 seconds to  establish an LISL between two satellites for the first time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Once  the orbital parameters are exchanged between satellites, it takes 2  seconds to setup an LISL for every next time [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Tesat [13] and  General Atomics [14] have LCTs for LEO/VLEO constellations  which have LISL setup delay in the range of tens of seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  In any communications network, the end-to-end latency from  source to destination typically has four components: propagation  delay, transmission delay, queuing delay, and processing delay  [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Based on this latency model, authors of [2] compared the  latency performance of FSOSNs and OFTNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' As stated earlier  that latency-wise, FSOSNs can be a better alternative to OFTN for  longer communication distances [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' On that regard, authors of  [12] and [16] have come up with a concept of crossover distance  to determine that for a certain terrestrial distance, which one will  provide a better latency performance among FSOSN and OFTN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Authors of [17] have suggested ground stations as relays as a  substitute of ISLs where satellites have transparent payload.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' With  this network architecture, they proved that constellations like Star-  link can provide better latency performance compared to OFTN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  In addition to that, idle user terminals can also be used which will  provide further improvement in latency performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' However,  [18] shows that exploiting ISLs can reduce variation in latency  performance as well as reduce the effects of weather impairments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  To analyze network delay, authors of [19] have modeled each  satellite node as M/M/1 queue in a multihop scenario where  each satellite can receive packets from ground station as well as  other satellite node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Authors of [20] highlighted the importance  of temporary LISLs (defined as LISLs which are established  temporarily with satellites that are within LISL range) in order  to achieve better latency performance compared to static LISLs  in FSOSNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' They showed that with temporary LISLs, there exist  more number of LISLs which will provide better routing options.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  They also reported that temporary LISLs are more useful at lower  LISL ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Authors of [12] and [20] mentioned about LISL  setup delay in FSOSNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' With that respect, in FSOSNs, along  with the other four end-to-end latency components discussed  earlier, we introduce LISL setup delay to the latency model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' METHODOLOGY  To quantify LISL setup delay, calculate end-to-end latency  from source to destination with the LISL setup delay, investigate  the impact of LISL setup delay on overall latency, and present  design guidelines for LCT as a form of maximum tolerable value  of LISL setup delay, we simulate Starlink’s Phase I Version 2 con-  stellation in AGI’s Systems Tool Kit (STK) platform [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' This  constellation has a total of 1584 satellites consisting 24 orbital  planes with each of them having 66 satellites [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' The orbits are  at an inclination of 53° with respect to the equator and satellites  are at an altitude of 550 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' With these constellation parameters,  we generate this constellation’s satellites in STK with a certain  LISL range (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=', the range over which a satellite in an FSOSN  can establish an LISL with any other satellite within this range)  along with ground stations at New York, London, Istanbul, and  Hanoi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Next we extract the data from STK (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=', vertices, edges,  length of edges, etc) at every second for one hour simulation  period to Python platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Then we apply Dijkstra’s shortest  path algorithm [22] to find shortest path at every time slot (equal  to one second in duration) for the source to destination pairs:  New York–London, New York–Istanbul, and New York–Hanoi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  In our investigation, we consider 4 different values of LISL  range: 1500 km, 1700 km, 2500 km, and 5016 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' The minimum  range to have communication with nearest neighbor at the imme-  diate left and right orbital planes is 1500 km in Starlink’s Phase  I Version 2 constellation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' At this range, a satellite can connect to  two satellites in front and two at rear in the same orbital plane  making total 6 connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' At 1700 km range, a satellite can  connect to three immediate neighbors on the left, three immediate  neighbors on the right, and four intra-orbital plane neighbors  making a total of 10 possible connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' The maximum possible  LISL range for Starlink’s Phase 1 constellation can be calculated  as 5016 km [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' The 2500 km LISL range is taken as an  intermediate value between 1700 km and 5016 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Quantification of LISL Setup Delay  We define LISL setup delay indicator (a binary variable)  as follows: if the shortest paths of (i − 1)th time slot and  ith time slot are exactly same, no LISL setup delay is to be  included in the end-to-end latency, and the LISL setup delay  indicator, αi is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' If shortest path changes from (i−1)th to  ith time slot, αi is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Considering ηs as LISL setup delay, we  denote end-to-end latency without and with LISL setup delay  as ηLE(withoutηs) and ηLE(withηs), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In Table  I, we show shortest paths (satellite naming convention follows  [6]) and corresponding values of ηLE(without ηs), αi, and  ηLE(withηs) for first 6 time slots over the FSOSN for New  York to Istanbul inter-continental connection at an LISL range  of 1500 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' From Table I, we can see that shortest path could  change from time to time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' This is due to the fact that as LEO  satellites are moving at high orbital speeds, either a shortest path  at one time instance may even not exist in the next time instance  (due to one or multiple satellites moving out of range) or there  may become available a new shortest path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' ηLE(withoutηs) has  Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' ηLE(without ηs), αi, ηs, and ηLE(with ηs) of the shortest paths at first 6 time slots  over the FSOSN for New York–Istanbul inter-continental connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  ηLE  ηLE  Time  Shortest  (without  αi  ηs  (with  Slot  Path  ηs)  (ms)  ηs)  (ms)  (ms)  1  GS at New York, satellite x10919, x11115, x11312, x11509, x11609, x11611, x12166, GS at Istanbul  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='09  0  0  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='09  2  GS at New York, satellite x11503, x11505, x11507, x11509, x11609, x11611, x12166, GS at Istanbul  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='08  1  100  138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='08  3  GS at New York, satellite x11503,x11505, x11507, x11509, x11609, x11611, x12166, GS at Istanbul  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='07  0  0  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='07  4  GS at New York, satellite x11503,x11505, x11507, x11509, x11609, x11611, x12166, GS at Istanbul  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='06  0  0  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='06  5  GS at New York, satellite x11503,x11505, x11507, x11509, x11609, x11611, x12166, GS at Istanbul  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='05  0  0  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='05  6  GS at New York, satellite x11503, x11505, x11507, x11508, x11608, x11903, x12166, GS at Istanbul  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='00  1  100  138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='00  two major components: propagation delay and node delay (sum  of processing and queuing delay is node delay).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' We calculate  propagation delay as sum of lengths of all the laser links in  the shortest path divided by speed of light in vacuum and we  consider node delay as 1 ms [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' From Table I, it is evident that  shortest paths are not same for 1st and 2nd time slots, so α2 =1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Considering ηs =100 ms, ηLE(withηs) will be 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='08+100, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=',  138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='08 ms at time slot 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' The shortest path remains unchanged  from time slot 3 to 5, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=', α3 =α4 =α5 =0 and corresponding  ηLE(withηs) values remain same as ηLE(withoutηs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Then  again at time slot 6, shortest path changes which makes α6 =1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Path Change Rate  We simulate for 3600 time slots, one time slot being equal  to 1 second in duration and we define the path change rate,  λ as the average number of instances the shortest path from  source to destination changes (represented in percentage) and  mathematically it can be calculated as  λ=  1  3600  3600  �  i=1  αi ×100%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (1)  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' End-to-End Latency  Averaging ηLE(with ηs) and ηLE(without ηs) over 3600  time slots, we get average end-to-end latency with and without  ηs as ηLE(withηs) and ηLE(withoutηs), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' They  are related to λ and ηs as follows:  ηLE(withηs)=ηLE(withoutηs)+ λ  100 ηs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (2)  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Impact of ηs  To measure the impact of LISL setup delay, ηs on average end-  to-end latency, we define β as percentage of delay introduced due  to ηs in average end-to-end latency and calculate it as follows:  β = ηLE(withηs)−ηLE(withoutηs)  ηLE(withηs)  ×100%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (3)  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Tolerable Value of ηs  For an inter-continental connection, it is meaningful to use  the FSOSN only when ηLE(withηs) is lesser than end-to-end  latency of the OFTN, ηLE,OF T N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Using (2), the following can  be written,  ηLE(withoutηs)+ λ  100 ηs ≤ηLE,OF T N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (4)  Now we define the maximum tolerable value of LISL setup  delay, ηs,max as the maximum value of ηs so that the average  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Path change rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  end-to-end latency of the FSOSN is lesser or equal to that of  the OFTN and calculate it from (4) as follows:  ηs,max = ηLE,OF T N −ηLE(withoutηs)  λ/100  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (5)  To calculate ηLE,OF T N, first we determine the distance  from the source ground station to the destination ground  station along the surface of the Earth using Haversine formula  [24] from latitudes and longitudes of source and destination  ground stations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Later we find ηLE,OF T N as that distance  divided by speed of light in the optical fiber (having refractive  index=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4675), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=', 204,287,876 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' RESULTS  We consider three inter-continental connections: New York to  London (low inter-continental distance connection with terrestrial  distance=5593 km), New York to Istanbul (mid inter-continental  distance connection with terrestrial distance=8079 km), and  New York to Hanoi (high inter-continental distance connection  with terrestrial distance=13164 km).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For the metrics λ, ηLE,  and β, we show bar plots for the four LISL ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' To clearly  show both high and low values in the same figure, we use log  scale in the y-axis in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1 to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Path Change Rate  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1, we plot λ with LISL range varying along x-axis for  the three inter-continental connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For any inter-continental  connection, we can observe that λ reduces as LISL range  increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Also note that for a particular LISL range, the more  the inter-continental distance, the higher the value of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' End-to-End Latency  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2 shows end-to-end latency for the three inter-continental  connections averaged over one hour of simulation period  without considering ηs and with four ηs values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' As LISL range  increases along x-axis, both ηLE(withoutηs) (black bars) and  ηLE(withηs) (other bars) decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For a certain LISL range, the  102  New York to London  New York to Istanbul  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='1  New York to Hanoi  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  (%)  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='8  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  101  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='8  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='8  100  1500  1700  2500  5016  LISL Range (km)(a) New York to London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (b) New York to Istanbul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (c) New York to Hanoi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Average end-to-end latency performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  more the value of ηs, the more the overall latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For example, in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2a with LISL range of 1700 km, ηLE(withηs) is 123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9 ms  for ηs=1 sec and it reduces to 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7 ms when ηs is considered to  be 100 ms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Also, for a certain LISL range with a certain ηs value,  the more the inter-continental distance, the more the end-to-end  latency for both the cases: ηLE(withoutηs) and ηLE(withηs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  It is interesting to note that with the increase of LISL range,  ηLE(with ηs) reduces faster compared to ηLE(without ηs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  For example, considering Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2a, ηLE(withoutηs) drops from  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9 ms to 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6 ms when LISL range increases from 1700  km to 2500 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' If we take the ratio and term the ratio as  reduction ratio, for this case it will be 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6 =1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='053.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Similarly,  for ηLE(with ηs), the reduction ratio will be 123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='1 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='345  which is greater than that of ηLE(withoutηs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Impact of ηs  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 3, we show the variation of β with LISL range for  four ηs values in the three inter-continental connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' As we  see, β reduces as LISL range increases for a certain ηs value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Also, at a certain LISL range, β reduces as ηs reduces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For  example, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 3b with LISL range of 2500 km, β is 71%  for ηs=1 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' However, when ηs reduces to 100 ms, β reduces  to 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In addition, for a certain LISL range with a particular  ηs value, β reduces as inter-continental distance increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For  example, assuming 1700 km of LISL range and ηs as 1 sec, β  reduces from 77% to 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='1% when inter-continental connection  changes from New York–Istanbul to New York–Hanoi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Tolerable Value of ηs  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4, we plot ηLE(withηs) and ηLE,OF T N against ηs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Note that, ηLE(withηs) is a straight line with a constant slope  and as LISL range increases, the slope reduces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' The significance  of this figure is where ηLE(withηs) for a certain LISL range  cuts ηLE,OF T N, the x-coordinate value of the intersection point  is ηs,max as beyond that point, ηLE(with ηs) will be greater  than ηLE,OF T N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' To show the intersection points clearly, we  only present ηs values on the x-axis varying from 1 ms to  100 ms where we mention the coordinates of the intersection  points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' If we substitute ηLE,OF T N =39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='55 ms (from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4b),  ηLE(without ηs) = 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9 ms (from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2b), and λ = 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5%  (from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1) for New York to Istanbul inter-continental  connection with 1500 km LISL range in (5), we get ηs,max  as 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4 ms which matches with Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Also, we should observe  from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4 that, as LISL range increases, ηs,max also increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Interesting point to note in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4c is that it only shows two  intersection points because ηLE(withηs) for 1500 km and 1700  km LISL range straight lines (black and blue lines) never intersect  with ηLE,OF T N for ηs >1 ms values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For 1500 km LISL range,  ηLE(withoutηs)=66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5 ms (from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2c) and ηLE,OF T N=64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='44  ms (from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Putting these values in (5), we get negative  ηs,max value which does not exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Similarly, for 1700 km LISL  range, ηLE(withoutηs)≈ηLE,OF T N which makes ηs,max ≈0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' INSIGHTS AND DESIGN GUIDELINES  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Insights  1) Path Change Rate  As LISL range increases, there will be lesser hops, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=', lesser  number of satellites for the signal to reach from source to  destination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For example, in New York to Istanbul inter-  continental connection, average number of hops drops from  7 to 6 when LISL range increases from 1500 km to 1700 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  The lesser the number of hops, the lesser is the chance of a  new shortest path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' This in turn reduces λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Also, when the LISL  range increases, two satellites remain in communication range  for a longer time span.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' One of the reasons for the shortest  path to change is satellites going out of LISL range, and a  shortest path tends to change lesser with longer LISL range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Due to these two reasons, λ reduces as LISL range increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  For a certain LISL range, the longer the inter-continental  distance, the higher the average number of hops which leads  to more chances of a new shortest path, and this increases  the path change rate, λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  2) End-to-End Latency  Increase in LISL range reduces the number of hops which  reduces total node delays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' This decreases ηLE(withoutηs)  with the increase in LISL range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Now, as both λ and  ηLE(withoutηs) decrease with the increase of LISL range,  from (2), it is clear that ηLE(withηs) also decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  From (2), we can see that if ηs reduces, ηLE(with ηs)  reduces for a certain LISL range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  For a certain LISL range with a certain ηs value, when  inter-continental distance increases, λ increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' From (2), we  can say that ηLE(withηs) will increase with the increase of  λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For longer inter-continental connections, propagation delay  as well as node delay (due to more number of hops) is more  which increases ηLE(withoutηs) for longer inter-continental  connections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  We consider that at LISL range la and lb (lb > la), path  change rates are λa and λb, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Also, the average  end-to-end latencies without ηs are ηLEa(without ηs)  103  Without ns  With ns=1 sec  With ns=100 ms  365.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='1  Withns=10 ms  With ns=1 ms  (sw) 3u  123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  102  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='1  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  101  1500  2500  1700  5016  LiSL Range (km)103  Without ns  With ns=l sec  With ns=100 ms  413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  With ns=10 ms  With ns=1 ms  160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  (sw)  122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='8  113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  102  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='1  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  101  1500  1700  2500  5016  LISL Range (km)Without ns  With ns=1 sec  With ns=100 ms  103  With ns=10 ms  With ns=1 ms  457.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='8  (ms)  239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  nLE  153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='1  105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  102  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='8  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  101  1500  1700  2500  5016  LiSL Range (km)(a) New York to London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (b) New York to Istanbul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (c) New York to Hanoi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Impact of ηs on end-to-end latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (a) New York to London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (b) New York to Istanbul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (c) New York to Hanoi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Maximum tolerable value of ηs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  and ηLEb(without ηs), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' From Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1 and 2  values we observe that λa  λb > ηLEa(withoutηs)  ηLEb(withoutηs) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For example,  considering New York to Istanbul inter-continental connection,  assuming la=1500 km and lb=1700 km, λa  λb = 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='049  and ηLEa(withoutηs)  ηLEb(withoutηs) = 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9 =1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Now, we can write the  following:  λa  λb  > ηLEa(withoutηs)  ηLEb(withoutηs) ,  (6)  λa ηs/100  ηLEa(withoutηs) >  λb ηs/100  ηLEb(withoutηs),  (7)  1+  λa ηs/100  ηLEa(withoutηs) >1+  λb ηs/100  ηLEb(withoutηs),  (8)  ηLEa(withoutηs)+ λa  100 ηs  ηLEa(withoutηs)  > ηLEb(withoutηs)+ λb  100 ηs  ηLEb(withoutηs)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (9)  Assuming  average  end-to-end  latency  with  ηs  as  ηLEa(withηs) and ηLEb(withηs) for LISL range la and lb,  respectively and using (2) we can rewrite (9) as follows:  ηLEa(withηs)  ηLEb(withηs) > ηLEa(withoutηs)  ηLEb(withoutηs) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  (10)  3) Impact of ηs  We have seen that ηLE(with ηs) reduces faster compared  to ηLE(withoutηs) as LISL range increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Thus, the ratio  ηLE(withoutηs)  ηLE(withηs)  increases as LISL range increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' From (3),  as we can see that β is proportional to  �  1− ηLE(withoutηs)  ηLE(withηs)  �  ,  β reduces with the increase of LISL range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  ηLE(withηs) reduces when ηs reduces but ηLE(withoutηs)  remains the same which causes the ratio ηLE(withoutηs)  ηLE(withηs)  to  increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' As β is proportional to  �  1 − ηLE(withoutηs)  ηLE(withηs)  �  , it  decreases when ηs reduces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Let us consider that for inter-continental distance dx and dy  (dy >dx), path change rates are λx and λy, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Also,  average end-to-end latencies without ηs are ηLEx(withoutηs)  and ηLEy(without ηs), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' From Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1 and 2  values, we also observe that λx  λy > ηLEx(withoutηs)  ηLEy (withoutηs) (note that  in this discussion, we are varying inter-continental distance, not  LISL range).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For example, at 1700 km LISL range, for New  York to Istanbul and New York to Hanoi inter-continental con-  nection, λx, λy, ηLEx(without ηs), and ηLEy(without ηs)  are 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3%, 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5%, 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9 ms, and 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4 ms, respectively from  which we get λx  λy =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='703 and ηLEx(withoutηs)  ηLEy (withoutηs) =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='573.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Using  the approach in (6) – (10), we can come to the conclusion that  ηLEx(withoutηs)  ηLEx(withηs)  <  ηLEy (withoutηs)  ηLEy (withηs)  where ηLEx(withηs) and  ηLEy(withηs) are average end-to-end latencies considering ηs  for inter-continental distance dx and dy, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=', ηLE(withoutηs)  ηLE(withηs)  in-  creases as inter-continental distance increases which reduces β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  4) Tolerable Value of ηs  (2) represents an equation of a straight line with slope  proportional to λ considering ηLE(withηs) as y variable and  ηs as the x variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' As LISL range increases, λ decreases  which makes the slope of the straight lines to reduce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In  addition to λ, ηLE(without ηs) also reduces with the  110  FSOSN with LiSL Range=1500km  FSOSN with LISL Range=1700km  100  FSOSN with LISL Range=2500km  FSOSN with LISL Range=5016km  90  OFTN  (ms)  80  37u  70  (24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='58,64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='44)  (80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='63,64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='44)  60  50  20  40  60  80  100  ns (ms)92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  102  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='1  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  101  (%)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  B  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  1500  1700  2500  5016  LISL Range (km)Ns=l sec  ns=100 ms  ns=10 ms  ns=1 ms  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='8  102  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='8  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  101  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  (%)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  B  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  1500  1700  2500  5016  LiSL Range (km)85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  102  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='1  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='5  101  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  β  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='17  1500  2500  5016  1700  LISL Range (km)60  FSOSN with LISL Range=1500km  55  FSOSN with LISLRange=1700km  FSOSN with LISL Range=2500km  50  FSOSN with LISL Range=5016km  OFTN  45  (ms)  40  37  35  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='30,27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='38)  30  (15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='10,27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='38)  (40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='88,27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='38)  (70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='34,27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='38)  25  20  10  20  30  40  50  60  70  80  ns (ms)80  FSOSN with LISL Range=1500km  FSOSN with LISL Range=1700km  70  FSOSN withLISL Range=2500km  FSOSN with LISL Range=5016km  OFTN  60  (sw) u  50  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='40,39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='55)  (21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='54,39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='55)  (45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='40,39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='55)  40  (76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='87,39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='55)  30  20  40  60  80  100  Ns (ms)increase of LISL range, and from (5) we can say that ηs,max  increases with increase in LISL range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Design Guidelines  The values we get from (5) are exactly same as we  get from intersection points shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Given that  ηLE,OF T N, ηLE(withoutηs), and λ are known for a particular  inter-continental connection for a certain LISL range, (5) can  be used to design LCTs in order to exploit full potential of  NNG-FSOSNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' For example:  For New York to London inter-continental connection with  1500 km of LISL range, ηLE,OF T N, ηLE(withoutηs), and λ  are 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='38 ms, 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6 ms, and 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9%, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Putting these  values in (5), we get ηs,max as 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3 ms (same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  With 1700 km LISL range for New York to Istanbul  inter-continental connection, putting ηLE,OF T N=39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='55 ms,  ηLE(without ηs)=36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='9 ms, and λ=12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='3% in (5), we get  ηs,max=21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='54 ms, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=', exactly as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Considering New York to Hanoi inter-continental connection  with 5016 km of LISL range, values of ηLE,OF T N,  ηLE(withoutηs), and λ are 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='44 ms, 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='7 ms, and 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='6%,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Using these values in (5), we get ηs,max equal  to 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='63 ms (same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 4c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' CONCLUSION AND FUTURE WORK  Dynamic LISLs are essential to leverage the full potential  of NNG-FSOSNs due to their on-demand flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' However,  whenever a new LISL is established, LISL setup delay is added to  the end-to-end latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' To model the end-to-end latency including  LISL setup delay, we study the quantification of LISL setup delay,  and calculate the end-to-end latencies for low, medium, and high  inter-continental distance connections for different LISL setup  delay values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' We find that the end-to-end latency depends on path  change rate which reduces as LISL range increases but increases  as inter-continental distance increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' We also highlight the  impact of LISL setup delay on total end-to-end latency which  clearly indicates that LISL setup delay cannot be ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' We  observe that the impact of LISL setup delay reduces as LISL  range or inter-continental distance increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' We also deduce  the formula to find maximum tolerable value of LISL setup  delay which represents design guidelines for LCT manufacturers  so that FSOSNs can have better latency performance compared  to OFTN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' We see that for some LISL range, there does not  exist any such value of ηs,max.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' An interesting takeaway point is  that higher LISL range has two major benefits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Firstly, highest  possible LISL range has the best latency performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Secondly,  it has the highest value of ηs,max which can be attainable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  However, with high LISL range, the penalty is more satellite  transmission power and energy consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  It is evident that due to change of shortest path with time  slots, LISL setup delay is introduced which negatively impacts  the latency of an FSOSN using dynamic LISLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' In order to  minimize end-to-end latency, we need to minimize the path  change rate so that LISL setup delay is introduced less often.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  In future, we plan to develop algorithms to minimize the path  change rate for a better latency performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  ACKNOWLEDGMENT  This work was supported by the High Throughput and Secure  Networks Challenge Program at the National Research Council  of Canada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' The authors would also like to acknowledge Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Pablo Madoery for his technical help and feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  REFERENCES  [1] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Ahmmed, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Alidadi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Chaudhry, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Yanikomeroglu,  “The Digital Divide in Canada and the Role of LEO Satellites in Bridging the  Gap,” IEEE Communications Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 60(6), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 24–30, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Chaudhry and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Yanikomeroglu, “Optical Wireless Satellite  Networks versus Optical Fiber Terrestrial Networks: The Latency  Perspective–Invited Paper,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 30th Biennial Symposium on  Communications, Saskatoon, Canada, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Bhattacharjee, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Acharya, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Chakravarty, “Energy Efficient Data  Gathering in IoT Networks With Heterogeneous Traffic for Remote Area  Surveillance Applications: A Cross Layer Approach,” IEEE Transactions  on Green Communications and Networking, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 5(3), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1165–1178,  Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [4] 3GPP, “Technical Specification Group Radio Access Network, Study on  New Radio (NR) to Support Non-Terrestrial Networks (NTN),” Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2020,  TR 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='811, v15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='0, Release 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Chaudhry and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Yanikomeroglu, “Free Space Optics for  Next-Generation Satellite Networks,” IEEE Consumer Electronics  Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 10(6), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 21–31, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Chaudhry and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Yanikomeroglu, “Laser Intersatellite Links in  a Starlink Constellation: A Classification and Analysis,” IEEE Vehicular  Technology Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 16(2), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 48–56, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [7] SpaceX FCC update, 2018, “SpaceX Non-Geostationary Satellite  System,  Attachment  A,  Technical  Information  to  Supplement  Schedule  S,”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Available:  https://licensing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='fcc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='gov/myibfs/  download.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='do?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='attachment key=1569860, accessed on Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [8] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Kaushal, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Jain, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Kar, “Acquisition, Tracking, and Pointing,”  in Free Space Optical Communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  New Delhi: Springer-Verlag,  2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 119–137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [9] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Kaymak, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Rojas-Cessa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Feng, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Ansari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Zhou, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Zhang,  “A Survey on Acquisition, Tracking, and Pointing Mechanisms for Mobile  Free-Space Optical Communications,” IEEE Communications Surveys  & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 20(2), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1104–1123, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [10] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Carrizo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Knapek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Horwath, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Gonzalez, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Cornwell,  “Optical Inter-Satellite Link Terminals for Next Generation Satellite  Constellations,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Society of Photo-Optical Instrumentation  Engineers (SPIE), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 11272, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Handley, “Delay is Not an Option: Low Latency Routing in Space,”  in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 17th ACM Workshop on Hot Topics in Networks, Redmond, WA,  USA, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 85–91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Chaudhry and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Yanikomeroglu, “When to Crossover from Earth to  Space for Lower Latency Data Communications?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' IEEE Transactions on  Aerospace and Electronic Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 58(5), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 3962–3978, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [13] TESAT,  “Laser  products.”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='tesat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='de/products#laser, accessed on Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [14] General Atomics, “General Atomics Partners with Space Development  Agency to Demonstrate Optical Intersatellite Link,” Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2020, [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='ga.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='com/general-atomics-partners-with-space-  development-agency-to-demonstrate-optical-intersatellite-link, accessed  on Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Kurose and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Ross, Computer Networks: A Top Down Approach  Featuring the Internet, Boston: Addison-Wesley, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Chaudhry and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Yanikomeroglu, “On Crossover Distance for Optical  Wireless Satellite Networks and Optical Fiber Terrestrial Networks,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  2022 IEEE Future Networks World Forum, Montreal, Canada, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [17] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Handley, “Using Ground Relays for Low-Latency Wide-Area Routing  in Megaconstellations,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 18th ACM Workshop on Hot Topics in  Networks, New York, NY, USA, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 125–132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Hauri, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Bhattacherjee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Grossmann, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Singla, ““Internet from  Space” without Inter-Satellite Links?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 19th ACM Workshop on  Hot Topics in Networks, New York, NY, USA, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 205–211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [19] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Soret, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Ravikanti, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Popovski, “Latency and Timeliness  in Multi-Hop Satellite Networks,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2020 IEEE International  Conference on Communications (ICC), Dublin, Ireland, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Chaudhry and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Yanikomeroglu, “Temporary Laser Inter-Satellite  Links in Free-Space Optical Satellite Networks,” IEEE Open Journal  of the Communications Society, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1413–1427, Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [21] AGI,  “Systems  Tool  Kit  (STK),”  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='agi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='com/products/stk, accessed on Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [22] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Dijkstra, “A Note on Two Problems in Connexion with Graphs,”  Numerische Mathematik, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 269–271, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1959.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [23] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Hermenier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Kissling, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Donner, “A Delay Model for Satellite  Constellation Networks with Inter-Satellite Links,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 2009  International Workshop on Satellite and Space Communications, Siena,  Italy, 2009, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 3–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content='  [24] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' Robusto, “The Cosine-Haversine Formula,” The American  Mathematical Monthly, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 64(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 38–40, Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
+page_content=' 1957.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQf0w2N/content/2301.05285v1.pdf'}
diff --git a/4tAyT4oBgHgl3EQfpPhP/content/tmp_files/2301.00521v1.pdf.txt b/4tAyT4oBgHgl3EQfpPhP/content/tmp_files/2301.00521v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..73b037fc7aaaf9b26f23793b5ee1a6b78923b70b
--- /dev/null
+++ b/4tAyT4oBgHgl3EQfpPhP/content/tmp_files/2301.00521v1.pdf.txt
@@ -0,0 +1,3696 @@
+A RL-based Policy Optimization Method Guided by Adaptive Stability
+Certification
+Shengjie Wang 1 Fengbo Lan 1 Xiang Zheng 2 Yuxue Cao 3 Oluwatosin Oseni 4 Haotian Xu 1 Yang Gao 5
+Tao Zhang 1
+Abstract
+In contrast to the control-theoretic methods, the
+lack of stability guarantee remains a significant
+problem for model-free reinforcement learning
+(RL) methods. Jointly learning a policy and a
+Lyapunov function has recently become a promis-
+ing approach to ensuring the whole system with
+a stability guarantee. However, the classical Lya-
+punov constraints researchers introduced cannot
+stabilize the system during the sampling-based
+optimization. Therefore, we propose the Adap-
+tive Stability Certification (ASC), making the sys-
+tem reach sampling-based stability. Because the
+ASC condition can search for the optimal policy
+heuristically, we design the Adaptive Lyapunov-
+based Actor-Critic (ALAC) algorithm based on
+the ASC condition. Meanwhile, our algorithm
+avoids the optimization problem that a variety of
+constraints are coupled into the objective in cur-
+rent approaches. When evaluated on ten robotic
+tasks, our method achieves lower accumulated
+cost and fewer stability constraint violations than
+previous studies.
+1. Introduction
+Learning-based (especially Reinforcement-Learning-based)
+controllers have become increasingly popular and have
+achieved excellent performance in non-linear dynamic sys-
+tems (Hwangbo et al., 2019; Andrychowicz et al., 2020).
+However, a lack of some safety notions introduces addi-
+tional risks to the agents and environments. Stability is a
+crucial notion of safety, whose violation can cause unsafe
+behaviours (Jin et al., 2020). Fortunately, there exists an
+effective tool to assess the stability, Lyapunov functions, in
+1Department of Automation, Tsinghua University 2Department
+of Computer Science, City University of Hong Kong 3Beijing
+Institute of Control Engineering 4Covenant University 5Institute
+for Interdisciplinary Information Sciences,Tsinghua University.
+Correspondence to: Tao Zhang <taozhang@tsinghua.edu.cn>.
+State space
+𝑐! 𝑠 ≤ 𝑏
+𝑠"
+𝑐! 𝑠 = 0
+Diverging trajectory
+Optimal trajectory w/ stability
+Sub-optimal trajectory w/ stability
+Unstable trajectory
+Figure 1. Intuitive example showing the mean cost stabil-
+ity according to Definition 3.1. The figure shows the re-
+lationship between three sets, like the whole state space,
+{s | cπ(s) ≤ b} and {s | cπ(s) = 0}. The red line repre-
+sents a diverging trajectory. The yellow line represents a
+trajectory without the mean cost stability. The trajectories
+coloured cyan and purple remain stable, whereas the state in
+the purple trajectory reaches the set {s | cπ(s) = 0} more
+quickly. The task aims to obtain the policy that can generate
+the purple trajectory.
+control-theoretic approaches. Lyapunov functions can be
+designed for a linear system with specific criteria in the form
+of a quadratic positive-definite function. But how to find
+a suitable Lyapunov function remains an open challenge
+in the non-linear dynamic system (La Salle & Lefschetz,
+2012).
+Thanks to the emergence of deep learning, researchers no-
+ticed that the neural Lyapunov function had an outperform-
+ing representation ability, thereby making it possible to
+search for a feasible Lyapunov function. According to Lya-
+punov’s second method for stability, the neural Lyapunov
+function is trained by forcing the updating direction toward
+decreasing the Lyapunov function along an episode’s state
+trajectories (Chang et al., 2019). In the early stage of time,
+these methods are only suitable for the model-based setting
+because the difference of Lyapunov function with respect to
+time brings a requirement of dynamic model (Berkenkamp
+arXiv:2301.00521v1  [cs.RO]  2 Jan 2023
+
+Adaptive Stability Certification
+et al., 2017; Richards et al., 2018). In contrast to model-
+based methods, model-free reinforcement learning meth-
+ods have achieved superior performance on many complex
+robotic systems (Hwangbo et al., 2019; Andrychowicz et al.,
+2020). Therefore, researchers proposed some methods to
+overcome the above issue. Firstly, they applied the discrete
+Lyapunov stability condition directly in the optimization.
+Then, the Lyapunov conditions can be viewed as multiple
+constraints. Prior studies added those constraints into the ob-
+jective function. Specifically, the objective function enables
+the system to reach optimality and stability together. Fur-
+thermore, it is worth noting that current RL-based methods
+with stability guarantee have been applied in some practi-
+cal problems successfully, such as monitoring the security
+of interconnected microgrids (Huang et al., 2021), power
+system control (Zhao et al., 2021), automatic assembly (Li
+et al., 2022) and motion planning of autonomous vehicles
+(Zhang et al., 2021).
+Admittedly, RL-based approaches with the help of the Lya-
+punov function achieve promising performance. However,
+the discrete Lyapunov stability condition should be satisfied
+in the whole state space, which means infinity constraints
+for continuous control tasks. Due to the sampling-based
+optimization in RL, current approaches sample some data
+pairs randomly, which causes a serious problem that the
+discrete stability condition is not convincing. Furthermore,
+reaching optimality and stability together remains a chal-
+lenge for their objective function. Because the Lyapunov
+stability condition introduces various constraints in the ob-
+jective function, it is hard to balance the optimality and
+stability of the system. In practical experiments, we find
+that previous constraints are either loose to find ineffective
+Lyapunov functions or tight to make the policy trapped into
+a sub-optimal point. Therefore, to better improve the cur-
+rent research, we hope the Lyapunov-based constraint can
+facilitate the policy to reach the optima within the set of the
+sampling-based stability. To better understand the principle,
+we give an intuitive example in Figure 1.
+To address the above issues, we propose the Adaptive
+Lyapunov-based Actor-Critic algorithm (ALAC). Unlike
+the discrete Lyapunov stability condition, we propose a
+novel sampling-based stability condition called Adaptive
+Stability Certification (ASC). Meanwhile, the certifica-
+tion can guide the policy to search for the optimal point
+heuristically. Thus, based on the ASC condition, we de-
+sign the Adaptive Lyapunov-based Actor-Critic algorithm
+(ALAC) to reach the optimality and stability of the system.
+Thanks to the supervised learning for a Lyapunov candidate
+and the Lagrangian-based policy optimization, our method
+eliminates the coupling relationship between various con-
+straints and the objective function. Experiments show that
+our method provides promising results under stability con-
+straints on some robotic control problems, like walking of
+legged robots, trajectory planning of a free-floating space
+robot, and so on. Another interesting finding is that, in
+contrast to traditional RL algorithms, our method facilitates
+the controller to enhance the robustness, generalization, and
+efficiency of the whole system 1.
+2. Related works
+Due to the difficulty of a manual design, constructing a
+Lyapunov neural network has become increasingly popu-
+lar in a non-linear dynamic system. For the model-known
+situation, the approaches jointly learn a Lyapunov func-
+tion and a controller (Richards et al., 2018; Chang et al.,
+2019; Mittal et al., 2020; Dai et al., 2020; Lechner et al.,
+2021; Donti et al., 2020; Gaby et al., 2021). But it re-
+stricts the application of complex systems which are hard
+to obtain accurate models. Therefore, some researchers
+present model-learned methods with a stability guarantee,
+in which Gaussian Process or Neural Network approximates
+the model. The model-learned method can be separated into
+two types. The first one is learning dynamics models guided
+by a learnable Lyapunov function, in which policies are
+inherently included or learned by LQR method (Kashima
+et al., 2022; Zhou et al., 2022; Chen et al., 2021; Lawrence
+et al., 2020; Schlaginhaufen et al., 2021). Another approach
+is to construct a learnable policy network updated by a neu-
+ral Lyapunov function, thereby satisfying the stability of
+system (Berkenkamp et al., 2017; Dawson et al., 2022; Zhou
+et al., 2022; Dai et al., 2021; Lale et al., 2022). However, we
+notice that most model-learned methods are only verified
+in relatively easy environments. A possible reason is that
+the coupling of the Lyapunov function and dynamic model
+makes learning unstable or incompatible due to interdepen-
+dency.
+A promising direction is to study model-free methods with
+a stability guarantee. Recently, a large variety of methods
+have been proposed to address the issue. One method is that
+the policy is updated by a mixed objective with respect to the
+neural Lyapunov function and Q function. POLYC (Chang
+& Gao, 2021) introduced the necessary conditions required
+by the Lyapunov function into objectives to optimize the
+policy network. LBPO (Sikchi et al., 2021) applied the log-
+arithmic barrier function based on the form of the Lyapunov
+function. TNLF (Xiong et al., 2022) constructed Lyapunov
+V and Q functions trained by the stability certification. The
+other form is policy optimization with Lyapunov constraints.
+Chow et al. (2018) designed a constrained RL algorithm to
+project a policy in a trust region with Lyapunov stability.
+Han et al. (2020a) provided a novel constrained RL-based
+approach called LAC, using the prime-dual method to mod-
+ify the constraint. Their latter work verified them in both
+1See our project page at https://sites.google.com/view/adaptive-
+lyapunov-actor-critic.
+
+Adaptive Stability Certification
+on-policy and off-policy settings (Han et al., 2021; 2020b).
+In the previous study, there still exist two main drawbacks
+to obtaining the optimal policy and a suitable Lyapunov
+function. The discrete Lyapunov condition they used did
+not meet the demand for a sampling-based stability guar-
+antee in RL. Furthermore, a combined objective function
+via a simple addition causes a sub-optimal policy or invalid
+Lyapunov function, especially for multiple and complex
+constraints. In contrast, our method proposes the Adap-
+tive Lyapunov-based Actor-Critic algorithm to satisfy the
+sampling-based stability and search for the optimal policy
+heuristically.
+3. Problem Formulation
+The pre-process of implementing RL-based algorithms is to
+formulate robotic control problems as a Markov Decision
+Process (MDP). In our paper, MDP mainly consists of four
+elements, such as S, A, P, and C. Here, S is the state space,
+A is the action space, P is the dynamic transition function,
+and C is the cost function. At timestep t, st ∈ S represents
+the state the robot observes. Then, at ∈ A is the action
+executed by the agent(robot). Note that at is sampled from
+the agent’s policy π(at|st). According to P(st+1|st, at),
+the state of system transfers to the next state st+1 with a
+certain probability. At the same time, the agent receives the
+cost cπ(st) = Ea∼πC(st, at). Besides, the distribution of
+starting state denotes s0 ∼ ρ. And then, we can define the
+state distribution T :
+T (s|ρ,π, t + 1) =
+�
+S
+�
+A
+π(at|st)P(st+1|st, at) daT (s|ρ, π, t) ds
+(1)
+Note that T (s|ρ, π, 0) = ρ holds.
+The optimal objec-
+tive is to find the optimal polity π∗, which can minimize
+Eπ[�∞
+t=0 γtcπ(t)|s0 = s] where γ is a discounting factor.
+An MDP system corresponds to a deterministic, continuous-
+state, discrete-time dynamical system st+1 = f(s, a) with
+state space S and action space A. Therefore, the system’s
+stability can be verified by a classical tool, Lyapunov’s Sta-
+bility Function (see Appendix A.3). If a Lyapunov function
+exists, a discrete-time system can achieve stability in the
+sense of Lyapunov as depicted in Appendix A.1 and A.2.
+In order to search for a Lyapunov function, current ap-
+proaches attempt to train a Lyapunov network by min-
+imizing the requirements in Appendix A.3.
+However,
+optimization-based methods meet a common problem in
+that the trained Lyapunov function remains close to 0 along
+the whole trajectories, thus resulting in ineffective guidance
+for the policy. More importantly, the classical definition
+is based on the whole state space, so it is unsuitable for
+RL-based methods due to sampling optimization.
+Therefore, we should extend the stability to a reasonable
+case in RL. We notice that for most robotic tasks, cost
+functions are related to the stability of the closed-loop
+system. For example, the goal of stabilization tasks is
+to make the norm of state equal to zero finally, where
+the cost function is C(s, a) = EP (·|st,at)∥st+1∥. Another
+main task is the tracking task, which aims to achieve the
+reference state r. The cost function can be denoted as
+C(s, a) = EP (·|st,at)∥st+1 − r∥. In this context, we in-
+troduce a Mean Cost Stability to connect the stability and
+the cost.
+Definition 3.1 (Mean Cost Stability). A robotic system
+remains stable in mean cost when satisfying the following
+equation, where b is a constant (Han et al., 2020a).
+lim
+t→∞ Est∼T cπ(st) = 0, cπ(s0) ≤ b
+(2)
+More importantly, the above definition corresponds to the
+mean square stability when the cost function is chosen to
+be the norm of the state; it is also equivalent to the partial
+stability in tracking tasks (Han et al., 2020a).
+In the other direction, the stability definition with regard
+to cost avoids the inconsistent scale between the objective
+and constraint. Specifically, the problem formulation can be
+represented as follows:
+min
+π Eρ,π,P[
+∞
+�
+t=0
+γtcπ(st)]
+s.t. lim
+t→∞ Est∼T cπ(st) = 0
+(3)
+4. Adaptive Lyapunov-based Actor-Critic
+Algorithm
+To target the above-mentioned problem, we propose the
+Adaptive Lyapunov-based Actor-Critic algorithm (ALAC)
+in this section. The main contents are as follows: 1) we
+design an Adaptive Stability Certification (ASC), a union
+of two objectives guaranteeing a system’s mean cost sta-
+bility and guiding the policy to search the optimal point
+heuristically (Section 4.1); 2) we construct an Actor-Critic
+optimizing framework based on ASC and use a supervised
+learning method to update the parameters of the Lyapunov
+critic network(Section 4.2); 3) we apply the prime-dual
+method to update the parameters of the policy network and
+tune the parameters of ASC adaptively (Section 4.3).
+4.1. Adaptive Stability Certification
+In order to achieve the mean cost stability in Definition
+3.1, we first give a reasonable assumption to ensure that the
+starting state is sampled in the region of attraction, which is
+represented as the starting state space.
+
+Adaptive Stability Certification
+Assumption 4.1 (Region of Attraction). There exists a pos-
+itive constant b such that ρ(s) > 0, ∀s ∈ {s|cπ(s) ≤ b}.
+Another assumption is the existence of the stationary state
+distribution, which is generally exploited in the RL litera-
+ture.
+Assumption 4.2 (Ergodic Property). The Markov Chain
+driven by the policy π is ergodic, which means the following
+equation holds.
+ωπ(s) = lim
+t→∞ T (s|ρ, π, t)
+(4)
+Furthermore, we define a new variable Uπ for further deriva-
+tion.
+Uπ = lim
+T →∞
+1
+T
+T
+�
+t=0
+T (s | ρ, π, t)
+(5)
+Based on these mild assumptions, we formalize the
+sampling-based Lyapunov stability that meets the mean
+cost stability in Theorem 4.3 below, proven in Appendix
+B.1.
+Theorem 4.3 (Sampling-based Lyapunov Stability). An
+MDP system is stable with regard to the mean cost, if there
+exists a function L : S → R meets the following conditions:
+αcπ(s) ≤ L(s) ≤ βcπ(s)
+(6)
+L(s) ≥ cπ(s) + λEs′∼PπL(s′)
+(7)
+Es∼Uπ[Es′∼PπL(s′) − L(s)]
+≤ −k[Es∼Uπ[L(s) − λEs′∼PπL(s′)]]
+(8)
+where α, β, λ and k is positive constants. Among them,
+Pπ(s′|s) =
+�
+A π(a|s)P(s′|s, a) da holds.
+In practice, our method constructs sampling-based require-
+ments for the Lyapunov function. Taking advantage of the
+sampling-based stability, we can learn the policy that guar-
+antees the system’s stability in RL framework. Moreover,
+finding a Lyapunov function directly remains a challenge
+when the search space becomes large due to the increas-
+ing dimension of the state. To mitigate the issue, we use a
+Lyapunov candidate which is related to the sum of cost or
+value function. it has been proven to be a valid Lyapunov
+candidate in a previous study for stability analysis (Mayne
+et al., 2000). Thus, we can denote a Lyapunov candidate as:
+Lπ(s) = Eπ[
+∞
+�
+t=0
+γtcπ(st)|s0 = s]
+(9)
+It is noteworthy that the Lyapunov candidate naturally meets
+the constraints in Equation (6) and (7) when λ ≤ γ holds.
+Please see Appendix A.2 for a detailed demonstration.
+∞
+{𝑊(𝑡)}!"#
+$
+{𝑅(𝑡)}!"#
+$
+𝑡
+𝑡 + 1
+𝑘(𝑊(𝑡) − 𝑅(𝑡))
+𝑊(𝑡 + 1)
+𝜆 ↓
+𝜆 ↓
+𝑅(𝑡)
+𝑊(𝑡)	
+Figure 2. Illustrative example of how ASC condition can
+minimize L(s).
+Note that {W(t)}∞
+t=0 = {EL(s)}∞
+t=0
+and {R(t)}∞
+t=0 = = {λEL(s′)}∞
+t=0. The blue point de-
+notes W(t), and the orange point denotes R(t), respectively.
+W(t + 1) should decrease by k(W(t) − R(t)) according to
+the ASC condition. Besides, as {R(t)}∞
+t=0 decreases with
+λ, {W(t)}∞
+t=0 decreases together. When λ remains at the
+minimum value, the ASC condition will help the policy
+minimize L(s).
+Recalling the optimization problem (3), we find that
+the constraint part equals Equation (8) with respect to
+Lπ(s), as well as the objective part can be rewritten as
+minπ Es∼ρLπ(s). The Lyapunov candidate builds a bridge
+between the constraint and the objective. A common ap-
+proach is to use the lagrangian-based method to achieve the
+trade-off. However, making the constraints soft poses a chal-
+lenge to the guarantee of mean cost stability. Accordingly,
+we hope to propose a method which guides the policy to find
+the optimal point on the premise of the stability guarantee.
+Fortunately, we find that Equation (8) can achieve the goal
+when finding the minimum value of λ adaptively. We call
+this the Adaptive Stability Certification (ASC) that pro-
+vides promising insight into searching for the optimal policy
+heuristically without violating stability. In the following,
+we illustrate the underlying reasons based on an interesting
+lemma in a continuous-time system.
+Lemma 4.4 (Finite Tracking Time). In a continuous-time
+system, a trajectory W(t) tracks the reference R(t). W(t)
+can track the reference within a finite time T, such that
+R(t) = W(t), t ≥ T, if the following conditions holds.
+∇tW(t) ≤ −k(W(t) − R(t)), ∀t ∈ [0, T]
+(10)
+Note that the gradient of R(t) should be bounded, meaning
+that ∇tR(t) ≤ µ. The proof see Appendix B.2
+It can be seen that Equation (8) is very similar to Equation
+(10). Although the discrete-time condition does not have a
+finite tracking time unlike the continuous-time setting, the
+same principle comes from the feedback control. To some
+extent, we can think Equation (8) as a special tracking task
+
+Adaptive Stability Certification
+that the sequence {W(t)}∞
+t=0 = {EL(s)}∞
+t=0 tracks the ref-
+erence sequence {R(t)}∞
+t=0 = {λEL(s′)}∞
+t=0. To explain
+it intuitively, Figure 2 depicts an illustrative example. As
+we can see, the value of W(t + 1) needs to decrease by
+k(W(t) − R(t)) at time t + 1. If λ decreases, {R(t)}∞
+t=0
+forces {W(t)}∞
+t=0 to minimize L(s) along the whole se-
+quence. Because of the introduction of the Lyapunov can-
+didate, minimizing L(s) equals the previous objective part
+in Equation (3). Therefore, we can find the optimal policy
+based on the certification by finding the minimum value of λ
+adaptively. To sum up, the optimization problem is modified
+to find the minimum value of λ as well as make Equation (8)
+holds. Note that we do not provide an in-depth theoretical
+analysis of the heuristic method. Thus, it leaves room for
+our future work, indicating that meeting ASC corresponds
+to finding the optimal policy.
+4.2. Lyapunov Critic Learning
+We leverage a traditional Actor-Critic framework to solve
+the optimization problem mentioned above. First, we con-
+struct two neural networks, namely actor πφ(a|s) and Lya-
+punov critic Lθ(s, a). Among them, φ and θ represent
+the parameters of two networks, respectively. The actor
+πφ(a|s) maps a given state s to a distribution over action.
+The action distribution is modelled as a Gaussian, with a
+state-dependent mean µφ(s) and diagonal covariance matrix
+Σφ(s). Unlike traditional Actor-Critic methods, our critic
+network is related to the Lyapunov candidate Lπ(s). As a
+matter of fact, Lπ(s) is the expectation of Lθ(s, a) over the
+distribution of actions. Specifically, EπLθ(s, a) = Lπ(s)
+holds. In the context of this property, the above theoretical
+results about Lπ(s) are also suitable for our critic network.
+For the training of Lθ(s, a), because we choose the value
+function as the Lyapunov candidate illustrated in Equation
+(9), we can update θ according to the TD error:
+θk+1 = θk + αθ(∇θ(Lθ(s, a) − (cπ + γL′(s′, π′(·|s′))))2)
+(11)
+where k is the number of iterations. L′ and π′ are the target
+networks parameterized by θ′ and φ′, respectively. In the
+Actor-Critic method, the parameters θ′ and φ′ are usually
+updated through exponentially moving average of weights
+controlled by a hyper-parameter σ ∈ (0, 1), which is shown
+as:
+θ′
+k+1 ← σθk + (1 − σ)θ′
+k; φ′
+k+1 ← σφk + (1 − σ)φ′
+k
+(12)
+Furthermore, we introduce an interesting mechanism on
+the Lyapunov critic network to speed up the learning pro-
+cess. Admittedly, the Lyapunov candidate Lπ(s) meets
+some requirements sufficiently shown in Appendix A.2,
+which means the output of the critic network can guarantee
+them eventually based on TD-like updating. In order to
+encourage accurate and efficient learning, we construct a
+constrained critic network. Concretely, we denote the output
+of a neural network as f(s, a). And then, Lθ(s, a) can be
+described by:
+Lθ(s, a) = (Gs(f(s, a)))(Gs(f(s, a)))⊤
+(13)
+where Gs is a linear transformation, which guarantees
+Gs=se(f(s = se, a)) = 0 (se is an equilibrium point de-
+fined in Definition A.1.). Note that Gs contains no parame-
+ters to be learned, so the operator does not cause harm to the
+representation ability of the neural network. For the details,
+see Appendix B.3. To this end, the constrained network
+ensures that the output is non-negative and the Lyapunov
+value should be zero when the state is an equilibrium point.
+4.3. Lagrangian-based Policy Learning
+Policy learning aims to search feasible parameters of the
+policy network to make the output of the Lyapunov network
+meet the requirements of the ASC condition.
+For optimizing the policy πφ(a|s), we denote the specific
+constrained condition as follows according to Equation (8).
+∆Lπφ(s, a) = Lθ(s′, πφ(· | s′)) − Lθ(s, a)
++ k[Lθ(s, a) − λLθ(s′, πφ(· | s′))] ≤ 0
+(14)
+We can see that the current policy’s parameters can be up-
+dated due to the embedding of πφ. Meanwhile, because of
+the sampling-based stability theorem (Theorem 4.3), it is
+convenient to efficiently implement the random sampling in
+the replay buffer D that stores the interaction data. More-
+over, the optimal policy can be obtained, when we maxi-
+mize ∆Lπφ(s, a) by finding the minimum λ according to
+the ASC condition. Specifically, The optimization problem
+in Equation (3) can be reformulated as follows.
+max
+λ,πφ
+ED∆Lπφ(s, a)
+s.t. ED∆Lπφ(s, a) ≤ 0
+(15)
+First, we focus on the sub-problem of finding πφ under
+satisfying the constraint with arbitrary λ, which is shown as:
+find πφ
+s.t. ED∆Lπφ(s, a) ≤ 0
+(16)
+Applying the Lagrangian-based method (Stooke et al.,
+2020), the parameters of πφ are updated by:
+φk+1 = φk + αφ(λl∇a∆Lπφ(s, a)∇φπφ(s, a))
+(17)
+where αφ is the learning rate of φ. λl represents the La-
+grange multiplier of the constraint. During the training, λl
+
+Adaptive Stability Certification
+is updated by gradient ascent to maximize ∆Lπφ(s, a).
+λk+1
+l
+= λk
+l + αλl∆Lπφ(s, a)
+(18)
+Note that λl should always be positive. αλl is the learning
+rate. It is worth noting that λl is clipped by 0 and 1, to
+bound the value. In addition, to improve the exploration
+efficiency, we add a constraint about the minimum entropy
+as the same as the maximum entropy RL algorithms.
+4.3.1. THE CHOICE OF λ
+However, how to maximize ∆Lπφ(s, a) in Equation (15)
+remains to be an unsolved problem. Finding the maximum
+value of ∆Lπφ(s, a) equals finding the minimum value of
+λ. First, The range of λ is from γ to 0 in the ASC condition,
+and γ is very close to 1 in practical usage. Moreover, we
+find the Lagrange multiplier λl ranges from 0 to 1, and it
+decreases with the constraint’s satisfaction. Therefore, we
+can update λ by the following method.
+λ ← min(λl, γ)
+(19)
+To be specific, when satisfying the constraint, λ decreases
+toward 0 to maximize ∆Lπφ(s, a). When λ remains at a
+stable level, the minimum value of λ realizes the aim of
+maximizing ∆Lπφ(s, a). Until now, we have constructed
+the whole training process for the optimization problem in
+Equation (15).
+4.3.2. THE CHOICE OF k
+For the choice of k, we also use a heuristics approach to
+adjust the value of k dynamically, k ← 1 − λl. There is
+an essential advantage to the approach. As we can see, λl
+is close to 1 at the early stage of training; thus, k leads to
+slow tracking according to Lemma 4.4. When λl decreases,
+it indicates the current constraint is loose. In the setup,
+kl increases instead, and the constraint forces the tracking
+process to be performed more quickly. Besides, It offers
+another benefit we explain in Section 4.4.
+We have designed the complete ALAC algorithm, and the
+pseudo-code of the proposed algorithm is shown in Ap-
+pendix C.
+4.4. Theoretical Analysis
+A common fact we notice is that there exists a bias be-
+tween the practical computing and theoretical analysis about
+Uπ in Theorem 4.3. To estimate the distribution Uπ, we
+need an infinite number of trajectories with infinite time
+steps, whereas in practice, only M trajectories of T time
+steps are accessible. To better illustrate the issue, we de-
+fine a finite sampling distribution UT
+π , apparently where
+UT
+π = 1
+T
+�T
+t=0 T (s | ρ, π, t). Besides, we introduce a new
+variable ∆Lπ(s) about the Lyapunov candidate to simplify
+the expression of derivation.
+∆Lπ(s) =Est+1∼PπLπ(st+1) − Lπ(st)
++ k[Lπ(st) − λEst+1∼PπLπ(st+1)]
+(20)
+First, we provide a quantitative bound of expectation from
+Uπ and UT
+π .
+Theorem 4.5. Suppose that the length of sampling trajecto-
+ries is T, then the bound can be expressed as:
+|Es∼Uπ∆Lπ(s) − Es∼UT
+π ∆Lπ(s)| ≤ 2(k + 1)cπ
+1 − γ
+T q−1
+(21)
+where cπ is the maximum of cost and q is a constant in
+(0, 1). For proof see Appendix B.4.
+Next, we take the number of trajectories into considera-
+tion and derive the probabilistic bound of the difference of
+∆Lπ(s) estimated by UT
+π distribution and M trajectories.
+Theorem 4.6. Suppose that the length of sampling trajec-
+tories is T and the number of trajectories is M, then there
+exists the following upper bound:
+P(| 1
+MT
+M
+�
+m=1
+T
+�
+t=1
+∆Lπ(sm
+t ) − Es∼UT
+π ∆Lπ(s)| ≥ α)
+≤ 2 exp(−
+Mα2(1 − γ)2
+((1 − kλ)2 + (k − 1)2)cπ2 )
+(22)
+where sm
+t represents the state in the m-th trajectory at the
+timestep t. For proof see Appendix B.5.
+Theorem 4.5 suggests that if k is close to 0, the gap becomes
+small in practice. Alternatively, Theorem 4.6 indicates that
+k has better to be 1. That means the best choice of k ranges
+from 0 to 1. Thus, the updating method of k in Section 4.3.2
+balances the impacts of each other efficiently. Furthermore,
+two theorems illustrate the theoretical gap between infinite
+and finite samples in practical usage, thus making Theorem
+4.3 more complete.
+5. Experiments
+In this section, we demonstrate empirical evidence that
+ALAC captures an improved trade-off between optimal-
+ity and stability compared to the baseline approaches.
+We test our method and baselines in ten robotic control
+environments, including Cartpole-cost,Point-circle-cost,
+Halfcheetah-cost, Swimmer-cost, Ant-cost, Humanoid-
+cost, Minitaur-cost, Spacereach-cost, Spacerandom-
+cost and Spacedualarm-cost. Details of the environments
+are given in Appendix D.1. Furthermore, we benchmark
+the ALAC method against five algorithms with a neu-
+ral Lyapunov function. The algorithms can be separated
+
+Adaptive Stability Certification
+Table 1. Performance evaluations of the cultivated costs and stability constraint violations on ten environments compared with six baselines.
+All quantities are provided in a scale of 0.1. Standard errors are provided in brackets. (if the mean constraints are less than 0.2, the sign is
+↓ else ↑.‘-’ indicates the algorithm does not contain the stability constraints.)
+Task
+Metrics
+ALAC
+SAC-cost
+SPPO
+LAC
+LAC∗
+POLYC
+LBPO
+TNLF
+Cartpole-cost
+Cost Return
+26.2(7.0)
+22.7(12.6)
+102.3(59.3)
+31.0(10.1)
+31.5(5.1)
+104.8(70.7)
+205.3(27.0)
+33.5(24.5)
+Violation
+↓
+-
+↑
+↓
+↓
+↓
+-
+↓
+Point-circle-cost
+Cost Return
+111.1(4.5)
+111.8(2.4)
+247.9(58.2)
+958.6(15.5)
+112.0(5.0)
+207.0(62.4)
+722.1(126.1)
+145.8(38.0)
+Violation
+↓
+-
+↑
+↓
+↑
+↓
+-
+↓
+Halfcheetah-cost
+Cost Return
+1.7(0.7)
+16.6(25.2)
+144.0(14.6)
+119.5(37.3)
+1.8(0.5)
+168.8(10.7)
+37.8(24.8)
+6.5(1.4)
+Violation
+↓
+-
+↑
+↓
+↓
+↓
+-
+↓
+Swimmer-cost
+Cost Return
+44.6(4.8)
+53.7(12.4)
+52.5(4.2)
+47.5(1.3)
+44.8(3.0)
+104.7(11.0)
+52.3(11.3)
+46.5(2.4)
+Violation
+↓
+-
+↑
+↓
+↑
+↓
+-
+↓
+Ant-cost
+Cost Return
+101.0(42.1)
+155.2(29.9)
+255.0(31.2)
+166.9(13.6)
+125.6(12.5)
+259.8(37.1)
+114.6(26.1)
+186.8(11.0)
+Violation
+↓
+-
+↑
+↓
+↑
+↓
+-
+↓
+Humanoid-cost
+Cost Return
+354.6(97.1)
+441.9(18.3)
+531.8(22.9)
+431.3(14.9)
+368.3(76.6)
+490.4(32.5)
+452.4(13.9)
+317.7(31.1)
+Violation
+↓
+-
+↑
+↓
+↑
+↓
+-
+↓
+Minitaur-cost
+Cost Return
+493.0(67.9)
+692.2(93.0)
+950.0(72.3)
+612.2(47.8)
+666.6(306.7)
+608.3(65.6)
+838.3(237.0)
+382.9(62.6)
+Violation
+↓
+-
+↑
+↓
+↑
+↓
+-
+↓
+Spacereach-cost
+Cost Return
+1.6(0.2)
+8.9(8.8)
+19.4(2.5)
+35.2(1.6)
+1.8(0.4)
+125.7(20.8)
+31.0(19.1)
+112.1(53.0)
+Violation
+↓
+-
+↓
+↓
+↓
+↓
+-
+↓
+Spacerandom-cost
+Cost Return
+2.3(0.3)
+38.4(28.6)
+53.2(32.7)
+33.9(3.5)
+2.8(0.9)
+112.8(19.4)
+35.82.9)
+85.9(42.3)
+Violation
+↓
+-
+↓
+↓
+↓
+↓
+-
+↓
+Spacedualarm-cost
+Cost Return
+26.1(3.5)
+36.1(8.3)
+201.9(48.8)
+66.3(10.6)
+63.6(62.1)
+140.6(17.4)
+37.87.5)
+280.1(99.3)
+Violation
+↓
+-
+↓
+↓
+↓
+↓
+-
+↓
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+300
+350
+400
+450
+500
+550
+Cost Return
+Humanoid-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+0
+5
+10
+15
+20
+25
+30
+Violation
+Humanoid-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+400
+600
+800
+1000
+Cost Return
+Minitaur-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+0
+2
+4
+6
+8
+10
+12
+Violation
+Minitaur-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+Figure 3. Ablation studies of the ASC condition. ALAC(original) shows comparable or the best performance compared with
+other certifications on each task.
+into two categories, optimizing policy with a mixed ob-
+jective and Lyapunov-like constraints. The first one con-
+tains POLYC (Chang & Gao, 2021), LBPO(Sikchi et al.,
+2021) and TNLF(Xiong et al., 2022). The second one in-
+cludes SPPO(Chow et al., 2019), LAC (Han et al., 2020a)
+2.
+We also take the SAC-cost (Haarnoja et al., 2018)
+method into account because the method is very close to
+our method without the ASC condition. For the detailed
+hyper-parameter settings see Appendix D.2.1 and D.2.2.
+5.1. Comparing with Baselines
+In this part, we evaluate the optimality and stability of our
+methods and baselines. The results demonstrate ALAC out-
+2We find LAC with a large α3 (see Appendix D.2.1) performs
+better, so we call it LAC∗ for the distinction between them.
+performs baselines. To fairly evaluate the performance of
+the methods mentioned above, we run the experiments over
+5 rollouts and 5 seeds for all algorithms. We use the accu-
+mulated cost in a testing episode as the metric of optimality
+and the stability constraint violations as the stability metric.
+Although the metric of stability violations depends on each
+algorithm’s design, the best value should be close to 0. Ta-
+ble 1 shows the performance on all tasks, and the training
+curves for different algorithms are in Appendix D.3. Results
+confirm that ALAC outperforms state-of-the-art baselines
+on all tasks except for Cartpole-cost, Humanoid-cost and
+Minitaur-cost where our method doesn’t outperform SAC-
+cost and TNLF, respectively. Furthermore, although LAC∗
+using tighter constraints achieves comparable performance
+with our method in contrast to LAC, the stability violations
+in LAC∗ remain at a high level on some tasks. Admittedly,
+TNLF achieves lower cost than ALAC on Minitaur-cost,
+
+Adaptive Stability Certification
+Cartpole-cost
+HalfCheetah-cost
+Minitaur-cost
+𝑔𝑜𝑎𝑙!
+𝑔𝑜𝑎𝑙"
+𝑔𝑜𝑎𝑙#
+Spacerandom-cost
+Steps
+𝜑
+𝜑 ̇
+ℒ!!
+Values
+Figure 4. Visualization of states for ALAC method by t-SNE and phase trajectory techniques. The top row of the figure
+depicts the t-SNE dimension reduction technique. (Cartpole-Cost is visualized within 2 dims while others within 3 dims.)
+The bottom row shows the phase trajectories and Lyapunov-value surfaces of environments. ψ and ˙ψ denotes the angular
+position and velocity respectively.
+Table 2. Average evaluation score and standard deviation on our environments for ALAC with and without the feedback under different
+biases of goals. (w/ errors means using errors between the desired and achieved goals as extra states for the agent)
+Task
+Point-circle-cost
+Halfcheetah-cost
+Spacereach-cost
+Biases of goals
+-20%
+0%
+20%
+-20%
+0%
+20%
+-20%
+0%
+20%
+ALAC w/ errors
+85.2(4.5)
+110.1(3.9)
+148.5(12.2)
+3.9(0.8)
+2.5(0.6)
+8.3(4.7)
+6.4(1.7)
+2.4(1.4)
+8.7(1.7)
+ALAC w/o errors
+178.8(7.8)
+118.9(11.4)
+247.8(11.9)
+10.1(2.1)
+3.3(1.2)
+13.4(2.1)
+11.9(0.4)
+1.6(0.2)
+11.5(0.3)
+SAC-cost w/ errors
+84.2(4.2)
+109.3(2.2)
+140.1(3.0)
+60.1(27.5)
+81.6(50.2)
+129.5(85.6)
+21.9(12.3)
+22.1(16.9)
+20.6(18.1)
+SAC-cost w/o errors
+180.9(6.3)
+115.3(4.0)
+240.3(3.7)
+15.9(15.7)
+16.7(25.5)
+33.5(34.0)
+16.1(6.2)
+8.8(8.8)
+15.0(7.2)
+but TNLF converges to suboptimal policies on many tasks.
+According to Figure 11, we notice that TNLF satisfies the
+stability constraints quickly during the training. Neverthe-
+less, the reason is that the trained Lyapunov function is close
+to 0 quickly. To this end, it does not provide dense guid-
+ance for the policy, thus leading it to a suboptimal solution.
+To recap, ALAC strikes an efficient balance between the
+optimality and stability of the system.
+5.2. Ablation Studies
+To better demonstrate the effectiveness of the ASC condi-
+tion, we do the ablation studies about different certifications
+in ALAC. We compare the performance of the original
+ALAC with a version that uses ∆L1
+πφ and ∆L2
+πφ, and with
+a version where k is a constant throughout training. The de-
+tails of ∆L1
+πφ and ∆L2
+πφ are given in Appendix D.4. In con-
+trast to ∆Lπφ, ∆L1
+πφ and ∆L2
+πφ represents the upper bound
+and lower bound of the constraint, respectively. Figure 3 and
+Figure 10 (see Appendix D.4) depict the accumulated cost
+and constraint violations on all tasks, where the algorithms
+are modified from ALAC directly. ALAC(∆L2
+πφ) achieve
+lower performance than ALAC, while ALAC(∆L1
+πφ) per-
+forms the tasks comparably with ALAC. Nevertheless, more
+strict constraints (ALAC(∆L1
+πφ)) negatively affect its per-
+formance on constraint violations, as shown in Figure 3.
+This is because there doesn’t exist a reasonable policy
+that meets such strict constraints. Moreover, the results of
+ALAC(k = 0.1) comparing with ALAC demonstrate that
+the heuristics updating of k is effective during the training.
+The slight gap between ALAC(Tanh) with the Lyapunov
+function activated by the Tanh function and ALAC shows
+our method is not sensitive to the form of the Lyapunov
+function.
+
+Adaptive Stability Certification
+5.3. Evaluation Results
+In this section, we describe the impacts of the stability condi-
+tion more concretely by using various visualization methods.
+Furthermore, we verify that ALAC achieves excellent ro-
+bustness, generalization, and efficiency with the aid of the
+ASC condition.
+5.3.1. ANALYSIS OF VISUALIZATION
+First, we use the t-SNE method to indicate the visualization
+of the state in 3 dimensions in order to illustrate better the
+stability of the system learned by ALAC (Cartpole-cost
+in 2 dimensions). As we can see, the top row of Figure 4
+shows the states in the final stage of an episode converge
+to a point or circle. Basically, we recognize that those
+patterns happen in a stable system. Furthermore, experts
+can judge a system’s stability from a phase space of the
+system. Therefore, we also introduce various phase space
+trajectories of the system to analyze stability. The second
+row of Figure 4 shows the phase trajectories with variance
+according to the state pairs of joint angular position and
+velocity. Concretely, ψ and ˙ψ represent an angular position
+and velocity, respectively. It can be found that the angular
+velocity starts from 0 to 0, and the angular position starts
+from the beginning to an equilibrium point. (For more
+details see Figure 6). Based on the above phenomenons, it
+suggests the trained systems using the ALAC method satisfy
+focal stability or stable limit cycles. More importantly, we
+observe that the Lyapunov value decreases while learning
+and consistently falls to its lowest point at the end of an
+episode, as shown in Figure 4 (bottom row). Furthermore,
+it can facilitate the policy to achieve promising results on
+robustness and generalization, which is demonstrated in
+further analysis. More implementation details for t-SNE
+and phase trajectories are given in Appendix D.5.
+5.3.2. VERIFICATION OF PROPERTIES
+Robustness
+Generally speaking, stability has a potential
+relationship with robustness to some extent (Chang & Gao,
+2021). Thus, we add external disturbances with different
+magnitudes in each environment and observe the perfor-
+mance difference. To be concrete, we introduce periodic
+external disturbances with different magnitudes in each task.
+Furthermore, we omit the algorithms which do not converge
+to a reasonable solution in each task. Figure 8 (see Appendix
+D.6.1) shows in all scenarios, ALAC enjoys superior per-
+formance over other methods.
+Generalization
+Previous studies focus on the robustness
+of a system to demonstrate the effectiveness of Lyapunov
+constraints. In this paper, we build some interesting exper-
+iments to verify whether the policy can generalize well to
+follow previously unseen reference signals or not. We in-
+Table 3. Comparisons on the performance of ALAC and SAC-cost
+methods under different actor structures.
+Task
+Halfcheetah-cost
+Actor structure
+[64,64]
+[32,32]
+[16,16]
+ALAC
+1.7(0.7)
+2.9(1.7)
+5.0(1.9)
+SAC-cost
+16.6(25.2)
+94.1(38.4)
+86.6(57.8)
+Task
+Minitaur-cost
+Actor structure
+[64,64]
+[32,32]
+[16,16]
+ALAC
+492.9(67.9)
+403.5(85.7)
+571.7(116.1)
+SAC-cost
+692.1(92.9)
+664.9(115.3)
+934.1(149.3)
+Task
+Spaceramdom-cost
+Actor structure
+[64,64]
+[32,32]
+[16,16]
+ALAC
+3.6 (1.0)
+8.3(6.0)
+12.1(4.9)
+SAC-cost
+28.7(9.5)
+30.6(13.9)
+38.4(28.6)
+troduce the error between the desired and achieved goals as
+additional information in the state. Because the Lyapunov
+function is significantly related to the error, ALAC w/ er-
+rors gains remarkable performance improvement on gen-
+eralization as Table 2 illustrated. We choose the SAC-cost
+algorithm as a comparison since SAC-cost is very similar
+to our method without the ASC condition. For more ex-
+perimental results, see Appendix D.6.2. In particular, the
+gap between each other enlarges with the increasing biases.
+Furthermore, we observe that the errors have a negative
+impact on the performance of SAC-cost on complex tasks
+like Halfcheetah-cost and Spacereach-cost. The reason
+can be that SAC-cost does not efficiently capture the error
+information without the guidance of a Lyapunov function.
+Efficiency
+Our method also offers a positive effect on the
+limited network size. Results in Table 3 suggest ALAC
+method consistently achieves comparable performance un-
+der different actor structures. Compared with the SAC-cost
+method, the ALAC method brings another benefit, perform-
+ing the task more efficiently with limited parameters of
+controllers. It is because the adaptive stability certification
+provides efficient guidance for policy optimization.
+6. Discussion and Future Work
+We propose the Adaptive Stability Certification (ASC),
+which meets the sampling-based stability of mean cost.
+Meanwhile, it guides the current policy to approaches to
+the optimal point heuristically in the context of classical
+feedback control. Based on the Actor-Critic framework and
+Lagrangian-based optimization, We present a practical algo-
+rithm, namely the Adaptive Lyapunov-based Actor-Critic
+algorithm (ALAC). Furthermore, empirical results show that
+our method outperforms baselines on diverse robotic tasks
+with two metrics, stability constraint violations and mean
+costs. Furthermore, the controller trained by our method
+
+Adaptive Stability Certification
+achieves higher generalization ability compared with the
+method without the stability guarantee. By making a heuris-
+tic formulation, we provide an interesting method to com-
+bine the policy’s optimality with the system’s stability in
+model-free RL. In this work, we focus on the system’s sta-
+bility; an exciting direction for future work would be to
+combine ASC with some safe RL algorithms.
+References
+Achiam, J., Held, D., Tamar, A., and Abbeel, P. Constrained
+policy optimization. In International conference on ma-
+chine learning, pp. 22–31. PMLR, 2017.
+Andrychowicz, O. M., Baker, B., Chociej, M., Jozefowicz,
+R., McGrew, B., Pachocki, J., Petron, A., Plappert, M.,
+Powell, G., Ray, A., et al. Learning dexterous in-hand
+manipulation.
+The International Journal of Robotics
+Research, 39(1):3–20, 2020.
+Berkenkamp, F., Turchetta, M., Schoellig, A., and Krause,
+A. Safe model-based reinforcement learning with stability
+guarantees. Advances in neural information processing
+systems, 30, 2017.
+Brockman, G., Cheung, V., Pettersson, L., Schneider, J.,
+Schulman, J., Tang, J., and Zaremba, W. Openai gym.
+arXiv preprint arXiv:1606.01540, 2016.
+Chang, Y.-C. and Gao, S. Stabilizing neural control using
+self-learned almost lyapunov critics. In 2021 IEEE Inter-
+national Conference on Robotics and Automation (ICRA),
+pp. 1803–1809. IEEE, 2021.
+Chang, Y.-C., Roohi, N., and Gao, S. Neural lyapunov con-
+trol. Advances in neural information processing systems,
+32, 2019.
+Chen, S., Fazlyab, M., Morari, M., Pappas, G. J., and Pre-
+ciado, V. M. Learning region of attraction for nonlinear
+systems. In 2021 60th IEEE Conference on Decision and
+Control (CDC), pp. 6477–6484. IEEE, 2021.
+Chow,
+Y.,
+Nachum,
+O.,
+Duenez-Guzman,
+E.,
+and
+Ghavamzadeh, M. A lyapunov-based approach to safe
+reinforcement learning. Advances in neural information
+processing systems, 31, 2018.
+Chow, Y., Nachum, O., Faust, A., Duenez-Guzman, E.,
+and Ghavamzadeh, M.
+Lyapunov-based safe policy
+optimization for continuous control.
+arXiv preprint
+arXiv:1901.10031, 2019.
+Coumans, E. and Bai, Y. Pybullet, a python module for
+physics simulation for games, robotics and machine learn-
+ing. 2016.
+Dai, H., Landry, B., Pavone, M., and Tedrake, R. Counter-
+example guided synthesis of neural network lyapunov
+functions for piecewise linear systems. In 2020 59th
+IEEE Conference on Decision and Control (CDC), pp.
+1274–1281. IEEE, 2020.
+Dai, H., Landry, B., Yang, L., Pavone, M., and Tedrake, R.
+Lyapunov-stable neural-network control. arXiv preprint
+arXiv:2109.14152, 2021.
+
+Adaptive Stability Certification
+Dawson, C., Qin, Z., Gao, S., and Fan, C. Safe nonlinear
+control using robust neural lyapunov-barrier functions. In
+Conference on Robot Learning, pp. 1724–1735. PMLR,
+2022.
+Donti, P. L., Roderick, M., Fazlyab, M., and Kolter, J. Z.
+Enforcing robust control guarantees within neural net-
+work policies. In International Conference on Learning
+Representations, 2020.
+Gaby, N., Zhang, F., and Ye, X. Lyapunov-net: A deep
+neural network architecture for lyapunov function ap-
+proximation. arXiv preprint arXiv:2109.13359, 2021.
+Haarnoja, T., Zhou, A., Abbeel, P., and Levine, S. Soft
+actor-critic: Off-policy maximum entropy deep reinforce-
+ment learning with a stochastic actor. In International
+conference on machine learning, pp. 1861–1870. PMLR,
+2018.
+Han, M., Zhang, L., Wang, J., and Pan, W. Actor-critic re-
+inforcement learning for control with stability guarantee.
+IEEE Robotics and Automation Letters, 5(4):6217–6224,
+2020a.
+Han, M., Zhou, Z., Zhang, L., Wang, J., and Pan, W. Rein-
+forcement learning for control with probabilistic stability
+guarantee. 2020b.
+Han, M., Tian, Y., Zhang, L., Wang, J., and Pan, W. Rein-
+forcement learning control of constrained dynamic sys-
+tems with uniformly ultimate boundedness stability guar-
+antee. Automatica, 129:109689, 2021.
+Huang, T., Gao, S., Long, X., and Xie, L. A neural lya-
+punov approach to transient stability assessment in inter-
+connected microgrids. In HICSS, pp. 1–10, 2021.
+Hwangbo, J., Lee, J., Dosovitskiy, A., Bellicoso, D., Tsou-
+nis, V., Koltun, V., and Hutter, M. Learning agile and
+dynamic motor skills for legged robots. Science Robotics,
+4(26):eaau5872, 2019.
+Jin, W., Wang, Z., Yang, Z., and Mou, S.
+Neural
+certificates for safe control policies.
+arXiv preprint
+arXiv:2006.08465, 2020.
+Kashima, K., Yoshiuchi, R., and Kawano, Y.
+Learn-
+ing stabilizable deep dynamics models. arXiv preprint
+arXiv:2203.09710, 2022.
+La Salle, J. and Lefschetz, S. Stability by Liapunov’s Direct
+Method with Applications by Joseph L Salle and Solomon
+Lefschetz. Elsevier, 2012.
+Lale, S., Shi, Y., Qu, G., Azizzadenesheli, K., Wierman, A.,
+and Anandkumar, A. Kcrl: Krasovskii-constrained rein-
+forcement learning with guaranteed stability in nonlinear
+dynamical systems. arXiv preprint arXiv:2206.01704,
+2022.
+Lawrence, N., Loewen, P., Forbes, M., Backstrom, J., and
+Gopaluni, B. Almost surely stable deep dynamics. Ad-
+vances in Neural Information Processing Systems, 33:
+18942–18953, 2020.
+Lechner, M., Žikeli´c, Ð., Chatterjee, K., and Henzinger,
+T. A.
+Stability verification in stochastic control sys-
+tems via neural network supermartingales. arXiv preprint
+arXiv:2112.09495, 2021.
+Li, X., Xiao, J., Cheng, Y., and Liu, H. An actor-critic learn-
+ing framework based on lyapunov stability for automatic
+assembly. Applied Intelligence, pp. 1–12, 2022.
+Mayne, D. Q., Rawlings, J. B., Rao, C. V., and Scokaert,
+P. O. Constrained model predictive control: Stability and
+optimality. Automatica, 36(6):789–814, 2000.
+Mittal, M., Gallieri, M., Quaglino, A., Salehian, S. S. M.,
+and Koutník, J. Neural lyapunov model predictive control.
+2020.
+Murray, R. M., Li, Z., and Sastry, S. S. A mathematical
+introduction to robotic manipulation. CRC press, 2017.
+Richards, S. M., Berkenkamp, F., and Krause, A.
+The
+lyapunov neural network: Adaptive stability certification
+for safe learning of dynamical systems. In Conference on
+Robot Learning, pp. 466–476. PMLR, 2018.
+Schlaginhaufen, A., Wenk, P., Krause, A., and Dorfler, F.
+Learning stable deep dynamics models for partially ob-
+served or delayed dynamical systems. Advances in Neural
+Information Processing Systems, 34:11870–11882, 2021.
+Schulman, J., Levine, S., Abbeel, P., Jordan, M., and Moritz,
+P. Trust region policy optimization. In International
+conference on machine learning, pp. 1889–1897. PMLR,
+2015.
+Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and
+Klimov, O. Proximal policy optimization algorithms.
+arXiv preprint arXiv:1707.06347, 2017.
+Sikchi, H., Zhou, W., and Held, D. Lyapunov barrier policy
+optimization. arXiv preprint arXiv:2103.09230, 2021.
+Stooke, A., Achiam, J., and Abbeel, P. Responsive safety
+in reinforcement learning by pid lagrangian methods. In
+International Conference on Machine Learning, pp. 9133–
+9143. PMLR, 2020.
+Wang, S., Cao, Y., Zheng, X., and Zhang, T. Collision-free
+trajectory planning for a 6-dof free-floating space robot
+via hierarchical decoupling optimization. IEEE Robotics
+and Automation Letters, 7(2):4953–4960, 2022.
+
+Adaptive Stability Certification
+Xiong, Z., Eappen, J., Qureshi, A. H., and Jagannathan,
+S. Model-free neural lyapunov control for safe robot
+navigation. arXiv preprint arXiv:2203.01190, 2022.
+Zhang, L., Zhang, R., Wu, T., Weng, R., Han, M., and Zhao,
+Y. Safe reinforcement learning with stability guarantee
+for motion planning of autonomous vehicles. IEEE Trans-
+actions on Neural Networks and Learning Systems, 32
+(12):5435–5444, 2021.
+Zhao, T., Wang, J., Lu, X., and Du, Y. Neural lyapunov con-
+trol for power system transient stability: A deep learning-
+based approach. IEEE Transactions on Power Systems,
+37(2):955–966, 2021.
+Zhou, R., Quartz, T., De Sterck, H., and Liu, J. Neural
+lyapunov control of unknown nonlinear systems with
+stability guarantees. arXiv preprint arXiv:2206.01913,
+2022.
+Zou, S., Xu, T., and Liang, Y. Finite-sample analysis for
+sarsa with linear function approximation. Advances in
+neural information processing systems, 32, 2019.
+
+Adaptive Stability Certification
+A. Preliminary Remarks
+A.1. Lyapunov function
+Definition A.1 (Equilibrium Point). A state se is an equilibrium point if ∃ action ae ∈ A such that f(se, ae) = se. (Murray
+et al., 2017)
+Definition A.2 (Stabilizable in the sense of Lyapunov). A system is stabilizable if ∀ϵ > 0, ∃δ such that for all s0 ∈ S such
+that ||s0 − se|| ≤ δ, there exists {at}∞
+t=0 such that the resulting {st}∞
+t=0 satisfies ||st − se|| ≤ ϵ ∀t ≥ 0.(Murray et al., 2017)
+Definition A.3 (Lyapunov Function). A continuous and radially unbounded function L : S → R is a Lyapunov function if
+the following conditions hold:
+1. ∀s ∈ S, ∃a ∈ A, s.t. L(s) ≥ L(f(s, a)),
+2. ∀s ̸= 0, L > 0; L(0) = 0.
+If a Lyapunov function exists, a discrete-time system can achieve stability in the sense of Lyapunov without considering the
+physical energy.
+A.2. Lyapunov Candidate Bound
+In this part, we show that the Lyapunov candidate Lπ(s) meets the property in Theorem 4.3, which can be formulated as:
+cπ(s) + λEs′∼PπL(s′) ≤ L(s) ≤ βcπ(s)
+(23)
+where we omit the lower bound αcπ(s) which is naturally satisfied by Lπ(s).
+Firstly, according to the definition of Lπ(s), we have
+Lπ(s) = Eπ[
+∞
+�
+t=0
+γtcπ(st)|s0 = s]
+= Eπ[cπ(s0) +
+∞
+�
+t=1
+γtcπ(st)|s0 = s]
+= cπ(s) + Eπ[
+∞
+�
+t=1
+γtcπ(st)]
+= cπ(s) + γEπ,s′∼Pπ[
+∞
+�
+t=0
+γtcπ(st)|s0 = s′]
+= cπ(s) + γEs′∼PπL(s′)
+(24)
+Considering the left-hand side of Equation (6), we can find that if λ ≤ γ holds, the lower bound of the Lyapunov function
+can be satisfied. This is because the Lyapunov candidate Lπ(s) is positive at each state. Furthermore, the right-hand side of
+Equation 6 illustrates the higher bound of the Lyapunov function exists. The condition is also guaranteed for our Lyapunov
+candidate shown in the following process.
+Lπ(s) = Eπ[
+∞
+�
+t=0
+γtcπ(st)|s0 = s]
+≤
+∞
+�
+t=0
+γtEπ[cπ(st)|s0 = s]
+≤
+cπ
+1 − γ
+(25)
+Note that cπ denotes the maximum cost. The second row of the inequality holds due to Jensen inequality. Only if the
+maximum cost exists, ∃β ∈ R+,
+cπ
+1−γ ≤ βcπ(s) holds.
+
+Adaptive Stability Certification
+B. Details of Theoretical Analysis
+B.1. Proof of Theorem 4.3
+Theorem B.1 (Sampling-based Lyapunov Stability). An MDP system is stable with regard to the mean cost, if there exists a
+function L : S → R meets the following conditions:
+αcπ(s) ≤ L(s) ≤ βcπ(s)
+(26)
+L(s) ≥ cπ(s) + λEs′∼PπL(s′)
+(27)
+Es∼Uπ[Es′∼PπL(s′) − L(s)] ≤ −k[Es∼Uπ[L(s) − λEs′∼PπL(s′)]]
+(28)
+where α, β, λ and k is positive constants. Among them, Pπ(s′|s) =
+�
+A π(a|s)P(s′|s, a) da holds.
+Proof. Firstly, we simplify the left side of the Equation (28) with reference to (Han et al., 2020a). Introducing the definition
+of Uπ(s) leads to
+Es∼Uπ[Es′∼PπLπ(s′) − Lπ(s)]
+=
+�
+S
+lim
+T →∞
+1
+T
+T
+�
+t=0
+T (s | ρ, π, t)(
+�
+S
+Pπ(s′|s)Lπ(s′)ds′ − Lπ(s))ds
+(29)
+Due to the boundedness of Lπ, we apply the Lebesgue’s Dominated convergence theorem. To be specific, when |Fn(s)| ≤
+B(s), ∀s ∈ S, ∀n holds, we have
+lim
+n→∞
+�
+S
+Fn(s)ds =
+�
+S
+lim
+n→∞ Fn(s)ds
+(30)
+Hence, we get
+Es∼Uπ[Es′∼PπLπ(s′) − Lπ(s)]
+=
+�
+S
+lim
+T →∞
+1
+T
+T
+�
+t=0
+T (s | ρ, π, t)(
+�
+S
+Pπ(s′|s)Lπ(s′)ds′ − Lπ(s))ds
+= lim
+T →∞
+�
+S
+1
+T
+T
+�
+t=0
+T (s | ρ, π, t)(
+�
+S
+Pπ(s′|s)Lπ(s′)ds′ − Lπ(s))ds
+= lim
+T →∞
+1
+T (
+T +1
+�
+t=1
+ET (s|ρ,π,t)Lπ(s) −
+T
+�
+t=0
+ET (s|ρ,π,t)Lπ(s))
+= lim
+T →∞
+1
+T (ET (s|ρ,π,T +1)Lπ(s) − ET (s|ρ,π,t=0)Lπ(s))
+(31)
+Note that T (s|ρ, π, t = 0) is equal to ρ. Since the expectation of Lπ(s) is a finite value, the left side of Equation (28) is
+zero.
+Now, we turn to the right side of Equation (28). According to the Equation (31), we have
+−k[Es∼Uπ[L(s) − λEs′∼PπL(s′)]] ≥ 0
+Es∼Uπ[L(s) − λEs′∼PπL(s′)] ≤ 0
+(32)
+
+Adaptive Stability Certification
+Since L(s) ≥ cπ(s) + λEs′∼PπL(s′) holds, we get
+Es∼Uπcπ(s) ≤ 0
+(33)
+Based on the Abelian theorem, we know there exists
+Uπ(s) = lim
+T →∞
+1
+T
+T
+�
+t=0
+T (s | ρ, π, t)
+= lim
+t→∞ T (s|ρ, π, t)
+= ωπ(s)
+(34)
+Thus, we get
+Es∼ωπ[cπ(s)] ≤ 0
+(35)
+The last row of inequality holds because of Equation (34). Based on the definition of ωπ(s), we have
+lim
+t→∞ ET (s|ρ,π,t)cπ(s) ≤ 0
+(36)
+Suppose that there exists a starting state s0
+∈
+{s0
+|
+cπ(s0)
+≤
+b} and a positive constant d such that
+limt→∞ ET (s|ρ,π,t)cπ(s) = d or limt→∞ ET (s|ρ,π,t)cπ(s) = ∞. Consider that ρ(s0) > 0 for all starting states in
+{s0 | cπ(s0) ≤ b} (Assumption 4.1), then limt→∞ Es∼T (·|ρ,π,t)cπ(s) > 0 , which is contradictory with Equation (36).
+Thus ∀s0 ∈ {s0 | cπ(s0) ≤ b}, limt→∞ ET (s|ρ,π,t)cπ(s) = 0. Thus the system meets the mean cost stability by Definition
+3.1.
+Furthermore, we find that when L(s) = cπ(s) + λEs′∼PπL(s′) holds, our theorem is corresponding to the Theorem 1 in
+(Han et al., 2020a). That means we extend the previous method to a more general case. To be specific, the introduction of
+λ enlarges the solution space of the policy. Thus, it facilitates the policy to find the optimal point as well as maintain the
+system’s stability.
+B.2. Proof of Lemma 4.4
+Lemma B.2 (Finite Tracking Time). In a continuous-time system, a trajectory W(t) tracks the reference R(t). W(t) can
+track the reference within a finite time T, such that R(t) = W(t), t ≥ T, if the following conditions holds.
+∇tW(t) ≤ −k(W(t) − R(t)), ∀t ∈ [0, T]
+(37)
+Note that the gradient of R(t) is bounded, meaning that ∇tR(t) ≤ µ holds.
+Proof. First, we build the mean square error V (t) between them.
+V = 1
+2(W(t) − R(t))2
+(38)
+Then, we can derive the difference of V (t) as follows
+∇tV = (W − R)(∇tW − ∇tR)
+≤ (W − R)(−k(W − R) − ∇tR)
+≤ −k|W − R|2 − (W − R)∇tR
+(39)
+
+Adaptive Stability Certification
+Introducing the Assumption that the bounded gradient of R(t) , we have
+∇tV ≤ −2k |W − R|2
+2
+−
+√
+2µ|W − R|
+2
+≤ −2kV −
+√
+2µ
+√
+V
+(40)
+Observe that the above formulation belongs to a form of the Bernoulli differential equation. In this case, we can reduce the
+Bernoulli equation to a linear differential equation by substituting z =
+√
+V . Then, the general solution for z is
+z =
+√
+V ≤ −
+√
+2
+2
+µ
+k + Ce−kt
+(41)
+Applying the initial condition V (t = 0) = vt0, we have
+C = √vt0 +
+√
+2
+2
+µ
+k
+(42)
+Finally, the convergence time T can be represented as:
+T = 1
+k ln
+� √
+2
+2
+µ
+k + √vt0
+√
+2
+2
+µ
+k
+�
++ t0
+(43)
+B.3. Constrained Lyapunov Critic Network
+In this work, the output of the neural network of the Lyapunov critic is described by:
+f(s, a) = hO(hO−1(· · · h2(h1(< s, a >))))
+(44)
+where each ho(z) has the same form:
+ho(z) = ψo(Woz + bo)
+(45)
+Here, O represents the number of layers, and ψo is the non-linear activation function used in the o-th layer. Furthermore,
+{Wo, bo} is the weight and bias of the o-th layer.
+First of all, to meet the demand of Lθ(se, a) = 0, we introduce a linear transformation Gs, one of whose possible forms can
+be
+Gs(f) =
+1
+�I
+i δsi + ϵ
+�δs1
+δs2
+· · ·
+δsI
+�
+�
+��
+f1
+f1
+· · ·
+fv
+f1
+f1
+· · ·
+fv
+· · ·
+· · ·
+· · ·
+· · ·
+f1
+f1
+· · ·
+fv
+�
+��
+(46)
+where I denotes the number of elements of the state, and v is the number of units of the output layer. ϵ is a constant close to 0
+to avoid singularity. Note that δs = s − se, which indicates the difference between the current state and an equilibrium point.
+As we can see, when each element of δs is zero, the multiplication of matrices is zero. Thus, Gs=se(f(s = se, a)) = 0
+holds. Furthermore, it brings another benefit having no impact on the training of networks.
+B.4. Proof of Theorem 4.5
+Theorem B.3. Suppose that the length of sampling trajectories is T, then the bound can be expressed as:
+|Es∼Uπ∆Lπ(s) − Es∼UT
+π ∆Lπ(s)| ≤ 2(k + 1)cπ
+1 − γ
+T q−1
+(47)
+where q is a constant in (0, 1).
+
+Adaptive Stability Certification
+Proof. First, we can get the following equation by introducing the definitions of Uπ and UT
+π .
+Es∼Uπ∆Lπ(s) − Es∼UT
+π ∆Lπ(s)
+=
+�
+S
+(Uπ(s) − 1
+T
+T
+�
+t=1
+T (s | ρ, π, t))∆Lπ(s)ds
+= 1
+T
+T
+�
+t=1
+�
+S
+(Uπ(s) − T (s | ρ, π, t))∆Lπ(s)ds
+(48)
+Then, eliminating the integral operator, we obtain
+|Es∼Uπ∆Lπ(s) − Es∼UT
+π ∆Lπ(s)|
+≤ 1
+T
+T
+�
+t=1
+∥Uπ(s) − T (s | ρ, π, t)∥1∥∆Lπ(s)∥∞
+(49)
+Thus, the next step is to get the bounds of ∥Uπ(s) − T (s | ρ, π, t)∥1 and ∥∆Lπ(s)∥∞.
+For the first part, we introduce the assumption that first is mentioned in (Zou et al., 2019), shown as follows:
+T
+�
+t=1
+∥Uπ(s) − T (s | ρ, π, t)∥1 ≤ 2T q, ∀T ∈ Z+, ∃q ∈ (0, 1)
+(50)
+Frankly speaking, the assumption is easily satisfied because the L1 distance between two distributions is bounded by 2. At
+the same time, T (s | ρ, π, t) converges to Uπ(s) with time approaching.
+For the second part, we can get the bound of ∆Lπ(s) according to Equation 25.
+∆Lπ(s) = Es′∼PπLπ(s′) − Lπ(s) + k(Lπ(s) − λEs′∼Pπ(s′))
+≤
+cπ
+1 − γ − 0 + k( cπ
+1 − γ − 0)
+(51)
+Then, we have
+∥∆Lπ(s)∥∞ ≤ (k + 1) cπ
+1 − γ
+(52)
+Adding results in Equation 53, we finally get
+|Es∼Uπ∆Lπ(s) − Es∼UT
+π ∆Lπ(s)| ≤ 2(k + 1)cπ
+1 − γ
+T q−1
+(53)
+B.5. Proof of Theorem 4.6
+Theorem B.4. Suppose that the length of sampling trajectories is T and the number of trajectories is M, then there exists
+the following upper bound:
+P(| 1
+MT
+M
+�
+m=1
+T
+�
+t=1
+∆Lπ(sm
+t ) − Es∼UT
+π ∆Lπ(s)| ≥ α)
+≤ 2 exp(−
+Mα2(1 − γ)2
+((1 − kλ)2 + (k − 1)2)cπ2 )
+(54)
+where sm
+t represents the state in the m-th trajectory at the timestep t.
+
+Adaptive Stability Certification
+Proof. First, eliminating ∆Lπ(s) by Equation 20, we rewrites the left side of Equation 54 as
+δ = P(| 1
+MT
+M
+�
+m=1
+T
+�
+t=1
+∆Lπ(sm
+t ) − Es∼UT
+π ∆Lπ(s)| ≥ α)
+= P(| 1
+MT
+M
+�
+m=1
+T
+�
+t=1
+(Lπ(st+1) − Lπ(st) + kl(Lπ(st) − λLπ(st+1))) − Es∼UT
+π ∆Lπ(s)| ≥ α)
+= P(| 1
+MT
+M
+�
+m=1
+T
+�
+t=1
+((1 − kλ)Lπ(st+1) + (k − 1)Lπ(st)) − Es∼UT
+π ∆Lπ(s)| ≥ α)
+(55)
+Here Es∼UT
+π ∆Lπ(s) is expected value of
+1
+MT
+�M
+m=1
+�T
+t=1 ∆Lπ(sm
+t ). In addition, the bounds of (1 − kλ)Lπ(st+1) and
+(k − 1)Lπ(st) can be obtained easily by Equation 25. Thus, we obtain the Theorem 4.6 by applying Hoeffding’s inequality.
+δ ≤ 2 exp(−
+2M 2α2
+M((1 − kλ)2 + (k − 1)2)
+cπ2
+(1−γ)2
+)
+≤ 2 exp(−
+Mα2(1 − γ)2
+((1 − kλ)2 + (k − 1)2)cπ2 )
+(56)
+C. Details of Algorithms
+As mentioned in the main text, we introduce a minimum entropy as a constraint in policy optimization and apply the
+primal-dual method to update the policy and the Lagrange multiplier λe. To be specific, the constraint can be expressed as
+log πφ(a|s) ≤ −Ze
+(57)
+where Ze is the minimum value of policy entropy, usually, Ze corresponds to the dimension of action space in the
+environment.
+Algorithm 1: Adaptive Lyapunov-based Actor-Critic Algorithm (ALAC)
+Orthogonal initialize the parameters of actor and critic networks with φ, θ
+Initialize replay buffer D and λl, λe
+Initialize the parameters of target network with φ′ ← φ and θ′ ← θ
+for episode m = 1, M do
+Sample an initial state s0
+for step t = 0, T − 1 do
+Sample an action from πφ(at|st)
+Execute the action at and observe a new state st+1
+Store < st, at, ct, st+1 > into D
+end for
+for iteration n = 1, N do
+Sample a minibatch B from the replay buffer D
+Update θ according to Eq.(11) using minibatch B
+Update φ, λl, λe according to Eq.(17),(18),(57) using minibatch B
+Update the parameters of target networks, θ′, φ′, according to Eq. (12)
+end for
+end for
+D. Details of Experiments
+We test our method and baselines in ten robotic control environments, including Cartpole-cost,Point-circle-cost,
+Halfcheetah-cost, Swimmer-cost, Ant-cost, Humanoid-cost, Minitaur-cost, Spacereach-cost, Spacerandom-cost and
+
+Adaptive Stability Certification
+Cartpole-cost
+Point-circle-cost
+Swimmer-cost
+Halfcheetah-cost
+Ant-cost
+Humanoid-cost
+Minitaur-cost
+Spacereach-cost
+Spacerandom-cost
+Spacedualarm-cost
+Figure 5. Overview of our environments.
+Spacedualarm-cost. Most tasks in ten environments are goal-oriented, tracking a target position or speed, which corre-
+sponds to most control tasks. Furthermore, the latter four environments involve models of practical robots like a quadruped
+robot and a robotic arm, making them relatively more difficult. It is worth noting that the task of Spacedualarm-cost is
+trajectory planning of a free-floating dual-arm space robot. The coupling property of the base and the robotic arms brings
+hardship for both traditional control and RL-based methods (Wang et al., 2022).
+D.1. Environmental Design
+Cartpole-cost
+This task aims to maintain the pole vertically at a target position. The environment is inherited from (Han
+et al., 2020b). The state and action space are the same as the default settings in OpenAI Gym(Brockman et al., 2016), so we
+omit the description. The cost function is c =
+�
+x
+xthreshold
+�2
++ 20 ∗
+�
+θ
+θthreshold
+�2
+, where xthreshold = 10 and θthreshold = 20◦. The
+other settings can be found in Table 4.
+Point-circle-cost
+This task aims to allow a sphere to track a circular trajectory. The environment is inherited from (Achiam
+et al., 2017). The sphere is initialized at the original point. The cost function is represented as c = d, where d denotes the
+distance between the current position and the reference. The other settings can be found in Table 4.
+Table 4. Hyper-parameters of non-linear dynamic environments
+Hyper-parameters
+Cartpole-cost
+Point-circle-cost
+State shape
+4
+7
+Action shape
+2
+2
+Length of an episode
+250 steps
+65 steps
+Maximum steps
+3e5 steps
+3e5 steps
+Actor network
+(64, 64)
+(64, 64)
+Critic network
+(64, 64, 16)
+(64, 64, 16)
+Halfcheetah-cost
+The goal of this task is to make a HalfCheetah (a 2-legged simulated robot) to track the desired velocity.
+The environment is inherited from (Han et al., 2020b). The state and action space are the same as the default settings in
+
+A
+c300mm
+300mm
+300mmAdaptive Stability Certification
+Table 5. Hyper-parameters of mujoco environments
+Hyper-parameters
+Swimmer-cost
+Halfcheetah-cost
+Ant-cost
+Humanoid-cost
+State shape
+8
+17
+27
+376
+Action shape
+2
+6
+8
+8
+Length of an episode
+250 steps
+200 steps
+200 steps
+500 steps
+Maximum steps
+3e5 steps
+1e6 steps
+1e6 steps
+1e6 steps
+Actor network
+(64, 64)
+(64, 64)
+(64, 64)
+(256, 256)
+Critic network
+(64, 64, 16)
+(256, 256, 16)
+(64, 64, 16)
+(256, 256, 128)
+OpenAI Gym(Brockman et al., 2016), so we omit the description. The cost function is c = (v − 1)2, where 1 represents the
+desired velocity. The other settings can be found in Table 5.
+Swimmer-cost
+This task aims to make a multi-joint snake robot to track the desired velocity. The environment is inherited
+from (Han et al., 2020b). The state and action space are the same as the default settings in OpenAI Gym(Brockman et al.,
+2016), so we omit the description. The cost function is c = (v − 1)2, where 1 represents the desired velocity. The other
+settings can be found in Table 5.
+Ant-cost
+This task aims to make an Ant (a quadrupedal simulated robot) track the desired velocity. The environment is
+inherited from (Brockman et al., 2016). The state and action space are the same as the default settings in OpenAI Gym
+(Brockman et al., 2016), so we omit the description. The cost function is c = (v − 1)2, where 1 represents the desired
+velocity. The other settings can be found in Table 5.
+Humanoid-cost
+This task aims to make a humanoid robot to track the desired velocity. The environment is inherited from
+(Brockman et al., 2016). The state and action space are the same as the default settings in OpenAI Gym (Brockman et al.,
+2016), so we omit the description. The cost function is c = (v − 1)2, where 1 represents the desired velocity. The other
+settings can be found in Table 5.
+Minitaur-cost
+This task aims to control the Ghost Robotics Minitaur quadruped to run forward at the desired velocity.
+The environment is inherited from (Coumans & Bai, 2016). The state and action space are the same as the default settings
+in PyBullet environment(Coumans & Bai, 2016), so we omit the description. The cost function is c = (v − 1)2, where 1
+represents the desired velocity. The other settings can be found in Table 6.
+Spacereach-cost
+This task aims to make a free-floating single-arm space robot’s end-effector reach a fixed goal position.
+Since the base satellite is uncontrolled, collisions will cause system instability once collisions occur. Therefore, it is critical
+to plan a collision-free path while maintaining the stability of the base. The agent can obtain the state, including the angular
+positions and velocities of joints, the position of the end-effector, and the position of the reference point. Then, the agent
+outputs the desired velocities of joints. In low-level planning, a PD controller converts the desired velocities into torques,
+and then controls the manipulator. The cost function is defined as c = d, where d is the distance between the goal and
+end-effector. The other settings can be found in Table 6.
+Spacerandom-cost
+This task aims to make a free-floating single-arm space robot’s end-effector reach a random goal
+position. The agent can obtain the state, including the angular positions and velocities of joints, the position of the
+end-effector, and the position of the reference point. Then, the agent outputs the desired velocities of joints. In low-level
+planning, a PD controller converts the desired velocities into torques to control the manipulator. The cost function is defined
+as c = d, where d is the distance between goal and end-effector. The other settings can be found in Table 6.
+Spacedualarm-cost
+This task aims to make a free-floating dual-arm space robot’s end-effectors reach random goal
+positions. The complexity of the task increases dramatically due to two arms’ coupling effects on the base. The agent can
+obtain the state, including the angular positions and velocities of joints, the positions of end-effectors, and the position
+of target points of two manipulators. Then, the agent outputs the desired velocities of joints. In low-level planning, a PD
+controller converts the desired velocities into torques to control the manipulators. The cost function is defined as follows:
+c = d0 + d1, where di is the distance between goal and end-effector of Arm-i. The other settings can be found in Table 6.
+
+Adaptive Stability Certification
+Table 6. Hyper-parameters of robotic environments
+Hyper-parameters
+Minitaur-cost
+Spacereach-cost
+Spacerandom-cost
+Spacedualarm-cost
+State shape
+27
+18
+18
+54
+Action shape
+8
+6
+6
+12
+Length of an episode
+500 steps
+200 steps
+200 steps
+200 steps
+Maximum steps
+1e6 steps
+3e5 steps
+5e5 steps
+5e5 steps
+Actor network
+(256, 256)
+(256, 256)
+(256, 256)
+(512, 512)
+Critic network
+(256, 256, 16)
+(256, 256, 128)
+(256, 256, 128)
+(512, 512, 256)
+D.2. Implementation Details
+D.2.1. BASELINES
+SAC-cost
+Soft Actor-Critic(SAC) is an off-policy maximum entropy actor-critic algorithm (Haarnoja et al., 2018). The
+main contribution is to add a maximum entropy objective into standard algorithms. The soft Q and V functions are trained
+to minimize the soft Bellman residual, and the policy can be learned by directly minimizing the expected KL-divergence.
+The only difference between SAC and SAC-cost is replacing maximizing a reward function with minimizing a cost function.
+The hyper-parameters of SAC-cost is illustrated in Table 7.
+Table 7. Hyper-parameters of SAC-cost
+Hyper-parameters
+SAC-cost
+Learning rate of actor
+1.e-4
+Learning rate of critic
+3.e-4
+Optimizer
+Adam
+ReplayBuffer size
+106
+Discount (γ)
+0.995
+Polyak (1 − τ)
+0.995
+Entropy coefficient
+1
+Batch size
+256
+SPPO
+Safe proximal policy optimization (SPPO) is a Lyapunov-based safe policy optimization algorithm. The neural
+Lyapunov network is constructed to prevent unsafe behaviors. Actually, the safe projection method is inspired by the TRPO
+algorithm (Schulman et al., 2015). In this paper, we modify it to apply the Lyapunov constraints on the MDP tasks, similar
+to the process in (Han et al., 2020a). The hyper-parameters of SPPO is illustrated in Table 8.
+Table 8. Hyper-parameters of SPPO
+Hyper-parameters
+SPPO
+Learning rate of actor
+1.e-4
+Learning rate of Lyapunov
+3.e-4
+Optimizer
+Adam
+Discount (γ)
+0.995
+GAE parameter (λ)
+0.95
+Clipping range
+0.2
+KL constraint (δ)
+0.2
+Fisher estimation fraction
+0.1
+Conjugate gradient steps
+10
+Conjugate gradient damping
+0.1
+Backtracking steps
+10
+Timesteps per iteration
+2000
+
+Adaptive Stability Certification
+LAC
+Lyapunov-based Actor-Critic(LAC) algorithm is an actor-critic RL-based algorithm jointly learning a neural
+controller and Lyapunov function (Han et al., 2020a). Particularly, they propose a data-driven stability condition on the
+expected value over the state space. Moreover, they have found that the method achieves high generalization and robustness.
+The hyper-parameters of LAC is illustrated in Table 9. Among them, α3 is 0.1 in LAC, while it is changed as 1 in LAC∗.
+Table 9. Hyperparameters of LAC
+Hyperparameters
+LAC
+Learning rate of actor
+1.e-4
+Learning rate of Lyapunov
+3.e-4
+Learning rate of Larange multiplier
+3.e-4
+Optimizer
+Adam
+ReplayBuffer size
+106
+Discount (γ)
+0.995
+Polyak (1 − τ)
+0.995
+Parameter of Lyapunov constraint (α3)
+0.1
+Batch size
+256
+POLYC
+Policy Optimization with Self-Learned Almost Lyapunov Critics (POLYC) algorithm is built on the standard
+PPO algorithm (Schulman et al., 2017). Introducing a Lyapunov function without access to the cost allows the agent to
+self-learn the Lyapunov critic function by minimizing the Lyapunov risk. The hyper-parameters of POLYC is illustrated in
+Table 10.
+Table 10. Hyper-parameters of POLYC
+Hyper-parameters
+POLYC
+Learning rate of actor
+1.e-4
+Learning rate of critic
+3.e-4
+Learning rate of Lyapunov
+3.e-4
+Optimizer
+Adam
+Discount (γ)
+0.995
+GAE parameter (λ)
+0.95
+Weight of Lyapunov constraint (β)
+0.1
+Clipping range
+0.2
+Timesteps per iteration
+2000
+LBPO
+Lyapunov Barrier Policy Optimization (LBPO) algorithm (Sikchi et al., 2021) is built on SPPO algorithm (Chow
+et al., 2019). However, the core improvement uses a Lyapunov-based barrier function to restrict the policy update to a safe
+set for each training iteration. Compared with the SPPO algorithm, the method avoids backtracking to ensure safety. For
+the implementation in our paper, the process is similar to that of the SPPO algorithm. The hyperparameters of LBPO is
+illustrated in Table 11.
+TNLF
+Twin Neural Lyapunov Function (TNLF) algorithm is proposed to deal with safe robot navigation in (Xiong et al.,
+2022). Different from other approaches, the TNLF method defines a Lyapunov V function and Lyapunov Q function, which
+are trained by minimizing the Lyapunov risk. In effect, the Lyapunov risk is similar to that of (Chang & Gao, 2021). Since
+the Lyapunov function strictly decreases over time, the robot starting with any state in a Region of Attraction (RoA) will
+always stay in the RoA in the future. It should be pointed out that as our environments only support the cost function,
+the objective, except for Lyapunov risk, is to minimize the cumulative return of cost. The hyper-parameters of TNLF is
+illustrated in Table 12.
+D.2.2. OUR METHOD
+ALAC
+Our method offers a significant advantage in contrast to baselines, which is to use fewer hyperparameters. The
+main hyperparameters are illustrated in Table 13. We notice that these parameters control networks’ learning without
+
+Adaptive Stability Certification
+Table 11. Hyperparameters of LBPO
+Hyperparameters
+LBPO
+Learning rate of actor
+1.e-4
+Learning rate of critic
+1.e-4
+Learning rate of Lyapunov
+3.e-4
+Optimizer
+Adam
+Discount (γ)
+0.99
+GAE parameter (λ)
+0.97
+Clipping range
+0.2
+KL constraint
+0.012
+Fisher estimation fraction
+0.1
+Conjugate gradient steps
+10
+Conjugate gradient damping
+0.1
+Backtracking steps
+10
+Weight of Lyapunov constraint (β)
+0.01
+Timesteps per iteration
+2000
+Table 12. Hyper-parameters of TNLF
+Hyper-parameters
+TNLF
+Learning rate of actor
+1.e-4
+Learning rate of critic
+3.e-4
+Learning rate of Lyapunov V functiob
+3.e-4
+Learning rate of Lyapunov functiob
+3.e-4
+Optimizer
+Adam
+ReplayBuffer size
+106
+Discount (γ)
+0.995
+Polyak (1 − τ)
+0.995
+Weight of Lyapunov constraint (α)
+0.1
+Variance of noise distribution
+1
+Batch size
+256
+including the parameters of constraints. The reason is they are automatically updated according to Lagrange multipliers, λl,
+and λe. The initial value of Lagrange multipliers is set to 1, common usage in previous constrained methods.
+D.3. More Results on Comparison
+Figure 11 shows the learning curves of the accumulated cost and constraint violations of ALAC and other baselines in ten
+environments.
+D.4. More Results on Ablation Study
+We provide the specific formulation of ∆L1
+πφ and ∆L2
+πφ. Compared with ∆Lπφ in Equation 14, we intuitively find
+that ∆L1
+πφ and ∆L2
+πφ are lower and higher bound of ∆Lπφ respectively. In other words, ∆L1
+πφ represents the strongest
+constraint, while ∆L2
+πφ represents the loosest constraint. The comparison between them can demonstrate that the ASC
+condition (∆Lπφ) has a positive effect on the performance of optimality and stability.
+∆L1
+πφ(s, a) = Lθ(s′, πφ(·|s′)) − Lθ(s, a) + k[Lθ(s, a) − 0]
+∆L2
+πφ(s, a) = Lθ(s′, πφ(·|s′)) − Lθ(s, a) + k[Lθ(s, a) − Lθ(s′, πφ(·|s′))]
+(58)
+The ablation experiments on other tasks are shown in Figure 10.
+
+Adaptive Stability Certification
+Table 13. Hyper-parameters of ALAC
+Hyper-parameters
+ALAC
+Learning rate of actor
+1.e-4
+Learning rate of Lyapunov
+3.e-4
+Learning rate of Lagrange multipliers (λl and λe)
+3.e-4
+Optimizer
+Adam
+ReplayBuffer size
+106
+Discount (γ)
+0.995
+Polyak (1 − τ)
+0.995
+Batch size
+256
+1
+n_components=2 or 3 ,
+2
+e a r l y _ e x a g g e r a t i o n =12 ,
+3
+l e a r n i n g _ r a t e =200.0 ,
+4
+n _ i t e r =1000 ,
+5
+n _ i t e r _ w i t h o u t _ p r o g r e s s =300 ,
+6
+min_grad_norm=1e −7 ,
+7
+p e r p l e x i t y =30 ,
+8
+me tric ="euclidean" ,
+9
+n_jobs =None ,
+10
+random_state =42 ,
+11
+verbose =True ,
+12
+i n i t =’pca’
+Table 14. Other hyper-parameters of t-SNE method.
+D.5. Details of Visualization
+Our RL-based policy optimization method guided by adaptive stability is difficult to express the latent laws of states in the
+convergent process of different environments as the high-dimension states-space. To find and show the state’s change laws
+in the convergent process:
+• We use the t-SNE dimension reduction technique to visualize the state-space.
+• We plot the phase trajectory with variance according to the state pairs of joint angular position and velocity.
+• We plot the Lyapunov-value surface and its shadow with the phase trajectory and values in the convergence process.
+T-SNE Visualization
+The top row of Figure 4 shows the results of the t-SNE state plotting with SciKit-Learn
+tools(i.e.sklearn.manifold.TSNE function) with varying parameters(e.g. early_exaggeration, min_ grad_norm). Cartpole-
+Cost is visualized with n_components=2 while other environments with n_components=3. The hyper-parameters for t-SNE
+are shown in Table 14.
+Phase Trajectories of Systems
+We select the angular position and velocity of a joint in the state space in each environment
+and plot the phase trajectory with variance in Figure 6. The convergent process is shown as the angular velocity starts from
+0 to 0, and the joint angle starts from the beginning to the convergence position.
+Lyapunov Functions of Systems
+We visualize the change of Lyapunov-value in 3 dimensions based on the phase
+trajectory. The second row of Figure 4 shows the Lyapunov-value surface. The curves of values along the phase trajectory
+are mapped to the whole plane with down-sampled and smoothed by a Gaussian filter; we add the values and the phase
+trajectory shadows correspondingly simultaneously.
+
+Adaptive Stability Certification
+0.10
+0.05
+0.00
+0.05
+0.10
+0.15
+Angular Position
+1.5
+1.0
+0.5
+0.0
+0.5
+1.0
+Angular Velocity
+Cartpole-cost phase trajectory
+0.30
+0.35
+0.40
+0.45
+0.50
+Angular Position
+0
+1
+2
+3
+4
+Angular Velocity
+Halfcheetah-cost phase trajectory
+1.6
+1.8
+2.0
+2.2
+2.4
+Angular Position
+15
+10
+5
+0
+5
+10
+Angular Velocity
+Minitaur-cost phase trajectory
+1.75
+1.50
+1.25
+1.00
+0.75
+0.50
+0.25
+0.00
+Angular Position
+0.3
+0.2
+0.1
+0.0
+0.1
+Angular Velocity
+Spacerandom-cost phase trajectory
+Figure 6. Phase trajectories of the systems trained by ALAC. (we report the results of 20 trials and select a joint to graph the
+phase trajectory in each task.)
+D.6. More Results on Evaluation
+D.6.1. ROBUSTNESS
+We verify that ALAC achieves excellent robustness on most tasks. It is worth noting that we introduce periodic external
+disturbances with different magnitudes in each task. Furthermore, we omit the algorithms which do not converge to a
+reasonable solution in each task.
+D.6.2. GENERALIZATION
+We verify that ALAC achieves excellent generalization with the feedback of errors. In particular, the gap between each other
+enlarges with the increasing biases. Furthermore, we observe that the errors bring a negative impact on the performance of
+SAC-cost. The reason can be that SAC-cost does not capture the error information without the guidance of a Lyapunov
+function. Note that the number of environment steps in Halfcheetah-cost is 5e5 in this section.
+D.6.3. EFFICIENCY
+We verify that ALAC achieves comparable performance under different network structures of the actor on three tasks. By
+contrast, the network structure significantly impacts the performance of SAC-cost.
+
+Adaptive Stability Certification
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+25
+50
+75
+100
+125
+150
+175
+Cost Return
+Cartpole-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+200
+400
+600
+800
+1000
+Cost Return
+Pointcircle-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+20
+40
+60
+80
+100
+120
+Cost Return
+Swimmer-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+25
+50
+75
+100
+125
+150
+175
+Cost Return
+HalfCheetah-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+50
+100
+150
+200
+250
+300
+350
+Cost Return
+Ant-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+100
+200
+300
+400
+500
+600
+Cost Return
+Humanoid-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+200
+400
+600
+800
+1000
+Cost Return
+Minitaur-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+20
+40
+60
+80
+100
+120
+140
+160
+Cost Return
+Spacereach-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+20
+40
+60
+80
+100
+120
+140
+Cost Return
+Spacerandom-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+Magnitude
+0
+50
+100
+150
+200
+250
+300
+350
+400
+Cost Return
+Spacedualarm-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SAC-cost
+SPPO
+TNLF
+Figure 7. Performance of ALAC method and other baselines under persistent disturbances with different magnitudes. (The
+X-axis indicates the magnitude of the applied disturbance. We evaluate the trained policies for 20 trials in each setting.)
+-20%
+-10%
+0%
+10%
+20%
+Biases of goals
+75
+100
+125
+150
+175
+200
+225
+250
+Cost Return
+Pointcircle-cost
+ALAC w/ error
+ALAC w/o error
+SAC-cost w/ error
+SAC-cost w/o error
+-20%
+-10%
+0%
+10%
+20%
+Biases of goals
+0
+50
+100
+150
+200
+Cost Return
+HalfCheetah-cost
+ALAC w/ error
+ALAC w/o error
+SAC-cost w/ error
+SAC-cost w/o error
+-20%
+-10%
+0%
+10%
+20%
+Biases of goals
+0
+5
+10
+15
+20
+25
+30
+35
+40
+Cost Return
+Spacereach-cost
+ALAC w/ error
+ALAC w/o error
+SAC-cost w/ error
+SAC-cost w/o error
+Figure 8. Evaluation of ALAC and SAC-cost methods in the presence of different biases of goals. (The X-axis indicates the
+magnitude of the applied shifting. We evaluate the trained policies for 20 trials in each setting.)
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0
+50
+100
+150
+200
+Cost Return
+HalfCheetah-cost
+ALAC(64x64)
+ALAC(32x32)
+ALAC(16x16)
+SAC-cost(64x64)
+SAC-cost(32x32)
+SAC-cost(16x16)
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+400
+600
+800
+1000
+1200
+Cost Return
+Minitaur-cost
+ALAC(64x64)
+ALAC(32x32)
+ALAC(16x16)
+SAC-cost(64x64)
+SAC-cost(32x32)
+SAC-cost(16x16)
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0
+50
+100
+150
+200
+Cost Return
+HalfCheetah-cost
+ALAC(64x64)
+ALAC(32x32)
+ALAC(16x16)
+SAC-cost(64x64)
+SAC-cost(32x32)
+SAC-cost(16x16)
+Figure 9. Learning curves of ALAC and SAC-cost methods with different network structures of the actor on Halfcheetah-cost,
+Minitaur-cost, and Spaceramdom-cost tasks.
+
+Adaptive Stability Certification
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+50
+100
+150
+200
+250
+Cost Return
+Cartpole-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+200
+400
+600
+800
+1000
+Cost Return
+Pointcircle-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0
+25
+50
+75
+100
+125
+150
+175
+200
+Cost Return
+HalfCheetah-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+45
+50
+55
+60
+65
+70
+75
+80
+Cost Return
+Swimmer-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Violation
+Cartpole-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0
+1
+2
+3
+4
+5
+6
+Violation
+Pointcircle-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+Violation
+HalfCheetah-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0.00
+0.25
+0.50
+0.75
+1.00
+1.25
+1.50
+1.75
+Violation
+Swimmer-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+60
+80
+100
+120
+140
+160
+180
+200
+220
+Cost Return
+Ant-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0
+10
+20
+30
+40
+50
+60
+70
+80
+Cost Return
+Spacereach-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0
+10
+20
+30
+40
+50
+60
+70
+Cost Return
+Spacerandom-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+25
+50
+75
+100
+125
+150
+175
+200
+225
+Cost Return
+Spacedualarm-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+0
+1
+2
+3
+4
+5
+Violation
+Ant-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+Violation
+Spacereach-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+Violation
+Spacerandom-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0
+1
+2
+3
+4
+5
+6
+7
+Violation
+Spacedualarm-cost
+ALAC(original)
+ALAC(
+1 )
+ALAC(
+2 )
+ALAC(Tanh)
+ALAC(kl = 0.1)
+Figure 10. Ablation studies of the ASC condition. ALAC(original) shows comparable or the best performance compared
+with other certifications on each task.
+
+Adaptive Stability Certification
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+50
+100
+150
+200
+250
+300
+Cost Return
+Cartpole-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+200
+400
+600
+800
+1000
+Cost Return
+Pointcircle-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0
+50
+100
+150
+200
+250
+300
+Cost Return
+HalfCheetah-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+40
+60
+80
+100
+120
+Cost Return
+Swimmer-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0
+2
+4
+6
+8
+10
+Violation
+Cartpole-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0
+2
+4
+6
+8
+Violation
+Pointcircle-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+Violation
+HalfCheetah-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+Violation
+Swimmer-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+50
+100
+150
+200
+250
+300
+Cost Return
+Ant-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+300
+350
+400
+450
+500
+550
+600
+Cost Return
+Humanoid-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+400
+600
+800
+1000
+1200
+Cost Return
+Minitaur-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0
+25
+50
+75
+100
+125
+150
+175
+Cost Return
+Spacereach-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+0
+1
+2
+3
+4
+5
+Violation
+Ant-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+0
+2
+4
+6
+8
+10
+12
+Violation
+Humanoid-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Timestep
+1e6
+0
+1
+2
+3
+4
+5
+6
+7
+Violation
+Minitaur-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Timestep
+1e5
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+Violation
+Spacereach-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0
+20
+40
+60
+80
+100
+120
+140
+160
+Cost Return
+Spacerandom-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
+4.0
+Violation
+Spacerandom-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+50
+100
+150
+200
+250
+300
+350
+400
+Cost Return
+Spacedualarm-cost
+ALAC(ours)
+LAC
+LAC*
+LBPO
+POLYC
+SAC-cost
+SPPO
+TNLF
+0
+1
+2
+3
+4
+5
+Timestep
+1e5
+0
+1
+2
+3
+4
+5
+6
+7
+Violation
+Spacedualarm-cost
+ALAC(ours)
+LAC
+LAC*
+POLYC
+SPPO
+TNLF
+Figure 11. Performance comparison on ten tasks. The ALAC method finds a good trade-off between minimizing the
+accumulated cost and constraint violations in contrast to their rivals.
+
diff --git a/4tAyT4oBgHgl3EQfpPhP/content/tmp_files/load_file.txt b/4tAyT4oBgHgl3EQfpPhP/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e9598e09f3087ee2b77b26956a2db8b0b86e4083
--- /dev/null
+++ b/4tAyT4oBgHgl3EQfpPhP/content/tmp_files/load_file.txt
@@ -0,0 +1,1957 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf,len=1956
+page_content='A RL-based Policy Optimization Method Guided by Adaptive Stability  Certification  Shengjie Wang 1 Fengbo Lan 1 Xiang Zheng 2 Yuxue Cao 3 Oluwatosin Oseni 4 Haotian Xu 1 Yang Gao 5  Tao Zhang 1  Abstract  In contrast to the control-theoretic methods, the  lack of stability guarantee remains a significant  problem for model-free reinforcement learning  (RL) methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Jointly learning a policy and a  Lyapunov function has recently become a promis-  ing approach to ensuring the whole system with  a stability guarantee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' However, the classical Lya-  punov constraints researchers introduced cannot  stabilize the system during the sampling-based  optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Therefore, we propose the Adap-  tive Stability Certification (ASC), making the sys-  tem reach sampling-based stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Because the  ASC condition can search for the optimal policy  heuristically, we design the Adaptive Lyapunov-  based Actor-Critic (ALAC) algorithm based on  the ASC condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Meanwhile, our algorithm  avoids the optimization problem that a variety of  constraints are coupled into the objective in cur-  rent approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' When evaluated on ten robotic  tasks, our method achieves lower accumulated  cost and fewer stability constraint violations than  previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Introduction  Learning-based (especially Reinforcement-Learning-based)  controllers have become increasingly popular and have  achieved excellent performance in non-linear dynamic sys-  tems (Hwangbo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Andrychowicz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  However, a lack of some safety notions introduces addi-  tional risks to the agents and environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Stability is a  crucial notion of safety, whose violation can cause unsafe  behaviours (Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Fortunately, there exists an  effective tool to assess the stability, Lyapunov functions, in  1Department of Automation, Tsinghua University 2Department  of Computer Science, City University of Hong Kong 3Beijing  Institute of Control Engineering 4Covenant University 5Institute  for Interdisciplinary Information Sciences,Tsinghua University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Correspondence to: Tao Zhang <taozhang@tsinghua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='cn>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  State space  𝑐!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 𝑠 ≤ 𝑏  𝑠"  𝑐!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 𝑠 = 0  Diverging trajectory  Optimal trajectory w/ stability  Sub-optimal trajectory w/ stability  Unstable trajectory  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Intuitive example showing the mean cost stabil-  ity according to Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The figure shows the re-  lationship between three sets, like the whole state space,  {s | cπ(s) ≤ b} and {s | cπ(s) = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The red line repre-  sents a diverging trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The yellow line represents a  trajectory without the mean cost stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The trajectories  coloured cyan and purple remain stable, whereas the state in  the purple trajectory reaches the set {s | cπ(s) = 0} more  quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The task aims to obtain the policy that can generate  the purple trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  control-theoretic approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lyapunov functions can be  designed for a linear system with specific criteria in the form  of a quadratic positive-definite function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' But how to find  a suitable Lyapunov function remains an open challenge  in the non-linear dynamic system (La Salle & Lefschetz,  2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Thanks to the emergence of deep learning, researchers no-  ticed that the neural Lyapunov function had an outperform-  ing representation ability, thereby making it possible to  search for a feasible Lyapunov function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' According to Lya-  punov’s second method for stability, the neural Lyapunov  function is trained by forcing the updating direction toward  decreasing the Lyapunov function along an episode’s state  trajectories (Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In the early stage of time,  these methods are only suitable for the model-based setting  because the difference of Lyapunov function with respect to  time brings a requirement of dynamic model (Berkenkamp  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='00521v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='RO]  2 Jan 2023  Adaptive Stability Certification  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Richards et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In contrast to model-  based methods, model-free reinforcement learning meth-  ods have achieved superior performance on many complex  robotic systems (Hwangbo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Andrychowicz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Therefore, researchers proposed some methods to  overcome the above issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Firstly, they applied the discrete  Lyapunov stability condition directly in the optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Then, the Lyapunov conditions can be viewed as multiple  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Prior studies added those constraints into the ob-  jective function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Specifically, the objective function enables  the system to reach optimality and stability together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Fur-  thermore, it is worth noting that current RL-based methods  with stability guarantee have been applied in some practi-  cal problems successfully, such as monitoring the security  of interconnected microgrids (Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021), power  system control (Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021), automatic assembly (Li  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2022) and motion planning of autonomous vehicles  (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Admittedly, RL-based approaches with the help of the Lya-  punov function achieve promising performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' However,  the discrete Lyapunov stability condition should be satisfied  in the whole state space, which means infinity constraints  for continuous control tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Due to the sampling-based  optimization in RL, current approaches sample some data  pairs randomly, which causes a serious problem that the  discrete stability condition is not convincing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore,  reaching optimality and stability together remains a chal-  lenge for their objective function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Because the Lyapunov  stability condition introduces various constraints in the ob-  jective function, it is hard to balance the optimality and  stability of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In practical experiments, we find  that previous constraints are either loose to find ineffective  Lyapunov functions or tight to make the policy trapped into  a sub-optimal point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Therefore, to better improve the cur-  rent research, we hope the Lyapunov-based constraint can  facilitate the policy to reach the optima within the set of the  sampling-based stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To better understand the principle,  we give an intuitive example in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  To address the above issues, we propose the Adaptive  Lyapunov-based Actor-Critic algorithm (ALAC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Unlike  the discrete Lyapunov stability condition, we propose a  novel sampling-based stability condition called Adaptive  Stability Certification (ASC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Meanwhile, the certifica-  tion can guide the policy to search for the optimal point  heuristically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Thus, based on the ASC condition, we de-  sign the Adaptive Lyapunov-based Actor-Critic algorithm  (ALAC) to reach the optimality and stability of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Thanks to the supervised learning for a Lyapunov candidate  and the Lagrangian-based policy optimization, our method  eliminates the coupling relationship between various con-  straints and the objective function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Experiments show that  our method provides promising results under stability con-  straints on some robotic control problems, like walking of  legged robots, trajectory planning of a free-floating space  robot, and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Another interesting finding is that, in  contrast to traditional RL algorithms, our method facilitates  the controller to enhance the robustness, generalization, and  efficiency of the whole system 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Related works  Due to the difficulty of a manual design, constructing a  Lyapunov neural network has become increasingly popu-  lar in a non-linear dynamic system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' For the model-known  situation, the approaches jointly learn a Lyapunov func-  tion and a controller (Richards et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Mittal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lechner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Donti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Gaby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' But it re-  stricts the application of complex systems which are hard  to obtain accurate models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Therefore, some researchers  present model-learned methods with a stability guarantee,  in which Gaussian Process or Neural Network approximates  the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The model-learned method can be separated into  two types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The first one is learning dynamics models guided  by a learnable Lyapunov function, in which policies are  inherently included or learned by LQR method (Kashima  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lawrence  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Schlaginhaufen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Another approach  is to construct a learnable policy network updated by a neu-  ral Lyapunov function, thereby satisfying the stability of  system (Berkenkamp et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Dawson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Zhou  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lale et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' However, we  notice that most model-learned methods are only verified  in relatively easy environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A possible reason is that  the coupling of the Lyapunov function and dynamic model  makes learning unstable or incompatible due to interdepen-  dency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  A promising direction is to study model-free methods with  a stability guarantee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Recently, a large variety of methods  have been proposed to address the issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' One method is that  the policy is updated by a mixed objective with respect to the  neural Lyapunov function and Q function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' POLYC (Chang  & Gao, 2021) introduced the necessary conditions required  by the Lyapunov function into objectives to optimize the  policy network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' LBPO (Sikchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021) applied the log-  arithmic barrier function based on the form of the Lyapunov  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' TNLF (Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2022) constructed Lyapunov  V and Q functions trained by the stability certification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The  other form is policy optimization with Lyapunov constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Chow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (2018) designed a constrained RL algorithm to  project a policy in a trust region with Lyapunov stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (2020a) provided a novel constrained RL-based  approach called LAC, using the prime-dual method to mod-  ify the constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Their latter work verified them in both  1See our project page at https://sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='com/view/adaptive-  lyapunov-actor-critic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  on-policy and off-policy settings (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  In the previous study, there still exist two main drawbacks  to obtaining the optimal policy and a suitable Lyapunov  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The discrete Lyapunov condition they used did  not meet the demand for a sampling-based stability guar-  antee in RL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, a combined objective function  via a simple addition causes a sub-optimal policy or invalid  Lyapunov function, especially for multiple and complex  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In contrast, our method proposes the Adap-  tive Lyapunov-based Actor-Critic algorithm to satisfy the  sampling-based stability and search for the optimal policy  heuristically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Problem Formulation  The pre-process of implementing RL-based algorithms is to  formulate robotic control problems as a Markov Decision  Process (MDP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In our paper, MDP mainly consists of four  elements, such as S, A, P, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Here, S is the state space,  A is the action space, P is the dynamic transition function,  and C is the cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' At timestep t, st ∈ S represents  the state the robot observes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Then, at ∈ A is the action  executed by the agent(robot).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Note that at is sampled from  the agent’s policy π(at|st).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' According to P(st+1|st, at),  the state of system transfers to the next state st+1 with a  certain probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' At the same time, the agent receives the  cost cπ(st) = Ea∼πC(st, at).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Besides, the distribution of  starting state denotes s0 ∼ ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' And then, we can define the  state distribution T :  T (s|ρ,π, t + 1) =  �  S  �  A  π(at|st)P(st+1|st, at) daT (s|ρ, π, t) ds  (1)  Note that T (s|ρ, π, 0) = ρ holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The optimal objec-  tive is to find the optimal polity π∗, which can minimize  Eπ[�∞  t=0 γtcπ(t)|s0 = s] where γ is a discounting factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  An MDP system corresponds to a deterministic, continuous-  state, discrete-time dynamical system st+1 = f(s, a) with  state space S and action space A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Therefore, the system’s  stability can be verified by a classical tool, Lyapunov’s Sta-  bility Function (see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' If a Lyapunov function  exists, a discrete-time system can achieve stability in the  sense of Lyapunov as depicted in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1 and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  In order to search for a Lyapunov function, current ap-  proaches attempt to train a Lyapunov network by min-  imizing the requirements in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  However,  optimization-based methods meet a common problem in  that the trained Lyapunov function remains close to 0 along  the whole trajectories, thus resulting in ineffective guidance  for the policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' More importantly, the classical definition  is based on the whole state space, so it is unsuitable for  RL-based methods due to sampling optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Therefore, we should extend the stability to a reasonable  case in RL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' We notice that for most robotic tasks, cost  functions are related to the stability of the closed-loop  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' For example, the goal of stabilization tasks is  to make the norm of state equal to zero finally, where  the cost function is C(s, a) = EP (·|st,at)∥st+1∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Another  main task is the tracking task, which aims to achieve the  reference state r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function can be denoted as  C(s, a) = EP (·|st,at)∥st+1 − r∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In this context, we in-  troduce a Mean Cost Stability to connect the stability and  the cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1 (Mean Cost Stability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A robotic system  remains stable in mean cost when satisfying the following  equation, where b is a constant (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  lim  t→∞ Est∼T cπ(st) = 0, cπ(s0) ≤ b  (2)  More importantly, the above definition corresponds to the  mean square stability when the cost function is chosen to  be the norm of the state;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' it is also equivalent to the partial  stability in tracking tasks (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  In the other direction, the stability definition with regard  to cost avoids the inconsistent scale between the objective  and constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Specifically, the problem formulation can be  represented as follows:  min  π Eρ,π,P[  ∞  �  t=0  γtcπ(st)]  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' lim  t→∞ Est∼T cπ(st) = 0  (3)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Adaptive Lyapunov-based Actor-Critic  Algorithm  To target the above-mentioned problem, we propose the  Adaptive Lyapunov-based Actor-Critic algorithm (ALAC)  in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The main contents are as follows: 1) we  design an Adaptive Stability Certification (ASC), a union  of two objectives guaranteeing a system’s mean cost sta-  bility and guiding the policy to search the optimal point  heuristically (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 2) we construct an Actor-Critic  optimizing framework based on ASC and use a supervised  learning method to update the parameters of the Lyapunov  critic network(Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 3) we apply the prime-dual  method to update the parameters of the policy network and  tune the parameters of ASC adaptively (Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Adaptive Stability Certification  In order to achieve the mean cost stability in Definition  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1, we first give a reasonable assumption to ensure that the  starting state is sampled in the region of attraction, which is  represented as the starting state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  Assumption 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1 (Region of Attraction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' There exists a pos-  itive constant b such that ρ(s) > 0, ∀s ∈ {s|cπ(s) ≤ b}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Another assumption is the existence of the stationary state  distribution, which is generally exploited in the RL litera-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Assumption 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2 (Ergodic Property).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The Markov Chain  driven by the policy π is ergodic, which means the following  equation holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  ωπ(s) = lim  t→∞ T (s|ρ, π, t)  (4)  Furthermore, we define a new variable Uπ for further deriva-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Uπ = lim  T →∞  1  T  T  �  t=0  T (s | ρ, π, t)  (5)  Based on these mild assumptions, we formalize the  sampling-based Lyapunov stability that meets the mean  cost stability in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3 below, proven in Appendix  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3 (Sampling-based Lyapunov Stability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' An  MDP system is stable with regard to the mean cost, if there  exists a function L : S → R meets the following conditions:  αcπ(s) ≤ L(s) ≤ βcπ(s)  (6)  L(s) ≥ cπ(s) + λEs′∼PπL(s′)  (7)  Es∼Uπ[Es′∼PπL(s′) − L(s)]  ≤ −k[Es∼Uπ[L(s) − λEs′∼PπL(s′)]]  (8)  where α, β, λ and k is positive constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Among them,  Pπ(s′|s) =  �  A π(a|s)P(s′|s, a) da holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  In practice, our method constructs sampling-based require-  ments for the Lyapunov function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Taking advantage of the  sampling-based stability, we can learn the policy that guar-  antees the system’s stability in RL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Moreover,  finding a Lyapunov function directly remains a challenge  when the search space becomes large due to the increas-  ing dimension of the state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To mitigate the issue, we use a  Lyapunov candidate which is related to the sum of cost or  value function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' it has been proven to be a valid Lyapunov  candidate in a previous study for stability analysis (Mayne  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Thus, we can denote a Lyapunov candidate as:  Lπ(s) = Eπ[  ∞  �  t=0  γtcπ(st)|s0 = s]  (9)  It is noteworthy that the Lyapunov candidate naturally meets  the constraints in Equation (6) and (7) when λ ≤ γ holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Please see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2 for a detailed demonstration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  ∞  {𝑊(𝑡)}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' "#  $  {𝑅(𝑡)}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' "#  $  𝑡  𝑡 + 1  𝑘(𝑊(𝑡) − 𝑅(𝑡))  𝑊(𝑡 + 1)  𝜆 ↓  𝜆 ↓  𝑅(𝑡)  𝑊(𝑡)  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Illustrative example of how ASC condition can  minimize L(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Note that {W(t)}∞  t=0 = {EL(s)}∞  t=0  and {R(t)}∞  t=0 = = {λEL(s′)}∞  t=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The blue point de-  notes W(t), and the orange point denotes R(t), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  W(t + 1) should decrease by k(W(t) − R(t)) according to  the ASC condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Besides, as {R(t)}∞  t=0 decreases with  λ, {W(t)}∞  t=0 decreases together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' When λ remains at the  minimum value, the ASC condition will help the policy  minimize L(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Recalling the optimization problem (3), we find that  the constraint part equals Equation (8) with respect to  Lπ(s), as well as the objective part can be rewritten as  minπ Es∼ρLπ(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The Lyapunov candidate builds a bridge  between the constraint and the objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A common ap-  proach is to use the lagrangian-based method to achieve the  trade-off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' However, making the constraints soft poses a chal-  lenge to the guarantee of mean cost stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Accordingly,  we hope to propose a method which guides the policy to find  the optimal point on the premise of the stability guarantee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Fortunately, we find that Equation (8) can achieve the goal  when finding the minimum value of λ adaptively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' We call  this the Adaptive Stability Certification (ASC) that pro-  vides promising insight into searching for the optimal policy  heuristically without violating stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In the following,  we illustrate the underlying reasons based on an interesting  lemma in a continuous-time system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4 (Finite Tracking Time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In a continuous-time  system, a trajectory W(t) tracks the reference R(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' W(t)  can track the reference within a finite time T, such that  R(t) = W(t), t ≥ T, if the following conditions holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  ∇tW(t) ≤ −k(W(t) − R(t)), ∀t ∈ [0, T]  (10)  Note that the gradient of R(t) should be bounded, meaning  that ∇tR(t) ≤ µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The proof see Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  It can be seen that Equation (8) is very similar to Equation  (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Although the discrete-time condition does not have a  finite tracking time unlike the continuous-time setting, the  same principle comes from the feedback control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To some  extent, we can think Equation (8) as a special tracking task  Adaptive Stability Certification  that the sequence {W(t)}∞  t=0 = {EL(s)}∞  t=0 tracks the ref-  erence sequence {R(t)}∞  t=0 = {λEL(s′)}∞  t=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To explain  it intuitively, Figure 2 depicts an illustrative example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' As  we can see, the value of W(t + 1) needs to decrease by  k(W(t) − R(t)) at time t + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' If λ decreases, {R(t)}∞  t=0  forces {W(t)}∞  t=0 to minimize L(s) along the whole se-  quence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Because of the introduction of the Lyapunov can-  didate, minimizing L(s) equals the previous objective part  in Equation (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Therefore, we can find the optimal policy  based on the certification by finding the minimum value of λ  adaptively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To sum up, the optimization problem is modified  to find the minimum value of λ as well as make Equation (8)  holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Note that we do not provide an in-depth theoretical  analysis of the heuristic method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Thus, it leaves room for  our future work, indicating that meeting ASC corresponds  to finding the optimal policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lyapunov Critic Learning  We leverage a traditional Actor-Critic framework to solve  the optimization problem mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' First, we con-  struct two neural networks, namely actor πφ(a|s) and Lya-  punov critic Lθ(s, a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Among them, φ and θ represent  the parameters of two networks, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The actor  πφ(a|s) maps a given state s to a distribution over action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The action distribution is modelled as a Gaussian, with a  state-dependent mean µφ(s) and diagonal covariance matrix  Σφ(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Unlike traditional Actor-Critic methods, our critic  network is related to the Lyapunov candidate Lπ(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' As a  matter of fact, Lπ(s) is the expectation of Lθ(s, a) over the  distribution of actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Specifically, EπLθ(s, a) = Lπ(s)  holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In the context of this property, the above theoretical  results about Lπ(s) are also suitable for our critic network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  For the training of Lθ(s, a), because we choose the value  function as the Lyapunov candidate illustrated in Equation  (9), we can update θ according to the TD error:  θk+1 = θk + αθ(∇θ(Lθ(s, a) − (cπ + γL′(s′, π′(·|s′))))2)  (11)  where k is the number of iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' L′ and π′ are the target  networks parameterized by θ′ and φ′, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In the  Actor-Critic method, the parameters θ′ and φ′ are usually  updated through exponentially moving average of weights  controlled by a hyper-parameter σ ∈ (0, 1), which is shown  as:  θ′  k+1 ← σθk + (1 − σ)θ′  k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' φ′  k+1 ← σφk + (1 − σ)φ′  k  (12)  Furthermore, we introduce an interesting mechanism on  the Lyapunov critic network to speed up the learning pro-  cess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Admittedly, the Lyapunov candidate Lπ(s) meets  some requirements sufficiently shown in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2,  which means the output of the critic network can guarantee  them eventually based on TD-like updating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In order to  encourage accurate and efficient learning, we construct a  constrained critic network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Concretely, we denote the output  of a neural network as f(s, a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' And then, Lθ(s, a) can be  described by:  Lθ(s, a) = (Gs(f(s, a)))(Gs(f(s, a)))⊤  (13)  where Gs is a linear transformation, which guarantees  Gs=se(f(s = se, a)) = 0 (se is an equilibrium point de-  fined in Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Note that Gs contains no parame-  ters to be learned, so the operator does not cause harm to the  representation ability of the neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' For the details,  see Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To this end, the constrained network  ensures that the output is non-negative and the Lyapunov  value should be zero when the state is an equilibrium point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lagrangian-based Policy Learning  Policy learning aims to search feasible parameters of the  policy network to make the output of the Lyapunov network  meet the requirements of the ASC condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  For optimizing the policy πφ(a|s), we denote the specific  constrained condition as follows according to Equation (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  ∆Lπφ(s, a) = Lθ(s′, πφ(· | s′)) − Lθ(s, a)  + k[Lθ(s, a) − λLθ(s′, πφ(· | s′))] ≤ 0  (14)  We can see that the current policy’s parameters can be up-  dated due to the embedding of πφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Meanwhile, because of  the sampling-based stability theorem (Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3), it is  convenient to efficiently implement the random sampling in  the replay buffer D that stores the interaction data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' More-  over, the optimal policy can be obtained, when we maxi-  mize ∆Lπφ(s, a) by finding the minimum λ according to  the ASC condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Specifically, The optimization problem  in Equation (3) can be reformulated as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  max  λ,πφ  ED∆Lπφ(s, a)  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ED∆Lπφ(s, a) ≤ 0  (15)  First, we focus on the sub-problem of finding πφ under  satisfying the constraint with arbitrary λ, which is shown as:  find πφ  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ED∆Lπφ(s, a) ≤ 0  (16)  Applying the Lagrangian-based method (Stooke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  2020), the parameters of πφ are updated by:  φk+1 = φk + αφ(λl∇a∆Lπφ(s, a)∇φπφ(s, a))  (17)  where αφ is the learning rate of φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' λl represents the La-  grange multiplier of the constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' During the training, λl  Adaptive Stability Certification  is updated by gradient ascent to maximize ∆Lπφ(s, a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  λk+1  l  = λk  l + αλl∆Lπφ(s, a)  (18)  Note that λl should always be positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' αλl is the learning  rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' It is worth noting that λl is clipped by 0 and 1, to  bound the value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In addition, to improve the exploration  efficiency, we add a constraint about the minimum entropy  as the same as the maximum entropy RL algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' THE CHOICE OF λ  However, how to maximize ∆Lπφ(s, a) in Equation (15)  remains to be an unsolved problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Finding the maximum  value of ∆Lπφ(s, a) equals finding the minimum value of  λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' First, The range of λ is from γ to 0 in the ASC condition,  and γ is very close to 1 in practical usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Moreover, we  find the Lagrange multiplier λl ranges from 0 to 1, and it  decreases with the constraint’s satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Therefore, we  can update λ by the following method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  λ ← min(λl, γ)  (19)  To be specific, when satisfying the constraint, λ decreases  toward 0 to maximize ∆Lπφ(s, a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' When λ remains at a  stable level, the minimum value of λ realizes the aim of  maximizing ∆Lπφ(s, a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Until now, we have constructed  the whole training process for the optimization problem in  Equation (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' THE CHOICE OF k  For the choice of k, we also use a heuristics approach to  adjust the value of k dynamically, k ← 1 − λl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' There is  an essential advantage to the approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' As we can see, λl  is close to 1 at the early stage of training;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' thus, k leads to  slow tracking according to Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' When λl decreases,  it indicates the current constraint is loose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In the setup,  kl increases instead, and the constraint forces the tracking  process to be performed more quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Besides, It offers  another benefit we explain in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  We have designed the complete ALAC algorithm, and the  pseudo-code of the proposed algorithm is shown in Ap-  pendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Theoretical Analysis  A common fact we notice is that there exists a bias be-  tween the practical computing and theoretical analysis about  Uπ in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To estimate the distribution Uπ, we  need an infinite number of trajectories with infinite time  steps, whereas in practice, only M trajectories of T time  steps are accessible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To better illustrate the issue, we de-  fine a finite sampling distribution UT  π , apparently where  UT  π = 1  T  �T  t=0 T (s | ρ, π, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Besides, we introduce a new  variable ∆Lπ(s) about the Lyapunov candidate to simplify  the expression of derivation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  ∆Lπ(s) =Est+1∼PπLπ(st+1) − Lπ(st)  + k[Lπ(st) − λEst+1∼PπLπ(st+1)]  (20)  First, we provide a quantitative bound of expectation from  Uπ and UT  π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Suppose that the length of sampling trajecto-  ries is T, then the bound can be expressed as:  |Es∼Uπ∆Lπ(s) − Es∼UT  π ∆Lπ(s)| ≤ 2(k + 1)cπ  1 − γ  T q−1  (21)  where cπ is the maximum of cost and q is a constant in  (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' For proof see Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Next, we take the number of trajectories into considera-  tion and derive the probabilistic bound of the difference of  ∆Lπ(s) estimated by UT  π distribution and M trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Suppose that the length of sampling trajec-  tories is T and the number of trajectories is M, then there  exists the following upper bound:  P(| 1  MT  M  �  m=1  T  �  t=1  ∆Lπ(sm  t ) − Es∼UT  π ∆Lπ(s)| ≥ α)  ≤ 2 exp(−  Mα2(1 − γ)2  ((1 − kλ)2 + (k − 1)2)cπ2 )  (22)  where sm  t represents the state in the m-th trajectory at the  timestep t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' For proof see Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5 suggests that if k is close to 0, the gap becomes  small in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Alternatively, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6 indicates that  k has better to be 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' That means the best choice of k ranges  from 0 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Thus, the updating method of k in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  balances the impacts of each other efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore,  two theorems illustrate the theoretical gap between infinite  and finite samples in practical usage, thus making Theorem  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3 more complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Experiments  In this section, we demonstrate empirical evidence that  ALAC captures an improved trade-off between optimal-  ity and stability compared to the baseline approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  We test our method and baselines in ten robotic control  environments, including Cartpole-cost,Point-circle-cost,  Halfcheetah-cost, Swimmer-cost, Ant-cost, Humanoid-  cost, Minitaur-cost, Spacereach-cost, Spacerandom-  cost and Spacedualarm-cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Details of the environments  are given in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, we benchmark  the ALAC method against five algorithms with a neu-  ral Lyapunov function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The algorithms can be separated  Adaptive Stability Certification  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Performance evaluations of the cultivated costs and stability constraint violations on ten environments compared with six baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  All quantities are provided in a scale of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Standard errors are provided in brackets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (if the mean constraints are less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2, the sign is  ↓ else ↑.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='‘-’ indicates the algorithm does not contain the stability constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=')  Task  Metrics  ALAC  SAC-cost  SPPO  LAC  LAC∗  POLYC  LBPO  TNLF  Cartpole-cost  Cost Return  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2(7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  Violation  ↓ ↑  ↓  ↓  ↓ ↓  Point-circle-cost  Cost Return  111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  958.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  722.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  Violation  ↓ ↑  ↓  ↑  ↓ ↓  Halfcheetah-cost  Cost Return  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  Violation  ↓ ↑  ↓  ↓  ↓ ↓  Swimmer-cost  Cost Return  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  Violation  ↓ ↑  ↓  ↑  ↓ ↓  Ant-cost  Cost Return  101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2(29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  259.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  Violation  ↓ ↑  ↓  ↑  ↓ ↓  Humanoid-cost  Cost Return  354.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  441.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  531.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  431.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  368.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  490.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4(32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  452.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4(13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  Violation  ↓ ↑  ↓  ↑  ↓ ↓  Minitaur-cost  Cost Return  493.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2(93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  950.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2(47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  838.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(237.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  382.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  Violation  ↓ ↑  ↓  ↑  ↓ ↓  Spacereach-cost  Cost Return  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  Violation  ↓ ↓  ↓  ↓  ↓ ↓  Spacerandom-cost  Cost Return  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4(28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2(32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  Violation  ↓ ↓  ↓  ↓  ↓ ↓  Spacedualarm-cost  Cost Return  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  Violation  ↓ ↓  ↓  ↓  ↓ ↓  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  300  350  400  450  500  550  Cost Return  Humanoid-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  0  5  10  15  20  25  30  Violation  Humanoid-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  400  600  800  1000  Cost Return  Minitaur-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  0  2  4  6  8  10  12  Violation  Minitaur-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Ablation studies of the ASC condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ALAC(original) shows comparable or the best performance compared with  other certifications on each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  into two categories, optimizing policy with a mixed ob-  jective and Lyapunov-like constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The first one con-  tains POLYC (Chang & Gao, 2021), LBPO(Sikchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  2021) and TNLF(Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The second one in-  cludes SPPO(Chow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2019), LAC (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020a)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  We also take the SAC-cost (Haarnoja et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2018)  method into account because the method is very close to  our method without the ASC condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' For the detailed  hyper-parameter settings see Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1 and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Comparing with Baselines  In this part, we evaluate the optimality and stability of our  methods and baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The results demonstrate ALAC out-  2We find LAC with a large α3 (see Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1) performs  better, so we call it LAC∗ for the distinction between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  performs baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To fairly evaluate the performance of  the methods mentioned above, we run the experiments over  5 rollouts and 5 seeds for all algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' We use the accu-  mulated cost in a testing episode as the metric of optimality  and the stability constraint violations as the stability metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Although the metric of stability violations depends on each  algorithm’s design, the best value should be close to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Ta-  ble 1 shows the performance on all tasks, and the training  curves for different algorithms are in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Results  confirm that ALAC outperforms state-of-the-art baselines  on all tasks except for Cartpole-cost, Humanoid-cost and  Minitaur-cost where our method doesn’t outperform SAC-  cost and TNLF, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, although LAC∗  using tighter constraints achieves comparable performance  with our method in contrast to LAC, the stability violations  in LAC∗ remain at a high level on some tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Admittedly,  TNLF achieves lower cost than ALAC on Minitaur-cost,  Adaptive Stability Certification  Cartpole-cost  HalfCheetah-cost  Minitaur-cost  𝑔𝑜𝑎𝑙!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  𝑔𝑜𝑎𝑙"  𝑔𝑜𝑎𝑙#  Spacerandom-cost  Steps  𝜑  𝜑 ̇  ℒ!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Values  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Visualization of states for ALAC method by t-SNE and phase trajectory techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The top row of the figure  depicts the t-SNE dimension reduction technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (Cartpole-Cost is visualized within 2 dims while others within 3 dims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=')  The bottom row shows the phase trajectories and Lyapunov-value surfaces of environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ψ and ˙ψ denotes the angular  position and velocity respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Average evaluation score and standard deviation on our environments for ALAC with and without the feedback under different  biases of goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (w/ errors means using errors between the desired and achieved goals as extra states for the agent)  Task  Point-circle-cost  Halfcheetah-cost  Spacereach-cost  Biases of goals  20%  0%  20%  20%  0%  20%  20%  0%  20%  ALAC w/ errors  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  ALAC w/o errors  178.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  SAC-cost w/ errors  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  129.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  SAC-cost w/o errors  180.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8(8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  but TNLF converges to suboptimal policies on many tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  According to Figure 11, we notice that TNLF satisfies the  stability constraints quickly during the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Neverthe-  less, the reason is that the trained Lyapunov function is close  to 0 quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To this end, it does not provide dense guid-  ance for the policy, thus leading it to a suboptimal solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  To recap, ALAC strikes an efficient balance between the  optimality and stability of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Ablation Studies  To better demonstrate the effectiveness of the ASC condi-  tion, we do the ablation studies about different certifications  in ALAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' We compare the performance of the original  ALAC with a version that uses ∆L1  πφ and ∆L2  πφ, and with  a version where k is a constant throughout training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The de-  tails of ∆L1  πφ and ∆L2  πφ are given in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In con-  trast to ∆Lπφ, ∆L1  πφ and ∆L2  πφ represents the upper bound  and lower bound of the constraint, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Figure 3 and  Figure 10 (see Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4) depict the accumulated cost  and constraint violations on all tasks, where the algorithms  are modified from ALAC directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ALAC(∆L2  πφ) achieve  lower performance than ALAC, while ALAC(∆L1  πφ) per-  forms the tasks comparably with ALAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Nevertheless, more  strict constraints (ALAC(∆L1  πφ)) negatively affect its per-  formance on constraint violations, as shown in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  This is because there doesn’t exist a reasonable policy  that meets such strict constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Moreover, the results of  ALAC(k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1) comparing with ALAC demonstrate that  the heuristics updating of k is effective during the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The slight gap between ALAC(Tanh) with the Lyapunov  function activated by the Tanh function and ALAC shows  our method is not sensitive to the form of the Lyapunov  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Evaluation Results  In this section, we describe the impacts of the stability condi-  tion more concretely by using various visualization methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Furthermore, we verify that ALAC achieves excellent ro-  bustness, generalization, and efficiency with the aid of the  ASC condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ANALYSIS OF VISUALIZATION  First, we use the t-SNE method to indicate the visualization  of the state in 3 dimensions in order to illustrate better the  stability of the system learned by ALAC (Cartpole-cost  in 2 dimensions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' As we can see, the top row of Figure 4  shows the states in the final stage of an episode converge  to a point or circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Basically, we recognize that those  patterns happen in a stable system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, experts  can judge a system’s stability from a phase space of the  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Therefore, we also introduce various phase space  trajectories of the system to analyze stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The second  row of Figure 4 shows the phase trajectories with variance  according to the state pairs of joint angular position and  velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Concretely, ψ and ˙ψ represent an angular position  and velocity, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' It can be found that the angular  velocity starts from 0 to 0, and the angular position starts  from the beginning to an equilibrium point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (For more  details see Figure 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Based on the above phenomenons, it  suggests the trained systems using the ALAC method satisfy  focal stability or stable limit cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' More importantly, we  observe that the Lyapunov value decreases while learning  and consistently falls to its lowest point at the end of an  episode, as shown in Figure 4 (bottom row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore,  it can facilitate the policy to achieve promising results on  robustness and generalization, which is demonstrated in  further analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' More implementation details for t-SNE  and phase trajectories are given in Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' VERIFICATION OF PROPERTIES  Robustness  Generally speaking, stability has a potential  relationship with robustness to some extent (Chang & Gao,  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Thus, we add external disturbances with different  magnitudes in each environment and observe the perfor-  mance difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To be concrete, we introduce periodic  external disturbances with different magnitudes in each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Furthermore, we omit the algorithms which do not converge  to a reasonable solution in each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Figure 8 (see Appendix  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1) shows in all scenarios, ALAC enjoys superior per-  formance over other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Generalization  Previous studies focus on the robustness  of a system to demonstrate the effectiveness of Lyapunov  constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In this paper, we build some interesting exper-  iments to verify whether the policy can generalize well to  follow previously unseen reference signals or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' We in-  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Comparisons on the performance of ALAC and SAC-cost  methods under different actor structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Task  Halfcheetah-cost  Actor structure  [64,64]  [32,32]  [16,16]  ALAC  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  SAC-cost  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2)  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4)  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8)  Task  Minitaur-cost  Actor structure  [64,64]  [32,32]  [16,16]  ALAC  492.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5(85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7)  571.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  SAC-cost  692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  664.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9(115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  934.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(149.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3)  Task  Spaceramdom-cost  Actor structure  [64,64]  [32,32]  [16,16]  ALAC  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3(6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1(4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  SAC-cost  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='7(9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5)  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6(13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='9)  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4(28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6)  troduce the error between the desired and achieved goals as  additional information in the state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Because the Lyapunov  function is significantly related to the error, ALAC w/ er-  rors gains remarkable performance improvement on gen-  eralization as Table 2 illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' We choose the SAC-cost  algorithm as a comparison since SAC-cost is very similar  to our method without the ASC condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' For more ex-  perimental results, see Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In particular, the  gap between each other enlarges with the increasing biases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Furthermore, we observe that the errors have a negative  impact on the performance of SAC-cost on complex tasks  like Halfcheetah-cost and Spacereach-cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The reason  can be that SAC-cost does not efficiently capture the error  information without the guidance of a Lyapunov function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Efficiency  Our method also offers a positive effect on the  limited network size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Results in Table 3 suggest ALAC  method consistently achieves comparable performance un-  der different actor structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Compared with the SAC-cost  method, the ALAC method brings another benefit, perform-  ing the task more efficiently with limited parameters of  controllers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' It is because the adaptive stability certification  provides efficient guidance for policy optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Discussion and Future Work  We propose the Adaptive Stability Certification (ASC),  which meets the sampling-based stability of mean cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Meanwhile, it guides the current policy to approaches to  the optimal point heuristically in the context of classical  feedback control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Based on the Actor-Critic framework and  Lagrangian-based optimization, We present a practical algo-  rithm, namely the Adaptive Lyapunov-based Actor-Critic  algorithm (ALAC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, empirical results show that  our method outperforms baselines on diverse robotic tasks  with two metrics, stability constraint violations and mean  costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, the controller trained by our method  Adaptive Stability Certification  achieves higher generalization ability compared with the  method without the stability guarantee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' By making a heuris-  tic formulation, we provide an interesting method to com-  bine the policy’s optimality with the system’s stability in  model-free RL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In this work, we focus on the system’s sta-  bility;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' an exciting direction for future work would be to  combine ASC with some safe RL algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  References  Achiam, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Held, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Tamar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Abbeel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Constrained  policy optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In International conference on ma-  chine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 22–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' PMLR, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Andrychowicz, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Baker, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Chociej, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Jozefowicz,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', McGrew, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Pachocki, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Petron, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Plappert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  Powell, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Ray, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Learning dexterous in-hand  manipulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The International Journal of Robotics  Research, 39(1):3–20, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Berkenkamp, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Turchetta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Schoellig, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Krause,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Safe model-based reinforcement learning with stability  guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Advances in neural information processing  systems, 30, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Brockman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Cheung, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Pettersson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Schneider, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  Schulman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Tang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Zaremba, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Openai gym.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  arXiv preprint arXiv:1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='01540, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Chang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' and Gao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Stabilizing neural control using  self-learned almost lyapunov critics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In 2021 IEEE Inter-  national Conference on Robotics and Automation (ICRA),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 1803–1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Chang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Roohi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Gao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Neural lyapunov con-  trol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Advances in neural information processing systems,  32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Fazlyab, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Morari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Pappas, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Pre-  ciado, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Learning region of attraction for nonlinear  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In 2021 60th IEEE Conference on Decision and  Control (CDC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 6477–6484.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' IEEE, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Chow,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  Nachum,  O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  Duenez-Guzman,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  and  Ghavamzadeh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A lyapunov-based approach to safe  reinforcement learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Advances in neural information  processing systems, 31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Chow, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Nachum, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Faust, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Duenez-Guzman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  and Ghavamzadeh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Lyapunov-based safe policy  optimization for continuous control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  arXiv preprint  arXiv:1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10031, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Coumans, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' and Bai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Pybullet, a python module for  physics simulation for games, robotics and machine learn-  ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Dai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Landry, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Pavone, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Tedrake, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Counter-  example guided synthesis of neural network lyapunov  functions for piecewise linear systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In 2020 59th  IEEE Conference on Decision and Control (CDC), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  1274–1281.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' IEEE, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Dai, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Landry, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Pavone, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Tedrake, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Lyapunov-stable neural-network control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' arXiv preprint  arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='14152, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  Dawson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Qin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Gao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Fan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Safe nonlinear  control using robust neural lyapunov-barrier functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In  Conference on Robot Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 1724–1735.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' PMLR,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Donti, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Roderick, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Fazlyab, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Kolter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Enforcing robust control guarantees within neural net-  work policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In International Conference on Learning  Representations, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Gaby, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Zhang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Ye, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lyapunov-net: A deep  neural network architecture for lyapunov function ap-  proximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' arXiv preprint arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='13359, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Haarnoja, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Zhou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Abbeel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Levine, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Soft  actor-critic: Off-policy maximum entropy deep reinforce-  ment learning with a stochastic actor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In International  conference on machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 1861–1870.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' PMLR,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Han, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Pan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Actor-critic re-  inforcement learning for control with stability guarantee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  IEEE Robotics and Automation Letters, 5(4):6217–6224,  2020a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Han, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Zhou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Pan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Rein-  forcement learning for control with probabilistic stability  guarantee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 2020b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Han, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Tian, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Pan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Rein-  forcement learning control of constrained dynamic sys-  tems with uniformly ultimate boundedness stability guar-  antee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Automatica, 129:109689, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Huang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Gao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Long, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Xie, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A neural lya-  punov approach to transient stability assessment in inter-  connected microgrids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In HICSS, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 1–10, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Hwangbo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Dosovitskiy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Bellicoso, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Tsou-  nis, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Koltun, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Hutter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Learning agile and  dynamic motor skills for legged robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Science Robotics,  4(26):eaau5872, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Jin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Mou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Neural  certificates for safe control policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  arXiv preprint  arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='08465, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Kashima, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Yoshiuchi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Kawano, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Learn-  ing stabilizable deep dynamics models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' arXiv preprint  arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='09710, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  La Salle, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' and Lefschetz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Stability by Liapunov’s Direct  Method with Applications by Joseph L Salle and Solomon  Lefschetz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Elsevier, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Lale, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Shi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Qu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Azizzadenesheli, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Wierman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  and Anandkumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Kcrl: Krasovskii-constrained rein-  forcement learning with guaranteed stability in nonlinear  dynamical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' arXiv preprint arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='01704,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Lawrence, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Loewen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Forbes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Backstrom, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and  Gopaluni, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Almost surely stable deep dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Ad-  vances in Neural Information Processing Systems, 33:  18942–18953, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Lechner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Žikeli´c, Ð.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Chatterjee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Henzinger,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Stability verification in stochastic control sys-  tems via neural network supermartingales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' arXiv preprint  arXiv:2112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='09495, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Xiao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Cheng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' An actor-critic learn-  ing framework based on lyapunov stability for automatic  assembly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Applied Intelligence, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 1–12, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Mayne, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Rawlings, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Rao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Scokaert,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Constrained model predictive control: Stability and  optimality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Automatica, 36(6):789–814, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Mittal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Gallieri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Quaglino, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Salehian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  and Koutník, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Neural lyapunov model predictive control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Murray, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Sastry, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A mathematical  introduction to robotic manipulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' CRC press, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Richards, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Berkenkamp, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Krause, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The  lyapunov neural network: Adaptive stability certification  for safe learning of dynamical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In Conference on  Robot Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 466–476.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' PMLR, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Schlaginhaufen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Wenk, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Krause, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Dorfler, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Learning stable deep dynamics models for partially ob-  served or delayed dynamical systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Advances in Neural  Information Processing Systems, 34:11870–11882, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Schulman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Levine, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Abbeel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Jordan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Moritz,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Trust region policy optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In International  conference on machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 1889–1897.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' PMLR,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Schulman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Wolski, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Dhariwal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Radford, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and  Klimov, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Proximal policy optimization algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  arXiv preprint arXiv:1707.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='06347, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Sikchi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Zhou, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Held, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lyapunov barrier policy  optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' arXiv preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='09230, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Stooke, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Achiam, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Abbeel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Responsive safety  in reinforcement learning by pid lagrangian methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In  International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' 9133–  9143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Zheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Collision-free  trajectory planning for a 6-dof free-floating space robot  via hierarchical decoupling optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' IEEE Robotics  and Automation Letters, 7(2):4953–4960, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  Xiong, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Eappen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Qureshi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Jagannathan,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Model-free neural lyapunov control for safe robot  navigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' arXiv preprint arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='01190, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Wu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Weng, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Han, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Zhao,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Safe reinforcement learning with stability guarantee  for motion planning of autonomous vehicles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' IEEE Trans-  actions on Neural Networks and Learning Systems, 32  (12):5435–5444, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Zhao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Du, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Neural lyapunov con-  trol for power system transient stability: A deep learning-  based approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' IEEE Transactions on Power Systems,  37(2):955–966, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Zhou, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Quartz, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', De Sterck, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Neural  lyapunov control of unknown nonlinear systems with  stability guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' arXiv preprint arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='01913,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Zou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', Xu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', and Liang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Finite-sample analysis for  sarsa with linear function approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Advances in  neural information processing systems, 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Preliminary Remarks  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lyapunov function  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1 (Equilibrium Point).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A state se is an equilibrium point if ∃ action ae ∈ A such that f(se, ae) = se.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (Murray  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2017)  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2 (Stabilizable in the sense of Lyapunov).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A system is stabilizable if ∀ϵ > 0, ∃δ such that for all s0 ∈ S such  that ||s0 − se|| ≤ δ, there exists {at}∞  t=0 such that the resulting {st}∞  t=0 satisfies ||st − se|| ≤ ϵ ∀t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (Murray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2017)  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3 (Lyapunov Function).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' A continuous and radially unbounded function L : S → R is a Lyapunov function if  the following conditions hold:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ∀s ∈ S, ∃a ∈ A, s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' L(s) ≥ L(f(s, a)),  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ∀s ̸= 0, L > 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' L(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  If a Lyapunov function exists, a discrete-time system can achieve stability in the sense of Lyapunov without considering the  physical energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Lyapunov Candidate Bound  In this part, we show that the Lyapunov candidate Lπ(s) meets the property in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3, which can be formulated as:  cπ(s) + λEs′∼PπL(s′) ≤ L(s) ≤ βcπ(s)  (23)  where we omit the lower bound αcπ(s) which is naturally satisfied by Lπ(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Firstly, according to the definition of Lπ(s), we have  Lπ(s) = Eπ[  ∞  �  t=0  γtcπ(st)|s0 = s]  = Eπ[cπ(s0) +  ∞  �  t=1  γtcπ(st)|s0 = s]  = cπ(s) + Eπ[  ∞  �  t=1  γtcπ(st)]  = cπ(s) + γEπ,s′∼Pπ[  ∞  �  t=0  γtcπ(st)|s0 = s′]  = cπ(s) + γEs′∼PπL(s′)  (24)  Considering the left-hand side of Equation (6), we can find that if λ ≤ γ holds, the lower bound of the Lyapunov function  can be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' This is because the Lyapunov candidate Lπ(s) is positive at each state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, the right-hand side of  Equation 6 illustrates the higher bound of the Lyapunov function exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The condition is also guaranteed for our Lyapunov  candidate shown in the following process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Lπ(s) = Eπ[  ∞  �  t=0  γtcπ(st)|s0 = s]  ≤  ∞  �  t=0  γtEπ[cπ(st)|s0 = s]  ≤  cπ  1 − γ  (25)  Note that cπ denotes the maximum cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The second row of the inequality holds due to Jensen inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Only if the  maximum cost exists, ∃β ∈ R+,  cπ  1−γ ≤ βcπ(s) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Details of Theoretical Analysis  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1 (Sampling-based Lyapunov Stability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' An MDP system is stable with regard to the mean cost, if there exists a  function L : S → R meets the following conditions:  αcπ(s) ≤ L(s) ≤ βcπ(s)  (26)  L(s) ≥ cπ(s) + λEs′∼PπL(s′)  (27)  Es∼Uπ[Es′∼PπL(s′) − L(s)] ≤ −k[Es∼Uπ[L(s) − λEs′∼PπL(s′)]]  (28)  where α, β, λ and k is positive constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Among them, Pπ(s′|s) =  �  A π(a|s)P(s′|s, a) da holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Firstly, we simplify the left side of the Equation (28) with reference to (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Introducing the definition  of Uπ(s) leads to  Es∼Uπ[Es′∼PπLπ(s′) − Lπ(s)]  =  �  S  lim  T →∞  1  T  T  �  t=0  T (s | ρ, π, t)(  �  S  Pπ(s′|s)Lπ(s′)ds′ − Lπ(s))ds  (29)  Due to the boundedness of Lπ, we apply the Lebesgue’s Dominated convergence theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To be specific,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' when |Fn(s)| ≤  B(s),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ∀s ∈ S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ∀n holds,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' we have  lim  n→∞  �  S  Fn(s)ds =  �  S  lim  n→∞ Fn(s)ds  (30)  Hence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' we get  Es∼Uπ[Es′∼PπLπ(s′) − Lπ(s)]  =  �  S  lim  T →∞  1  T  T  �  t=0  T (s | ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' π,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' t)(  �  S  Pπ(s′|s)Lπ(s′)ds′ − Lπ(s))ds  = lim  T →∞  �  S  1  T  T  �  t=0  T (s | ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' π,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' t)(  �  S  Pπ(s′|s)Lπ(s′)ds′ − Lπ(s))ds  = lim  T →∞  1  T (  T +1  �  t=1  ET (s|ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='π,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='t)Lπ(s) −  T  �  t=0  ET (s|ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='π,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='t)Lπ(s))  = lim  T →∞  1  T (ET (s|ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='π,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='T +1)Lπ(s) − ET (s|ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='π,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='t=0)Lπ(s))  (31)  Note that T (s|ρ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' π,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' t = 0) is equal to ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Since the expectation of Lπ(s) is a finite value, the left side of Equation (28) is  zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Now, we turn to the right side of Equation (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' According to the Equation (31), we have  −k[Es∼Uπ[L(s) − λEs′∼PπL(s′)]] ≥ 0  Es∼Uπ[L(s) − λEs′∼PπL(s′)] ≤ 0  (32)  Adaptive Stability Certification  Since L(s) ≥ cπ(s) + λEs′∼PπL(s′) holds, we get  Es∼Uπcπ(s) ≤ 0  (33)  Based on the Abelian theorem, we know there exists  Uπ(s) = lim  T →∞  1  T  T  �  t=0  T (s | ρ, π, t)  = lim  t→∞ T (s|ρ, π, t)  = ωπ(s)  (34)  Thus, we get  Es∼ωπ[cπ(s)] ≤ 0  (35)  The last row of inequality holds because of Equation (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Based on the definition of ωπ(s), we have  lim  t→∞ ET (s|ρ,π,t)cπ(s) ≤ 0  (36)  Suppose that there exists a starting state s0  ∈  {s0  |  cπ(s0)  ≤  b} and a positive constant d such that  limt→∞ ET (s|ρ,π,t)cπ(s) = d or limt→∞ ET (s|ρ,π,t)cπ(s) = ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Consider that ρ(s0) > 0 for all starting states in  {s0 | cπ(s0) ≤ b} (Assumption 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1), then limt→∞ Es∼T (·|ρ,π,t)cπ(s) > 0 , which is contradictory with Equation (36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Thus ∀s0 ∈ {s0 | cπ(s0) ≤ b}, limt→∞ ET (s|ρ,π,t)cπ(s) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Thus the system meets the mean cost stability by Definition  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Furthermore, we find that when L(s) = cπ(s) + λEs′∼PπL(s′) holds, our theorem is corresponding to the Theorem 1 in  (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' That means we extend the previous method to a more general case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To be specific, the introduction of  λ enlarges the solution space of the policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Thus, it facilitates the policy to find the optimal point as well as maintain the  system’s stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2 (Finite Tracking Time).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In a continuous-time system, a trajectory W(t) tracks the reference R(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' W(t) can  track the reference within a finite time T, such that R(t) = W(t), t ≥ T, if the following conditions holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  ∇tW(t) ≤ −k(W(t) − R(t)), ∀t ∈ [0, T]  (37)  Note that the gradient of R(t) is bounded, meaning that ∇tR(t) ≤ µ holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' First, we build the mean square error V (t) between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  V = 1  2(W(t) − R(t))2  (38)  Then, we can derive the difference of V (t) as follows  ∇tV = (W − R)(∇tW − ∇tR)  ≤ (W − R)(−k(W − R) − ∇tR)  ≤ −k|W − R|2 − (W − R)∇tR  (39)  Adaptive Stability Certification  Introducing the Assumption that the bounded gradient of R(t) , we have  ∇tV ≤ −2k |W − R|2  2  −  √  2µ|W − R|  2  ≤ −2kV −  √  2µ  √  V  (40)  Observe that the above formulation belongs to a form of the Bernoulli differential equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In this case, we can reduce the  Bernoulli equation to a linear differential equation by substituting z =  √  V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Then, the general solution for z is  z =  √  V ≤ −  √  2  2  µ  k + Ce−kt  (41)  Applying the initial condition V (t = 0) = vt0, we have  C = √vt0 +  √  2  2  µ  k  (42)  Finally, the convergence time T can be represented as:  T = 1  k ln  � √  2  2  µ  k + √vt0  √  2  2  µ  k  �  + t0  (43)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Constrained Lyapunov Critic Network  In this work, the output of the neural network of the Lyapunov critic is described by:  f(s, a) = hO(hO−1(· · · h2(h1(< s, a >))))  (44)  where each ho(z) has the same form:  ho(z) = ψo(Woz + bo)  (45)  Here, O represents the number of layers, and ψo is the non-linear activation function used in the o-th layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore,  {Wo, bo} is the weight and bias of the o-th layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  First of all, to meet the demand of Lθ(se, a) = 0, we introduce a linear transformation Gs, one of whose possible forms can  be  Gs(f) =  1  �I  i δsi + ϵ  �δs1  δs2  · ·  δsI  �  �  ��  f1  f1  · ·  fv  f1  f1  · ·  fv  · ·  · ·  · ·  · ·  f1  f1  · ·  fv  �  ��  (46)  where I denotes the number of elements of the state, and v is the number of units of the output layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ϵ is a constant close to 0  to avoid singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Note that δs = s − se, which indicates the difference between the current state and an equilibrium point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  As we can see, when each element of δs is zero, the multiplication of matrices is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Thus, Gs=se(f(s = se, a)) = 0  holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, it brings another benefit having no impact on the training of networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Suppose that the length of sampling trajectories is T, then the bound can be expressed as:  |Es∼Uπ∆Lπ(s) − Es∼UT  π ∆Lπ(s)| ≤ 2(k + 1)cπ  1 − γ  T q−1  (47)  where q is a constant in (0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' First, we can get the following equation by introducing the definitions of Uπ and UT  π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Es∼Uπ∆Lπ(s) − Es∼UT  π ∆Lπ(s)  =  �  S  (Uπ(s) − 1  T  T  �  t=1  T (s | ρ, π, t))∆Lπ(s)ds  = 1  T  T  �  t=1  �  S  (Uπ(s) − T (s | ρ, π, t))∆Lπ(s)ds  (48)  Then, eliminating the integral operator, we obtain  |Es∼Uπ∆Lπ(s) − Es∼UT  π ∆Lπ(s)|  ≤ 1  T  T  �  t=1  ∥Uπ(s) − T (s | ρ, π, t)∥1∥∆Lπ(s)∥∞  (49)  Thus, the next step is to get the bounds of ∥Uπ(s) − T (s | ρ, π, t)∥1 and ∥∆Lπ(s)∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  For the first part, we introduce the assumption that first is mentioned in (Zou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2019), shown as follows:  T  �  t=1  ∥Uπ(s) − T (s | ρ, π, t)∥1 ≤ 2T q, ∀T ∈ Z+, ∃q ∈ (0, 1)  (50)  Frankly speaking, the assumption is easily satisfied because the L1 distance between two distributions is bounded by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' At  the same time, T (s | ρ, π, t) converges to Uπ(s) with time approaching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  For the second part, we can get the bound of ∆Lπ(s) according to Equation 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  ∆Lπ(s) = Es′∼PπLπ(s′) − Lπ(s) + k(Lπ(s) − λEs′∼Pπ(s′))  ≤  cπ  1 − γ − 0 + k( cπ  1 − γ − 0)  (51)  Then, we have  ∥∆Lπ(s)∥∞ ≤ (k + 1) cπ  1 − γ  (52)  Adding results in Equation 53, we finally get  |Es∼Uπ∆Lπ(s) − Es∼UT  π ∆Lπ(s)| ≤ 2(k + 1)cπ  1 − γ  T q−1  (53)  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Proof of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  Theorem B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Suppose that the length of sampling trajectories is T and the number of trajectories is M, then there exists  the following upper bound:  P(| 1  MT  M  �  m=1  T  �  t=1  ∆Lπ(sm  t ) − Es∼UT  π ∆Lπ(s)| ≥ α)  ≤ 2 exp(−  Mα2(1 − γ)2  ((1 − kλ)2 + (k − 1)2)cπ2 )  (54)  where sm  t represents the state in the m-th trajectory at the timestep t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' First, eliminating ∆Lπ(s) by Equation 20, we rewrites the left side of Equation 54 as  δ = P(| 1  MT  M  �  m=1  T  �  t=1  ∆Lπ(sm  t ) − Es∼UT  π ∆Lπ(s)| ≥ α)  = P(| 1  MT  M  �  m=1  T  �  t=1  (Lπ(st+1) − Lπ(st) + kl(Lπ(st) − λLπ(st+1))) − Es∼UT  π ∆Lπ(s)| ≥ α)  = P(| 1  MT  M  �  m=1  T  �  t=1  ((1 − kλ)Lπ(st+1) + (k − 1)Lπ(st)) − Es∼UT  π ∆Lπ(s)| ≥ α)  (55)  Here Es∼UT  π ∆Lπ(s) is expected value of  1  MT  �M  m=1  �T  t=1 ∆Lπ(sm  t ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In addition, the bounds of (1 − kλ)Lπ(st+1) and  (k − 1)Lπ(st) can be obtained easily by Equation 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Thus, we obtain the Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6 by applying Hoeffding’s inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  δ ≤ 2 exp(−  2M 2α2  M((1 − kλ)2 + (k − 1)2)  cπ2  (1−γ)2  )  ≤ 2 exp(−  Mα2(1 − γ)2  ((1 − kλ)2 + (k − 1)2)cπ2 )  (56)  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Details of Algorithms  As mentioned in the main text, we introduce a minimum entropy as a constraint in policy optimization and apply the  primal-dual method to update the policy and the Lagrange multiplier λe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To be specific, the constraint can be expressed as  log πφ(a|s) ≤ −Ze  (57)  where Ze is the minimum value of policy entropy, usually, Ze corresponds to the dimension of action space in the  environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Algorithm 1: Adaptive Lyapunov-based Actor-Critic Algorithm (ALAC)  Orthogonal initialize the parameters of actor and critic networks with φ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' θ  Initialize replay buffer D and λl,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' λe  Initialize the parameters of target network with φ′ ← φ and θ′ ← θ  for episode m = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' M do  Sample an initial state s0  for step t = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' T − 1 do  Sample an action from πφ(at|st)  Execute the action at and observe a new state st+1  Store < st,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' at,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ct,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' st+1 > into D  end for  for iteration n = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' N do  Sample a minibatch B from the replay buffer D  Update θ according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (11) using minibatch B  Update φ, λl, λe according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (17),(18),(57) using minibatch B  Update the parameters of target networks, θ′, φ′, according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (12)  end for  end for  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Details of Experiments  We test our method and baselines in ten robotic control environments, including Cartpole-cost,Point-circle-cost,  Halfcheetah-cost, Swimmer-cost, Ant-cost, Humanoid-cost, Minitaur-cost, Spacereach-cost, Spacerandom-cost and  Adaptive Stability Certification  Cartpole-cost  Point-circle-cost  Swimmer-cost  Halfcheetah-cost  Ant-cost  Humanoid-cost  Minitaur-cost  Spacereach-cost  Spacerandom-cost  Spacedualarm-cost  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Overview of our environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Spacedualarm-cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Most tasks in ten environments are goal-oriented, tracking a target position or speed, which corre-  sponds to most control tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, the latter four environments involve models of practical robots like a quadruped  robot and a robotic arm, making them relatively more difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' It is worth noting that the task of Spacedualarm-cost is  trajectory planning of a free-floating dual-arm space robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The coupling property of the base and the robotic arms brings  hardship for both traditional control and RL-based methods (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Environmental Design  Cartpole-cost  This task aims to maintain the pole vertically at a target position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The environment is inherited from (Han  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The state and action space are the same as the default settings in OpenAI Gym(Brockman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2016), so we  omit the description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is c =  �  x  xthreshold  �2  + 20 ∗  �  θ  θthreshold  �2  , where xthreshold = 10 and θthreshold = 20◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The  other settings can be found in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Point-circle-cost  This task aims to allow a sphere to track a circular trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The environment is inherited from (Achiam  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The sphere is initialized at the original point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is represented as c = d, where d denotes the  distance between the current position and the reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The other settings can be found in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyper-parameters of non-linear dynamic environments  Hyper-parameters  Cartpole-cost  Point-circle-cost  State shape  4  7  Action shape  2  2  Length of an episode  250 steps  65 steps  Maximum steps  3e5 steps  3e5 steps  Actor network  (64, 64)  (64, 64)  Critic network  (64, 64, 16)  (64, 64, 16)  Halfcheetah-cost  The goal of this task is to make a HalfCheetah (a 2-legged simulated robot) to track the desired velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The environment is inherited from (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The state and action space are the same as the default settings in  A  c300mm  300mm  300mmAdaptive Stability Certification  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyper-parameters of mujoco environments  Hyper-parameters  Swimmer-cost  Halfcheetah-cost  Ant-cost  Humanoid-cost  State shape  8  17  27  376  Action shape  2  6  8  8  Length of an episode  250 steps  200 steps  200 steps  500 steps  Maximum steps  3e5 steps  1e6 steps  1e6 steps  1e6 steps  Actor network  (64, 64)  (64, 64)  (64, 64)  (256, 256)  Critic network  (64, 64, 16)  (256, 256, 16)  (64, 64, 16)  (256, 256, 128)  OpenAI Gym(Brockman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2016), so we omit the description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is c = (v − 1)2, where 1 represents the  desired velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The other settings can be found in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Swimmer-cost  This task aims to make a multi-joint snake robot to track the desired velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The environment is inherited  from (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The state and action space are the same as the default settings in OpenAI Gym(Brockman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  2016), so we omit the description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is c = (v − 1)2, where 1 represents the desired velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The other  settings can be found in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Ant-cost  This task aims to make an Ant (a quadrupedal simulated robot) track the desired velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The environment is  inherited from (Brockman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The state and action space are the same as the default settings in OpenAI Gym  (Brockman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2016), so we omit the description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is c = (v − 1)2, where 1 represents the desired  velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The other settings can be found in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Humanoid-cost  This task aims to make a humanoid robot to track the desired velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The environment is inherited from  (Brockman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The state and action space are the same as the default settings in OpenAI Gym (Brockman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  2016), so we omit the description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is c = (v − 1)2, where 1 represents the desired velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The other  settings can be found in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Minitaur-cost  This task aims to control the Ghost Robotics Minitaur quadruped to run forward at the desired velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The environment is inherited from (Coumans & Bai, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The state and action space are the same as the default settings  in PyBullet environment(Coumans & Bai, 2016), so we omit the description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is c = (v − 1)2, where 1  represents the desired velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The other settings can be found in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Spacereach-cost  This task aims to make a free-floating single-arm space robot’s end-effector reach a fixed goal position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Since the base satellite is uncontrolled, collisions will cause system instability once collisions occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Therefore, it is critical  to plan a collision-free path while maintaining the stability of the base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The agent can obtain the state, including the angular  positions and velocities of joints, the position of the end-effector, and the position of the reference point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Then, the agent  outputs the desired velocities of joints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In low-level planning, a PD controller converts the desired velocities into torques,  and then controls the manipulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is defined as c = d, where d is the distance between the goal and  end-effector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The other settings can be found in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Spacerandom-cost  This task aims to make a free-floating single-arm space robot’s end-effector reach a random goal  position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The agent can obtain the state, including the angular positions and velocities of joints, the position of the  end-effector, and the position of the reference point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Then, the agent outputs the desired velocities of joints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In low-level  planning, a PD controller converts the desired velocities into torques to control the manipulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is defined  as c = d, where d is the distance between goal and end-effector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The other settings can be found in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Spacedualarm-cost  This task aims to make a free-floating dual-arm space robot’s end-effectors reach random goal  positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The complexity of the task increases dramatically due to two arms’ coupling effects on the base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The agent can  obtain the state, including the angular positions and velocities of joints, the positions of end-effectors, and the position  of target points of two manipulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Then, the agent outputs the desired velocities of joints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In low-level planning, a PD  controller converts the desired velocities into torques to control the manipulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The cost function is defined as follows:  c = d0 + d1, where di is the distance between goal and end-effector of Arm-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The other settings can be found in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyper-parameters of robotic environments  Hyper-parameters  Minitaur-cost  Spacereach-cost  Spacerandom-cost  Spacedualarm-cost  State shape  27  18  18  54  Action shape  8  6  6  12  Length of an episode  500 steps  200 steps  200 steps  200 steps  Maximum steps  1e6 steps  3e5 steps  5e5 steps  5e5 steps  Actor network  (256, 256)  (256, 256)  (256, 256)  (512, 512)  Critic network  (256, 256, 16)  (256, 256, 128)  (256, 256, 128)  (512, 512, 256)  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Implementation Details  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' BASELINES  SAC-cost  Soft Actor-Critic(SAC) is an off-policy maximum entropy actor-critic algorithm (Haarnoja et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The  main contribution is to add a maximum entropy objective into standard algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The soft Q and V functions are trained  to minimize the soft Bellman residual, and the policy can be learned by directly minimizing the expected KL-divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The only difference between SAC and SAC-cost is replacing maximizing a reward function with minimizing a cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The hyper-parameters of SAC-cost is illustrated in Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyper-parameters of SAC-cost  Hyper-parameters  SAC-cost  Learning rate of actor  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of critic  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Optimizer  Adam  ReplayBuffer size  106  Discount (γ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  Polyak (1 − τ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  Entropy coefficient  1  Batch size  256  SPPO  Safe proximal policy optimization (SPPO) is a Lyapunov-based safe policy optimization algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The neural  Lyapunov network is constructed to prevent unsafe behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Actually, the safe projection method is inspired by the TRPO  algorithm (Schulman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In this paper, we modify it to apply the Lyapunov constraints on the MDP tasks, similar  to the process in (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The hyper-parameters of SPPO is illustrated in Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyper-parameters of SPPO  Hyper-parameters  SPPO  Learning rate of actor  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of Lyapunov  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Optimizer  Adam  Discount (γ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  GAE parameter (λ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='95  Clipping range  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  KL constraint (δ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  Fisher estimation fraction  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  Conjugate gradient steps  10  Conjugate gradient damping  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  Backtracking steps  10  Timesteps per iteration  2000  Adaptive Stability Certification  LAC  Lyapunov-based Actor-Critic(LAC) algorithm is an actor-critic RL-based algorithm jointly learning a neural  controller and Lyapunov function (Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Particularly, they propose a data-driven stability condition on the  expected value over the state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Moreover, they have found that the method achieves high generalization and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  The hyper-parameters of LAC is illustrated in Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Among them, α3 is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1 in LAC, while it is changed as 1 in LAC∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyperparameters of LAC  Hyperparameters  LAC  Learning rate of actor  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of Lyapunov  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of Larange multiplier  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Optimizer  Adam  ReplayBuffer size  106  Discount (γ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  Polyak (1 − τ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  Parameter of Lyapunov constraint (α3)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  Batch size  256  POLYC  Policy Optimization with Self-Learned Almost Lyapunov Critics (POLYC) algorithm is built on the standard  PPO algorithm (Schulman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Introducing a Lyapunov function without access to the cost allows the agent to  self-learn the Lyapunov critic function by minimizing the Lyapunov risk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The hyper-parameters of POLYC is illustrated in  Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyper-parameters of POLYC  Hyper-parameters  POLYC  Learning rate of actor  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of critic  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of Lyapunov  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Optimizer  Adam  Discount (γ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  GAE parameter (λ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='95  Weight of Lyapunov constraint (β)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  Clipping range  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  Timesteps per iteration  2000  LBPO  Lyapunov Barrier Policy Optimization (LBPO) algorithm (Sikchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2021) is built on SPPO algorithm (Chow  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' However, the core improvement uses a Lyapunov-based barrier function to restrict the policy update to a safe  set for each training iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Compared with the SPPO algorithm, the method avoids backtracking to ensure safety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' For  the implementation in our paper, the process is similar to that of the SPPO algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The hyperparameters of LBPO is  illustrated in Table 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  TNLF  Twin Neural Lyapunov Function (TNLF) algorithm is proposed to deal with safe robot navigation in (Xiong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=',  2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Different from other approaches, the TNLF method defines a Lyapunov V function and Lyapunov Q function, which  are trained by minimizing the Lyapunov risk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In effect, the Lyapunov risk is similar to that of (Chang & Gao, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Since  the Lyapunov function strictly decreases over time, the robot starting with any state in a Region of Attraction (RoA) will  always stay in the RoA in the future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' It should be pointed out that as our environments only support the cost function,  the objective, except for Lyapunov risk, is to minimize the cumulative return of cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The hyper-parameters of TNLF is  illustrated in Table 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' OUR METHOD  ALAC  Our method offers a significant advantage in contrast to baselines, which is to use fewer hyperparameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The  main hyperparameters are illustrated in Table 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' We notice that these parameters control networks’ learning without  Adaptive Stability Certification  Table 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyperparameters of LBPO  Hyperparameters  LBPO  Learning rate of actor  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of critic  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of Lyapunov  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Optimizer  Adam  Discount (γ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='99  GAE parameter (λ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='97  Clipping range  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  KL constraint  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='012  Fisher estimation fraction  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  Conjugate gradient steps  10  Conjugate gradient damping  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  Backtracking steps  10  Weight of Lyapunov constraint (β)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='01  Timesteps per iteration  2000  Table 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyper-parameters of TNLF  Hyper-parameters  TNLF  Learning rate of actor  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of critic  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of Lyapunov V functiob  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of Lyapunov functiob  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Optimizer  Adam  ReplayBuffer size  106  Discount (γ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  Polyak (1 − τ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  Weight of Lyapunov constraint (α)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  Variance of noise distribution  1  Batch size  256  including the parameters of constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The reason is they are automatically updated according to Lagrange multipliers, λl,  and λe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The initial value of Lagrange multipliers is set to 1, common usage in previous constrained methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' More Results on Comparison  Figure 11 shows the learning curves of the accumulated cost and constraint violations of ALAC and other baselines in ten  environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' More Results on Ablation Study  We provide the specific formulation of ∆L1  πφ and ∆L2  πφ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Compared with ∆Lπφ in Equation 14, we intuitively find  that ∆L1  πφ and ∆L2  πφ are lower and higher bound of ∆Lπφ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In other words, ∆L1  πφ represents the strongest  constraint, while ∆L2  πφ represents the loosest constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The comparison between them can demonstrate that the ASC  condition (∆Lπφ) has a positive effect on the performance of optimality and stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  ∆L1  πφ(s, a) = Lθ(s′, πφ(·|s′)) − Lθ(s, a) + k[Lθ(s, a) − 0]  ∆L2  πφ(s, a) = Lθ(s′, πφ(·|s′)) − Lθ(s, a) + k[Lθ(s, a) − Lθ(s′, πφ(·|s′))]  (58)  The ablation experiments on other tasks are shown in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  Table 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Hyper-parameters of ALAC  Hyper-parameters  ALAC  Learning rate of actor  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of Lyapunov  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Learning rate of Lagrange multipliers (λl and λe)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e-4  Optimizer  Adam  ReplayBuffer size  106  Discount (γ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  Polyak (1 − τ)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='995  Batch size  256  1  n_components=2 or 3 ,  2  e a r l y _ e x a g g e r a t i o n =12 ,  3  l e a r n i n g _ r a t e =200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0 ,  4  n _ i t e r =1000 ,  5  n _ i t e r _ w i t h o u t _ p r o g r e s s =300 ,  6  min_grad_norm=1e −7 ,  7  p e r p l e x i t y =30 ,  8  me tric ="euclidean" ,  9  n_jobs =None ,  10  random_state =42 ,  11  verbose =True ,  12  i n i t =’pca’  Table 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Other hyper-parameters of t-SNE method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Details of Visualization  Our RL-based policy optimization method guided by adaptive stability is difficult to express the latent laws of states in the  convergent process of different environments as the high-dimension states-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' To find and show the state’s change laws  in the convergent process:  We use the t-SNE dimension reduction technique to visualize the state-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  We plot the phase trajectory with variance according to the state pairs of joint angular position and velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  We plot the Lyapunov-value surface and its shadow with the phase trajectory and values in the convergence process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  T-SNE Visualization  The top row of Figure 4 shows the results of the t-SNE state plotting with SciKit-Learn  tools(i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='sklearn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='TSNE function) with varying parameters(e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' early_exaggeration, min_ grad_norm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Cartpole-  Cost is visualized with n_components=2 while other environments with n_components=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The hyper-parameters for t-SNE  are shown in Table 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Phase Trajectories of Systems  We select the angular position and velocity of a joint in the state space in each environment  and plot the phase trajectory with variance in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The convergent process is shown as the angular velocity starts from  0 to 0, and the joint angle starts from the beginning to the convergence position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Lyapunov Functions of Systems  We visualize the change of Lyapunov-value in 3 dimensions based on the phase  trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The second row of Figure 4 shows the Lyapunov-value surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The curves of values along the phase trajectory  are mapped to the whole plane with down-sampled and smoothed by a Gaussian filter;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' we add the values and the phase  trajectory shadows correspondingly simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='15  Angular Position  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Angular Velocity  Cartpole-cost phase trajectory  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='40  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='45  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='50  Angular Position  0  1  2  3  4  Angular Velocity  Halfcheetah-cost phase trajectory  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  Angular Position  15  10  5  0  5  10  Angular Velocity  Minitaur-cost phase trajectory  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='00  Angular Position  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  Angular Velocity  Spacerandom-cost phase trajectory  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Phase trajectories of the systems trained by ALAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (we report the results of 20 trials and select a joint to graph the  phase trajectory in each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=')  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' More Results on Evaluation  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ROBUSTNESS  We verify that ALAC achieves excellent robustness on most tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' It is worth noting that we introduce periodic external  disturbances with different magnitudes in each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, we omit the algorithms which do not converge to a  reasonable solution in each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' GENERALIZATION  We verify that ALAC achieves excellent generalization with the feedback of errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' In particular, the gap between each other  enlarges with the increasing biases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Furthermore, we observe that the errors bring a negative impact on the performance of  SAC-cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The reason can be that SAC-cost does not capture the error information without the guidance of a Lyapunov  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Note that the number of environment steps in Halfcheetah-cost is 5e5 in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' EFFICIENCY  We verify that ALAC achieves comparable performance under different network structures of the actor on three tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' By  contrast, the network structure significantly impacts the performance of SAC-cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  25  50  75  100  125  150  175  Cost Return  Cartpole-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  200  400  600  800  1000  Cost Return  Pointcircle-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  20  40  60  80  100  120  Cost Return  Swimmer-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  25  50  75  100  125  150  175  Cost Return  HalfCheetah-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  50  100  150  200  250  300  350  Cost Return  Ant-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  100  200  300  400  500  600  Cost Return  Humanoid-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  200  400  600  800  1000  Cost Return  Minitaur-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  20  40  60  80  100  120  140  160  Cost Return  Spacereach-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  20  40  60  80  100  120  140  Cost Return  Spacerandom-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Magnitude  0  50  100  150  200  250  300  350  400  Cost Return  Spacedualarm-cost  ALAC(ours)  LAC  LAC*  POLYC  SAC-cost  SPPO  TNLF  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Performance of ALAC method and other baselines under persistent disturbances with different magnitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (The  X-axis indicates the magnitude of the applied disturbance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' We evaluate the trained policies for 20 trials in each setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=')  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='20%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='20%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Biases of goals  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='75  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='125  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='150  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='175  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='225  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='250  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Cost Return  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Pointcircle-cost  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC w/ error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC w/o error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost w/ error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost w/o error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='20%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='20%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Biases of goals  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='150  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Cost Return  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='HalfCheetah-cost  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC w/ error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC w/o error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost w/ error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost w/o error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='20%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='20%  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Biases of goals  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Cost Return  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Spacereach-cost  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC w/ error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC w/o error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost w/ error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost w/o error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Evaluation of ALAC and SAC-cost methods in the presence of different biases of goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' (The X-axis indicates the  magnitude of the applied shifting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' We evaluate the trained policies for 20 trials in each setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=')  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Timestep  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1e5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='150  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Cost Return  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='HalfCheetah-cost  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC(64x64)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC(32x32)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC(16x16)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost(64x64)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost(32x32)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost(16x16)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Timestep  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1e5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='600  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='800  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Cost Return  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Minitaur-cost  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC(64x64)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC(32x32)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC(16x16)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost(64x64)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost(32x32)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost(16x16)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Timestep  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1e5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='150  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Cost Return  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='HalfCheetah-cost  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC(64x64)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC(32x32)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='ALAC(16x16)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost(64x64)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost(32x32)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='SAC-cost(16x16)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Learning curves of ALAC and SAC-cost methods with different network structures of the actor on Halfcheetah-cost,  Minitaur-cost, and Spaceramdom-cost tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  50  100  150  200  250  Cost Return  Cartpole-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  200  400  600  800  1000  Cost Return  Pointcircle-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0  1  2  3  4  5  Timestep  1e5  0  25  50  75  100  125  150  175  200  Cost Return  HalfCheetah-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  45  50  55  60  65  70  75  80  Cost Return  Swimmer-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Violation  Cartpole-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0  1  2  3  4  5  6  Violation  Pointcircle-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0  1  2  3  4  5  Timestep  1e5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Violation  HalfCheetah-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='75  Violation  Swimmer-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  60  80  100  120  140  160  180  200  220  Cost Return  Ant-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0  10  20  30  40  50  60  70  80  Cost Return  Spacereach-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0  1  2  3  4  5  Timestep  1e5  0  10  20  30  40  50  60  70  Cost Return  Spacerandom-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0  1  2  3  4  5  Timestep  1e5  25  50  75  100  125  150  175  200  225  Cost Return  Spacedualarm-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  0  1  2  3  4  5  Violation  Ant-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Violation  Spacereach-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0  1  2  3  4  5  Timestep  1e5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Violation  Spacerandom-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  0  1  2  3  4  5  Timestep  1e5  0  1  2  3  4  5  6  7  Violation  Spacedualarm-cost  ALAC(original)  ALAC(  1 )  ALAC(  2 )  ALAC(Tanh)  ALAC(kl = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='1)  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Ablation studies of the ASC condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' ALAC(original) shows comparable or the best performance compared  with other certifications on each task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='  Adaptive Stability Certification  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  50  100  150  200  250  300  Cost Return  Cartpole-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  200  400  600  800  1000  Cost Return  Pointcircle-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0  1  2  3  4  5  Timestep  1e5  0  50  100  150  200  250  300  Cost Return  HalfCheetah-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  40  60  80  100  120  Cost Return  Swimmer-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0  2  4  6  8  10  Violation  Cartpole-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0  2  4  6  8  Violation  Pointcircle-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  0  1  2  3  4  5  Timestep  1e5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  Violation  HalfCheetah-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  Violation  Swimmer-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  50  100  150  200  250  300  Cost Return  Ant-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  300  350  400  450  500  550  600  Cost Return  Humanoid-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  400  600  800  1000  1200  Cost Return  Minitaur-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0  25  50  75  100  125  150  175  Cost Return  Spacereach-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  0  1  2  3  4  5  Violation  Ant-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  0  2  4  6  8  10  12  Violation  Humanoid-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e6  0  1  2  3  4  5  6  7  Violation  Minitaur-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Timestep  1e5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Violation  Spacereach-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  0  1  2  3  4  5  Timestep  1e5  0  20  40  60  80  100  120  140  160  Cost Return  Spacerandom-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0  1  2  3  4  5  Timestep  1e5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content='0  Violation  Spacerandom-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  0  1  2  3  4  5  Timestep  1e5  50  100  150  200  250  300  350  400  Cost Return  Spacedualarm-cost  ALAC(ours)  LAC  LAC*  LBPO  POLYC  SAC-cost  SPPO  TNLF  0  1  2  3  4  5  Timestep  1e5  0  1  2  3  4  5  6  7  Violation  Spacedualarm-cost  ALAC(ours)  LAC  LAC*  POLYC  SPPO  TNLF  Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' Performance comparison on ten tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
+page_content=' The ALAC method finds a good trade-off between minimizing the  accumulated cost and constraint violations in contrast to their rivals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4tAyT4oBgHgl3EQfpPhP/content/2301.00521v1.pdf'}
diff --git a/79E1T4oBgHgl3EQfTwOd/content/tmp_files/2301.03082v1.pdf.txt b/79E1T4oBgHgl3EQfTwOd/content/tmp_files/2301.03082v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a81a2850b80e30b27fa74137f07d80e7a5a53d54
--- /dev/null
+++ b/79E1T4oBgHgl3EQfTwOd/content/tmp_files/2301.03082v1.pdf.txt
@@ -0,0 +1,295 @@
+Noname manuscript No.
+(will be inserted by the editor)
+Przemys�law Ko´scik
+On the Exponential Decay of Strongly Interacting
+Cold Atoms from a Double-Well Potential
+the date of receipt and acceptance should be inserted later
+Abstract In this article, we study an exponential decay for the gas of bosons with strong repulsive
+delta interactions from a double-well potential. We consider an exactly solvable model comprising an
+infinite wall and two Dirac delta barriers. We explore its features both within the exact method and
+with the resonance expansion approach. The study reveals the effect of the splitting barrier on the
+decay rate in dependence on the number of particles. Among other things, we find that the effect of the
+splitting barrier on the decay rate is most pronounced in systems with odd particle numbers. During
+exponential decay, the spatial correlations in an internal region are well captured by the ”radiating
+state”.
+1 Introduction
+Over the past few years there has been a growing interest in understanding the decay properties
+of unstable quantum states [1,2,3,4,5,6,7,8]. In particular, recent progress in fabricating systems of
+interacting particles has inspired the theoretical community to study the decay properties of unstable
+many-particle states [9,10,11,12,13,14]. A simple model to study the decay process of many-particle
+states is the system of bosons with infinitely strong delta-contact interactions, i.e., the so-called Tonks-
+Girardeau (TG) gas [15]. Considerable effort has been made already to understand the decay properties
+of such systems. Among other works, the relevant for exponential and long-time decays were presented
+in [12] and [13], respectively. A recent paper [14] went even further and explained the decay mechanism
+of TG gases at intermediate stages of the time evolution (between exponential and long-time regimes).
+In the present paper, we provide a deeper insight into the exponential decay of TG gases from the
+double-well trap. As a model, we consider the potential in the form [14]
+V (x) =
+�
+∞,
+if x ≤ −L
+αδ(x) + ηδ(x − L)
+otherwise.
+(1)
+Note that the model is a modification of the celebrated Winter model [3], to which a Delta barrier at
+x = 0 was added, see Fig.1. The remainder of this article is structured as follows. Section 2 discusses
+the theoretical tools for studying the time evolution of the decaying TG gas and focuses on the results.
+Section 3 presents some concluding remarks.
+2 Results
+The scenario we consider is typical of controllable studies of the tunnelling phenomena in modern
+experiments. In the case studied, the system is initially prepared (t < 0) in the ground state of the
+University of Applied Sciences, Department of Computer Sciences, ul. Mickiewicza 8, PL-33100 Tarn´ow, Poland
+arXiv:2301.03082v1  [cond-mat.quant-gas]  8 Jan 2023
+
+2
+Fig. 1 Ilustrative diagram of double-well structure in Eq. (1)
+TG gas in a hard-wall split trap (η = ∞). At t = 0, the strength of the right barrier is changed to a
+finite value of η. As a result, the initial state is no longer stationary and begins to evaluate in time.
+According to Bose-Fermi mapping [15], the time-dependent TG wave function is given by
+Ψ(x1, x2, ..., xN, t) =
+= Πk<lsgn(xk − xl)
+1
+√
+N!
+detN
+i,j[φi(xj, t)],
+(2)
+where the one-particle state φk(x, t) is governed by the Schr¨odinger equation,
+Iℏ∂φk(x, t)
+∂t
+= [− ℏ2
+2m
+∂2
+∂x2 + V (x)]φk(x, t),
+(3)
+with the initial condition as the bound-state eigenfunction of the hard-wall split trap, ϕk(x), that
+is, φk(x, t)|t=0 = ϕk(x). From here we set L = ℏ = m = 1 so that the spatial coordinates, time
+coordinates, and energies are measured in units of L and mL2/ℏ, in and ℏ2/(mL2), respectively. The
+system under consideration has a nice feature where both eigenfunctions of the hard-wall split trap,
+ϕk(x) and continuum wave functions (η < ∞) ψp(x) (normalised to a delta Dirac distribution) can be
+obtained in closed analytical forms. For further detail, we refer readers to the papers [14,16], in which
+the relevant formulas are reported. Thanks to those, the solutions to Eq. (3) can be condensed in a
+Fourier series as follows:
+φk(x, t) =
+� ∞
+0
+ck(p)ψp(x)e− Itp2
+2 dp,
+(4)
+where ck(p),
+ck(p) =
+� 1
+−1
+ϕk(x)ψp(x)dx,
+(5)
+is given in closed analytical form [14]. Nonetheless, numerical computations are required to evaluate
+the integrals in Eq. (4). We conduct our analysis in terms of the non-escape probability,
+P (N)(t) =
+�
+∆N |Ψ(x1, x2, ..., xN, t)|2dx1...dxN,
+(6)
+
+4
+3.5
+V(x)
+3
+2.5
+8
+n (x-L)
+2
+1.5
+α (x)
+1
+0.5
+0
+x=-L
+x=0
+x=L
+x3
+∆N = [−1, 1]N (internal region), which informs us of the probability that N bosons remain in the
+internal region at time t. For the TG wavefunction in Eq. (2), the N-particle non-escape probabil-
+ity can be reduced to the matrix form [12,13] P (N)(t) = detN
+k,l[Pkl(t)] with the entries Pkl(t) =
+� 1
+−1 ψ∗
+k(x, t)ψl(x, t)dx. The diagonal elements Pkk(t) are nothing but the non-escape probabilities
+of the one-particle states. We denote Pk(t) = Pkk(t). Within the resonance expansion method [4],
+the one-particle state that experiences an exponential decay follows in the region ∆ of the approx-
+imation: ψk(x, t) ≈ Mk(x)e−Γkt/2−Iεkt with Γk = −Im{p2
+k}, εk = (Im{pk}2 − Re{pk}2)/2, and
+Mk(x) = 2πIrespk{ck(p)ψp(x)}, where pk are the roots of the denominator in the integrand in Eq.(4)
+on the fourth quadrant of the complex p-plane (the proper poles) and respk{f} stands for the residue
+of f at a pole pk. Then, the corresponding non-escape probability is Pk(t) ≈ mke−Γkt, where mk =
+� 1
+−1 |Mk(x)|2dx. If mk ≈ 1(Pk(0) ≈ 1), then the exponential decay starts at about t = 0 and the state
+|ψk(t)⟩ can well be approximated by the so-called ”radiating state”: |ψk(t)⟩ ≈ e−Γkt/2−Iεkt |ψk(0)⟩.
+When taking this approach, the time-dependent TG wavefunction in the region ∆N takes the form:
+Ψ(x1, x2, ..., xN, t) ≈ e−Γ (N)t/2−Iε(N)tΠk<lsgn(xk − xl)
+1
+√
+N!
+detN
+i,j[φi(xj, 0)],
+(7)
+with Γ (N) = �N
+k=1 Γk, ε(N) = �N
+k=1 εk. Consequently its validity is expected to hold when mk ≈ 1
+for k = 1, ..., N ( M (N) = ΠN
+k=1mk ≈ 1). The corresponding N-particle non-escape probability is:
+P (N)(t) ≈ e−Γ (N)t.
+(8)
+Now, we focus on examining when the above approximations are satisfied and what follows from their
+applicability. Our resuls are summarised in Fig. 2. Fig. 2 (a) shows the behaviour of M (N) as a function
+of N. We can observe a local minimum with a value slightly smaller than one. As a result, there is a
+value where N = Nc(greater than where the minimum occurs) such that M (Nc) ≈ 1. Starting from
+N = Nc the deviation of M (N)from 1 rapidly increases as N increases. This suggests that the point
+N = Nc can be viewed as a transition point to the regime in which the non-escape probability begins to
+diverge significantly from its approximation in Eq. (8). To clarify this, Fig. 2 (b) offers a comparison of
+the results obtained from Eq. (8) with the results of the exact numerical calculations, where to support
+the presentation only case η = 10, α = 0 is shown. As the results indicate, the period in which the
+decay is consistent with the ”radiating state” shrinks with increasing N. When N exceeds the critical
+value Nc = 10 (see Fig. 2 (a)), the decay of the N-particle state switches to the non-exponential regime
+at a very small t value. When the splitting barrier is present an effect of the parity of a number of
+particles appears. This is demonstrated in Fig. 2 (c) which displays the behaviour of a relative change
+defined as γ(N) = (Γ (N) − Γ (N)
+α=0) : Γ (N)
+α=0, where Γ (N)
+α=0 represents the decay rate for a system without
+the splitting barrier. We conclude that the change in the decay process caused by the addition of the
+splitting barrier is most pronounced for systems with odd numbers of particles and in the small N
+regime, i. e. where γ(N) exhibits its most rapid variation. When there is instead an even number of
+particles, the decay rate becomes almost insensitive to changes in α. It is worth mentioning that the
+coherence of the initial state depends on α in the opposite way [16]. That is to say, it strongly depends
+on α only when N is even. To determine whether Eq. (7) can capture the correlation in the internal
+region, we tested its ability to reproduce a function n(x, t) defined as P (N)(t) =
+� 1
+−1 n(x, t)dx,
+n(x, t) =
+�
+∆N−1 |Ψ(x, x2, ..., xN, t)|2dx2...dxN.
+(9)
+If n(x, t) is divided by the corresponding value of P (N)(t), then the resulting quantity can be interpreted
+as the probability density of finding a particle, provided that all the particles remain in the region ∆.
+The correctness of the ”radiating state” in reproducing the spatial correlation is confirmed in Fig. 2 (d),
+where the results for n(x, t) obtained using it and the exact wave function are compared. The results
+imply that during exponential decay, spatial correlations in the internal region are indeed consistent
+with those in the initial state. More details regarding the correlation in the initial state (i.e. in the TG
+ground state in the hard-wall split trap) can be found in [16].
+
+4
+Fig. 2 Results for different quantities as discussed in the text, when investigating transparent control pa-
+rameter values. (a) Results for M (N) as a function of N. (b) N- particle non-escape probability, where the
+continuous lines represent the results of Eq.(8) and the markers the results of exact calculations. (c) Behaviour
+of the relative change γ(N). (d) Results for n(x, t), obtained for N = 3 particles at t = 10 from the numerically
+exact wave function (markers) and its approximation in Eq. (7)(continuous lines)
+
+4
+(a)
+n=10
+n=15
+3.5
+--α=0
+-α=0
+*:α=5
+0:α=5
+3
+0
+(N)
+2.5
+M
+2
+1.5
+*
+5
+10
+15
+20
+25
+30
+N0
+(b)
+N=5
+-50
+N=8
+-100
+X
++
+N=15
+:11
+X
+-150
+X
+-200
+n=10
+α=0
+0
+2
+4
+6
+8
+10
+t(c)
+0.2
+n=10
+x:α=1
+0.15
+0:α=3
+*:α=5
+(N)
+0.1
+0.05
+0
+2
+4
+6
+8
+10
+12
+14
+16
+18
+20
+N0.04 N=3,t=10
+(d)
+0.035
+0.03
+0.025
+('x)u
+X
+n=10
+0.02
+x:α=0
+0:α=3
+0.015
+0.01
+x
+0
+0.005
+x
+x5
+3 Conclusions
+In this article, we have studied the exponential decay of N bosons with strong delta interactions from
+the double-well structure. Using the resonance expansion approach, we have analysed the effect of the
+splitting barrier on the decay rate of the N-particle system in dependence on N. We have found that
+the splitting barrier strongly affects the decay rates of systems with odd numbers of particles. In such
+systems, the coherence of the initial state behaves differently and is insensitive to changes in the height
+of the splitting barrier. Our results have shown that in the exponential regime the ”radiating state”
+effectively reproduces the spatial correlations in the internal region.
+References
+1. G. Gamow,Z. Phys. 51, 204 (1928)
+2. E. U. Condon, R. W. Gurney, Nature London 112, 439 (1928)
+3. R. G. Winter, Phys. Rev. 123, 1503 (1961)
+4. G. Garcia-Calder´on, J. L. Mateos, M. Moshinsky, Phys. Rev. Lett. 74, 337 (1995)
+5. A.Wyrzykowski, Acta Physica Polonica B, 51,11 (2020)
+6. F. Giacosa, P. Ko´scik, and T. Sowi´nski, Phys. Rev. A 102, 022204 (2020)
+7. D. R. Jim´enez, N. G. Kelkar,Phys. Rev. A 104.2, 022214 (2021)
+8. G. Garcia-Calder´on, R. Romo, Annals of Physics, 424, 168348 (2021)
+9. G. Garcia-Calder´on, L. G. Mendoza-Luna, Phys. Rev. A 84, 032106 (2011)
+10. J. Dobrzyniecki, T. Sowi´nski, Phys. Rev. A 98, 013634 (2018)
+11. I. S. Ishmukhamedov, Physica E: Low-dimensional Systems and Nanostructures 142, 11522 (2022)
+12. M. Pons, D. Sokolovski, A. del Campo, Phys. Rev. A 85, 022107 (2012)
+13. A. del Campo, Phys. Rev. A 84, 012113 (2011)
+14. P. Ko´scik, Phys. Rev. A 102, 033308 (2020)
+15. M. D. Girardeau, J. Math. Phys. 1, 516 (1960)
+16. X. Yin, Y. Hao, S. Chen, and Y. Zhang, Phys. Rev. A 78, 013604 (2008)
+
diff --git a/79E1T4oBgHgl3EQfTwOd/content/tmp_files/load_file.txt b/79E1T4oBgHgl3EQfTwOd/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7f4ffc2bfc9be73abf2f4a364c0ff8234fcd9a91
--- /dev/null
+++ b/79E1T4oBgHgl3EQfTwOd/content/tmp_files/load_file.txt
@@ -0,0 +1,216 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf,len=215
+page_content='Noname manuscript No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  (will be inserted by the editor)  Przemys�law Ko´scik  On the Exponential Decay of Strongly Interacting  Cold Atoms from a Double-Well Potential  the date of receipt and acceptance should be inserted later  Abstract In this article, we study an exponential decay for the gas of bosons with strong repulsive  delta interactions from a double-well potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' We consider an exactly solvable model comprising an  infinite wall and two Dirac delta barriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' We explore its features both within the exact method and  with the resonance expansion approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' The study reveals the effect of the splitting barrier on the  decay rate in dependence on the number of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Among other things, we find that the effect of the  splitting barrier on the decay rate is most pronounced in systems with odd particle numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' During  exponential decay, the spatial correlations in an internal region are well captured by the ”radiating  state”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  1 Introduction  Over the past few years there has been a growing interest in understanding the decay properties  of unstable quantum states [1,2,3,4,5,6,7,8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' In particular, recent progress in fabricating systems of  interacting particles has inspired the theoretical community to study the decay properties of unstable  many-particle states [9,10,11,12,13,14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A simple model to study the decay process of many-particle  states is the system of bosons with infinitely strong delta-contact interactions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=', the so-called Tonks-  Girardeau (TG) gas [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Considerable effort has been made already to understand the decay properties  of such systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Among other works, the relevant for exponential and long-time decays were presented  in [12] and [13], respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A recent paper [14] went even further and explained the decay mechanism  of TG gases at intermediate stages of the time evolution (between exponential and long-time regimes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  In the present paper, we provide a deeper insight into the exponential decay of TG gases from the  double-well trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' As a model, we consider the potential in the form [14]  V (x) =  �  ∞,  if x ≤ −L  αδ(x) + ηδ(x − L)  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  (1)  Note that the model is a modification of the celebrated Winter model [3], to which a Delta barrier at  x = 0 was added, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' The remainder of this article is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Section 2 discusses  the theoretical tools for studying the time evolution of the decaying TG gas and focuses on the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  Section 3 presents some concluding remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  2 Results  The scenario we consider is typical of controllable studies of the tunnelling phenomena in modern  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' In the case studied, the system is initially prepared (t < 0) in the ground state of the  University of Applied Sciences, Department of Computer Sciences, ul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Mickiewicza 8, PL-33100 Tarn´ow, Poland  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='03082v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='quant-gas]  8 Jan 2023  2  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 1 Ilustrative diagram of double-well structure in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (1)  TG gas in a hard-wall split trap (η = ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' At t = 0, the strength of the right barrier is changed to a  finite value of η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' As a result, the initial state is no longer stationary and begins to evaluate in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  According to Bose-Fermi mapping [15], the time-dependent TG wave function is given by  Ψ(x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=', xN, t) =  = Πk<lsgn(xk − xl)  1  √  N!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  detN  i,j[φi(xj, t)],  (2)  where the one-particle state φk(x, t) is governed by the Schr¨odinger equation,  Iℏ∂φk(x, t)  ∂t  = [− ℏ2  2m  ∂2  ∂x2 + V (x)]φk(x, t),  (3)  with the initial condition as the bound-state eigenfunction of the hard-wall split trap, ϕk(x), that  is, φk(x, t)|t=0 = ϕk(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' From here we set L = ℏ = m = 1 so that the spatial coordinates, time  coordinates, and energies are measured in units of L and mL2/ℏ, in and ℏ2/(mL2), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' The  system under consideration has a nice feature where both eigenfunctions of the hard-wall split trap,  ϕk(x) and continuum wave functions (η < ∞) ψp(x) (normalised to a delta Dirac distribution) can be  obtained in closed analytical forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' For further detail, we refer readers to the papers [14,16], in which  the relevant formulas are reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Thanks to those, the solutions to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (3) can be condensed in a  Fourier series as follows:  φk(x, t) =  � ∞  0  ck(p)ψp(x)e− Itp2  2 dp,  (4)  where ck(p),  ck(p) =  � 1  −1  ϕk(x)ψp(x)dx,  (5)  is given in closed analytical form [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Nonetheless, numerical computations are required to evaluate  the integrals in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' We conduct our analysis in terms of the non-escape probability,  P (N)(t) =  �  ∆N |Ψ(x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=', xN, t)|2dx1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='dxN,  (6)  4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='5  V(x)  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='5  8  n (x-L)  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='5  α (x)  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='5  0  x=-L  x=0  x=L  x3  ∆N = [−1, 1]N (internal region), which informs us of the probability that N bosons remain in the  internal region at time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' For the TG wavefunction in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (2), the N-particle non-escape probabil-  ity can be reduced to the matrix form [12,13] P (N)(t) = detN  k,l[Pkl(t)] with the entries Pkl(t) =  � 1  −1 ψ∗  k(x, t)ψl(x, t)dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' The diagonal elements Pkk(t) are nothing but the non-escape probabilities  of the one-particle states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' We denote Pk(t) = Pkk(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Within the resonance expansion method [4],  the one-particle state that experiences an exponential decay follows in the region ∆ of the approx-  imation: ψk(x, t) ≈ Mk(x)e−Γkt/2−Iεkt with Γk = −Im{p2  k}, εk = (Im{pk}2 − Re{pk}2)/2, and  Mk(x) = 2πIrespk{ck(p)ψp(x)}, where pk are the roots of the denominator in the integrand in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (4)  on the fourth quadrant of the complex p-plane (the proper poles) and respk{f} stands for the residue  of f at a pole pk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Then, the corresponding non-escape probability is Pk(t) ≈ mke−Γkt, where mk =  � 1  −1 |Mk(x)|2dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' If mk ≈ 1(Pk(0) ≈ 1), then the exponential decay starts at about t = 0 and the state  |ψk(t)⟩ can well be approximated by the so-called ”radiating state”: |ψk(t)⟩ ≈ e−Γkt/2−Iεkt |ψk(0)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  When taking this approach, the time-dependent TG wavefunction in the region ∆N takes the form:  Ψ(x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=', xN, t) ≈ e−Γ (N)t/2−Iε(N)tΠk<lsgn(xk − xl)  1  √  N!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  detN  i,j[φi(xj, 0)],  (7)  with Γ (N) = �N  k=1 Γk, ε(N) = �N  k=1 εk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Consequently its validity is expected to hold when mk ≈ 1  for k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=', N ( M (N) = ΠN  k=1mk ≈ 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' The corresponding N-particle non-escape probability is:  P (N)(t) ≈ e−Γ (N)t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  (8)  Now, we focus on examining when the above approximations are satisfied and what follows from their  applicability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Our resuls are summarised in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 2 (a) shows the behaviour of M (N) as a function  of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' We can observe a local minimum with a value slightly smaller than one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' As a result, there is a  value where N = Nc(greater than where the minimum occurs) such that M (Nc) ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Starting from  N = Nc the deviation of M (N)from 1 rapidly increases as N increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' This suggests that the point  N = Nc can be viewed as a transition point to the regime in which the non-escape probability begins to  diverge significantly from its approximation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' To clarify this, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 2 (b) offers a comparison of  the results obtained from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (8) with the results of the exact numerical calculations, where to support  the presentation only case η = 10, α = 0 is shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' As the results indicate, the period in which the  decay is consistent with the ”radiating state” shrinks with increasing N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' When N exceeds the critical  value Nc = 10 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 2 (a)), the decay of the N-particle state switches to the non-exponential regime  at a very small t value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' When the splitting barrier is present an effect of the parity of a number of  particles appears.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' This is demonstrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 2 (c) which displays the behaviour of a relative change  defined as γ(N) = (Γ (N) − Γ (N)  α=0) : Γ (N)  α=0, where Γ (N)  α=0 represents the decay rate for a system without  the splitting barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' We conclude that the change in the decay process caused by the addition of the  splitting barrier is most pronounced for systems with odd numbers of particles and in the small N  regime, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' where γ(N) exhibits its most rapid variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' When there is instead an even number of  particles, the decay rate becomes almost insensitive to changes in α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' It is worth mentioning that the  coherence of the initial state depends on α in the opposite way [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' That is to say, it strongly depends  on α only when N is even.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' To determine whether Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (7) can capture the correlation in the internal  region, we tested its ability to reproduce a function n(x, t) defined as P (N)(t) =  � 1  −1 n(x, t)dx,  n(x, t) =  �  ∆N−1 |Ψ(x, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=', xN, t)|2dx2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='dxN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  (9)  If n(x, t) is divided by the corresponding value of P (N)(t), then the resulting quantity can be interpreted  as the probability density of finding a particle, provided that all the particles remain in the region ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  The correctness of the ”radiating state” in reproducing the spatial correlation is confirmed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 2 (d),  where the results for n(x, t) obtained using it and the exact wave function are compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' The results  imply that during exponential decay, spatial correlations in the internal region are indeed consistent  with those in the initial state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' More details regarding the correlation in the initial state (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' in the TG  ground state in the hard-wall split trap) can be found in [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  4  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 2 Results for different quantities as discussed in the text, when investigating transparent control pa-  rameter values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (a) Results for M (N) as a function of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (b) N- particle non-escape probability, where the  continuous lines represent the results of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (8) and the markers the results of exact calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (c) Behaviour  of the relative change γ(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (d) Results for n(x, t), obtained for N = 3 particles at t = 10 from the numerically  exact wave function (markers) and its approximation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' (7)(continuous lines)  4  (a)  n=10  n=15  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='5  --α=0  α=0  :α=5  0:α=5  3  0  (N)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='5  M  2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='5 5  10  15  20  25  30  N0  (b)  N=5  50  N=8  100  X  +  N=15  :11  X  150  X  200  n=10  α=0  0  2  4  6  8  10  t(c)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='2  n=10  x:α=1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='15  0:α=3  :α=5  (N)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='05  0  2  4  6  8  10  12  14  16  18  20  N0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='04 N=3,t=10  (d)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='035  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content="025  ('x)u  X  n=10  0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='02  x:α=0  0:α=3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='015  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='01  x  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='005  x  x5  3 Conclusions  In this article, we have studied the exponential decay of N bosons with strong delta interactions from  the double-well structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Using the resonance expansion approach, we have analysed the effect of the  splitting barrier on the decay rate of the N-particle system in dependence on N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' We have found that  the splitting barrier strongly affects the decay rates of systems with odd numbers of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' In such  systems, the coherence of the initial state behaves differently and is insensitive to changes in the height  of the splitting barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Our results have shown that in the exponential regime the ”radiating state”  effectively reproduces the spatial correlations in the internal region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Gamow,Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 51, 204 (1928)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Condon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Gurney, Nature London 112, 439 (1928)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Winter, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 123, 1503 (1961)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Garcia-Calder´on, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Mateos, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Moshinsky, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 74, 337 (1995)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='Wyrzykowski, Acta Physica Polonica B, 51,11 (2020)  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Giacosa, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Ko´scik, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Sowi´nski, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A 102, 022204 (2020)  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Jim´enez, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Kelkar,Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content='2, 022214 (2021)  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Garcia-Calder´on, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Romo, Annals of Physics, 424, 168348 (2021)  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Garcia-Calder´on, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Mendoza-Luna, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A 84, 032106 (2011)  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Dobrzyniecki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Sowi´nski, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A 98, 013634 (2018)  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Ishmukhamedov, Physica E: Low-dimensional Systems and Nanostructures 142, 11522 (2022)  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Pons, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Sokolovski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' del Campo, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A 85, 022107 (2012)  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' del Campo, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A 84, 012113 (2011)  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Ko´scik, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A 102, 033308 (2020)  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Girardeau, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' 1, 516 (1960)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Yin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Hao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Chen, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Zhang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
+page_content=' A 78, 013604 (2008)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/79E1T4oBgHgl3EQfTwOd/content/2301.03082v1.pdf'}
diff --git a/9dE1T4oBgHgl3EQfoAQF/content/tmp_files/2301.03314v1.pdf.txt b/9dE1T4oBgHgl3EQfoAQF/content/tmp_files/2301.03314v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b9befe4cca34a6966b566e14f4f8fc40ed54dd6f
--- /dev/null
+++ b/9dE1T4oBgHgl3EQfoAQF/content/tmp_files/2301.03314v1.pdf.txt
@@ -0,0 +1,818 @@
+.
+SIGN INVOLUTIONS ON PARA-ABELIAN VARIETIES
+JAKOB BERGQVIST, THUONG DANG, AND STEFAN SCHR¨OER
+9 January 2023
+Abstract. We study the so-called sign involutions on twisted forms of abelian
+varieties, and show that such a sign involution exists if and only if the class in the
+Weil–Chˆatelet group is annihilated by two. If these equivalent conditions hold,
+we prove that the Picard scheme of the quotient is ´etale and contains no points
+of finite order. In dimension one, such quotients are Brauer–Severi curves, and
+we analyze the ensuing embeddings of the genus-one curve into twisted forms of
+Hirzebruch surfaces and weighted projective spaces.
+Contents
+Introduction
+1
+1.
+The scheme of sign involutions
+3
+2.
+The Picard scheme of the quotient
+6
+3.
+Morphisms to Brauer–Severi curves
+9
+References
+13
+Introduction
+Recall that an abelian variety A over a ground field k is a group scheme that
+is proper, smooth, and with h0(OA) = 1. It then follows that the group law is
+commutative, such that A comes with a canonical automorphism x �→ −x. This
+sign involution plays a prominent role in the theory of abelian varieties, because it
+gives rise to the notion of symmetric invertible sheaves. Furthermore, one can form
+the quotient A/G for the corresponding group G = {±1} of order two. In dimension
+g = 1 this gives the projective line, whereas for g = 2 we get Kummer surfaces. In
+characteristic p ̸= 2 this is a K3 surface with rational double points. The case p = 2
+requires extra attention, because than A/G may also be a rational surface with an
+elliptic singularity ([35] and [16]).
+In this paper we investigate the existence of sign involutions σ on twisted forms
+X of abelian varieties A, over general ground fields k of arbitrary characteristic
+p ≥ 0. These σ are involutions on X that become a sign involutions with respect to
+a suitable group law that arises on some base-change. The following point of view,
+developed by Laurent and the third author [18], is most suitable: A para-abelian
+variety is a proper scheme X such that X ⊗ k′ admits the structure of an abelian
+variety, for some field extension k ⊂ k′. It then turns out that the the subgroup
+scheme A ⊂ AutX/k that acts trivially on the numerically trivial part Picτ
+X/k is an
+abelian variety, and that the canonical A-action on X is free and transitive. In
+2010 Mathematics Subject Classification. 14L30, 14K15, 14K30, 14J26.
+1
+arXiv:2301.03314v1  [math.AG]  9 Jan 2023
+
+SIGN INVOLUTIONS
+2
+turn, one may view the scheme X as a torsor with respect to the abelian variety A,
+and obtains a class [X] in the Weil–Chˆatelet group H1(k, A). Our first main result
+relates these cohomology classes with the kernel A[2] for the multiplication-by-two
+map and the existence of sign involutions on X:
+Theorem. (See Thm. 1.2) Let X be a para-abelian variety. Then the following are
+equivalent:
+(i) There is a sign involution σ : X → X.
+(ii) We have 2 · [X] = 0 in the Weil–Chˆatelet group H1(k, A).
+(iii) There is an torsor P with respect to H = A[2] such that X ≃ P ∧H A.
+Here P ∧H A denotes the quotient of P × A by the diagonal H-action, usually
+called contracted product or associated fiber bundle. The main idea idea for the above
+result is to introduce the scheme of sign involutions Invsgn
+X/k ⊂ AutX/k, analyze the
+effect of the conjugacy action on this subscheme, and derive consequences using the
+general machinery of twisted forms and non-abelian cohomology.
+Now suppose X is a para-abelian variety admitting a sign involution σ : X → X.
+We then can form the quotient B = X/G with respect to the cyclic group G = {e, σ}
+of order two. In particular in characteristic two, not much seems to be known on
+this proper normal scheme. Our second main result is concerned with Picτ
+B/k, the
+numerically trivial part of the Picard scheme:
+Theorem. (See Thm. 2.1) In the above situation, the group scheme Picτ
+B/k is trivial.
+This relies on Grothendieck’s two spectral sequences abutting to equivariant coho-
+mology groups [11]. The result is not difficult in the tame case p ̸= 2, but requires a
+careful analysis in the wild case p = 2. In dimension g = 1 the para-abelian varieties
+X are usually called genus-one curves; we like to call them para-elliptic curves. The
+above shows that the quotient by any sign involution is a Brauer–Severi curve, that
+is, a twisted form of P1.
+Our third main result deals with the converse situation: Suppose there is a degree-
+two morphism f : X → B from a para-elliptic curve X to some Brauer–Severi
+curve B. Then the projectivization S = P(E ) of the rank-two sheaf E = f∗(OX)
+is a twisted form of a Hirzebruch surface with invariant e = 2, and comes with
+a contraction to a normal surface S′, having a unique singularity, which is often
+factorial. The geometry of the situation is as follows:
+Theorem. (See Section 3) Assumptions as above. Then f : X → B is the quotient
+by some sign involution σ on the para-elliptic curve X, and the latter embeds into
+both S and S′ as an anti-canonical curve. Moreover, S′ is the anti-canonical model
+of S, and also a twisted form of the weighted projective space P(1, 1, 2).
+We also show that if there are two different sign involutions σ1 ̸= σ2, the ensuing
+diagonal map gives an embedding X ⊂ B1 × B2 into a product of Brauer–Severi
+curves.
+Such products where studied by Koll´ar [17] and Hogadi [15].
+Again X
+becomes an anti-canonical curve, and it turns out that B1 × B2 embeds into P3 if
+and only if the factors are isomorphic.
+The paper is structured as follows: In Section 1 we recall the theory of para-abelian
+varieties X, introduces the scheme of sign involutions Invsgn
+X/k ⊂ AutX/k, analyze
+
+SIGN INVOLUTIONS
+3
+the conjugacy action, and establish the link between sign involutions, cohomology
+classes, and structure reductions. Section 2 is devoted to the Picard scheme of the
+quotient B = X/G of a para-abelian variety X of arbitrary dimension g ≥ 0 by a
+sign involution. In Section 3 we consider the case g = 1, and unravel the geometry
+attached to degree-two maps X → B from a para-elliptic curve X to a Brauer–Severi
+curve B.
+Acknowledgement. The research was conducted in the framework of the research
+training group GRK 2240: Algebro-Geometric Methods in Algebra, Arithmetic and
+Topology. The first two authors where financially supported by the Deutsche For-
+schungsgemeinschaft with a PhD grant in GRK 2240/1, the first author also with a
+PhD grant in GRK 2240/2.
+1. The scheme of sign involutions
+Let k be a ground field of characteristic p ≥ 0, and X be a proper scheme. Then
+the group scheme AutX/k is locally of finite type, and the connected component
+Aut0
+X/k of the neutral element e = idX is of finite type ([19], Theorem 3.7). By
+the Yoneda Lemma, the map σ �→ σ2 defines a morphism of the scheme AutX/k to
+itself, which usually disrespects the group law. The scheme of involutions InvX/k is
+defined via a cartesian diagram
+InvX/k
+−−−→ AutX/k
+���
+���σ�→σ2
+Spec(k) −−−→
+e
+AutX/k .
+It contains the neutral element and is stable under the inverse map σ �→ σ−1, but
+otherwise carries no further structure in general.
+Now suppose that X can be endowed with the structure of an abelian variety.
+Recall that for each rational point x0 ∈ X, there is a unique group law that turns X
+into an abelian variety, with origin 0 = x0. Fix such a datum, and write A for the
+abelian variety obtained by endowing X with the ensuing group law. Note that A
+can also be regarded as the pair (X, x0). The automorphism group scheme becomes
+a semidirect product
+AutX/k = A ⋊ AutA/k,
+where the normal subgroup on the left acts on X by translations x �→ a + x. The
+cokernel AutA/k on the right is an ´etale group scheme with countably many points,
+acting on A in the canonical way. Its rational points are the automorphisms σ :
+X → X fixing the origin x0. It contains a canonical element, namely the standard
+sign involution x �→ −x. This defines a morphism (−1) : Spec(k) → AutA/k. Its
+fiber with respect to the canonical projection A ⋊ AutA/k → AutA/k is denoted by
+A ⊗ κ(−1).
+Lemma 1.1. The closed subscheme A ⊗ κ(−1) ⊂ AutX/k is invariant under the
+conjugacy action of AutX/k, lies inside InvX/k, and does not depend on the choice
+of the origin x0 ∈ X.
+
+SIGN INVOLUTIONS
+4
+Proof. Let x, a, b ∈ A(R) and ϕ ∈ AutA/k(R) be R-valued points, for some k-algebra
+R. Then x �→ a − x is some R-valued point of A ⊗ κ(−1). Conjugation by (b, id) is
+(1)
+x �−→ −b + x �−→ a − (−b + x) �−→ (a + 2b) − x,
+whereas conjugation by (0, ϕ) takes the form
+x �−→ ϕ−1(x) �−→ a − ϕ−1(x) �−→ ϕ(a) − x.
+Both are R-valued points of A⊗κ(−1). Furthermore, the composition x �→ a−x �→
+a − (a − x) is the identity. With the Yoneda Lemma, we see that A ⊗ κ(−1) is
+invariant under conjugacy, and must be contained in InvX/k.
+Now let a0 ∈ X be another origin. The ensuing new group law and negation are
+given by
+x ⊕ y = x + y − x′
+0
+and
+⊖ x = −x + 2a0,
+and thus a ⊖ x = (a + a0) − x. This shows that the closed subscheme A ⊗ κ(−1) ⊂
+AutX/k does not depend on the choice of origin.
+□
+Recall that a proper scheme X is called a para-abelian variety if there is a field
+extension k ⊂ k′ such that the base-change X′ = X ⊗ k′ admits the structure
+of an abelian variety. This notation was introduced and studied by Laurent and
+the third author [18]. According to loc. cit., Proposition 5.2, the closed subscheme
+A ⊂ AutX/k that acts trivial on Picτ
+X/k is an abelian variety, and the canonical
+A-action on X is free and transitive. The resulting class
+[X] ∈ H1(k, A)
+in the Weil–Chˆatelet group is called the cohomology class of the para-abelian variety.
+Note that since A is smooth, the ´etale and fppf topology yield the same cohomology
+groups ([13], Theorem 11.7). Consequently, the class [X] has some finite order; this
+number is usually called period per(X) ≥ 1.
+Conversely, if H is any commutative group scheme, with a torsor P and a homo-
+morphism H → A, we get a para-abelian variety X = P ∧H X0. The latter denotes
+the quotient of P × X0 by the diagonal action h · (p, x) = (h · p, h + x), and X0 is
+the underlying scheme of the abelian variety A. By construction, this X is a twisted
+form of X0.
+Recall that the index ind(X) ≥ 1 is the greatest common divisor of the degrees
+[κ(a) : k] for the closed points a ∈ X. This is indeed the index for the image of the
+degree map CH0(X) → Z on the Chow group of zero-cycles. Note that in dimension
+one this can also be seen as the degree map on the Picard group. According to [21],
+Proposition 5 the divisibility property per(X) | ind(X) holds, and both numbers
+have the same prime factors.
+As explained in [36], Section 3, the group scheme AutX/k is a twisted form of
+AutX0/k with respect to the conjugacy action.
+In turn, the conjugacy-invariant
+closed subscheme A ⊗ κ(−1) ⊂ AutX0/k becomes a closed subscheme
+Invsgn
+X/k ⊂ AutX/k,
+which we call the scheme of sign involutions.
+Any automorphism σ : X → X
+belonging to Invsgn
+X/k is called a sign involution.
+
+SIGN INVOLUTIONS
+5
+Theorem 1.2. For each para-abelian variety X of dimension g ≥ 0, the following
+three conditions are equivalent:
+(i) There is a sign involution σ : X → X.
+(ii) We have 2 · [X] = 0 in the Weil–Chˆatelet group H1(k, A).
+(iii) There is an torsor P with respect to H = A[2] such that X ≃ P ∧H A.
+It these conditions hold we have the divisibility property ind(X) | 4g.
+Proof. We start with some general observations: The first projection
+AutX0/k = A ⋊ AutA/k −→ A
+identifies the scheme of sign involutions Z0 = Invsgn
+X0/k = A ⊗ κ(−1) with a copy of
+X0 = A. According to (1), the kernel for the conjugacy homomorphism A → AutZ0/k
+is A[2], so this factors over multiplication-by-two map A
+2→ A. It is now convenient
+to write X = T ∧A X0 for some A-torsor T. Note that since the X0 is the trivial
+A-torsor, one actually has T = X. What is important now is that the scheme of sign
+involutions Z = Invsgn
+X/k coincides with Z = T ∧A Z0, and the latter is the quotient
+of T × Z0 by the A-action a · (t, z0) = (a + t, 2a + z0).
+This quotient can be computed as successive quotients, first for the action of
+H = A[2] and then for the induced action of A/A[2]. The group H acts trivially on
+the second factor, hence H\(T × X0) = (H\T) × X0. In light of the short exact
+sequence
+(2)
+0 −→ H −→ A
+2
+−→ A −→ 0,
+we may regard ¯T = H\T as the A-torsor induced from T with respect to A
+2→ A.
+In other words Z = ¯T ∧ ¯
+A Z0, where we write ¯A = A/H = A to indicate the nature
+of the action. By construction, the ¯A-action on Z0 is free and transitive, so the
+projection ¯T ⊗ κ(−1) → Z is an isomorphism. We conclude that there is a rational
+point σ ∈ Z if and only if the torsor ¯T is trivial.
+From the short exact sequence (2) we get a long exact sequence
+H0(k, A)
+2
+−→ H0(k, A) −→ H1(k, H) −→ H1(k, A)
+2
+−→ H1(k, A).
+It follows that the element [X] = [T] in H1(k, A) is annihilated by two if and only
+if there is an H-torsor P such that such that X ≃ P ∧H X0, giving the equivalence
+of (ii) and (iii). Similarly, we see that [X] = [T] is annihilated by two if and only if
+¯T is trivial. Together with the previous paragraph this gives the equivalence of (i)
+and (ii).
+It remains to verify the divisibility property of the index. This is just a special
+case of general fact: Suppose X has period n ≥ 1. From the long exact sequence
+for the multiplication-by-n map we see that the quotient of X by A[n] contains a
+rational point, so its fiber Z ⊂ X is a torsor with respect to A[n]. According to
+[24], page 147 the kernel A[n] is finite of length l = n2g. Clearly, the torsor Z has
+the same length, hence X contains a zero-cycle of degree n2g. Now if (ii) holds, we
+have n | 2, and thus ind(X) | 4g.
+□
+Recall that for each m ≥ 1 there is an identification H1(k, µm) = k×/k×m. Sup-
+pose now that k contains a primitive m-th root of unity, such that µn ≃ (Z/mZ)k.
+Let us recall the following result of Lang and Tate ([21], Theorem 8): Assume that
+
+SIGN INVOLUTIONS
+6
+the ground field k, the abelian variety A, and the integer m ≥ 0 satisfies the fol-
+lowing conditions: The Z/mZ-module k×/k×m contains a free module of infinite
+rank, the quotient A(k)/mA(k) is finite, and A(k) contains an element of order m.
+Then the Weil–Chˆatelet group H1(k, A) contains infinitely many elements X whose
+period and index equals m. Note that for global fields k, the first two conditions
+are automatic, and the third can be obtained after a finite extension, provided the
+abelian variety has dimension g ≥ 1 and the characteristic exponent p ≥ 1 of k is
+prime to m.
+2. The Picard scheme of the quotient
+Let X be a para-abelian variety having a sign involution σ : X → X. Write
+G ⊂ Aut(X) the corresponding subgroup of order two. The quotient B = X/G is
+a projective scheme that is geometrically integral and geometrically normal, with
+h0(OB) = 1. Following [9], Section 2, we write Sing(B/k) for the locus of non-
+smoothness. In contrast to the locus of non-regularity Sing(B), it comes with a
+scheme structure, defined via Fitting ideals for K¨ahler differentials.
+Let Picτ
+B/k be the open-and-closed subgroup scheme inside the Picard scheme
+comprising numerically trivial invertible sheaves. Its Lie algebra is H1(B, OB), and
+the group scheme of connected components is the torsion part of the N´eron–Severi
+group scheme. It therefore encodes important information on B.
+Theorem 2.1. The group scheme Picτ
+B/k is trivial. Moreover, Sing(B/k) is finite,
+and is contained in the image of the fixed scheme Xσ.
+Proof. It suffices to treat the case that k is algebraically closed, and we choose the
+origin so that X = A is an abelian variety with σ(x) = −x. Write q : A → B for
+the quotient map, let U ⊂ A be the complement of the fixed scheme, and V = q(U)
+be its image. The induced map q : U → V is a G-torsor, in particular smooth.
+According to [12], Theorem 17.11.1 the smoothness of U ensures the smoothness of
+V . Thus Sing(B/k) is contained in the image of Aσ = A[2], and is therefore finite.
+The structure sheaf OA has a G-linearization, and thus comes with equivariant
+cohomology groups Hi(A, G, OA), and likewise we get Hi(A, G, O×
+A). According to
+[11], Section 5.2 there are two spectral sequences
+(3)
+Ers
+2 = Hr(G, Hs(A, O×
+A))
+and
+Ers
+2 = Hr(B, Hs(G, O×
+A),
+both with equivariant cohomology Hr+s(A, G, O×
+A) as abutment.
+This gives two
+exact sequences forming a diagram
+(4)
+0
+Pic(B)
+Pic(A)G
+H2(G, k×)
+H1(A, G, O×
+A)
+0
+H1(G, k×)
+H0(B, F)
+H2(B, O×
+B),
+where the abelian sheaf F = H1(G, O×
+A) is supported by the singular locus of B.
+Recall that the cohomology groups for the cyclic group G = {e, σ} are given by
+H2j+1(G, M) = Ker(σ + id)
+Im(σ − id)
+and
+H2j+2(G, M) = Ker(σ − id)
+Im(σ + id) ,
+
+SIGN INVOLUTIONS
+7
+for any G-module M. It follows that H2(G, k×) vanishes, because G acts trivially
+on k×, and k× = k×2, whereas H1(G, k×) = µ2(k) = {±1}.
+According to (4)
+the kernel for Picτ(B) → Picτ(A) is the intersection of Pic(B) ∩ H1(G, k×) inside
+the equivariant cohomology group, whereas the image is contained in Pic(A)[2] =
+Pic(A)G. This already shows that the group scheme Picτ
+B/k must be finite. It also
+solves the case of dimension g = 1: Now B is a normal curve with finite Picard
+scheme. The latter is smooth, according to [23], Section 27 because H2(B, OB) = 0.
+Consequently B = P1, and thus Picτ
+B/k = 0.
+From now on, we assume that we are in dimension g ≥ 2. At each a ∈ A[2], the
+induced G-action on the local ring OA,a is ramified only at the origin, and it follows
+from [22], Proposition 3.2 that the local ring at the image b ∈ B is singular, and that
+the finite degree-two extension OB,b ⊂ OA,a is not flat. Consequently, the quotient
+map q : A → B induces a bijection between A[2] and Sing(B). Furthermore, the
+short exact sequence 0 → OB → q∗(OA) → F → 0 defines a coherent sheaf F that
+is invertible on the open set V = Reg(B), but not at the points b ∈ Sing(B).
+We claim that the canonical map Pic(B) → Pic(A)[2] is injective. Equivalently,
+the intersection Pic(B) ∩ H1(G, k×) inside H1(A, G, O×
+A) is trivial.
+The group
+H1(G, k×) = µ2(k) vanishes in characteristic two, so only the case p ̸= 2 requires
+attention. Then the trace map gives a splitting q∗(OA) = OB ⊕ F, thus F satis-
+fies Serre’s Condition (S2). The canonical identification FV ⊗ F ∨
+V = OV yields an
+element in Γ(V, q∗(OA) ⊗ F ∨) = Γ(U, q∗(F ∨)) without zeros, and it follows that
+the invertible sheaf F|V becomes trivial on U. Using the diagram (4) for the quo-
+tient V = U/G instead of B = A/G, we conclude that F|V generates the kernel
+of Pic(V ) → Pic(U). Seeking a contradiction, we now assume that there is a non-
+trivial invertible sheaf L on B that becomes trivial on Y , we therefore must have
+L |V = F|V . Using that both L and F satisfies Serre’s Condition (S2) together
+with [14], Theorem 1.12 we infer that L = F, contradicting that F is not invert-
+ible. This establishes our claim. We therefor may regard the canonical map as an
+inclusion Picτ(B) ⊂ Pic(A)[2].
+We next check that for p ̸= 2 the finite group scheme Picτ
+B/k is reduced. Equiv-
+alently, its Lie algebra H1(B, OB) vanishes. To see this, consider the spectral se-
+quences (3) with the additive sheaf OA instead the multiplicative sheaf O×
+A. For
+i ≥ 1, the vector spaces Hi(G, k) are annihilated by the group order |G| = 2. For
+p ̸= 2 they consequently vanish, and we obtain inclusions
+H1(B, OB) ⊂ H1(A, G, OA) ⊂ H1(A, OA)G.
+Moreover, the term on the right also vanishes because G acts via the sign involution
+on the cohomology group, according ([27], proof of Proposition 2.3). This establishes
+the claim.
+To proceed we use the fact that for any finite commutative group scheme N the
+isomorphism classes of N-torsors B′ → B corresponds to homomorphisms of group
+schemes N ∗ → PicB/k, where N ∗ = Hom(N, Gm) denotes the Cartier dual (see [26],
+Proposition 6.2.1, and also the discussion in [33], Section 4).
+The constant group scheme N = (Z/2Z)k has Cartier dual N ∗ = µ2. Suppose we
+have an inclusion µ2 ⊂ Picτ
+B/k such that the composite map µ2 → Picτ
+A/k remains
+a monomorphism. The corresponding N-torsor B′ → B thus induces a non-trivial
+
+SIGN INVOLUTIONS
+8
+N-torsor A′ → A. According to the Serre–Lang Theorem ([24], page 167), there is
+a unique structure of an abelian variety for A′ so that A′ → A is a homomorphisms.
+This gives an embedding N ⊂ A′ defined by a 2-division point a′ ∈ A′.
+The
+composite A′ → B is the quotient for the action of N ⋊ {±1}. Since this semidirect
+product is actually a direct product, the projection A′ → B′ must be the quotient
+by G = {±1}. Now choose a closed point x′ ∈ A′ with 2x′ = a′. It follows that
+the orbit G · x′ = {±x′}, viewed as a rational point on B′, is fixed by the the N-
+action, contradiction. This settles the case p ̸= 2: Then µ2 = (Z/2Z)k, and we see
+that Picτ(B) ⊂ Pic(A)[2] is trivial. We already saw in the previous paragraph that
+Picτ
+B/k is reduced, and infer that it must be trivial.
+It remains to treat the case p = 2, where the arguments in some sense run parallel
+to the preceding paragraph. At each a ∈ A[2], the local ring at the image b ∈ B
+is singular, with depth(OB,b) = 2, according to [22], Proposition 3.2. Note that is
+in stark contrast to the situation p ̸= 2, when such rings of invariants are Cohen–
+Macaulay. Again we consider the short exact sequence 0 → OB → q∗(OA) → F → 0
+of coherent sheaves on B. According to [8], Section 1 we have F|V = OV . The
+short exact sequence of local cohomology
+H0
+b (B, q∗(OA)) −→ H0
+b (B, F) −→ H1
+b (B, OB)
+reveals that F is torsion-free.
+So the adjunction map F → i∗(F|V ) = OB is
+injective, hence F is a sheaf of ideals.
+Using that F is not invertible we infer
+H0(B, F) = 0. The exact sequence
+H0(B, F) −→ H1(B, OB) −→ H1(A, OA)
+ensures that the map on the right is injective. On the other hand, its kernel is the
+Lie algebra for the kernel of Picτ
+B/k → PicA/k[2]. It follows that this map is actually
+a closed embedding Picτ
+B/k ⊂ PicA/k[2].
+Now we use that the Lie algebra of any group scheme in characteristic p > 0
+carries as additional structure the p-map x �→ x[p] and becomes a restricted Lie
+algebra (see [36], Section 1 for more details). Suppose H1(B, OB) ̸= 0. Then there
+is a p-closed vector x ̸= 0, in other words x[p] is a multiple of x. The case x[p] ̸= 0
+yields an inclusion of µp ⊂ B where the composite map µp → A is injective. We saw
+above that this is impossible. In turn we must have x[p] = 0. This gives an inclusion
+of N ∗ = αp into B where the composite map αp → A remains injective. The Cartier
+dual is N = αp. Thus we get a non-trivial αp-torsor B′ → B for αp whose base-
+change A′ → A remains non-trivial. A similar situation with N ∗ = (Z/2Z)k and
+N = µp arise if there is a point of order two on PicB/k. In both cases the discussion
+in [27], beginning of Section 2 shows that A′ has the structure of an abelian variety
+so that the projection A′ → A is a homomorphism, and we get an inclusion N ⊂ A′.
+The composition A′ → B is the quotient by the group scheme N ⋊ {±1}. Again
+this is actually a direct product. In the cartesian diagram
+A′ −−−→ B′
+���
+���
+A −−−→ B
+
+SIGN INVOLUTIONS
+9
+the vertical maps are quotients by the action of the infinitesimal group scheme N,
+and the horizontal maps are quotients by G = {±1}. Fix some a′ ∈ A′[2], with
+image b′ ∈ Sing(B′), and consider the ring of invariants OB′,b′ ⊂ OA′,a′. According
+to [22], Lemma 3.3 no element f ∈ mA′,a′ ∖ m2
+a′ is G-invariant.
+It follows that
+the infinitesimal neighborhood Spec(OA′,a′/m2
+a′) maps to Z′ = Spec(OB′,b′/mb′), and
+therefore the same holds for the orbit N · {a′}. In light of the above commutative
+diagram, the N-action on B′ is not free, contradiction.
+□
+Para-abelian varieties X of dimension g = 1 are usually called genus-one curves.
+Throughout, we shall prefer the term para-elliptic curves. These are twisted forms
+of elliptic curves. The moduli stack of such curves was studied by the second author
+[6]. Recall that the Brauer–Severi varieties Y are twisted forms of projective space
+Pn, for some n ≥ 0. For more details we refer to [3]. In case n = 1 we also say that
+Y is a Brauer–Severi curve.
+Corollary 2.2. Assumption as in the proposition, and suppose additionally g = 1.
+Then the corresponding quotient B = X/G is a Brauer–Severi curve.
+Proof. The scheme B is geometrically normal and of dimension one, hence smooth.
+According to the theorem, the Picard scheme is discrete. It follows that the tangent
+space H1(B, OB) vanishes. If there is a rational point a ∈ X, the resulting invertible
+sheaf L = OB(a) is very ample, with h0(L ) = 2, and we obtain an isomorphism
+B → P1.
+□
+In dimension g = 2 and characteristic p ̸= 2, the quotient B = A/{±1} is called
+a Kummer surface, and is a K3 surface with rational double points. For p = 2,
+the quotient B is either a K3 surface with rational double points, or a rational
+surface with an elliptic singularity. This was discovered by Shioda [35], see also [16],
+[31], [32] and [20]. The formation of such quotients is studied by the first author
+[5]. Little seems to be know on the quotient in higher dimensions, in particular in
+characteristic two, compare Schilson’s investigation [29], [30].
+3. Morphisms to Brauer–Severi curves
+Let X be a para-elliptic curve over a ground field k. If there is a sign involution
+σ : X → X, the quotient B by the corresponding group of order two is a Brauer–
+Severi curve, according to Corollary 2.2. In this section we conversely assume that
+our para-elliptic curve X admits a morphism f : X → B of degree two to some
+Brauer–Severi curve B, and derive several geometric consequences.
+First note that the corresponding function field extension k(B) ⊂ k(X) has degree
+two. It must be separable, because X and B are smooth of different genus. So this
+is a Galois extension, and the Galois group G is cyclic of order two. Let σ ∈ G be
+the generator.
+Proposition 3.1. The automorphism σ : X → X is a sign involution.
+Proof. It suffices to treat the case that k is algebraically closed. The action is not
+free, because χ(OX) = 0 ̸= 2 = |G|·χ(OB). Choose a fixed point x0 ∈ X, and regard
+E = (X, x0) as an elliptic curve. If Aut(E) is cyclic, there is a unique element of
+order two, and we infer that σ equals the sign involution. Suppose now that Aut(E)
+is non-cyclic. According to [7], Proposition 5.9 this group is either the semi-direct
+
+SIGN INVOLUTIONS
+10
+product Z/3Z ⋊ µ4(k) in characteristic p = 3, or Q ⋊ µ3(k) in characteristic p = 2,
+where Q = {±1, ±i, ±j ± k} denotes the quaternion group. In these groups, the
+respective elements (0, −1) and (−1, 1) are the only ones of order two, and we again
+conclude that σ coincides with the sign involution.
+□
+Proposition 3.2. The cokernel for the inclusion OB ⊂ f∗(OX) is isomorphic to
+ωB, and the resulting extension 0 → OB → f∗(OX) → ωB → 0 of coherent sheaves
+splits.
+Proof. The sheaf f∗(OX) has rank two and is torsion-free, hence is locally free. The
+inclusion of OB is locally a direct summand, so the cokernel L is invertible. We
+have 0 = χ(OX) = χ(OB) + χ(L ) = 2 + deg(L ) and conclude deg(L ) = −2. Since
+deg : Pic(B) → Z is injective, this gives L ≃ ωB. The extension yields a class in
+Ext1(ωB, OB) = H1(X, ω⊗−1
+B
+), which vanishes by Serre Duality. So the extension
+splits.
+□
+Choose a splitting and set E = f∗(OX) = OB ⊕ ωB. The smooth surface
+S = P(E ) = Proj(Sym• E )
+is a twisted form of the Hirzebruch surface S0 = P(E0), where E0 = OP1 ⊕ OP1(−2).
+Let us call S the twisted Hirzebruch surface attached to the Brauer–Severi curve B.
+Since f : X → B is affine, the invertible sheaf OX is relatively very ample, and we
+get a closed embedding X ⊂ S. By abuse of notation we also write f : S → B for
+the extension of our original morphism on X.
+Recall that each invertible quotient E → N defines a section s : B → S, whose
+image D has self-intersection D2 = deg(N ) − deg(N ′), where N ′ ⊂ E is the
+kernel. For more details we refer to [10], Section 6. In particular, pr1 : E → OB
+yields a curve D ⊂ S with D2 = 2, whereas pr2 : E → ωB gives some E ⊂ S
+with E2 = −2, and the two sections are disjoint. The Adjunction Formula gives
+(ωS ·D) = −4 and (ωS ·E) = 0. Hence ωS = f ∗(ω⊗2
+B )⊗OS(−2E), because both sides
+have the same intersection numbers with D and E. In particular c2
+1 = (ωS · ωS) =
+−8 · deg(ωB) + 4 · E2 = 8. Setting
+ω⊗1/2
+S
+= f ∗(ωB) ⊗ OS(−E),
+we get an invertible sheaf whose square is isomorphic to the dualizing sheaf. In other
+words, the surface S comes with a canonical theta characteristic, or spin structure,
+compare [4] and [25].
+Proposition 3.3. The dual sheaf L = ω⊗−1/2
+S
+is globally generated with h0(L ) = 4.
+The image of the resulting r : S → P3 is an integral normal surface S′ ⊂ P3 of degree
+two, and the induced morphism r : S → S′ is the contraction of E. Moreover, the
+image a = r(E) is a rational point, the local ring OS′,a is singular, and the restriction
+r|X is a closed embedding.
+Proof. Our sheaf has intersection numbers (L · L ) = 2 and (L · E) = 0. Serre
+Duality gives h2(L ) = h0(ω⊗3/2
+S
+) = 0, and Riemann–Roch yields
+h0(L ) ≥ χ(L ) = c2
+1/4 + c2
+1/2
+2
++ χ(OS) = (2 + 4)/2 + 1 = 4.
+
+SIGN INVOLUTIONS
+11
+The base locus Bs(L ) is contained in E, because ω⊗−1
+B
+is globally generated. The
+short exact sequence 0 → f ∗(ω⊗−1
+B
+) → L → L |E → 0 yields an exact sequence
+0 −→ H0(S, f ∗(ω⊗−1
+B
+)) −→ H0(S, L ) −→ H0(E, OE),
+consequently h0(L ) ≤ h0(ωB) + h0(OE) = 4. This ensures h0(L ) = 4, and that L
+is globally generated.
+In turn, our spin structure yields a morphism r : S → P3 with r∗(OP3(1)) =
+ω⊗1/2
+S
+. It therefore contracts E. Moreover, the image S′ ⊂ P3 is integral and two-
+dimensional, of some degree n ≥ 1. This image is not a plane, because the morphism
+is defined by the complete linear system H0(S, L ). From 2 = (L ·L ) = deg(S/S′)·n
+we infer that S → S′ is birational and n = 2.
+The Adjunction Formula gives
+ωS′ = OS′(2), consequently r∗(ωS′) = ωS. It follows that the birational morphism
+r : S → S′ is in Stein factorization. Since Pic(S) has rank two, the exceptional
+divisor is irreducible, whence must coincide with E.
+The image a = r(E) is a rational point, because h0(OE) = 1. The local ring OS′,a
+must be singular, because otherwise S = Bla(S′), such that E = r−1(a) must be a
+projective line with E2 = −1, contradiction.
+It remains to verify that the curves X, E ⊂ S are disjoint. Since deg(X/B) = 2
+we have ωS = OS(−X)⊗f ∗(N ) for some invertible sheaf N on B. The Adjunction
+Formula gives
+0 = (ωS · X) + X2 = −X2 + 2 deg(N ) + X2.
+Consequently N
+is trivial, and ωS = OS(−X).
+This gives X2 = c2
+1 = 8, and
+furthermore (X · E) = −(ωS · E) = 0. Thus the integral curves X and E must be
+disjoint, hence r|X is a closed embedding.
+□
+Note that the local ring OS′,a is factorial provided that B ̸≃ P1. The above also
+shows that the image S′ = r(S) can also be viewed as the anti-canonical model
+P(S, −KS) of the scheme S, which is defined as the homogeneous spectrum of the
+anti-canonical ring R(S, −KS) = �
+t≥0 H0(S, ω⊗t
+S ).
+Recall that the weighted projective space P(d0, . . . , dn) is the homogeneous spec-
+trum of k[U0, . . . , Un], where the generators have degrees di = deg(Ui). The case
+d0 = . . . = dn = 1 gives back the standard projective space Pn. Let us say that a
+closed subscheme of a Gorenstein surface is an anti-canonical curve if its sheaf of
+ideals is isomorphic to the dualizing sheaf.
+Proposition 3.4. The anti-canonical model S′ = P(S, −KS) is a twisted form of
+the weighted projective space P(1, 1, 2). Moreover, X ⊂ S and the resulting inclusion
+X ⊂ S′ are anti-canonical curves.
+Proof. It suffices to treat the case that k is algebraically closed. We claim that S′ is
+defined inside P3 = Proj k[T0, . . . , T3] by the equation T 2
+0 − T1T2 = 0, for a suitable
+choice of homogeneous coordinates. The main challenge is the case p = 2: According
+to [1], Satz 2 our quadric X ⊂ P3 must be defined by an equation of the form
+r
+�
+i=1
+(αiX2
+i + XiYi + γiY 2
+i ) +
+s
+�
+j=1
+δjZ2
+j = 0,
+with 1 ≤ 2r + s ≤ 4, and non-zero coefficients δj. Since k is algebraically closed, we
+can make a change of variables and achieve δj = 1, and furthermore αi = γi = 0.
+
+SIGN INVOLUTIONS
+12
+On now immediately sees that only for r = s = 1 the quadric S′ ⊂ P3 is normal
+and singular, and setting T0 = Z1 and T1 = X1 and T2 = Y1 gives the claim. For
+p ̸= 2 our quadric can be defined by an equation of the form �3
+j=0 δjZ2
+j = 0, and
+one argues similarly.
+Consider the graded ring A = k[U0, U1, U2] with weights (1, 1, 2). The Veronese
+subring A(2) is generated by the homogeneous elements U0U1, U 2
+0, U 2
+1, U2, which sat-
+isfy the relation (U0U1)2 = U 2
+0 · U 2
+1. This gives a surjection
+k[T0, T1, T2, T3]/(T 2
+0 − T1T2) −→ A(2),
+defined by the assignments T0 �→ U0U1 and T1 �→ U 2
+0 and T2 �→ U 2
+1 and T3 �→ U2.
+Both rings are integral of dimension three. Using Krull’s Principal Ideal Theorem,
+we infer that the above surjection is bijective. The homogeneous spectrum of A(2)
+coincides with P(1, 1, 2) = Proj(A), and by the above also with S′.
+We already saw in the previous proof that ωS = OS(−X), hence X ⊂ S is an
+anti-canonical curve. From the Theorem of Formal functions one infers f∗(ωS) is
+invertible, and this ensures that the direct image coincides with ωS′. Using X ∩E =
+∅ we infer ωS′ = OS′(−X).
+□
+Now suppose that we have two morphism B1
+f1
+← X
+f2
+→ B2 to Brauer–Severi curves,
+with deg(X/Bi) = 2. According to Proposition 3.1, they comes from sign involutions
+σ1 and σ2, respectively.
+Proposition 3.5. If σ1 ̸= σ2, the diagonal morphism i : X → B1 × B2 is a closed
+embedding, and its image is an anti-canonical curve.
+Proof. Let A ⊂ AutX/k be the subgroup scheme that fixes Picτ
+X/k. As discussed in
+Section 1, this is an elliptic curve, and the action on the para-elliptic curve X is free
+and transitive. Moreover, the dual abelian variety is identified with Pic0
+X/k. But
+note that the principal polarization stemming from the origin also gives A = Pic0
+X/k.
+We saw in the proof of Proposition 1.1 that the two rational points σ1, σ2 ∈ Invsgn
+X/k
+differ by the action of some non-zero a ∈ A(k). In other words, σ2(x) = a + σ1(x).
+It follows that there is no rational point x ∈ X with σ1(x) = σ2(x). In particular,
+the fixed schemes Xσ1 and Xσ2 are disjoint.
+To proceed, we assume that k is algebraically closed. Let x ∈ X be a closed
+point and write y = i(x) = (b1, b2). The inverse image i−1(y) is the intersection
+of the fibers f −1
+1 (b1) ∩ f −1
+2 (b2). This is just the spectrum of κ(x), by the previous
+paragraph. According to [12], Corollary 18.12.6 the finite morphism i : X → B1×B2
+is a closed embedding.
+By construction, we have deg(X/B1) = deg(X/B2) = 2. Set V = B1 × B2. Its
+Picard scheme PicV/k can seen as the Galois module Pic(V ⊗ksep) = Z×Z, compare
+the discussion in [34], Section 1. Obviously, the elements (2, 0) and (0, 2) are fixed
+by Gal(ksep/k), hence the whole Galois action is trivial, and thus PicV/k = (Z × Z)k
+is a constant group scheme. The dualizing sheaf ωV = pr∗
+1(ωB1) ⊗ pr∗
+2(ωB2) has class
+(2, 2), and we infer ωV = OS(−X).
+□
+Note that ωV is anti-ample, so the smooth surface V = B1 ×B2 coincides with its
+anti-canonical model P(V, −KV ). Products of Brauer–Severi curves were studied by
+Koll´ar [17] and Hogadi [15]. Let us close this paper with the following observation:
+
+SIGN INVOLUTIONS
+13
+Proposition 3.6. The surface V = B1 × B2 admits an embedding into P3 if and
+only if B1 ≃ B2.
+Proof. The Picard scheme is given by PicV/k = (Z × Z)k. The classes (−2, 0) and
+(0, −2) come from the preimages of the invertible sheaves on B1 and B2, and thus
+belong to the subgroup Pic(V ) ⊂ PicV/k(k).
+Suppose we have V ⊂ P3, and write d ≥ 1 for its degree. From ωV = OV (d − 4)
+we get 8 = (ωV · ωV ) = d(d − 4)2, and thus d = 2. In particular, V admits the spin
+structure ω⊗1/2
+V
+= OV (−1). The dual sheaf L = OV (1) has h0(L ) = 4, which easily
+follows from the short exact sequence 0 → OP3(−1) → OP3(1) → L → 0. Choose
+some non-zero global section s ̸= 0 from L , and let D ⊂ V the resulting effective
+Cartier divisor. Suppose D is reducible. Since deg(D) = 2 we see that there are
+two components. Since L has class (1, 1) in PicV/k(k), it follows that D = D1 +D2,
+where the summands are preimages of rational points on B1 and B2, respectively.
+Thus both Brauer–Severi curves are copies of P1. Suppose now that D is irreducible.
+Then deg(D/Bi) = 1, so the morphism D → Bi are birational. By Zariski’s Main
+Theorem, it must be an isomorphism, and therefore B1 ≃ B2.
+Conversely, suppose there is an isomorphism h : B1 → B2. Its graph defines
+an effective Cartier divisor D ⊂ B1 × B2 with class (1, 1) ∈ PicV/k(k). Set L =
+OV (D). Passing to the algebraic closure of k, we get L = pr∗
+1(OP1(1))⊗pr∗
+2(OP1(1)),
+and compute h0(L ) = 4. Moreover, L is very ample, and thus defines a closed
+embedding X ⊂ P3.
+□
+Given a sign involution σ : X → X and a non-zero rational point a ∈ A(k), we
+get another sign involution x �→ a + σ(x). We see that the situation B1
+f1
+← X
+f2
+→ B2
+with σ1 ̸= σ2 appears if and only if the set Invsgn
+X/k(k) is non-empty and the group
+A(k) is non-trivial.
+References
+[1] C. Arf: Untersuchungen ¨uber quadratische Formen in K¨orpern der Charakteristik 2. I. J.
+Reine Angew. Math. 183 (1941), 148–167.
+[2] M. Artin: Algebraization of formal moduli I. In: D. Spencer, S. Iyanaga (eds.), Global
+Analysis, pp. 21–71. Univ. Tokyo Press, Tokyo, 1969.
+[3] M. Artin: Brauer–Severi varieties. In: F. van Oystaeyen, A. Verschoren (eds.), Brauer
+groups in ring theory and algebraic geometry, pp. 194—210, Springer, Berlin-New York,
+1982.
+[4] M. Atiyah: Riemann surfaces and spin structures. Ann. Sci. ´Ecole Norm. Sup. 4 (1971),
+47–62.
+[5] J. Bergqvist: The Kummer constructions in families. Dissertation, D¨usseldorf, in prepara-
+tion.
+[6] T. Dang: Cohomology of certain Artin stacks. Dissertation, D¨usseldorf (2022), https://
+nbn-resolving.org/urn/resolver.pl?urn=urn:nbn:de:hbz:061-20220822-084645-3.
+[7] P. Deligne: Courbes elliptiques: formulaire d’apr`es J. Tate. In: B. Birch, W. Kuyk (eds.),
+Modular functions of one variable IV, pp. 53–73. Springer, Berlin, 1975.
+[8] T. Ekedahl: Canonical models of surfaces of general type in positive characteristic. Inst.
+Hautes ´Etudes Sci. Publ. Math. 67 (1988), 97–144.
+[9] A. Fanelli, S. Schr¨oer: Del Pezzo surfaces and Mori fiber spaces in positive characteristic.
+Trans. Amer. Math. Soc. 373 (2020), 1775–1843.
+
+SIGN INVOLUTIONS
+14
+[10] A. Fanelli, S. Schr¨oer: The maximal unipotent finite quotient, unusual torsion in Fano
+threefolds, and exceptional Enriques surfaces. ´Epijournal Geom. Alg´ebrique 4 (2020), Art.
+11.
+[11] A. Grothendieck: Sur quelques points d’alg`ebre homologique. Tohoku Math. J. 9 (1957),
+119–221.
+[12] A. Grothendieck: ´El´ements de g´eom´etrie alg´ebrique IV: ´Etude locale des sch´emas et des
+morphismes de sch´emas. Publ. Math., Inst. Hautes ´Etud. Sci. 32 (1967).
+[13] A. Grothendieck: Le groupe de Brauer III. In: J. Giraud (ed.) et al.: Dix expos´es sur la
+cohomologie des sch´emas, pp. 88–189. North-Holland, Amsterdam, 1968.
+[14] R. Hartshorne: Generalised divisors on Gorenstein schemes. K-Theory 8 (1994), 287–339.
+[15] A. Hogadi: Products of Brauer–Severi surfaces. Proc. Amer. Math. Soc. 137 (2009), 45–50.
+[16] T. Katsura: On Kummer surfaces in characteristic 2. In: M. Nagata (ed.), Proceedings of
+the international symposium on algebraic geometry, pp. 525–542. Kinokuniya Book Store,
+Tokyo, 1978.
+[17] J. Koll´ar: Conics in the Grothendieck ring. Adv. Math. 198 (2005), 27–35.
+[18] B. Laurent, S. Schr¨oer: Para-abelian varieties and Albanese maps. Preprint, arXiv:2101.
+10829.
+[19] H. Matsumura, F. Oort: Representability of group functors, and automorphisms of alge-
+braic schemes. Invent. Math. 4 (1967–68), 1–25.
+[20] S. Kondo, S. Schr¨oer: Kummer surfaces associated with group schemes. Manuscripta Math.
+166 (2021), 323–342.
+[21] S. Lang, J. Tate: Principal homogeneous spaces over abelian varieties. Amer. J. Math. 80
+(1958), 659–684.
+[22] D. Lorenzini, S. Schr¨oer: Moderately ramified actions in positive characteristic. Math. Z.
+295 (2020), 1095–1142.
+[23] D. Mumford:
+Lectures on curves on an algebraic surface. Princeton University Press,
+Princeton, 1966.
+[24] D. Mumford: Abelian varieties. Tata Institute of Fundamental Research Studies in Math-
+ematics 5. Oxford University Press, London, 1970.
+[25] D. Mumford: Theta characteristics of an algebraic curve. Ann. Sci. ´Ecole Norm. Sup. 4
+(1971), 181–192.
+[26] M. Raynaud: Sp´ecialisation du foncteur de Picard. Publ. Math., Inst. Hautes ´Etud. Sci. 38
+(1970), 27–76.
+[27] D. R¨ossler, S. Schr¨oer: Moret-Bailly families and non-liftable schemes. Algebr. Geom. 9
+(2022), 93–121.
+[28] T. Saito: The discriminant and the determinant of a hypersurface of even dimension. Math.
+Res. Lett. 19 (2012), 855–871.
+[29] B. Schilson: Singularit¨aten von Kummer-Variet¨aten in beliebiger Charakteristik. Disserta-
+tion, D¨usseldorf (2018), https://nbn-resolving.org/urn/resolver.pl?urn=urn:nbn:
+de:hbz:061-20181108-114448-1.
+[30] B. Schilson: Wild singularities of Kummer varieties. J. Singul. 20 (2020), 274–288.
+[31] S. Schr¨oer: Kummer surfaces for the selfproduct of the cuspidal rational curve. J. Algebraic
+Geom. 16 (2007), 305–346.
+[32] S. Schr¨oer: The Hilbert scheme of points for supersingular abelian surfaces. Arkiv Mat. 47
+(2009), 143–181.
+[33] S. Schr¨oer: Enriques surfaces with normal K3-like coverings. J. Math. Soc. Japan. 73 (2021),
+433–496.
+[34] S. Schr¨oer: There is no Enriques surface over the integers. Ann. of Math. 197 (2023), 1–63.
+[35] T. Shioda: Kummer surfaces in characteristic 2. Proc. Japan Acad. 50 (1974), 718–722.
+[36] N. Tziolas, S. Schr¨oer: The structure of Frobenius kernels for automorphism group schemes.
+arXiv:2105.07860, to appear in Algebra Number Theory.
+
+SIGN INVOLUTIONS
+15
+Mathematisches Institut, Heinrich-Heine-Universit¨at, 40204 D¨usseldorf, Ger-
+many
+Email address: Jakob.Bergqvist@hhu.de
+Mathematisches Institut, Heinrich-Heine-Universit¨at, 40204 D¨usseldorf, Ger-
+many
+Email address: dangt@uni-duesseldorf.de
+Mathematisches Institut, Heinrich-Heine-Universit¨at, 40204 D¨usseldorf, Ger-
+many
+Email address: schroeer@math.uni-duesseldorf.de
+
diff --git a/9dE1T4oBgHgl3EQfoAQF/content/tmp_files/load_file.txt b/9dE1T4oBgHgl3EQfoAQF/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..61e43a860b207b91c05b24a60c948c56acfccc5c
--- /dev/null
+++ b/9dE1T4oBgHgl3EQfoAQF/content/tmp_files/load_file.txt
@@ -0,0 +1,653 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf,len=652
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  SIGN INVOLUTIONS ON PARA-ABELIAN VARIETIES  JAKOB BERGQVIST, THUONG DANG, AND STEFAN SCHR¨OER  9 January 2023  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' We study the so-called sign involutions on twisted forms of abelian  varieties, and show that such a sign involution exists if and only if the class in the  Weil–Chˆatelet group is annihilated by two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' If these equivalent conditions hold,  we prove that the Picard scheme of the quotient is ´etale and contains no points  of finite order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In dimension one, such quotients are Brauer–Severi curves, and  we analyze the ensuing embeddings of the genus-one curve into twisted forms of  Hirzebruch surfaces and weighted projective spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Contents  Introduction  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The scheme of sign involutions  3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The Picard scheme of the quotient  6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Morphisms to Brauer–Severi curves  9  References  13  Introduction  Recall that an abelian variety A over a ground field k is a group scheme that  is proper, smooth, and with h0(OA) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It then follows that the group law is  commutative, such that A comes with a canonical automorphism x �→ −x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This  sign involution plays a prominent role in the theory of abelian varieties, because it  gives rise to the notion of symmetric invertible sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Furthermore, one can form  the quotient A/G for the corresponding group G = {±1} of order two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In dimension  g = 1 this gives the projective line, whereas for g = 2 we get Kummer surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In  characteristic p ̸= 2 this is a K3 surface with rational double points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The case p = 2  requires extra attention, because than A/G may also be a rational surface with an  elliptic singularity ([35] and [16]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  In this paper we investigate the existence of sign involutions σ on twisted forms  X of abelian varieties A, over general ground fields k of arbitrary characteristic  p ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' These σ are involutions on X that become a sign involutions with respect to  a suitable group law that arises on some base-change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The following point of view,  developed by Laurent and the third author [18], is most suitable: A para-abelian  variety is a proper scheme X such that X ⊗ k′ admits the structure of an abelian  variety, for some field extension k ⊂ k′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It then turns out that the the subgroup  scheme A ⊂ AutX/k that acts trivially on the numerically trivial part Picτ  X/k is an  abelian variety, and that the canonical A-action on X is free and transitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In  2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 14L30, 14K15, 14K30, 14J26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='03314v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='AG]  9 Jan 2023  SIGN INVOLUTIONS  2  turn, one may view the scheme X as a torsor with respect to the abelian variety A,  and obtains a class [X] in the Weil–Chˆatelet group H1(k, A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Our first main result  relates these cohomology classes with the kernel A[2] for the multiplication-by-two  map and the existence of sign involutions on X:  Theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' (See Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2) Let X be a para-abelian variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Then the following are  equivalent:  (i) There is a sign involution σ : X → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  (ii) We have 2 · [X] = 0 in the Weil–Chˆatelet group H1(k, A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  (iii) There is an torsor P with respect to H = A[2] such that X ≃ P ∧H A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Here P ∧H A denotes the quotient of P × A by the diagonal H-action, usually  called contracted product or associated fiber bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The main idea idea for the above  result is to introduce the scheme of sign involutions Invsgn  X/k ⊂ AutX/k, analyze the  effect of the conjugacy action on this subscheme, and derive consequences using the  general machinery of twisted forms and non-abelian cohomology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Now suppose X is a para-abelian variety admitting a sign involution σ : X → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  We then can form the quotient B = X/G with respect to the cyclic group G = {e, σ}  of order two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In particular in characteristic two, not much seems to be known on  this proper normal scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Our second main result is concerned with Picτ  B/k, the  numerically trivial part of the Picard scheme:  Theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' (See Thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='1) In the above situation, the group scheme Picτ  B/k is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  This relies on Grothendieck’s two spectral sequences abutting to equivariant coho-  mology groups [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The result is not difficult in the tame case p ̸= 2, but requires a  careful analysis in the wild case p = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In dimension g = 1 the para-abelian varieties  X are usually called genus-one curves;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' we like to call them para-elliptic curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The  above shows that the quotient by any sign involution is a Brauer–Severi curve, that  is, a twisted form of P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Our third main result deals with the converse situation: Suppose there is a degree-  two morphism f : X → B from a para-elliptic curve X to some Brauer–Severi  curve B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Then the projectivization S = P(E ) of the rank-two sheaf E = f∗(OX)  is a twisted form of a Hirzebruch surface with invariant e = 2, and comes with  a contraction to a normal surface S′, having a unique singularity, which is often  factorial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The geometry of the situation is as follows:  Theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' (See Section 3) Assumptions as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Then f : X → B is the quotient  by some sign involution σ on the para-elliptic curve X, and the latter embeds into  both S and S′ as an anti-canonical curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Moreover, S′ is the anti-canonical model  of S, and also a twisted form of the weighted projective space P(1, 1, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  We also show that if there are two different sign involutions σ1 ̸= σ2, the ensuing  diagonal map gives an embedding X ⊂ B1 × B2 into a product of Brauer–Severi  curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Such products where studied by Koll´ar [17] and Hogadi [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Again X  becomes an anti-canonical curve, and it turns out that B1 × B2 embeds into P3 if  and only if the factors are isomorphic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The paper is structured as follows: In Section 1 we recall the theory of para-abelian  varieties X, introduces the scheme of sign involutions Invsgn  X/k ⊂ AutX/k, analyze  SIGN INVOLUTIONS  3  the conjugacy action, and establish the link between sign involutions, cohomology  classes, and structure reductions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Section 2 is devoted to the Picard scheme of the  quotient B = X/G of a para-abelian variety X of arbitrary dimension g ≥ 0 by a  sign involution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In Section 3 we consider the case g = 1, and unravel the geometry  attached to degree-two maps X → B from a para-elliptic curve X to a Brauer–Severi  curve B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Acknowledgement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The research was conducted in the framework of the research  training group GRK 2240: Algebro-Geometric Methods in Algebra, Arithmetic and  Topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The first two authors where financially supported by the Deutsche For-  schungsgemeinschaft with a PhD grant in GRK 2240/1, the first author also with a  PhD grant in GRK 2240/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The scheme of sign involutions  Let k be a ground field of characteristic p ≥ 0, and X be a proper scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Then  the group scheme AutX/k is locally of finite type, and the connected component  Aut0  X/k of the neutral element e = idX is of finite type ([19], Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' By  the Yoneda Lemma, the map σ �→ σ2 defines a morphism of the scheme AutX/k to  itself, which usually disrespects the group law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The scheme of involutions InvX/k is  defined via a cartesian diagram  InvX/k  −−−→ AutX/k  ���  ���σ�→σ2  Spec(k) −−−→  e  AutX/k .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  It contains the neutral element and is stable under the inverse map σ �→ σ−1, but  otherwise carries no further structure in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Now suppose that X can be endowed with the structure of an abelian variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Recall that for each rational point x0 ∈ X, there is a unique group law that turns X  into an abelian variety, with origin 0 = x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Fix such a datum, and write A for the  abelian variety obtained by endowing X with the ensuing group law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Note that A  can also be regarded as the pair (X, x0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The automorphism group scheme becomes  a semidirect product  AutX/k = A ⋊ AutA/k,  where the normal subgroup on the left acts on X by translations x �→ a + x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The  cokernel AutA/k on the right is an ´etale group scheme with countably many points,  acting on A in the canonical way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Its rational points are the automorphisms σ :  X → X fixing the origin x0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It contains a canonical element, namely the standard  sign involution x �→ −x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This defines a morphism (−1) : Spec(k) → AutA/k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Its  fiber with respect to the canonical projection A ⋊ AutA/k → AutA/k is denoted by  A ⊗ κ(−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The closed subscheme A ⊗ κ(−1) ⊂ AutX/k is invariant under the  conjugacy action of AutX/k, lies inside InvX/k, and does not depend on the choice  of the origin x0 ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  SIGN INVOLUTIONS  4  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Let x, a, b ∈ A(R) and ϕ ∈ AutA/k(R) be R-valued points, for some k-algebra  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Then x �→ a − x is some R-valued point of A ⊗ κ(−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Conjugation by (b, id) is  (1)  x �−→ −b + x �−→ a − (−b + x) �−→ (a + 2b) − x,  whereas conjugation by (0, ϕ) takes the form  x �−→ ϕ−1(x) �−→ a − ϕ−1(x) �−→ ϕ(a) − x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Both are R-valued points of A⊗κ(−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Furthermore, the composition x �→ a−x �→  a − (a − x) is the identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' With the Yoneda Lemma, we see that A ⊗ κ(−1) is  invariant under conjugacy, and must be contained in InvX/k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Now let a0 ∈ X be another origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The ensuing new group law and negation are  given by  x ⊕ y = x + y − x′  0  and  ⊖ x = −x + 2a0,  and thus a ⊖ x = (a + a0) − x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This shows that the closed subscheme A ⊗ κ(−1) ⊂  AutX/k does not depend on the choice of origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  Recall that a proper scheme X is called a para-abelian variety if there is a field  extension k ⊂ k′ such that the base-change X′ = X ⊗ k′ admits the structure  of an abelian variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This notation was introduced and studied by Laurent and  the third author [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to loc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' cit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=', Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2, the closed subscheme  A ⊂ AutX/k that acts trivial on Picτ  X/k is an abelian variety, and the canonical  A-action on X is free and transitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The resulting class  [X] ∈ H1(k, A)  in the Weil–Chˆatelet group is called the cohomology class of the para-abelian variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Note that since A is smooth, the ´etale and fppf topology yield the same cohomology  groups ([13], Theorem 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Consequently, the class [X] has some finite order;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' this  number is usually called period per(X) ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Conversely, if H is any commutative group scheme, with a torsor P and a homo-  morphism H → A, we get a para-abelian variety X = P ∧H X0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The latter denotes  the quotient of P × X0 by the diagonal action h · (p, x) = (h · p, h + x), and X0 is  the underlying scheme of the abelian variety A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' By construction, this X is a twisted  form of X0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Recall that the index ind(X) ≥ 1 is the greatest common divisor of the degrees  [κ(a) : k] for the closed points a ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This is indeed the index for the image of the  degree map CH0(X) → Z on the Chow group of zero-cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Note that in dimension  one this can also be seen as the degree map on the Picard group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to [21],  Proposition 5 the divisibility property per(X) | ind(X) holds, and both numbers  have the same prime factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  As explained in [36], Section 3, the group scheme AutX/k is a twisted form of  AutX0/k with respect to the conjugacy action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  In turn, the conjugacy-invariant  closed subscheme A ⊗ κ(−1) ⊂ AutX0/k becomes a closed subscheme  Invsgn  X/k ⊂ AutX/k,  which we call the scheme of sign involutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Any automorphism σ : X → X  belonging to Invsgn  X/k is called a sign involution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  SIGN INVOLUTIONS  5  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' For each para-abelian variety X of dimension g ≥ 0, the following  three conditions are equivalent:  (i) There is a sign involution σ : X → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  (ii) We have 2 · [X] = 0 in the Weil–Chˆatelet group H1(k, A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  (iii) There is an torsor P with respect to H = A[2] such that X ≃ P ∧H A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  It these conditions hold we have the divisibility property ind(X) | 4g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' We start with some general observations: The first projection  AutX0/k = A ⋊ AutA/k −→ A  identifies the scheme of sign involutions Z0 = Invsgn  X0/k = A ⊗ κ(−1) with a copy of  X0 = A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to (1), the kernel for the conjugacy homomorphism A → AutZ0/k  is A[2], so this factors over multiplication-by-two map A  2→ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It is now convenient  to write X = T ∧A X0 for some A-torsor T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Note that since the X0 is the trivial  A-torsor, one actually has T = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' What is important now is that the scheme of sign  involutions Z = Invsgn  X/k coincides with Z = T ∧A Z0, and the latter is the quotient  of T × Z0 by the A-action a · (t, z0) = (a + t, 2a + z0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  This quotient can be computed as successive quotients, first for the action of  H = A[2] and then for the induced action of A/A[2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The group H acts trivially on  the second factor, hence H\\(T × X0) = (H\\T) × X0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In light of the short exact  sequence  (2)  0 −→ H −→ A  2  −→ A −→ 0,  we may regard ¯T = H\\T as the A-torsor induced from T with respect to A  2→ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  In other words Z = ¯T ∧ ¯  A Z0, where we write ¯A = A/H = A to indicate the nature  of the action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' By construction, the ¯A-action on Z0 is free and transitive, so the  projection ¯T ⊗ κ(−1) → Z is an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' We conclude that there is a rational  point σ ∈ Z if and only if the torsor ¯T is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  From the short exact sequence (2) we get a long exact sequence  H0(k, A)  2  −→ H0(k, A) −→ H1(k, H) −→ H1(k, A)  2  −→ H1(k, A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  It follows that the element [X] = [T] in H1(k, A) is annihilated by two if and only  if there is an H-torsor P such that such that X ≃ P ∧H X0, giving the equivalence  of (ii) and (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Similarly, we see that [X] = [T] is annihilated by two if and only if  ¯T is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Together with the previous paragraph this gives the equivalence of (i)  and (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  It remains to verify the divisibility property of the index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This is just a special  case of general fact: Suppose X has period n ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' From the long exact sequence  for the multiplication-by-n map we see that the quotient of X by A[n] contains a  rational point, so its fiber Z ⊂ X is a torsor with respect to A[n].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to  [24], page 147 the kernel A[n] is finite of length l = n2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Clearly, the torsor Z has  the same length, hence X contains a zero-cycle of degree n2g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Now if (ii) holds, we  have n | 2, and thus ind(X) | 4g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  Recall that for each m ≥ 1 there is an identification H1(k, µm) = k×/k×m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Sup-  pose now that k contains a primitive m-th root of unity, such that µn ≃ (Z/mZ)k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Let us recall the following result of Lang and Tate ([21], Theorem 8): Assume that  SIGN INVOLUTIONS  6  the ground field k, the abelian variety A, and the integer m ≥ 0 satisfies the fol-  lowing conditions: The Z/mZ-module k×/k×m contains a free module of infinite  rank, the quotient A(k)/mA(k) is finite, and A(k) contains an element of order m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Then the Weil–Chˆatelet group H1(k, A) contains infinitely many elements X whose  period and index equals m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Note that for global fields k, the first two conditions  are automatic, and the third can be obtained after a finite extension, provided the  abelian variety has dimension g ≥ 1 and the characteristic exponent p ≥ 1 of k is  prime to m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The Picard scheme of the quotient  Let X be a para-abelian variety having a sign involution σ : X → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Write  G ⊂ Aut(X) the corresponding subgroup of order two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The quotient B = X/G is  a projective scheme that is geometrically integral and geometrically normal, with  h0(OB) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Following [9], Section 2, we write Sing(B/k) for the locus of non-  smoothness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In contrast to the locus of non-regularity Sing(B), it comes with a  scheme structure, defined via Fitting ideals for K¨ahler differentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Let Picτ  B/k be the open-and-closed subgroup scheme inside the Picard scheme  comprising numerically trivial invertible sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Its Lie algebra is H1(B, OB), and  the group scheme of connected components is the torsion part of the N´eron–Severi  group scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It therefore encodes important information on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The group scheme Picτ  B/k is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Moreover, Sing(B/k) is finite,  and is contained in the image of the fixed scheme Xσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It suffices to treat the case that k is algebraically closed, and we choose the  origin so that X = A is an abelian variety with σ(x) = −x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Write q : A → B for  the quotient map, let U ⊂ A be the complement of the fixed scheme, and V = q(U)  be its image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The induced map q : U → V is a G-torsor, in particular smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  According to [12], Theorem 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='1 the smoothness of U ensures the smoothness of  V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Thus Sing(B/k) is contained in the image of Aσ = A[2], and is therefore finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The structure sheaf OA has a G-linearization, and thus comes with equivariant  cohomology groups Hi(A, G, OA), and likewise we get Hi(A, G, O×  A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to  [11], Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2 there are two spectral sequences  (3)  Ers  2 = Hr(G, Hs(A, O×  A))  and  Ers  2 = Hr(B, Hs(G, O×  A),  both with equivariant cohomology Hr+s(A, G, O×  A) as abutment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  This gives two  exact sequences forming a diagram  (4)  0  Pic(B)  Pic(A)G  H2(G, k×)  H1(A, G, O×  A)  0  H1(G, k×)  H0(B, F)  H2(B, O×  B),  where the abelian sheaf F = H1(G, O×  A) is supported by the singular locus of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Recall that the cohomology groups for the cyclic group G = {e, σ} are given by  H2j+1(G, M) = Ker(σ + id)  Im(σ − id)  and  H2j+2(G, M) = Ker(σ − id)  Im(σ + id) ,  SIGN INVOLUTIONS  7  for any G-module M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It follows that H2(G, k×) vanishes, because G acts trivially  on k×, and k× = k×2, whereas H1(G, k×) = µ2(k) = {±1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  According to (4)  the kernel for Picτ(B) → Picτ(A) is the intersection of Pic(B) ∩ H1(G, k×) inside  the equivariant cohomology group, whereas the image is contained in Pic(A)[2] =  Pic(A)G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This already shows that the group scheme Picτ  B/k must be finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It also  solves the case of dimension g = 1: Now B is a normal curve with finite Picard  scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The latter is smooth, according to [23], Section 27 because H2(B, OB) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Consequently B = P1, and thus Picτ  B/k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  From now on, we assume that we are in dimension g ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' At each a ∈ A[2], the  induced G-action on the local ring OA,a is ramified only at the origin, and it follows  from [22], Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2 that the local ring at the image b ∈ B is singular, and that  the finite degree-two extension OB,b ⊂ OA,a is not flat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Consequently, the quotient  map q : A → B induces a bijection between A[2] and Sing(B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Furthermore, the  short exact sequence 0 → OB → q∗(OA) → F → 0 defines a coherent sheaf F that  is invertible on the open set V = Reg(B), but not at the points b ∈ Sing(B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  We claim that the canonical map Pic(B) → Pic(A)[2] is injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Equivalently,  the intersection Pic(B) ∩ H1(G, k×) inside H1(A, G, O×  A) is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The group  H1(G, k×) = µ2(k) vanishes in characteristic two, so only the case p ̸= 2 requires  attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Then the trace map gives a splitting q∗(OA) = OB ⊕ F, thus F satis-  fies Serre’s Condition (S2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The canonical identification FV ⊗ F ∨  V = OV yields an  element in Γ(V, q∗(OA) ⊗ F ∨) = Γ(U, q∗(F ∨)) without zeros, and it follows that  the invertible sheaf F|V becomes trivial on U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Using the diagram (4) for the quo-  tient V = U/G instead of B = A/G, we conclude that F|V generates the kernel  of Pic(V ) → Pic(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Seeking a contradiction, we now assume that there is a non-  trivial invertible sheaf L on B that becomes trivial on Y , we therefore must have  L |V = F|V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Using that both L and F satisfies Serre’s Condition (S2) together  with [14], Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='12 we infer that L = F, contradicting that F is not invert-  ible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This establishes our claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' We therefor may regard the canonical map as an  inclusion Picτ(B) ⊂ Pic(A)[2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  We next check that for p ̸= 2 the finite group scheme Picτ  B/k is reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Equiv-  alently, its Lie algebra H1(B, OB) vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' To see this, consider the spectral se-  quences (3) with the additive sheaf OA instead the multiplicative sheaf O×  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' For  i ≥ 1, the vector spaces Hi(G, k) are annihilated by the group order |G| = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' For  p ̸= 2 they consequently vanish, and we obtain inclusions  H1(B, OB) ⊂ H1(A, G, OA) ⊂ H1(A, OA)G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Moreover, the term on the right also vanishes because G acts via the sign involution  on the cohomology group, according ([27], proof of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This establishes  the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  To proceed we use the fact that for any finite commutative group scheme N the  isomorphism classes of N-torsors B′ → B corresponds to homomorphisms of group  schemes N ∗ → PicB/k, where N ∗ = Hom(N, Gm) denotes the Cartier dual (see [26],  Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='1, and also the discussion in [33], Section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The constant group scheme N = (Z/2Z)k has Cartier dual N ∗ = µ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Suppose we  have an inclusion µ2 ⊂ Picτ  B/k such that the composite map µ2 → Picτ  A/k remains  a monomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The corresponding N-torsor B′ → B thus induces a non-trivial  SIGN INVOLUTIONS  8  N-torsor A′ → A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to the Serre–Lang Theorem ([24], page 167), there is  a unique structure of an abelian variety for A′ so that A′ → A is a homomorphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  This gives an embedding N ⊂ A′ defined by a 2-division point a′ ∈ A′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The  composite A′ → B is the quotient for the action of N ⋊ {±1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Since this semidirect  product is actually a direct product, the projection A′ → B′ must be the quotient  by G = {±1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Now choose a closed point x′ ∈ A′ with 2x′ = a′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It follows that  the orbit G · x′ = {±x′}, viewed as a rational point on B′, is fixed by the the N-  action, contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This settles the case p ̸= 2: Then µ2 = (Z/2Z)k, and we see  that Picτ(B) ⊂ Pic(A)[2] is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' We already saw in the previous paragraph that  Picτ  B/k is reduced, and infer that it must be trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  It remains to treat the case p = 2, where the arguments in some sense run parallel  to the preceding paragraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' At each a ∈ A[2], the local ring at the image b ∈ B  is singular, with depth(OB,b) = 2, according to [22], Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Note that is  in stark contrast to the situation p ̸= 2, when such rings of invariants are Cohen–  Macaulay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Again we consider the short exact sequence 0 → OB → q∗(OA) → F → 0  of coherent sheaves on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to [8], Section 1 we have F|V = OV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The  short exact sequence of local cohomology  H0  b (B, q∗(OA)) −→ H0  b (B, F) −→ H1  b (B, OB)  reveals that F is torsion-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  So the adjunction map F → i∗(F|V ) = OB is  injective, hence F is a sheaf of ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Using that F is not invertible we infer  H0(B, F) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The exact sequence  H0(B, F) −→ H1(B, OB) −→ H1(A, OA)  ensures that the map on the right is injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' On the other hand, its kernel is the  Lie algebra for the kernel of Picτ  B/k → PicA/k[2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It follows that this map is actually  a closed embedding Picτ  B/k ⊂ PicA/k[2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Now we use that the Lie algebra of any group scheme in characteristic p > 0  carries as additional structure the p-map x �→ x[p] and becomes a restricted Lie  algebra (see [36], Section 1 for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Suppose H1(B, OB) ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Then there  is a p-closed vector x ̸= 0, in other words x[p] is a multiple of x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The case x[p] ̸= 0  yields an inclusion of µp ⊂ B where the composite map µp → A is injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' We saw  above that this is impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In turn we must have x[p] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This gives an inclusion  of N ∗ = αp into B where the composite map αp → A remains injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The Cartier  dual is N = αp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Thus we get a non-trivial αp-torsor B′ → B for αp whose base-  change A′ → A remains non-trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' A similar situation with N ∗ = (Z/2Z)k and  N = µp arise if there is a point of order two on PicB/k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In both cases the discussion  in [27], beginning of Section 2 shows that A′ has the structure of an abelian variety  so that the projection A′ → A is a homomorphism, and we get an inclusion N ⊂ A′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The composition A′ → B is the quotient by the group scheme N ⋊ {±1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Again  this is actually a direct product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In the cartesian diagram  A′ −−−→ B′  ���  ���  A −−−→ B  SIGN INVOLUTIONS  9  the vertical maps are quotients by the action of the infinitesimal group scheme N,  and the horizontal maps are quotients by G = {±1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Fix some a′ ∈ A′[2], with  image b′ ∈ Sing(B′), and consider the ring of invariants OB′,b′ ⊂ OA′,a′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According  to [22], Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='3 no element f ∈ mA′,a′ ∖ m2  a′ is G-invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  It follows that  the infinitesimal neighborhood Spec(OA′,a′/m2  a′) maps to Z′ = Spec(OB′,b′/mb′), and  therefore the same holds for the orbit N · {a′}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In light of the above commutative  diagram, the N-action on B′ is not free, contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  Para-abelian varieties X of dimension g = 1 are usually called genus-one curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Throughout, we shall prefer the term para-elliptic curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' These are twisted forms  of elliptic curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The moduli stack of such curves was studied by the second author  [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Recall that the Brauer–Severi varieties Y are twisted forms of projective space  Pn, for some n ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' For more details we refer to [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In case n = 1 we also say that  Y is a Brauer–Severi curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Assumption as in the proposition, and suppose additionally g = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Then the corresponding quotient B = X/G is a Brauer–Severi curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The scheme B is geometrically normal and of dimension one, hence smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  According to the theorem, the Picard scheme is discrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It follows that the tangent  space H1(B, OB) vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' If there is a rational point a ∈ X, the resulting invertible  sheaf L = OB(a) is very ample, with h0(L ) = 2, and we obtain an isomorphism  B → P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  In dimension g = 2 and characteristic p ̸= 2, the quotient B = A/{±1} is called  a Kummer surface, and is a K3 surface with rational double points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' For p = 2,  the quotient B is either a K3 surface with rational double points, or a rational  surface with an elliptic singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This was discovered by Shioda [35], see also [16],  [31], [32] and [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The formation of such quotients is studied by the first author  [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Little seems to be know on the quotient in higher dimensions, in particular in  characteristic two, compare Schilson’s investigation [29], [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Morphisms to Brauer–Severi curves  Let X be a para-elliptic curve over a ground field k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' If there is a sign involution  σ : X → X, the quotient B by the corresponding group of order two is a Brauer–  Severi curve, according to Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In this section we conversely assume that  our para-elliptic curve X admits a morphism f : X → B of degree two to some  Brauer–Severi curve B, and derive several geometric consequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  First note that the corresponding function field extension k(B) ⊂ k(X) has degree  two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It must be separable, because X and B are smooth of different genus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' So this  is a Galois extension, and the Galois group G is cyclic of order two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Let σ ∈ G be  the generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The automorphism σ : X → X is a sign involution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It suffices to treat the case that k is algebraically closed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The action is not  free, because χ(OX) = 0 ̸= 2 = |G|·χ(OB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Choose a fixed point x0 ∈ X, and regard  E = (X, x0) as an elliptic curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' If Aut(E) is cyclic, there is a unique element of  order two, and we infer that σ equals the sign involution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Suppose now that Aut(E)  is non-cyclic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to [7], Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='9 this group is either the semi-direct  SIGN INVOLUTIONS  10  product Z/3Z ⋊ µ4(k) in characteristic p = 3, or Q ⋊ µ3(k) in characteristic p = 2,  where Q = {±1, ±i, ±j ± k} denotes the quaternion group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In these groups, the  respective elements (0, −1) and (−1, 1) are the only ones of order two, and we again  conclude that σ coincides with the sign involution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The cokernel for the inclusion OB ⊂ f∗(OX) is isomorphic to  ωB, and the resulting extension 0 → OB → f∗(OX) → ωB → 0 of coherent sheaves  splits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The sheaf f∗(OX) has rank two and is torsion-free, hence is locally free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The  inclusion of OB is locally a direct summand, so the cokernel L is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' We  have 0 = χ(OX) = χ(OB) + χ(L ) = 2 + deg(L ) and conclude deg(L ) = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Since  deg : Pic(B) → Z is injective, this gives L ≃ ωB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The extension yields a class in  Ext1(ωB, OB) = H1(X, ω⊗−1  B  ), which vanishes by Serre Duality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' So the extension  splits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  Choose a splitting and set E = f∗(OX) = OB ⊕ ωB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The smooth surface  S = P(E ) = Proj(Sym• E )  is a twisted form of the Hirzebruch surface S0 = P(E0), where E0 = OP1 ⊕ OP1(−2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Let us call S the twisted Hirzebruch surface attached to the Brauer–Severi curve B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Since f : X → B is affine, the invertible sheaf OX is relatively very ample, and we  get a closed embedding X ⊂ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' By abuse of notation we also write f : S → B for  the extension of our original morphism on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Recall that each invertible quotient E → N defines a section s : B → S, whose  image D has self-intersection D2 = deg(N ) − deg(N ′), where N ′ ⊂ E is the  kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' For more details we refer to [10], Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In particular, pr1 : E → OB  yields a curve D ⊂ S with D2 = 2, whereas pr2 : E → ωB gives some E ⊂ S  with E2 = −2, and the two sections are disjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The Adjunction Formula gives  (ωS ·D) = −4 and (ωS ·E) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Hence ωS = f ∗(ω⊗2  B )⊗OS(−2E), because both sides  have the same intersection numbers with D and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In particular c2  1 = (ωS · ωS) =  −8 · deg(ωB) + 4 · E2 = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Setting  ω⊗1/2  S  = f ∗(ωB) ⊗ OS(−E),  we get an invertible sheaf whose square is isomorphic to the dualizing sheaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In other  words, the surface S comes with a canonical theta characteristic, or spin structure,  compare [4] and [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The dual sheaf L = ω⊗−1/2  S  is globally generated with h0(L ) = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The image of the resulting r : S → P3 is an integral normal surface S′ ⊂ P3 of degree  two, and the induced morphism r : S → S′ is the contraction of E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Moreover, the  image a = r(E) is a rational point, the local ring OS′,a is singular, and the restriction  r|X is a closed embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Our sheaf has intersection numbers (L · L ) = 2 and (L · E) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Serre  Duality gives h2(L ) = h0(ω⊗3/2  S  ) = 0, and Riemann–Roch yields  h0(L ) ≥ χ(L ) = c2  1/4 + c2  1/2  2  + χ(OS) = (2 + 4)/2 + 1 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  SIGN INVOLUTIONS  11  The base locus Bs(L ) is contained in E, because ω⊗−1  B  is globally generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The  short exact sequence 0 → f ∗(ω⊗−1  B  ) → L → L |E → 0 yields an exact sequence  0 −→ H0(S, f ∗(ω⊗−1  B  )) −→ H0(S, L ) −→ H0(E, OE),  consequently h0(L ) ≤ h0(ωB) + h0(OE) = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This ensures h0(L ) = 4, and that L  is globally generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  In turn, our spin structure yields a morphism r : S → P3 with r∗(OP3(1)) =  ω⊗1/2  S  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It therefore contracts E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Moreover, the image S′ ⊂ P3 is integral and two-  dimensional, of some degree n ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This image is not a plane, because the morphism  is defined by the complete linear system H0(S, L ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' From 2 = (L ·L ) = deg(S/S′)·n  we infer that S → S′ is birational and n = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The Adjunction Formula gives  ωS′ = OS′(2), consequently r∗(ωS′) = ωS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It follows that the birational morphism  r : S → S′ is in Stein factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Since Pic(S) has rank two, the exceptional  divisor is irreducible, whence must coincide with E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  The image a = r(E) is a rational point, because h0(OE) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The local ring OS′,a  must be singular, because otherwise S = Bla(S′), such that E = r−1(a) must be a  projective line with E2 = −1, contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  It remains to verify that the curves X, E ⊂ S are disjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Since deg(X/B) = 2  we have ωS = OS(−X)⊗f ∗(N ) for some invertible sheaf N on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The Adjunction  Formula gives  0 = (ωS · X) + X2 = −X2 + 2 deg(N ) + X2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Consequently N  is trivial, and ωS = OS(−X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  This gives X2 = c2  1 = 8, and  furthermore (X · E) = −(ωS · E) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Thus the integral curves X and E must be  disjoint, hence r|X is a closed embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  Note that the local ring OS′,a is factorial provided that B ̸≃ P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The above also  shows that the image S′ = r(S) can also be viewed as the anti-canonical model  P(S, −KS) of the scheme S, which is defined as the homogeneous spectrum of the  anti-canonical ring R(S, −KS) = �  t≥0 H0(S, ω⊗t  S ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Recall that the weighted projective space P(d0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' , dn) is the homogeneous spec-  trum of k[U0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' , Un], where the generators have degrees di = deg(Ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The case  d0 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' = dn = 1 gives back the standard projective space Pn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Let us say that a  closed subscheme of a Gorenstein surface is an anti-canonical curve if its sheaf of  ideals is isomorphic to the dualizing sheaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The anti-canonical model S′ = P(S, −KS) is a twisted form of  the weighted projective space P(1, 1, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Moreover, X ⊂ S and the resulting inclusion  X ⊂ S′ are anti-canonical curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' It suffices to treat the case that k is algebraically closed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' We claim that S′ is  defined inside P3 = Proj k[T0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' , T3] by the equation T 2  0 − T1T2 = 0, for a suitable  choice of homogeneous coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The main challenge is the case p = 2: According  to [1], Satz 2 our quadric X ⊂ P3 must be defined by an equation of the form  r  �  i=1  (αiX2  i + XiYi + γiY 2  i ) +  s  �  j=1  δjZ2  j = 0,  with 1 ≤ 2r + s ≤ 4, and non-zero coefficients δj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Since k is algebraically closed, we  can make a change of variables and achieve δj = 1, and furthermore αi = γi = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  SIGN INVOLUTIONS  12  On now immediately sees that only for r = s = 1 the quadric S′ ⊂ P3 is normal  and singular, and setting T0 = Z1 and T1 = X1 and T2 = Y1 gives the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' For  p ̸= 2 our quadric can be defined by an equation of the form �3  j=0 δjZ2  j = 0, and  one argues similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Consider the graded ring A = k[U0, U1, U2] with weights (1, 1, 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The Veronese  subring A(2) is generated by the homogeneous elements U0U1, U 2  0, U 2  1, U2, which sat-  isfy the relation (U0U1)2 = U 2  0 · U 2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This gives a surjection  k[T0, T1, T2, T3]/(T 2  0 − T1T2) −→ A(2),  defined by the assignments T0 �→ U0U1 and T1 �→ U 2  0 and T2 �→ U 2  1 and T3 �→ U2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Both rings are integral of dimension three.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Using Krull’s Principal Ideal Theorem,  we infer that the above surjection is bijective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The homogeneous spectrum of A(2)  coincides with P(1, 1, 2) = Proj(A), and by the above also with S′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  We already saw in the previous proof that ωS = OS(−X), hence X ⊂ S is an  anti-canonical curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' From the Theorem of Formal functions one infers f∗(ωS) is  invertible, and this ensures that the direct image coincides with ωS′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Using X ∩E =  ∅ we infer ωS′ = OS′(−X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  Now suppose that we have two morphism B1  f1  ← X  f2  → B2 to Brauer–Severi curves,  with deg(X/Bi) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='1, they comes from sign involutions  σ1 and σ2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' If σ1 ̸= σ2, the diagonal morphism i : X → B1 × B2 is a closed  embedding, and its image is an anti-canonical curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Let A ⊂ AutX/k be the subgroup scheme that fixes Picτ  X/k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' As discussed in  Section 1, this is an elliptic curve, and the action on the para-elliptic curve X is free  and transitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Moreover, the dual abelian variety is identified with Pic0  X/k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' But  note that the principal polarization stemming from the origin also gives A = Pic0  X/k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  We saw in the proof of Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='1 that the two rational points σ1, σ2 ∈ Invsgn  X/k  differ by the action of some non-zero a ∈ A(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In other words, σ2(x) = a + σ1(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  It follows that there is no rational point x ∈ X with σ1(x) = σ2(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In particular,  the fixed schemes Xσ1 and Xσ2 are disjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  To proceed, we assume that k is algebraically closed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Let x ∈ X be a closed  point and write y = i(x) = (b1, b2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The inverse image i−1(y) is the intersection  of the fibers f −1  1 (b1) ∩ f −1  2 (b2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' This is just the spectrum of κ(x), by the previous  paragraph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' According to [12], Corollary 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='6 the finite morphism i : X → B1×B2  is a closed embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  By construction, we have deg(X/B1) = deg(X/B2) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Set V = B1 × B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Its  Picard scheme PicV/k can seen as the Galois module Pic(V ⊗ksep) = Z×Z, compare  the discussion in [34], Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Obviously, the elements (2, 0) and (0, 2) are fixed  by Gal(ksep/k), hence the whole Galois action is trivial, and thus PicV/k = (Z × Z)k  is a constant group scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The dualizing sheaf ωV = pr∗  1(ωB1) ⊗ pr∗  2(ωB2) has class  (2, 2), and we infer ωV = OS(−X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  Note that ωV is anti-ample, so the smooth surface V = B1 ×B2 coincides with its  anti-canonical model P(V, −KV ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Products of Brauer–Severi curves were studied by  Koll´ar [17] and Hogadi [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Let us close this paper with the following observation:  SIGN INVOLUTIONS  13  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The surface V = B1 × B2 admits an embedding into P3 if and  only if B1 ≃ B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The Picard scheme is given by PicV/k = (Z × Z)k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The classes (−2, 0) and  (0, −2) come from the preimages of the invertible sheaves on B1 and B2, and thus  belong to the subgroup Pic(V ) ⊂ PicV/k(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Suppose we have V ⊂ P3, and write d ≥ 1 for its degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' From ωV = OV (d − 4)  we get 8 = (ωV · ωV ) = d(d − 4)2, and thus d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In particular, V admits the spin  structure ω⊗1/2  V  = OV (−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' The dual sheaf L = OV (1) has h0(L ) = 4, which easily  follows from the short exact sequence 0 → OP3(−1) → OP3(1) → L → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Choose  some non-zero global section s ̸= 0 from L , and let D ⊂ V the resulting effective  Cartier divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Suppose D is reducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Since deg(D) = 2 we see that there are  two components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Since L has class (1, 1) in PicV/k(k), it follows that D = D1 +D2,  where the summands are preimages of rational points on B1 and B2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Thus both Brauer–Severi curves are copies of P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Suppose now that D is irreducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Then deg(D/Bi) = 1, so the morphism D → Bi are birational.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' By Zariski’s Main  Theorem, it must be an isomorphism, and therefore B1 ≃ B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Conversely, suppose there is an isomorphism h : B1 → B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Its graph defines  an effective Cartier divisor D ⊂ B1 × B2 with class (1, 1) ∈ PicV/k(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Set L =  OV (D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Passing to the algebraic closure of k, we get L = pr∗  1(OP1(1))⊗pr∗  2(OP1(1)),  and compute h0(L ) = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Moreover, L is very ample, and thus defines a closed  embedding X ⊂ P3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  □  Given a sign involution σ : X → X and a non-zero rational point a ∈ A(k), we  get another sign involution x �→ a + σ(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' We see that the situation B1  f1  ← X  f2  → B2  with σ1 ̸= σ2 appears if and only if the set Invsgn  X/k(k) is non-empty and the group  A(k) is non-trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  References  [1] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Arf: Untersuchungen ¨uber quadratische Formen in K¨orpern der Charakteristik 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Reine Angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 183 (1941), 148–167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Artin: Algebraization of formal moduli I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In: D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Spencer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Iyanaga (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' ), Global  Analysis, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 21–71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Tokyo Press, Tokyo, 1969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Artin: Brauer–Severi varieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In: F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' van Oystaeyen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Verschoren (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' ), Brauer  groups in ring theory and algebraic geometry, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 194—210, Springer, Berlin-New York,  1982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Atiyah: Riemann surfaces and spin structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' ´Ecole Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Sup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 4 (1971),  47–62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [5] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Bergqvist: The Kummer constructions in families.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Dissertation, D¨usseldorf, in prepara-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Dang: Cohomology of certain Artin stacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Dissertation, D¨usseldorf (2022), https://  nbn-resolving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='org/urn/resolver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='pl?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='urn=urn:nbn:de:hbz:061-20220822-084645-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [7] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Deligne: Courbes elliptiques: formulaire d’apr`es J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Tate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In: B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Birch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Kuyk (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' ),  Modular functions of one variable IV, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 53–73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Springer, Berlin, 1975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [8] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Ekedahl: Canonical models of surfaces of general type in positive characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Hautes ´Etudes Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 67 (1988), 97–144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Fanelli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: Del Pezzo surfaces and Mori fiber spaces in positive characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 373 (2020), 1775–1843.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  SIGN INVOLUTIONS  14  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Fanelli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: The maximal unipotent finite quotient, unusual torsion in Fano  threefolds, and exceptional Enriques surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' ´Epijournal Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Alg´ebrique 4 (2020), Art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Grothendieck: Sur quelques points d’alg`ebre homologique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Tohoku Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 9 (1957),  119–221.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Grothendieck: ´El´ements de g´eom´etrie alg´ebrique IV: ´Etude locale des sch´emas et des  morphismes de sch´emas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=', Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Hautes ´Etud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 32 (1967).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Grothendieck: Le groupe de Brauer III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In: J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Giraud (ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=') et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' : Dix expos´es sur la  cohomologie des sch´emas, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 88–189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' North-Holland, Amsterdam, 1968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [14] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Hartshorne: Generalised divisors on Gorenstein schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' K-Theory 8 (1994), 287–339.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Hogadi: Products of Brauer–Severi surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 137 (2009), 45–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [16] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Katsura: On Kummer surfaces in characteristic 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' In: M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Nagata (ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' ), Proceedings of  the international symposium on algebraic geometry, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 525–542.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Kinokuniya Book Store,  Tokyo, 1978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Koll´ar: Conics in the Grothendieck ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 198 (2005), 27–35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [18] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Laurent, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: Para-abelian varieties and Albanese maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Preprint, arXiv:2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  10829.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Matsumura, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Oort: Representability of group functors, and automorphisms of alge-  braic schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 4 (1967–68), 1–25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Kondo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: Kummer surfaces associated with group schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Manuscripta Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  166 (2021), 323–342.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Lang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Tate: Principal homogeneous spaces over abelian varieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 80  (1958), 659–684.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [22] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Lorenzini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: Moderately ramified actions in positive characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  295 (2020), 1095–1142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [23] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Mumford:  Lectures on curves on an algebraic surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Princeton University Press,  Princeton, 1966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [24] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Mumford: Abelian varieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Tata Institute of Fundamental Research Studies in Math-  ematics 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Oxford University Press, London, 1970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [25] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Mumford: Theta characteristics of an algebraic curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' ´Ecole Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Sup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 4  (1971), 181–192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Raynaud: Sp´ecialisation du foncteur de Picard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=', Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Hautes ´Etud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 38  (1970), 27–76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [27] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' R¨ossler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: Moret-Bailly families and non-liftable schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Algebr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 9  (2022), 93–121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [28] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Saito: The discriminant and the determinant of a hypersurface of even dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 19 (2012), 855–871.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [29] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schilson: Singularit¨aten von Kummer-Variet¨aten in beliebiger Charakteristik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Disserta-  tion, D¨usseldorf (2018), https://nbn-resolving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='org/urn/resolver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='pl?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='urn=urn:nbn:  de:hbz:061-20181108-114448-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [30] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schilson: Wild singularities of Kummer varieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Singul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 20 (2020), 274–288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [31] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: Kummer surfaces for the selfproduct of the cuspidal rational curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Algebraic  Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 16 (2007), 305–346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [32] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: The Hilbert scheme of points for supersingular abelian surfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Arkiv Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 47  (2009), 143–181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [33] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: Enriques surfaces with normal K3-like coverings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Japan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 73 (2021),  433–496.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: There is no Enriques surface over the integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 197 (2023), 1–63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [35] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Shioda: Kummer surfaces in characteristic 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Japan Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' 50 (1974), 718–722.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  [36] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Tziolas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content=' Schr¨oer: The structure of Frobenius kernels for automorphism group schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  arXiv:2105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='07860, to appear in Algebra Number Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='  SIGN INVOLUTIONS  15  Mathematisches Institut, Heinrich-Heine-Universit¨at, 40204 D¨usseldorf, Ger-  many  Email address: Jakob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='Bergqvist@hhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='de  Mathematisches Institut, Heinrich-Heine-Universit¨at, 40204 D¨usseldorf, Ger-  many  Email address: dangt@uni-duesseldorf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='de  Mathematisches Institut, Heinrich-Heine-Universit¨at, 40204 D¨usseldorf, Ger-  many  Email address: schroeer@math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='uni-duesseldorf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
+page_content='de' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/9dE1T4oBgHgl3EQfoAQF/content/2301.03314v1.pdf'}
diff --git a/AtFLT4oBgHgl3EQfFC_E/content/tmp_files/2301.11986v1.pdf.txt b/AtFLT4oBgHgl3EQfFC_E/content/tmp_files/2301.11986v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6d7567829dec60624af8965e760588ce9e8068e1
--- /dev/null
+++ b/AtFLT4oBgHgl3EQfFC_E/content/tmp_files/2301.11986v1.pdf.txt
@@ -0,0 +1,2817 @@
+1
+1
+FRA: A novel Face Representation Augmentation algorithm for face recognition
+Soroush Hashemifar1, Abdolreza Marefat2, Javad Hassannataj Joloudari3,*, Hamid Hassanpour4
+1School of Computer Engineering, Iran University of Science and Technology, Tehran, Iran
+2Department of Artificial Intelligence, Technical and Engineering Faculty, South Tehran Branch, Islamic 
+Azad University, Tehran, Irans
+3Department of Computer Engineering, Faculty of Engineering, University of Birjand, Birjand 
+9717434765, Iran 
+4Faculty of Computer Engineering & Information Technology, Shahrood University of Technology, P.O. 
+Box 316, Shahrood, Iran
+Corresponding author*: javad.hassannataj@birjand.ac.ir
+Abstract
+A low amount of training data for many state-of-the-art deep learning-based Face Recognition (FR) 
+systems causes a marked deterioration in their performance. Although a considerable amount of research 
+has addressed this issue by inventing new data augmentation techniques, using either input space 
+transformations or Generative Adversarial Networks (GAN) for feature space augmentations, these 
+techniques have yet to satisfy expectations. In this paper, we propose a novel method, named the Face 
+Representation Augmentation (FRA) algorithm, for augmenting face datasets. To the best of our 
+knowledge, FRA is the first method that shifts its focus towards manipulating the face embeddings 
+generated by any face representation learning algorithm in order to generate new embeddings 
+representing the same identity and facial emotion but with an altered posture. Extensive experiments 
+conducted in this study convince the efficacy of our methodology and its power to provide noiseless, 
+completely new facial representations to improve the training procedure of any FR algorithm. Therefore, 
+FRA is able to help the recent state-of-the-art FR methods by providing more data for training FR 
+systems. The proposed method, using experiments conducted on the Karolinska Directed Emotional Faces 
+(KDEF) dataset, improves the identity classification accuracies by 9.52 %, 10.04 %, and 16.60 %, in 
+comparison with the base models of MagFace, ArcFace, and CosFace, respectively.
+Keywords:
+Face Recognition, Face Embeddings, Face Representation Learning, Autoencoder, Vision Transformers, 
+Latent Space Data Augmentation, Facial Pose Reconstruction
+1.Introduction
+Face images are one of the most popular biometric modalities which have been continuously utilized in 
+Face Recognition (FR) systems [1]. It is used in a wide range of contexts with the aim of identity 
+authentication and its applications vary from daily life and finance to military and public security [2]. In 
+fact, in comparison with other biometrics, such as the fingerprint, iris, or retina which are ubiquitously 
+used for authorizing individuals, FR can provide us with the most convenient way to capture visual 
+information without the need for any extra activity from the subject. In recent years, FR has been one of 
+
+2
+2
+the most proactively studied areas in Computer Vision [3]. Particularly, with the advent of deep learning 
+and architectures like Convolutional Neural Networks (CNNs) [4], a large number of efficient facial 
+recognition methods with outstanding performance have been invented to address this challenge [5-12]. 
+These successful algorithms depend heavily on the performance of neural networks which use a cascade 
+of layers comprised of neurons that are able to learn different levels of abstractions and representations 
+from the input data [2]. These representations are more powerful substitutions for hand-crafted features 
+from facial attributes such as Scale-Invariant Feature Transform (SIFT) and Speeded Up Robust Features 
+(SURF) [13, 14]. Their principal advantage is that they obviate the need for manually and exhaustively 
+searching for the best features representing one’s face. Moreover, the process of learning representations 
+via deep learning-based algorithms makes the generated features surprisingly discriminative in that the 
+inter-class diversity and intra-class compactness within the training data are all taken into account by the 
+network itself [15]. 
+However, there are still problematic scenarios in which FR systems fail to realize the expectations. For 
+instance, in real-life situations, the imagery of a person’s face has a high chance of being in a variety of 
+facial expressions, occlusions, poor illumination, low resolution, etc. [16-18], and all these factors cause 
+substantial degradation of the overall performance of the current FR algorithms. Thus, different 
+approaches have been adopted to rectify the negative impact of such barriers in FR systems [19-21]. 
+Some have opted for experimenting and devising new loss functions whose capability to better feedback 
+to their neural network in the backpropagation step, enables the extracted deep features to be more 
+discriminative and clearly separable [2, 6, 9, 22-26]. In addition to these works, different architectures 
+have been implemented to extract feature maps which are more useful in terms of facial representations. 
+Moreover, developing larger and more variant datasets has been one of the main stimuli which have been 
+pushing the boundaries in recent FR systems [27]. Nevertheless, although some of these benchmark 
+datasets can be found in large volumes, we often lack such a training set of images when it comes to real 
+use cases. A typical case would be a situation in which the goal is to train a deep learning-based method 
+on a private, in-house set of identities that have been chosen by a multimedia organization for video 
+indexing purposes. The data-gathering phase can be very time and labor-consuming and sometimes even 
+impossible, and it acts as an impediment in the way of achieving a tailored amount of training datasets. 
+These have motivated researchers to pave the way by introducing different data augmentation techniques. 
+Data augmentation refers to a set of techniques that are used to increase the number of training datasets 
+without the loss of previously annotated data. The benefit of such methods is that it equips the trained 
+model with more generalizability and acts as a regularizer in the case of overfitting which is one of the 
+most frequent complications when dealing with a small amount of training data [28, 29]. Overall, there 
+are two mainstream categories of methods for augmenting data. The first set of methods has the aim of 
+manipulating the data in the input space in that they simply take the input image and apply different 
+geometric transformations such as translations, cropping, vertical and horizontal flipping, rotation, etc 
+[30]. Even though these methods are proven to be extremely useful in some other challenges like image 
+classification, object detection, and image captioning in computer vision, in the case of FR they cannot be 
+as helpful as they expected. The main reason is that in order for any FR system to capture a reliable visual 
+representation of a face crop image, the content should be aligned in terms of facial landmarks. This 
+means that any geometric alteration on these which conspicuously happens when one uses these classical 
+methods, can perturb the overall performance of FR pipeline. These challenges have motivated the 
+researchers to shift their studies’ direction toward more modern and domain-specific solutions [31-33], 
+leading to the second set of methods, which are known to be Generative Adversarial Networks (GANs) 
+
+3
+3
+[34]. These methods are the well-known type of generative models which are used with the objective of 
+transforming the input data in feature space with the aim of generating new augmented image data. This 
+group of models is capable of adjusting the facial attributes existent in a face image such as hair style, 
+expression, posture, skin color, etc. to a target style. However, in most cases, these generative models 
+cannot create realistic outputs and these models deal with the high complexities of reconstructing the 
+feature space to input space, without having any considerable improvement on the downstream task, 
+which in our case, is classification on the identity of the samples.
+In order to address these difficulties, in this paper we propose the Face Representation Augmentation 
+(FRA) algorithm. This algorithm augments the posture of a given face image in the latent space. This 
+means that, given a set of embeddings representing a specific person, the proposed approach alters the 
+embedding to sustain the identity-related features with a transformed pose feature. The FRA algorithm 
+can help the existing facial recognition systems especially when the number of training samples is 
+imbalanced or less than expected. Our main contributions in this paper are itemized in the following:
+1. A novel algorithm for facial posture augmentation inside the latent space to reduce the complexity of 
+the image augmentation problem.
+2. Generating noiseless, non-duplicated embeddings which are proved to be linearly separable.
+3. Extensive experiments were conducted on the Karolinska Directed Emotional Faces (KDEF) [35] 
+dataset and improved the identity classification accuracies in comparison with the base models of 
+MagFace, ArcFace, and CosFace, respectively. 
+The rest of the paper is organized as follows. In Section 2, we briefly review the related works on face-
+specific data augmentation and representation learning. Then, in Section 4, we present the details of our 
+proposed methodology. In Section 4, we demonstrate the results of our experiments in comparison with 
+other related state-of-the-art approaches. Finally, the conclusion will be drawn in Section 5. 
+2.Related works
+In this section, we present an overview of face-specific data augmentation techniques. These are 
+categorized into two groups classical and generative-based methods in 2.1. Additionally, we review the 
+related literature of FR algorithms in 2.2.
+2.1.Face-Specific Data Augmentation
+To begin with, five data augmentation techniques for face photos were reported by Lv et al. [29]. These 
+techniques were landmark perturbation, hairdo synthesis, glasses synthesis, postures synthesis, and 
+lighting synthesis. Vincent et al. [36] tried to synthesize more data by applying different types of noise 
+such as Gaussian and Salt-and-pepper with the objective of training Stacked Denoising Autoencoders on 
+more complicated samples. Wang et al. [37] addressed the issue of data augmentation in picture 
+classification using conventional transformation techniques and GANs. They also suggested a technique 
+for learning network-based augmentations that better enhance the classifier in the setting of generic 
+photos rather than face images. 
+Moreover, although the hair is not an intrinsic part of the human face, it interferes with facial recognition 
+since it obscures the face and changes its appearance. Using DiscoGAN, which was developed to find 
+cross-domain relationships using unpaired data, Kim et al. altered hair color. In addition to the color, Kim 
+et al. in [38], suggested changing the bang by transferring an unsupervised visual characteristic using a 
+reconfigurable GAN. An online compositing technique was used in the face synthesis system proposed by 
+Kemelmacher-Shlizerman et al. [39]. The system might produce a series of fresh photographs with the 
+
+4
+4
+input person's identification and the questioned look using one or more photos of their face and a text 
+query like curly hair. Jiang et al., in [40], proposed Pose and expression resilient Spatial aware GAN 
+(PSGAN). It starts by using Makeup Distill Network to separate the reference image's makeup into two 
+spatially aware makeup matrices. After that, a module called Attentive Makeup Morphing is developed to 
+let users describe how a pixel's appearance in the source picture is altered based on the reference image. 
+In order to ease applications in the real-world setting, PSGAN is the first to concurrently accomplish 
+partial, shade tunable, and pose/expression robust makeup transfer. In order to separate the makeup from 
+the reference picture as two makeup matrices, an MDNet is also included. The flexible partial and shade 
+adjustable transfer is made possible by the spatially aware makeup matrices. To learn all cosmetics 
+attributes [41], including color, form, texture, and position, it comprises an enhanced color transfer branch 
+and a new pattern transfer branch. They present makeup in this work as a combination of color 
+transformation and pattern addition, and they create a thorough makeup transfer technique that works for 
+both delicate and dramatic looks. They suggest using warped faces in the Ultraviolet (UV) space while 
+training two network branches to eliminate the disagreement between input faces in terms of form, head 
+posture, and expression. They also create a new architecture with two branches for color and pattern 
+transfer. They present brand-new cosmetics transfer datasets with extreme fashions that were not taken 
+into account in the earlier datasets.
+2.2.Representation Learning for Face Recognition 
+Representation learning refers to a set of algorithms that are designed to solve a variety of challenges like 
+image retrieval [42-44], the person [45, 46] and vehicle [47, 48] re-identification, landmark detection, and 
+fine-grained object recognition [49, 50]. The task of face recognition in computer vision is heavily 
+dependent on learning representations that have fine intra-class and large inter-class distances [51]. 
+Previous works [6, 22, 25, 52, 53] have mainly adopted different, more robust loss functions with the aim 
+of learning representations that satisfy the aforementioned requirements.
+In [52], a deep convolutional neural network, named FaceNet, was proposed which learns facial 
+representations with the help of triplet loss. The main objective of this work is to achieve an embedding 
+f(x) from an image x into a d-dimensional Euclidean space Rd. The obtained embedding is generated in a 
+way that the squared distance among the embeddings from one class is small and that of the embeddings 
+from different classes is large. This algorithm achieves 99.63% and 95.12% accuracy in LFW [54] and 
+YouTube Faces Database [55] respectively. Liu et al. [53] have proposed a new look at the loss functions 
+which are based on the Euclidean margin between the produced embeddings. For CNNs to learn 
+discriminative facial characteristics with clear and innovative geometric interpretation, they suggest the 
+A-Softmax loss. The assumption that faces also lie on a manifold is fundamentally compatible with the 
+learnt features' discriminative spread on a hypersphere manifold. In order to approximate the learning 
+problem that minimal inter-class distance is greater than maximum intra-class distance, they develop 
+lower the margin set between such classes.
+In [22], the authors have proposed ArcFace, a major modification of the Softmax loss to further improve 
+the robustness of the learned deep features. By utilizing the arc-cosine function to calculate the angle 
+between the current feature and the target weight and adding an additive angular margin to the target 
+angle, the target logit can be obtained. Then, these logits are rescaled by a fixed feature norm followed by 
+exactly the same steps in the Softmax loss function. Their approach has the following advantages over the 
+others. (1) Directly optimizing the geodesic distance margin (2) State-of-the-art performance in several 
+
+5
+5
+benchmark datasets: achieving 99.53% accuracy (3) Easiness in terms of implementation (4) Efficiency in 
+terms of computational complexity.
+In [25], the authors reformulated the Softmax loss as a cosine loss with the aim of introducing a novel 
+loss function, named Large Margin Cosine Loss (LMCL). Their improvement is to further maximize the 
+decision margin in the angular space by introducing and training a deep model called CosFace. In this 
+deep model, LMCL guides the convolutional layers to learn features with huge cosine margins. Their 
+results demonstrate that they have achieved 97.96% accuracy in face verification on the MegaFace 
+benchmark, which has been a major improvement in comparison to previous works.  
+Meng et al. [6] proposed a new set of losses that enable the network to learn embeddings whose 
+magnitude represents the quality of the given face. By extending ArcFace [22] and introducing the 
+MagFace loss function, they demonstrate that the more likely the subject is to be recognized, the bigger 
+the magnitude of the generated embedding becomes. MagFace learns to generate these universal 
+embeddings by pulling the easier samples within a class of identities to the class center and pushing them 
+away from the origin. This makes the embeddings robust to ambiguity and the absence of high 
+discriminative features which prevalently exist in unconstrained face images in real scenarios. They have 
+achieved 99.83% verification accuracy in the LFW benchmark dataset. In Table 1, a comparison of these 
+works is depicted.
+Table 1. Verification accuracy of MagFace, CosFace, ArcFace, and SphereFace. These models are 
+evaluated on CALFW, CPLFW, AgeDB, LFW, and CFP-FP datasets.
+Method
+CALFW [56]
+CPLFW [57]
+AgeDB [58]
+LFW [54]
+CFP-FP [59]
+MagFace [6]
+96.15
+92.87
+98.17
+99.83
+98.46
+CosFace [25]
+96.18
+92.18
+98.17
+99.78
+98.26
+ArcFace [22]
+95.96
+92.72
+98.05
+9981
+98.40
+SphereFace [53]
+95.58
+91.27
+97.05
+99.67
+96.84
+Moreover, although these approaches have significant performance, directly applying GAN approaches 
+appears to have a few disadvantages. Models collapse, difficulty in training and convergence problems, 
+and poor image generation effect, along with the unreliable results of the generator for unconstrained 
+input images, cause the generated image examples to be incapable of being utilized for industrial data 
+augmentation tasks ]60 ,61[.
+3.
+Proposed approach
+3.1.Overview
+This section presents the proposed FRA algorithm. As can be inferred from Figure 1, our method includes 
+four steps. These are as follows: face detection and alignment, input preparation: facial landmark and 
+representation extraction, pose feature extraction, and representation augmentation. Steps 1 and 2 
+comprise our data preprocessing pipeline which is explained in Section 3.2. Steps 3 and 4 represent our 
+main contribution to this paper and are explained in Section 3.4.
+
+6
+6
+Figure 1. The overall procedure of FRA. FRA is composed of four steps to generate a new representation 
+vector with identity i, emotion e, and posture p, by applying a target posture p on a base image with 
+identity i and emotion e.
+3.2. Dataset preprocessing and preparation
+Our data preprocessing step includes three main phases. These three phases are depicted in Figure 1. As is 
+seen in the first phase, we feed the raw face images to the Multi-task Cascaded Convolutional Networks 
+(MTCNN) algorithm [53] which is a robust face and landmark detector. MTCNN provides us with 5 
+landmark points, including the center of both eyes, the tip of the nose, and the left and right corners of the 
+lips, and a bounding box that perfectly encloses the face area within the image without any padding. In 
+this phase, we also align the face images by feeding the acquired facial landmarks along with the face 
+image itself to the method of warp affine which exists in OpenCV [62], a famous library with ready-to-
+use computer vision-related algorithms. 
+In the second phase, we feed the aligned face images to MLXTEND1 so as to determine more facial 
+landmarks. As is shown in Figure 1, MLXTEND outputs 68 facial key points which we use to construct 
+binarized images with pixel value 0 (completely black) for the background and 1 (completely white) for 
+facial landmarks. On the other hand, we need to have fixed-size embeddings for each sample within the 
+dataset. These embeddings are in fact the training data for the combiner module which will be explained 
+in Section 3.4. In our case, we use two of the most reliable and robust face representation learning 
+algorithms, namely MagFace [6] and FaceNet [52], for obtaining embeddings for each image. MagFace’s 
+learning procedure is for a universal embedding that is quality aware, meaning that the easier the sample 
+is for the recognition task, the closer its feature vector becomes to the center of the class. Furthermore, 
+FaceNet is an algorithm that directly learns a mapping from the samples to a compact Euclidean space 
+and the distances correlate to the similarity degree of a given pair of face images. In Phase 3, the 
+binarized images generated in Phase 2 are fed to the AE model in order to generate an embedding vector 
+1http://rasbt.github.io/mlxtend/  
+
+Faciallandmarkextraction
+1
+Face lancmark
+detector
+Encoder
+(MLXTEND)
+1
+-
+68facial
+1
+targetface
+-
+withposturep'
+landmarks
+512Dposefeatures
+Combiner
+1
+Facialrepresentationextraction
+1
+-
+1
+-
+512D augmented face
+Face
+Face
+-
+for identity i, emotion e,
+representation
+detector
+representation
+detector
+andposturep'
+(MTCNN)
+(FRL)
+1
+1
+sourceface
+with identity i,
+512Dfacial
+emotione,
+representation
+andposturep
+1
+1
+-
+1
+1
+a)alignandcrop
+b)inputspreparation
+c)posefeaturesextraction
+d)augmentedrepresentation7
+7
+representing posture features. Finally, in Phase 4, pose and face representation vectors are fed into the 
+combiner module to generate an augmented face representation vector.
+3.3.Facial Landmark Restoration using Autoencoders
+Autoencoders (AE)  are a particular type of neural networks whose main functionality is to encode the 
+input into a meaningfully compacted representation and decode this into the input space afterwards [63, 
+64]. Following this paradigm, in this paper, we have been inspired by  the work done by Meng et al. [65] 
+and decided to use an AE-based model for encoding our input space (binarized images of landmarks 
+explained in Section 3.2) into the latent space (embeddings), as shown in Figure 2. Given Si as a sample 
+of facial landmarks image, the output of F(Si) is a reconstructed image S’i, where F(Si) is. After the AE 
+model’s convergence, we can discard B (decoder) and take only A which has learned to encode the input 
+into an optimized and meaningful latent space representation denoted by Vi. It is worth mentioning that Vi 
+plays a vital role in our proposed method which is the latent representation of the posture of the face. 
+Figure 2 illustrates the proposed AE-based model and its architecture.
+Figure 2. A general architecture of an autoencoder-based model. FRA utilizes a typical convolutional 
+autoencoder with a bottleneck of size 512. This bottleneck vector is used in further steps.
+3.4.Combining Feature Vectors and Feature Extraction using Vision Transformers
+Vision Transformers (ViT) are deep learning models whose versatility in various fields such as natural 
+language processing, speech recognition and computer vision has made them a prominent choice for 
+researchers [66]. In comparison with the conventional CNNs, ViT models have achieved competitive 
+superior results in vision tasks like object detection [67], image recognition [68], image super-resolution 
+[69], and segmentation [70, 71].  
+At the core of ViT models, there is a mechanism of attention that has been probably one of the most 
+significant concepts in the domain of deep learning. Its inspiration is the biological attributes of human 
+beings in that, to recognize an object, we tend to focus on the most distinctive parts of that entity instead 
+of paying attention to all parts of it as a whole [72]. In terms of deep neural networks, this can be 
+interpreted as assigning importance scores for a given set of features where the higher scores are for more 
+relevant features and the lower ones for the features with less saliency [73]. As can be observed from 
+Figure 3, the model learns to have more focus on the parts which represent the target object in the image. 
+
+20
+5
+112x112x1
+56
+1@112x112
+112x112x1
+@
+4@
+Convolution
+Convoluton
++Max-Pool
+S
+Encoder (A)
+Decoder (B)8
+8
+Figure 3. The paradigm of combining two representation vectors using ViT. The combiner takes two 
+representation vectors with a size of 512 and combines them into a 32x32 matrix to be processed by a 
+vision-transformer component.
+Moreover, transformers [74] refer to a set of neural networks which use the mechanism of attention. 
+These models consist of multiple encoders and decoders whose architectures are identical to each other. 
+In these models, a multi-head self-attention (MSA) mechanism is used for encoding the input, followed 
+by decoders which include an extra attention layer in order to process the encoder’s output. Self-attention 
+is a function denoted in Equation (1). 
+  
+s.t.  
+(1)
+where , , and  are weight matrices used in linear transformations on inputs x to produce Q, K, and V. The 
+attention score is then calculated by  as the dot product of the query and each key, scaled by the 
+dimension dk of the key K. Put x = "x1, x2, x3, ... , xn" to calculate an answer based on a collection of 
+queries Q, keys K, and values V. In MSA, Q, K, and V are projected linearly and this is done for h 
+consecutive times with different learned weights. Then, by applying the self-attention mechanism on each 
+of the outputs in the previous step simultaneously, we obtain h outputs which are heads. Then, these 
+heads are concatenated to achieve the final output. The following demonstrates these computations in 
+mathematical terms. 
+ 
+s.t. 
+(2)
+MSAs, compared with CNNs, transform feature maps with huge data-specific kernels and this makes 
+them as expressive as the CNN-based architectures [75]. The key difference exists where convolutions 
+diversify feature maps whereas MSAs combine them. According to [76], the Fourier analysis of feature 
+maps demonstrates that convolutions boost high-frequency components whereas MSAs, on the other 
+hand, attenuate them. 
+Furthermore, finding elements that are more pertinent for the depiction of the altered posture is made 
+easier by the multi-head attention layer. In order to do this, the scaled dot product attention gives greater 
+weight to the characteristics of the input facial representation and encoded posture that is more pertinent 
+while providing less weight to the features that are less relevant [77]. The procedure chooses features 
+
+512Dpose
+Concatination and Reshape
+representation
+Normalization Layer
+512DAugmented
+Vision
+representation
+Transformer
+(ViT)
+512Dface
+representation9
+9
+from various input regions and aids in improving representation performance since there are several heads 
+in the attention layer.
+In this paper, we have opted for using a ViT-based architecture for extracting features. As stated before, 
+this policy ensures that the model is trained to attend to the most salient feature values within the identity 
+and posture-related feature vectors simultaneously.  Considering E of size  as the embedding obtained 
+from a pre-trained facial representation learning algorithm and Vi of shape  as the bottleneck vector 
+generated by the autoencoder part of FRA, we concatenate and reshape the produced feature vector to 
+make it of shape . 
+3.5.Generating Pose-Aware Face Embeddings
+After the ViT module in our proposed model, the output is normalized, making it into the range of 0-1, 
+after which it is fed to a fully connected layer. This layer helps us produce an output of a 1-d shape which 
+is also considered the embedding generated by our model. 
+3.6.Multi-Task Loss Function
+In the training procedure, we utilized a Multi-part Loss Function (MLF) as the learning objective. This 
+MLF comprises a Binary Cross-Entropy (BCE) loss function, which is used to train the autoencoder, so it 
+can reconstruct the posed style better. Since the activation function of the last layer of our autoencoder is 
+Sigmoid, it can lead to loss of saturation (plateau) [78]. This saturation could prevent gradient-based 
+learning algorithms from convergence. In order to avoid this issue, it would be better to have a logarithm 
+function in the objective function to undo the exponential function within the Sigmoid. This is why BCE is 
+preferred, because it uses a logarithm function, unlike Mean Squared Error (MSE).
+The second part of our loss function is a type of N-pair Loss [79]. N-pair loss generalizes triplet loss [52] 
+to include comparison with multiple negative samples. The objective of this function is to keep the 
+distance between the anchor and positive smaller than the distance between the anchor and negative 
+representations, as shown in Figure 4.
+Figure 4. Effect of the proposed loss function during the learning process. The N-pair loss allows the 
+model to distinguish between pose-variant representation vectors with the same identity and emotion, as 
+well as possible.
+The proposed multi-task loss function is defined as follows,
+
+10
+10
+(3)
+in which, yi and pi denote the reconstructed pose style and the original pose style, respectively, and also is 
+defined as
+(4)
+where m is a margin applied to impose the separability between genuine and imposter pairs, and f denotes 
+the proposed architecture. d is the euclidean distance applied on normalized features and it is given by 
+Equation (5).
+(5)
+In Equation (6), a and p denote the anchor (generated) representation and the positive (real) 
+representation, respectively. Additionally, , , and  denote the negative representation w.r.t pose, identity, 
+and emotion of the anchor face, respectively. Specifically, negative pose representations have the same 
+identity as the anchor, but with different poses. The same holds for negative emotion representation. But, 
+for negative identity representation, the representation of another person is chosen randomly, regardless 
+of what pose or emotion it has. The goal of the triplet loss is to achieve,
+(6)
+The optimal state for each single triplet loss is achieved when is equal to zero and  is greater than the 
+predefined margin.
+4.Results and Discussion
+In this section we first introduce the benchmark dataset that we have used for evaluating our proposed 
+method. Then, we elaborate the details of our implementation and introduce the metrics used in this 
+paper. Finally, we demonstrate our experimental results and discussion.
+4.1.Datasets
+With the object of benchmarking our results, we have used the KDEF dataset. It is a publicly available 
+dataset of 4900 face images, covering 140 unique identities. The images demonstrate face images with 
+varying pose and emotion styles. Some samples of these datasets are shown in Figure 5. 
+
+11
+11
+Figure 5. A few samples of the KDEF dataset. The KDEF dataset provides face images of 140 different 
+people in various postures and emotions.
+4.2.Implementation details
+We carried out our experiments on a machine with a Core i7-1165G7 @ 2.80GHz CPU with 64 
+Gigabytes of RAM and a GeForce RTX 2060 12 GB GPU. All models were implemented and trained 
+using the Pytorch framework. Table 2 shows the hyperparameter setting.
+Table 2. Details of the training procedure and the utilized FRLs. The hyperparameter settings are shown. 
+FRL arch.
+# epochs
+Init. learning rate
+Dropout 
+rate
+Triplet 
+margin
+ViT
+Embedding dim
+FC dim
+# Heads
+# Layers
+Patch 
+size
+MagFace
+255
+0.001
+0.4
+10.0
+256
+256
+4
+4
+8
+ArcFace
+320
+0.001
+0.4
+10.0
+CosFace
+157
+0.001
+0.05
+10.0
+Furthermore, with the object of fairly evaluating the proposed FRA, we divided KDEF datasets based 
+on identities with the following distributions:
+●
+We randomly selected all samples from 99 identities which nearly comprise 70.7 % of all 
+identities in KDEF as our training data.
+
+12
+12
+●
+We randomly selected all samples from 11 identities which nearly comprise 7.8 % of all identities 
+in KDEF as our validation data.
+●
+We randomly selected all samples from 30 identities which nearly comprise 21.5 % of all 
+identities in KDEF as our testing data.
+4.3.
+Experimental Results
+This section details our comprehensive experimental results. Table 3 shows the achieved 
+accuracy of the Support Vector Machine (SVM) [80] classifier on the embeddings generated in 
+three different experiments. These experiments are:
+(1) Pre-augmentation accuracy: In this experiment, the training happens on the embeddings extracted 
+using three different FRLs, namely MagFace, ArcFace, and CosFace, and the testing accuracy is 
+achieved on the testing partition of these embeddings (Train/Test split ratio is set 80/20). In this 
+experiment, we used no augmentation technique at all and this is done to find a baseline for the 
+quality of the original data in the chosen benchmark dataset.
+(2) Generated embeddings’ accuracy: In this experiment, we first augmented the original 
+embeddings to obtain the transformed embeddings. Then, we trained the SVM on the original data 
+and tested its performance on the generated embeddings by the proposed algorithm. This is done to 
+demonstrate how much the proposed model is able to sustain the identity, posture, and emotion-
+related features without any degradation. 
+(3) Post-augmentation accuracy: In this experiment, we have augmented the embeddings of the 
+training split using FRA, where the test split is the same as (1). Then, we trained the SVM classifier 
+on the training part and tested it on the testing one.
+Table3. Evaluation results of FRA. Pre-augmentation and post-augmentation accuracies show the 
+effectiveness of FRA. Generated embeddings’ accuracy denotes the sustainability of FRA.
+FRL
+Target
+(1) Pre-
+augmentation
+Accuracy (%)
+(2) Generated 
+embeddings’ 
+Accuracy 
+(%)  
+(3) Post-
+augmentation 
+Accuracy (%)
+MagFace
+Posture
+82.38
+98.12
+96.66
+Identity
+86.19
+93.61
+95.71
+Emotion
+44.76
+92.43
+99.04
+ArcFace 
+Posture
+89.12
+99.3
+97.9
+Identity
+86.61
+91.6
+96.65
+Emotion
+53.55
+92.98
+100
+CosFace
+Posture
+99.12
+99.91
+99.12
+Identity
+79.91
+88.11
+96.50
+Emotion
+54.14
+87.61
+97.37
+
+13
+13
+Based on Table 3, it is observed that our proposed algorithm improves the classification accuracy, not 
+only identity-wise but also in terms of emotion and posture. For instance, SVM outputs 86.19% accuracy 
+on the MagFace embeddings but after the augmentation, this score goes up to 95.71% in Post-
+augmentation. For the same data, the generated embeddings are much more representative which 
+improves the classification accuracy on the identity of the SVM outputs by 93.61%. This enhancement 
+can also be validated for ArcFace and CosFace since our algorithm increases the accuracy in all three 
+experiments. In addition, FRA can improve the accuracy of SVM embeddings remarkably. In addition to 
+improving the classification accuracy with respect to the identities of the embeddings, FRA improves that 
+pose and emotion-wise. Based on Table 5, the accuracy of the SVM classifier is increased from 86.19% 
+for MagFace embeddings to 95.71% after augmentation. This improvement for ArcFace and Cosface is 
+from 86.61% to 96.65% and from 79.91% to 97.37%, respectively.
+Furthermore, our generated embeddings should ensure the fact that they are linearly separable. This 
+means that the embeddings can be classified using a linear classifier such as SVM with a linear kernel. In 
+our experiments we used an SVM classifier with a linear kernel and based on Table 5, we can deduce that 
+FRA is able to improve the accuracy in Phase 2 and Phase 3 by a large margin, effectively enhancing the 
+performance of SVM with a linear kernel.
+Moreover, in order to show the independence of FRA from any FR algorithms, we adopted three such 
+approaches, namely MagFace, ArcFace, and CosFace. Based on Table 5, after augmenting the 
+embeddings generated by each of these algorithms, the classification accuracy of the SVM classifier is 
+increased significantly and this proves the fact that FRA is not dependent on any specific FR algorithm as 
+its requirements. 
+In addition, for our algorithms’ performance to be verified thoroughly, the reconstructed binary images 
+which are created by the AE part of the proposed approach are presented. These images are illustrated in 
+Figure 6, showing the original image, and the AE’s output when dealing with MagFace embeddings, 
+ArcFace embeddings, and CosFace embeddings. Also, the training and validation loss in the training 
+procedure of our proposed pipeline is shown in Figure 7. 
+
+14
+14
+Original landmarks
+AE-generated landmarks 
+for Magface FRL
+AE-generated landmarks 
+for Arcface FRL
+AE-generated landmarks 
+for Cosface FRL
+Figure 6. Some instances of reconstructed binarized facial landmark images. These reconstructed images 
+denote how good the AE is performing for each FRL model. The CosFace model reconstructs the most 
+landmarks more precisely.
+
+15
+15
+Total Loss Magface
+BCE Loss Magface
+Npair Loss Magface
+Total Loss Arcface
+BCE Loss Arcface
+Npair Loss Arcface
+Total Loss Cosface
+BCE Loss Cosface
+Npair Loss Cosface
+Figure 7. Total loss, BCE loss and Npair loss curves achieved by various FRL methods.
+The curves of Precision-Recall (PRC), Receiver Operating Characteristic (ROC), and confusion matrices 
+of all experiments for MagFace, ArcFace, and CosFace are shown in Figures 8-16.
+
+Train loss
+Validation loss
+20
+15
+Loss Error
+10
+5
+0
+0
+50 
+100
+150
+200
+250
+Epoch0.22
+Train BCE losS
+ValidationBCEloss
+0.20
+0.18
+0.16
+rror
+E
+0.14
+Loss
+0.12
+0.10
+0.08
+0.06
+0
+50
+100
+150
+200
+250
+EpochTrain Npair loss
+Validation Npair loss
+20
+15
+Loss Error
+10
+5
+0
+0
+50 
+100
+150
+200
+250
+EpochTrain loss
+Validation loss
+20
+15
+Error
+Loss
+10
+5
+0
+0
+50
+100
+150
+200
+250
+300
+EpochTrain BCE losS
+Validation BCE loss
+0.7
+0.6
+0.5
+rror
+E
+0.4
+LosS
+0.3
+0.2 
+0.1
+0
+50
+100
+150
+200
+250
+300
+EpochTrain Npair loss
+Validation Npair loss
+20
+15
+Loss Error
+10
+5
+0
+0
+50
+100
+150
+200
+250
+300
+EpochTrain loss
+14 
+Validation loss
+12 
+10
+Error
+8
+Loss
+6
+4
+2
+0
+0
+20
+40
+60
+80
+100
+120
+140
+160
+EpochTrain BCE losS
+Validation BCE loss
+0.18
+0.16
+0.14
+Loss Error
+0.12
+0.10
+0.08
+0.06
+0.04
+0
+20
+40
+60
+80
+100
+120
+140
+160
+EpochTrain Npair loss
+14
+Validation Npair loss
+12 
+10
+Error
+8
+Loss
+6
+4
+2
+0
+0
+20
+40
+60
+80
+100
+120
+140
+160
+Epoch16
+16
+a)
+Pre-augmentation PRC (pose)
+b)
+Pre-augmentation PRC (id)
+c)
+Pre-augmentation PRC 
+(emotion)
+d)
+Post-augmentation PRC 
+(pose)
+e)
+Post-augmentation PRC (id)
+f)
+Post-augmentation PRC 
+(emotion)
+Figure 8. PRC curves for MagFace FRL. As the curves indicate, post-augmentation PRC curves (d, e, and f) have 
+significant improvements in comparison to pre-augmentation PRC curves (a, b, and c) for pose, identity, and 
+emotion, respectively.
+
+precision vs.recall curve (pose)
+1.0
+0.8
+0.6
+precision
+0.4
+0.2 
+class FL
+class HL
+0.0
+class HR
+class S
+0.0
+0.2 
+0.4
+0.6
+0.8
+1.0
+recallprecision vs. recall curve (id)
+1.0
+0.9
+class AF05
+class BF04
+0.8
+clasS AM31
+classBM13
+class BF11
+class AF01
+class AM15
+0.7 
+class AF03
+class BM16
+precision
+class AF10
+class AM22
+0.6
+class AM13
+class BMo5
+class BM23
+class AM34
+class BF12
+0.5
+class AF07
+class AM05
+class AF27
+class BF14
+class BM29
+0.4
+class AMo1
+class AF16
+class AF32
+class AF26
+0.3
+class BM07
+class AF29
+class BF16
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+recallprecision vs.recall curve (emo)
+1.0
+0.8
+precision
+0.6
+0.4
+class AF
+class AN
+class DI
+class HA
+0.2
+class NE
+class SA
+class SU
+0.0
+0.2 
+0.4 
+0.6
+0.8 
+1.0
+recallprecision vs.recall curve (pose
+class FL
+1.0
+class HL
+class HR
+0.8
+0.6
+precision
+0.4
+0.2 
+0.0
+0.0
+0.2 
+0.4 
+0.6 
+0.8
+1.0
+recallprecision vs.recall curve (id)
+1.00
+0.95
+class AF05
+0.90
+class BF04
+class AM31
+class BM13
+class BF11
+class AF01
+0.85
+class AM15
+class AF03
+precision
+class BM16
+class AF10
+0.80
+class AM22
+class AM13
+class BM05
+class BM23
+0.75
+class AM34
+class BF12
+class AF07
+class AM05
+0.70
+class AF27
+class BF14
+class BM29
+class AM01
+0.65
+class AF16
+class AF32
+class AF26
+class BM07
+0.60
+class AF29
+class BF16
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+recallprecision vs.recall curve (emo)
+1.00
+0.99
+0.98
+precision
+0.97
+0.96
+0.95
+class AF
+class AN
+class DI
+class HA
+0.94
+class NE
+class SA
+class SU
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+recall17
+17
+a)
+Pre-augmentation ROC (pose)
+b)
+Pre-augmentation ROC (id)
+c)
+Pre-augmentation ROC 
+(emotion)
+d)
+Post-augmentation ROC 
+(pose)
+e)
+Post-augmentation ROC (id)
+f)
+Post-augmentation ROC 
+(emotion)
+Figure 9. ROC curves for MagFace FRL. As the curves indicate, post-augmentation ROC curves (d, e, and f) have 
+significant improvements in comparison to pre-augmentation ROC curves (a, b, and c) for pose, identity, and 
+emotion, respectively.
+
+RoCcurve(pose)
+1.0
+0.8
+0.6
+truepositive rate
+0.4
+0.2
+class FL (AUC = 0.9609)
+class FR (AUC = 0.999)
+class HL (AUC = 0.9991)
+0.0
+class HR (AUC = 1.0)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateROC curve (id)
+1.0
+class AM23 (AUC = 1.0)
+0.8 -
+class AF05 (AUC = 1.0)
+class BM13 (AUC = 1.0)
+classAF13(AUC =0.9892)
+class BF28 (AUC = 1.0)
+class BM08 (AUC = 1.0)
+class AF31 (AUC = 1.0)
+0.6
+class BM35 (AUC = 1.0)
+true positive rate
+class BF33 (AUC = 1.0)
+class BM18 (AUC = 1.0)
+class BF13 (AUC = 1.0)
+class AF19 (AUC = 0.9918)
+class AM26 (AUC = 0.9904)
+class BM12 (AUC = 1.0)
+0.4
+class AF16 (AUC = 1.0)
+class AF23 (AUC = 1.0)
+class BM01 (AUC = 1.0)
+class BM03 (AUC = 0.9938)
+class BF10 (AUC = 1.0)
+class BM19 (AUC = 1.0)
+class AF04 (AUC = 1.0)
+0.2
+class BF32 (AUC = 1.0)
+class AM08 (AUC =0.9939)
+class BF01 (AUC = 1.0)
+class BM06 (AUC = 1.0)
+class AM14 (AUC = 1.0)
+class BM07 (AUC = 1.0)
+0.0
+class BF15 (AUC =0.9949)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateROCcurve (emo)
+1.0
+0.8
+0.6
+true positive rate
+0.4
+0.2
+class AF (AUC =0.9948)
+classAN (AUC =0.9921)
+class DI (AUC = 0.9972)
+class HA (AUC = 0.9959)
+class NE (AUC = 0.9894)
+class SA (AUC = 0.9939)
+0.0
+classSU (AUC = 0.9916)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateRoC curve (pose)
+class FL (AUC = 0.459)
+1.0
+class FR (AUC = 0.4088)
+class HL (AUC = 0.0797)
+No skill
+0.8
+0.6
+true positive rate
+0.4
+0.2
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateROC curve (id)
+1.0
+class AM23 (AUC = 1.0)
+0.8 -
+class AF05 (AUC = 1.0)
+class BM13 (AUC = 1.0)
+class AF13 (AUC = 0.9951)
+class BF28 (AUC = 1.0)
+class BM08 (AUC = 1.0)
+class AF31 (AUC = 1.0)
+0.6
+class BM35 (AUC = 1.0)
+true positive rate
+class BF33 (AUC = 1.0)
+class BM18 (AUC = 1.0)
+class BF13 (AUC = 1.0)
+class AF19 (AUC =0.9961)
+class AM26 (AUC = 0.9961)
+class BM12 (AUC = 1.0)
+0.4
+class AF16 (AUC = 1.0)
+class AF23 (AUC = 1.0)
+class BM01 (AUC = 1.0)
+class BM03 (AUC = 0.9951)
+class BF10 (AUC = 1.0)
+class BM19 (AUC = 1.0)
+class AF04 (AUC = 1.0)
+0.2
+class BF32 (AUC = 1.0)
+class AM08 (AUC = 0.9989)
+class BF01 (AUC = 1.0)
+class BM06 (AUC = 1.0)
+class AM14 (AUC = 1.0)
+class BM07 (AUC = 1.0)
+0.0
+class BF15 (AUC =0.999)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateRoCcurve(emo)
+1.0
+0.8
+0.6
+true positive rate
+0.4
+0.2
+class AF (AUC = 1.0)
+class AN (AUC = 1.0)
+class DI (AUC = 1.0)
+class HA (AUC = 1.0)
+class NE (AUC = 1.0)
+class SA (AUC = 0.9996)
+0.0
+class SU (AUC = 1.0)
+No skill
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rate18
+18
+a) Pre-augmentation Confusion (pose)
+b) Pre-augmentation Confusion (id)
+c) Pre-augmentation Confusion 
+(emotion)
+d) Post-augmentation Confusion (pose)
+e) Post-augmentation Confusion (id)
+f) Post-augmentation Confusion 
+(emotion)
+Figure 10. Confusion matrices for MagFace FRL. As the confusion matrices indicate, post-augmentation matrices 
+(d, e, and f) have significant improvements in comparison to pre-augmentation matrices (a, b, and c) for pose, 
+identity, and emotion, respectively.
+
+Confusionmatrix(pose
+10000
+8000
+6000
+4000
+2000
+FL
+HL
+HR
+SConfusionmatrix(id)
+AF05
+BF04
+AM31
+BM13
+BF11
+1000
+AF01
+AM15
+AF03
+BM16
+AF10
+800
+AM22
+AM13
+BM05
+BM23
+600
+AM34 -
+BF12
+AF07
+AM05
+AF27
+400
+BF14 
+BM29
+AM01
+AF16
+AF32
+200
+AF26 
+BM07
+AF29
+BF16
+AF05
+BF04
+AM31
+BM13
+BF11
+AF01
+AM15
+AF03
+BM16
+AF10
+AM22
+AM13
+BM05
+BM23
+AM34
+BF12
+AF07
+AM05
+AF27
+BF14
+BM29
+AM01
+AF16
+AF32
+AF26
+BM07
+AF29
+BF16Confusionmatrix(emo)
+4
+4000
+3500
+3
+3000
+2500
+2000
+1500
+1000
+ SA
+500
+SU
+0
+AF
+AN
+DI
+HA
+NE
+SA
+SUConfusionmatrix(pose)
+60
+50
+40
+30
+20
+S
+10
+0
+HL
+HR
+SConfusionmatrix(id)
+10
+AF05
+BF04
+AM31
+BM13
+BF11
+AF01
+8
+AM15
+AF03
+BM16
+AF10
+AM22
+AM13
+6
+BM05
+BM23
+AM34 
+BF12
+AF07
+4
+AM05
+AF27
+BF14 
+BM29
+AM01
+AF16
+2
+AF32
+AF26
+BM07
+AF29
+BF16
+AF05
+BF04
+AM31
+BM13
+BF11
+AF01
+AM15
+AF03
+BM16
+AF10
+AM22
+AM13
+BM05
+BM23
+AM34
+BF12
+AF07
+AM05
+AF27
+BF14
+BM29
+AM01
+AF16
+AF32
+AF26
+BM07
+AF29
+BF16Confusionmatrix(emo)
+-35
+4
+30
+3
+ 25
+- 20
+15
+10
+ SA
+- 5
+SU
+0
+AF
+AN
+DI
+HA
+NE
+SA
+sU19
+19
+a)
+Pre-augmentation PRC (pose)
+b)
+Pre-augmentation PRC (id)
+c)
+Pre-augmentation PRC 
+(emotion)
+d)
+Post-augmentation PRC 
+(pose)
+e)
+Post-augmentation PRC (id)
+f)
+Post-augmentation PRC 
+(emotion)
+Figure 11. PRC curves for ArcFace FRL. As the curves indicate, post-augmentation PRC curves (d, e, and f) have 
+significant improvements in comparison to pre-augmentation PRC curves (a, b, and c) for pose, identity, and 
+emotion, respectively.
+
+precision vs.recall curve (pose
+1.0
+0.8
+0.6
+class FL
+precision
+class FR
+class HL
+class HR
+class S
+0.4
+0.2 
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+recallprecision vs.recall curve (id)
+1.0
+0.8
+class BM15
+class BF09
+class BM14
+class BF07
+class AM22
+class AM23
+0.6
+class BM18
+class BM26
+precision
+class AF14
+class BM11
+class AF10
+class BM16
+class AF33
+0.4
+class BF10
+class AF20
+class BF02
+class BM08
+class BF28
+class AM35
+class AM07
+0.2 
+class BF03
+class BM31
+class BF17
+class AM10
+class AF02
+class BM06
+0.0
+class BM23
+class BM13
+0.0
+0.2 
+0.4 
+0.6 
+0.8 
+1.0
+recallprecision vs.recall curve (emo)
+1.0
+0.8
+precision
+0.6
+0.4
+class AF
+class AN
+class DI
+class HA
+0.2
+class NE
+class SA
+class SU
+0.0
+0.2 
+0.4 
+0.6 
+0.8
+1.0
+recallprecision vs.recall curve (pose)
+class FL
+1.0
+class FR
+class HL
+0.8
+0.6
+precision
+0.4
+0.2 
+0.0
+0.0
+0.2 
+0.4
+0.6
+0.8
+1.0
+recallprecision vs.recall curve (id)
+1.0
+class BM15
+0.9
+class BF09
+class BM14
+class BF07
+class AM22
+class AM23
+class BM18
+class BM26
+precision
+class AF14
+0.8
+class BM11
+class AF10
+class BM16
+class AF33
+class BF10
+class AF20
+class BF02
+class BM08
+0.7
+class BF28
+class AM35
+class AM07
+class BF03
+class BM31
+class BF17
+class AM10
+class AF02
+0.6
+class BM06
+class BM23
+class BM13
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+recallprecision vs.recall curve (emo)
+1.2
+1.0
+0.8
+precision
+0.6
+0.4
+class AF
+0.2 
+class AN
+class DI
+class HA
+class NE
+class SA
+class SU
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+recall20
+20
+a)
+Pre-augmentation ROC (pose)
+b)
+Pre-augmentation ROC (id)
+c)
+Pre-augmentation ROC 
+(emotion)
+d)
+Post-augmentation ROC 
+(pose)
+e)
+Post-augmentation ROC (id)
+f)
+Post-augmentation ROC 
+(emotion)
+Figure 12. ROC curves for ArcFace FRL. As the curves indicate, post-augmentation ROC curves (d, e, and f) have 
+significant improvements in comparison to pre-augmentation ROC curves (a, b, and c) for pose, identity, and 
+emotion, respectively.
+
+RoCcurve(pose)
+1.0
+0.8
+0.6
+true positive rate
+0.4
+0.2
+class FL (AUC = 0.9978)
+class FR (AUC = 0.2198)
+class HL (AUC = 0.9953)
+class HR (AUC = 0.9998)
+0.0
+classS (AUC=0.9981)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateROC curve (id)
+1.0
+class BM15 (AUC = 1.0)
+0.8 -
+class BF09 (AUC = 1.0)
+class BM14 (AUC = 1.0)
+class BF07 (AUC = 1.0)
+class AM22 (AUC = 1.0)
+class AM23 (AUC = 0.9782)
+class BM18 (AUC = 1.0)
+0.6
+class BM26 (AUC = 1.0)
+true positive rate
+class AF14 (AUC = 1.0)
+class BM11 (AUC = 1.0)
+class AF10 (AUC = 0.9838)
+class BM16 (AUC = 1.0)
+class AF33 (AUC = 1.0)
+class BF10 (AUC = 0.9841)
+0.4
+class AF20 (AUC = 1.0)
+class BF02 (AUC = 0.9916)
+class BM08 (AUC = 1.0)
+class BF28 (AUC = 1.0)
+class AM35 (AUC = 1.0)
+class AM07 (AUC = 1.0)
+class BF03 (AUC = 1.0)
+0.2
+class BM31 (AUC = 1.0)
+class BF17 (AUC = 1.0)
+class AM10 (AUC = 1.0)
+class AF02 (AUC = 0.9875)
+class BM06 (AUC = 1.0)
+classBM23(AUC=0.9827)
+0.0
+class BM13 (AUC = 1.0)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateROCcurve (emo)
+1.0
+0.8
+0.6
+true positive rate
+0.4
+0.2
+classAF(AUC =0.9885)
+clasS AN (AUC = 0.9983)
+class DI (AUC = 0.9975)
+class HA (AUC = 0.9998)
+class NE (AUC =0.9901)
+class SA (AUC = 0.9947)
+0.0
+class SU (AUC = 0.9968)
+No skill
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateRoCcurve(pose)
+class FL (AUC = 0.1322)
+1.0
+class FR (AUC = 0.7495)
+class HL (AUC = 0.3596)
+No skill
+0.8
+0.6
+true positive rate
+0.4
+0.2
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+false positiverateROC curve (id)
+1.0
+class BM15 (AUC = 1.0)
+0.8 -
+class BF09 (AUC = 1.0)
+class BM14 (AUC = 1.0)
+class BF07 (AUC = 1.0)
+class AM22 (AUC = 1.0)
+class AM23 (AUC =0.9952)
+class BM18 (AUC = 1.0)
+0.6
+class BM26 (AUC = 1.0)
+true positive rate
+class AF14 (AUC = 1.0)
+class BM11 (AUC = 1.0)
+class AF10 (AUC = 0.9987)
+class BM16 (AUC = 1.0)
+class AF33 (AUC = 1.0)
+class BF10 (AUC = 0.9979)
+0.4
+class AF20 (AUC = 1.0)
+class BF02 (AUC = 1.0)
+class BM08 (AUC = 1.0)
+class BF28 (AUC = 1.0)
+class AM35 (AUC = 1.0)
+class AM07 (AUC = 1.0)
+class BF03 (AUC = 1.0)
+0.2
+claSs BM31 (AUC = 1.0)
+class BF17 (AUC = 1.0)
+class AM10 (AUC = 1.0)
+class AF02 (AUC = 1.0)
+class BM06 (AUC = 1.0)
+class BM23 (AUC = 0.994)
+0.0
+class BM13 (AUC = 1.0)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateRoCcurve(emo)
+1.0
+0.8
+0.6
+truepositive rate
+0.4
+0.2
+class AF (AUC = 1.0)
+class AN (AUC = 1.0)
+class DI (AUC = 1.0)
+class HA (AUC = 1.0)
+class NE (AUC = 1.0)
+class SA (AUC = 1.0)
+0.0
+class SU (AUC = 1.0)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rate21
+21
+a)
+Pre-augmentation Confusion 
+(pose)
+b)
+Pre-augmentation Confusion 
+(id)
+c)
+Pre-augmentation Confusion 
+(emotion)
+d)
+Post-augmentation Confusion 
+(pose)
+e)
+Post-augmentation Confusion 
+(id)
+f)
+Post-augmentation Confusion 
+(emotion)
+Figure 13. Confusion matrices for ArcFace FRL. As the confusion matrices indicate, post-augmentation matrices (d, 
+e, and f) have significant improvements in comparison to pre-augmentation matrices (a, b, and c) for pose, identity, 
+and emotion, respectively.
+
+Confusionmatrix(pose)
+10000
+L
+8000
+R
+6000
+主
+4000
+2000
+S
+FL
+FR
+HL
+HR
+sConfusionmatrix(id)
+BM15
+BF09
+BM14
+BF07
+AM22
+1000
+AM23
+BM18
+BM26
+AF14 
+800
+BM11
+AF10
+BM16
+AF33
+BF10
+600
+AF20 
+BF02
+BM08
+BF28
+AM35
+400
+AM07
+BF03
+BM31
+BF17
+AM10
+200
+AF02
+BM06
+BM23
+BM13
+BM15
+BF09
+BM14
+BF07
+AM22
+AM23
+BM18
+BM26
+AF14
+BM11
+AF10
+BM16
+AF33
+BF10
+AF20
+BF02
+BM08
+BF28
+AM35
+AM07
+BF03
+BM31
+BF17
+AM10
+AF02
+BM06
+BM23
+BM13Confusionmatrix(emo)
+4
+4000
+3
+3500
+3000
+2500
+2000
+NE
+1500
+1000
+ SA
+500
+SU
+0
+AF
+AN
+DI
+HA
+NE
+SA
+sUConfusion matrix(pose)
+80
+ 70
+60
+ 50
+40
+-30
+20
+S
+10
+0
+HL
+HR
+SConfusionmatrix(id)
+BM15
+BF09
+BM14
+10
+BF07
+AM22
+AM23
+BM18
+BM26
+AF14
+BM11
+AF10
+BM16
+AF33
+6
+BF10
+AF20 
+BF02
+BM08
+BF28
+AM35
+AM07
+BF03
+BM31
+BF17
+2
+AM10
+AF02
+BM06
+BM23
+BM13
+BM15
+BF09
+BM14
+BF07
+AM22
+AM23
+BM18
+BM26
+AF14
+BM11
+AF10
+BM16
+AF33
+BF10
+AF20
+BF02
+BM08
+BF28
+AM35
+AM07
+BF03
+BM31
+BF17
+AM10
+AF02
+BM06
+BM23
+BM13Confusionmatrix(emo)
+-35
+4
+30
+3
+25
+20
+15
+10
+5
+0
+AF
+AN
+DI
+HA
+NE
+SA
+sU22
+22
+a)
+Pre-augmentation PRC (pose)
+b)
+Pre-augmentation PRC (id)
+c)
+Pre-augmentation PRC 
+(emotion)
+d)
+Post-augmentation PRC 
+(pose)
+e)
+Post-augmentation PRC (id)
+f)
+Post-augmentation PRC 
+(emotion)
+Figure 14. PRC curves for CosFace FRL. As the curves indicate, post-augmentation PRC curves (d, e, and f) have 
+significant improvements in comparison to pre-augmentation PRC curves (a, b, and c) for pose, identity, and 
+emotion, respectively.
+
+precision vs.recall curve (pose)
+1.0
+0.8
+0.6
+class FL
+precision
+class FR
+class HL
+class HR
+class S
+0.4
+0.2 
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+recallprecision vs.recall curve (id)
+1.0
+0.8 
+class BF25
+class AM30
+classBM13
+class AM33
+class BM21
+class BF14
+class BM19
+class BM17
+0.6
+precision
+class BF15
+class BF06
+class AM18
+class AF35
+class BF13
+class BM22
+class BM23
+0.4
+class BM25
+class AF08
+class AF26
+class BM33
+class AM21
+class AMo1
+class AF14
+class AF32
+0.2
+class BM28
+class AM10
+class BM29
+class BM05
+class AM06
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+recallprecision vs.recall curve (emo)
+1.0
+0.9
+0.8
+0.7
+precision
+0.6
+0.5
+0.4 
+class AF
+0.3
+class AN
+class DI
+class HA
+class NE
+0.2
+class SA
+class SU
+0.0
+0.2 
+0.4 
+0.6 
+0.8 
+1.0
+recallprecision vs.recall curve (pose
+1.2
+class FL
+class FR
+class HL
+class HR
+class S
+1.0
+0.8
+precision
+0.6
+0.4
+0.2 
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+recallprecision vs.recall curve (id)
+1.0
+class E
+BF25
+class AM30
+class E
+BM13
+class AM33
+0.9
+class BM21
+class BF14
+class BM19
+class BM17
+class BF15
+class BF06
+0.8
+class AM18
+class AF35
+precision
+class BF13
+class BM22
+class BM23
+class BM25
+class AF08
+0.7
+class AF26
+class BM33
+class AM21
+class AMol
+class AF14
+class AF32
+class BM28
+0.6
+class AM10
+class BM29
+class BM05
+class AM06
+0.5
+0.0
+0.2 
+0.4 
+0.6
+0.8
+1.0
+recallprecision vs.recall curve (emo)
+1.0
+0.9
+0.8
+0.7
+recision
+ 0.6
+0.5
+0.4
+class AF
+class AN
+class DI
+class HA
+0.3
+class NE
+class SA
+class SU
+0.0
+0.2 
+0.4
+0.6
+0.8
+1.0
+recall23
+23
+a)
+Pre-augmentation ROC (pose)
+b)
+Pre-augmentation ROC (id)
+c)
+Pre-augmentation ROC 
+(emotion)
+d) Post-augmentation ROC (pose)
+e) Post-augmentation ROC (id)
+f) Post-augmentation ROC (emotion)
+Figure 15. ROC curves for CosFace FRL. As the curves indicate, post-augmentation ROC curves (d, e, and f) have 
+significant improvements in comparison to pre-augmentation ROC curves (a, b, and c) for pose, identity, and 
+emotion, respectively.
+
+RoC curve (pose)
+1.0
+0.8 -
+0.6
+true positive rate
+0.4
+0.2
+class FL (AUC = 0.5661)
+class FR (AUC = 0.7062)
+class HL (AUC = 0.9998)
+class HR (AUC =0.9997)
+0.0
+class S (AUC = 1.0)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateROC curve (id)
+1.0
+class BF25 (AUC = 0.9997)
+0.8
+class AM30 (AUC = 1.0)
+class BM13 (AUC = 0.9996)
+class AM33 (AUC = 0.9969)
+class BM21 (AUC = 0.9795)
+class BF14 (AUC = 0.9894)
+class BM19 (AUC = 0.9983)
+0.6
+class BM17 (AUC = 0.9998)
+truepositive rate
+classBF15(AUC =0.9907)
+class BF06 (AUC = 0.994)
+class AM18 (AUC = 0.9926)
+class AF35 (AUC =0.9998)
+class BF13 (AUC = 0.9998)
+class BM22 (AUC =0.9999)
+0.4
+class BM23 (AUC =0.9999)
+class BM25 (AUC =0.9997)
+class AF08 (AUC =0.9986)
+class AF26 (AUC =0.9952)
+class BM33 (AUC = 0.9912)
+class AM21 (AUC = 0.9817)
+class AM01 (AUC = 0.9994)
+0.2
+class AF14 (AUC =0.9908)
+class AF32 (AUC = 0.9996)
+class BM28 (AUC = 0.9996)
+class AM10 (AUC =0.9999)
+class BM29(AUC =0.9985)
+class BM05 (AUC =1.0)
+0.0
+class AM06 (AUC = 0.9988)
+No skill
+0.0 
+0.2 
+0.4
+0.6
+0.8
+1.0
+false positive rateROCcurve (emo)
+1.0
+0.8
+0.6
+true positive rate
+0.4
+0.2
+claSSAF (AUC =0.9749)
+class AN (AUC = 0.9835)
+class DI (AUC = 0.9897)
+class HA (AUC = 0.9994)
+class NE (AUC =0.9949)
+class SA (AUC = 0.9814)
+0.0
+class SU (AUC = 0.9931)
+No skill
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateROCcurve(pose)
+1.0
+0.8
+0.6
+true positive rate
+0.4
+0.2 
+class FL (AUC = 1.0)
+class FR (AUC = 1.0)
+class HL (AUC = 1.0)
+class HR (AUC = 1.0)
+0.0
+class S (AUC = 1.0)
+No skill
+0.0
+0.2 
+0.4
+0.6
+0.8
+1.0
+false positive rateROC curve (id)
+1.0
+class BF25 (AUC = 1.0)
+0.8 -
+class AM30 (AUC = 1.0)
+class BM13 (AUC = 1.0)
+class AM33 (AUC = 1.0)
+class BM21 (AUC = 1.0)
+class BF14 (AUC = 0.9932)
+class BM19 (AUC = 1.0)
+0.6
+class BM17 (AUC = 1.0)
+true positive rate
+class BF15 (AUC = 1.0)
+class BF06 (AUC = 1.0)
+class AM18 (AUC = 1.0)
+class AF35 (AUC = 1.0)
+class BF13 (AUC = 1.0)
+class BM22 (AUC = 1.0)
+0.4
+class BM23 (AUC = 1.0)
+class BM25 (AUC = 1.0)
+class AF08 (AUC = 1.0)
+class AF26 (AUC = 1.0)
+class BM33 (AUC = 1.0)
+class AM21 (AUC = 1.0)
+class AM01 (AUC = 1.0)
+0.2
+clasS AF14 (AUC = 0.9943)
+class AF32 (AUC = 1.0)
+class BM28 (AUC = 1.0)
+class AM10 (AUC = 1.0)
+class BM29 (AUC = 1.0)
+class BM05 (AUC = 1.0)
+0.0
+class AM06 (AUC = 1.0)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rateROCcurve (emo)
+1.0
+0.8
+0.6
+true positive rate
+0.4
+0.2
+classAF (AUC =0.9853)
+class AN (AUC = 0.9996)
+class DI (AUC = 0.9965)
+class HA (AUC = 1.0)
+class NE (AUC =0.9932)
+class SA (AUC = 0.9998)
+0.0
+class SU (AUC = 1.0)
+No skill
+0.0 
+0.2
+0.4
+0.6
+0.8
+1.0
+false positive rate24
+24
+a)
+Pre-augmentation Confusion 
+(pose)
+b)
+Pre-augmentation Confusion 
+(id)
+c)
+Pre-augmentation Confusion 
+(emotion)
+d)
+Post-augmentation Confusion 
+(pose)
+e)
+Post-augmentation Confusion 
+(id)
+f)
+Post-augmentation Confusion 
+(emotion)
+Figure 16. Confusion matrices for CosFace FRL. As the confusion matrices indicate, post-augmentation matrices 
+(d, e, and f) have significant improvements in comparison to pre-augmentation matrices (a, b, and c) for the pose, 
+identity, and emotion, respectively.
+4.4. Discussion
+FR has long been a popular field of study among specialists and academics in the field of biometric 
+recognition and it has the advantages of being non-contact, amiable, and simple to accept. Although 
+remarkable performance has been shown by some state-of-the-art approaches presented in the literature, 
+in real-world scenarios, there still exists the demand to improve such algorithms. For better handling such 
+uncontrolled contexts especially when we face a lack of data, DA techniques are introduced to increase 
+the number of training samples by applying different manipulations. Classical techniques for image 
+transformations such as rotation, skewing, flipping, blurring, etc., and also GAN-based ones which utilize 
+deep generative models and disentangled features to create more realistically transformed face images 
+have well been studied for DA in the domain of FR. However, these techniques have their drawbacks. 
+Classical techniques mostly manipulate face images in a way that distorts their alignment causing FR 
+algorithms’ performance when generating distinct representative embeddings dramatically decrease. To 
+prove this, we have experimented with four different transformations, namely, horizontal flip, skewing, 
+blurring, and notifying. We augmented samples in the KDEF dataset and increased the training dataset 
+size to be 4 times more than the original dataset and used different FR algorithms for generating 
+
+Confusion matrix (pose)
+10000
+8000
+R
+6000
+4000
+2000
+S
+FL
+FR
+HL
+HRConfusionmatrix(id)
+BF25
+AM30
+1200
+BM13
+AM33
+BM21
+BF14
+1000
+BM19
+BM17
+BF15
+BF06
+AM18
+800
+AF35
+BF13
+BM22
+BM23
+600
+BM25
+AF08
+AF26
+BM33
+400
+AM21
+AM01
+AF14
+AF32
+BM28
+200
+AM10
+BM29
+BM05
+AM06
+BF25
+AM30
+BM13
+AM33
+BM21
+BF14
+BM19
+BM17
+BF15
+BF06
+AM18
+AF35
+BF13
+BM22
+M23
+BM25
+AF08
+AF26
+BM33
+AM21
+AM01
+AF14
+AF32
+BM28
+AM10
+BM29
+BM05
+AM06Confusionmatrix(emo)
+4000
+4
+3500
+3
+3000
+2500
+2000
+NE
+1500
+1000
+ SA
+500
+SU
+0
+AF
+AN
+DI
+HA
+NE
+SA
+SUConfusion matrix (pose)
+- 80
+- 70
+60
+50
+-40
+-30
+- 20
+10
+0
+FL
+FR
+HL
+HR
+SConfusionmatrix(id)
+BF25
+AM30
+BM13
+10
+AM33
+BM21
+BF14 
+BM19
+BM17
+BF15
+BF06
+AM18
+AF35
+BF13
+6
+BM22
+BM23
+BM25
+AF08
+AF26
+BM33
+AM21
+AM01
+AF14
+AF32
+2
+BM28
+AM10
+BM29
+BM05
+AM06
+BF25
+AM30
+BM13
+AM33
+BM21
+BF14
+BM19
+BM17
+BF15
+BF06
+AM18
+AF35
+BF13
+BM22
+BM23
+BM25
+AF08
+AF26
+BM33
+AM21
+AM01
+AF14
+AF32
+BM28
+AM10
+BM29
+BM05
+AM06Confusionmatrix(emo)
+35
+4
+30
+3
+- 25
+20
+15
+10
+- 5
+0
+AF
+AN
+DI
+HA
+NE
+SA
+SU25
+25
+embeddings. Then we classified the embeddings using SVM with respect to their identities. Table 6 
+details the results achieved by this experiment. 
+ 
+Table 4. Evaluation of MagFace, ArcFace, and CosFace using traditional augmentation techniques on the 
+KDEF dataset. Post-augmentation accuracy scores achieved denote the ineffectiveness of these techniques 
+for FR tasks.
+FR Algorithm
+Accuracy Score
+Pre-augmentation
+Post-augmentation
+MagFace
+20.49%
+18.54%
+ArcFace
+20.12%
+17.01%
+CosFace
+18.19%
+11.33%
+Table 4 shows that augmenting the face images using the classical approaches does not result in any 
+improvement and they, in fact, degrade the quality of embeddings. For instance, for the MagFace 
+algorithm, the accuracy obtained by SVM is decreased by 2% after applying DA.
+Moreover, we conducted another experiment using three state-of-the-art generative-based algorithms 
+namely, CPM [41], AttGAN [81], and PSGAN [40]. Following the previous experiments, we augmented 
+the face images and obtained the classification accuracy before and after augmentation. Table 7 shows the 
+results achieved by this experiment.
+Table 5. Evaluation of augmentation techniques using GANs on the KDEF dataset. In the best case, the 
+post-augmentation accuracy has increased a little and in some cases, it has caused a degradation in 
+accuracy.
+Algorithm
+Accuracy Score
+Pre-augmentation
+Post-augmentation
+CPM [40]
+20.49 %
+17.82 %
+AttGAN
+20.49 %
+26.70 %
+PSGAN [39]
+20.49 %
+23.40 %
+Based on Table 5, it can be claimed that these generative models do not contribute to classification 
+accuracy improvement. Therefore, in order to address this issue, in this paper, we propose a new 
+algorithm, named FRA, which effectively augments the training data for FR algorithms. FRA functions 
+with original embeddings and manipulates them in a way to be representative of the same identity of the 
+embedding and also a differed postural information existent in these representational embeddings. Results 
+achieved by our extensive experiments indicate the efficacy of FRA in augmenting samples in the FR 
+domain.
+5.Conclusion
+
+26
+26
+Since data scarcity is a common problem in deep learning-based solutions, it can be very challenging to 
+build up FR systems that are robust enough to recognize face images with extreme diversity. In this paper, 
+we proposed a novel method that augments the face data in latent space. The proposed method utilizes 
+two major components, one of which is an autoencoder and the other is a ViT-based model. The former is 
+used to encode the binarized input images consisting of sparse facial landmarks into a latent space. The 
+latter is used for extracting features from the combined embeddings coming from a pre-trained FRL 
+algorithm and the autoencoder part of our model. Lastly, the output of the proposed model is an 
+embedding representing the main identity with the same emotion but with a different posture. This way, 
+we managed to improve the classification accuracy by 9.52, 10.04, and 16.60, in comparison with the 
+based models of MagFace, ArcFace, and CosFace, respectively.
+References
+[1] P. Terhorst, J.N. Kolf, N. Damer, F. Kirchbuchner, A. Kuijper, SER-FIQ: Unsupervised estimation of face image 
+quality based on stochastic embedding robustness,  Proceedings of the IEEE/CVF conference on computer 
+vision and pattern recognition2020, pp. 5651-5660.
+[2] M. Wang, W. Deng, Deep face recognition: A survey, Neurocomputing, 429 (2021) 215-244.
+[3] W. Ali, W. Tian, S.U. Din, D. Iradukunda, A.A. Khan, Classical and modern face recognition approaches: a 
+complete review, Multimedia tools and applications, 80 (2021) 4825-4880.
+[4] A. Krizhevsky, I. Sutskever, G.E. Hinton, Imagenet classification with deep convolutional neural networks, 
+Communications of the ACM, 60 (2017) 84-90.
+[5] Y. Taigman, M. Yang, M.A. Ranzato, L. Wolf, Deepface: Closing the gap to human-level performance in face 
+verification,  Proceedings of the IEEE conference on computer vision and pattern recognition2014, pp. 1701-
+1708.
+[6] Q. Meng, S. Zhao, Z. Huang, F. Zhou, Magface: A universal representation for face recognition and quality 
+assessment,  Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition2021, pp. 
+14225-14234.
+[7] Q. Cao, L. Shen, W. Xie, O.M. Parkhi, A. Zisserman, Vggface2: A dataset for recognising faces across pose and 
+age,  2018 13th IEEE international conference on automatic face & gesture recognition (FG 2018), IEEE2018, 
+pp. 67-74.
+[8] C. Yan, L. Meng, L. Li, J. Zhang, Z. Wang, J. Yin, J. Zhang, Y. Sun, B. Zheng, Age-invariant face recognition 
+by multi-feature fusionand decomposition with self-attention, ACM Transactions on Multimedia Computing, 
+Communications, and Applications (TOMM), 18 (2022) 1-18.
+[9] Y. Zheng, D.K. Pal, M. Savvides, Ring loss: Convex feature normalization for face recognition,  Proceedings of 
+the IEEE conference on computer vision and pattern recognition2018, pp. 5089-5097.
+[10] X. Zhang, Z. Fang, Y. Wen, Z. Li, Y. Qiao, Range loss for deep face recognition with long-tailed training data,  
+Proceedings of the IEEE International Conference on Computer Vision2017, pp. 5409-5418.
+[11] C. Peng, N. Wang, J. Li, X. Gao, DLFace: Deep local descriptor for cross-modality face recognition, Pattern 
+Recognition, 90 (2019) 161-171.
+[12] A. Bhattacharyya, S. Chatterjee, S. Sen, A. Sinitca, D. Kaplun, R. Sarkar, A deep learning model for classifying 
+human facial expressions from infrared thermal images, Scientific Reports, 11 (2021) 20696.
+[13] S. Gupta, K. Thakur, M. Kumar, 2D-human face recognition using SIFT and SURF descriptors of face’s feature 
+regions, The Visual Computer, 37 (2021) 447-456.
+[14] Y. Kortli, M. Jridi, A. Al Falou, M. Atri, A comparative study of CFs, LBP, HOG, SIFT, SURF, and BRIEF for 
+security and face recognition,  Advanced Secure Optical Image Processing for Communications, IOP 
+Publishing2018.
+[15] Y. Duan, J. Lu, J. Zhou, Uniformface: Learning deep equidistributed representation for face recognition,  
+Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition2019, pp. 3415-3424.
+
+27
+27
+[16] B. Lahasan, S.L. Lutfi, R. San-Segundo, A survey on techniques to handle face recognition challenges: 
+occlusion, single sample per subject and expression, Artificial Intelligence Review, 52 (2019) 949-979.
+[17] Y. Li, K. Guo, Y. Lu, L. Liu, Cropping and attention based approach for masked face recognition, Appl. Intell., 
+51 (2021) 3012-3025.
+[18] P. Li, L. Prieto, D. Mery, P.J. Flynn, On low-resolution face recognition in the wild: Comparisons and new 
+techniques, IEEE Transactions on Information Forensics and Security, 14 (2019) 2000-2012.
+[19] L. Song, D. Gong, Z. Li, C. Liu, W. Liu, Occlusion robust face recognition based on mask learning with 
+pairwise differential siamese network,  Proceedings of the IEEE/CVF International Conference on Computer 
+Vision2019, pp. 773-782.
+[20] Z. Lu, X. Jiang, A. Kot, Deep coupled resnet for low-resolution face recognition, IEEE Signal Processing 
+Letters, 25 (2018) 526-530.
+[21] J. Deng, S. Zafeririou, Arcface for disguised face recognition,  Proceedings of the IEEE/CVF International 
+Conference on Computer Vision Workshops2019, pp. 0-0.
+[22] J. Deng, J. Guo, N. Xue, S. Zafeiriou, Arcface: Additive angular margin loss for deep face recognition,  
+Proceedings of the IEEE/CVF conference on computer vision and pattern recognition2019, pp. 4690-4699.
+[23] Y. Srivastava, V. Murali, S.R. Dubey, A performance evaluation of loss functions for deep face recognition,  
+Computer Vision, Pattern Recognition, Image Processing, and Graphics: 7th National Conference, 
+NCVPRIPG 2019, Hubballi, India, December 22–24, 2019, Revised Selected Papers 7, Springer2020, pp. 322-
+332.
+[24] Y. Huang, Y. Wang, Y. Tai, X. Liu, P. Shen, S. Li, J. Li, F. Huang, Curricularface: adaptive curriculum 
+learning loss for deep face recognition,  proceedings of the IEEE/CVF conference on computer vision and 
+pattern recognition2020, pp. 5901-5910.
+[25] H. Wang, Y. Wang, Z. Zhou, X. Ji, D. Gong, J. Zhou, Z. Li, W. Liu, Cosface: Large margin cosine loss for 
+deep face recognition,  Proceedings of the IEEE conference on computer vision and pattern recognition2018, 
+pp. 5265-5274.
+[26] X. Wang, S. Wang, J. Wang, H. Shi, T. Mei, Co-mining: Deep face recognition with noisy labels,  Proceedings 
+of the IEEE/CVF International Conference on Computer Vision2019, pp. 9358-9367.
+[27] Z. Liu, P. Luo, X. Wang, X. Tang, Deep learning face attributes in the wild,  Proceedings of the IEEE 
+international conference on computer vision2015, pp. 3730-3738.
+[28] S.C. Wong, A. Gatt, V. Stamatescu, M.D. McDonnell, Understanding data augmentation for classification: 
+when to warp?,  2016 international conference on digital image computing: techniques and applications 
+(DICTA), IEEE2016, pp. 1-6.
+[29] J.-J. Lv, X.-H. Shao, J.-S. Huang, X.-D. Zhou, X. Zhou, Data augmentation for face recognition, 
+Neurocomputing, 230 (2017) 184-196.
+[30] I. Masi, A.T. Trần, T. Hassner, G. Sahin, G. Medioni, Face-specific data augmentation for unconstrained face 
+recognition, International Journal of Computer Vision, 127 (2019) 642-667.
+[31] D. Jiang, Y. Hu, S. Yan, L. Zhang, H. Zhang, W. Gao, Efficient 3D reconstruction for face recognition, Pattern 
+Recognition, 38 (2005) 787-798.
+[32] H. Mohammadzade, D. Hatzinakos, Projection into expression subspaces for face recognition from single 
+sample per person, IEEE Transactions on Affective Computing, 4 (2012) 69-82.
+[33] Y. Shen, P. Luo, J. Yan, X. Wang, X. Tang, Faceid-gan: Learning a symmetry three-player gan for identity-
+preserving face synthesis,  Proceedings of the IEEE conference on computer vision and pattern 
+recognition2018, pp. 821-830.
+[34] I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y. Bengio, 
+Generative adversarial networks, Communications of the ACM, 63 (2020) 139-144.
+[35] D. Lundqvist, A. Flykt, A. Öhman, Karolinska directed emotional faces, Cognition and Emotion, (1998).
+[36] P. Vincent, H. Larochelle, I. Lajoie, Y. Bengio, P.-A. Manzagol, L. Bottou, Stacked denoising autoencoders: 
+Learning useful representations in a deep network with a local denoising criterion, Journal of machine learning 
+research, 11 (2010).
+[37] J. Wang, L. Perez, The effectiveness of data augmentation in image classification using deep learning, 
+Convolutional Neural Networks Vis. Recognit, 11 (2017) 1-8.
+[38] T. Kim, M. Cha, H. Kim, J.K. Lee, J. Kim, Learning to discover cross-domain relations with generative 
+adversarial networks,  International conference on machine learning, PMLR2017, pp. 1857-1865.
+[39] I. Kemelmacher-Shlizerman, Transfiguring portraits, ACM Transactions on Graphics (TOG), 35 (2016) 1-8.
+
+28
+28
+[40] W. Jiang, S. Liu, C. Gao, J. Cao, R. He, J. Feng, S. Yan, Psgan: Pose and expression robust spatial-aware gan 
+for customizable makeup transfer,  Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern 
+Recognition2020, pp. 5194-5202.
+[41] T. Nguyen, A.T. Tran, M. Hoai, Lipstick ain't enough: beyond color matching for in-the-wild makeup transfer,  
+Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition2021, pp. 13305-
+13314.
+[42] C.-Y. Wu, R. Manmatha, A.J. Smola, P. Krahenbuhl, Sampling matters in deep embedding learning,  
+Proceedings of the IEEE international conference on computer vision2017, pp. 2840-2848.
+[43] Y. Movshovitz-Attias, A. Toshev, T.K. Leung, S. Ioffe, S. Singh, No fuss distance metric learning using 
+proxies,  Proceedings of the IEEE international conference on computer vision2017, pp. 360-368.
+[44] E. Ustinova, V. Lempitsky, Learning deep embeddings with histogram loss, Advances in Neural Information 
+Processing Systems, 29 (2016).
+[45] Q. Xiao, H. Luo, C. Zhang, Margin sample mining loss: A deep learning based method for person re-
+identification, arXiv preprint arXiv:1710.00478, (2017).
+[46] W. Chen, X. Chen, J. Zhang, K. Huang, Beyond triplet loss: a deep quadruplet network for person re-
+identification,  Proceedings of the IEEE conference on computer vision and pattern recognition2017, pp. 403-
+412.
+[47] A. Sanakoyeu, V. Tschernezki, U. Buchler, B. Ommer, Divide and conquer the embedding space for metric 
+learning,  Proceedings of the ieee/cvf conference on computer vision and pattern recognition2019, pp. 471-
+480.
+[48] Y. Bai, Y. Lou, F. Gao, S. Wang, Y. Wu, L.-Y. Duan, Group-sensitive triplet embedding for vehicle 
+reidentification, IEEE Transactions on Multimedia, 20 (2018) 2385-2399.
+[49] Y. Em, F. Gag, Y. Lou, S. Wang, T. Huang, L.-Y. Duan, Incorporating intra-class variance to fine-grained 
+visual recognition,  2017 IEEE International Conference on Multimedia and Expo (ICME), IEEE2017, pp. 
+1452-1457.
+[50] E. Smirnov, A. Oleinik, A. Lavrentev, E. Shulga, V. Galyuk, N. Garaev, M. Zakuanova, A. Melnikov, Face 
+representation learning using composite mini-batches,  Proceedings of the IEEE/CVF International Conference 
+on Computer Vision Workshops2019, pp. 0-0.
+[51] Y. Shi, X. Yu, K. Sohn, M. Chandraker, A.K. Jain, Towards universal representation learning for deep face 
+recognition,  Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition2020, pp. 
+6817-6826.
+[52] F. Schroff, D. Kalenichenko, J. Philbin, Facenet: A unified embedding for face recognition and clustering,  
+Proceedings of the IEEE conference on computer vision and pattern recognition2015, pp. 815-823.
+[53] W. Liu, Y. Wen, Z. Yu, M. Li, B. Raj, L. Song, Sphereface: Deep hypersphere embedding for face recognition,  
+Proceedings of the IEEE conference on computer vision and pattern recognition2017, pp. 212-220.
+[54] G.B. Huang, M. Mattar, T. Berg, E. Learned-Miller, Labeled faces in the wild: A database forstudying face 
+recognition in unconstrained environments,  Workshop on faces in'Real-Life'Images: detection, alignment, and 
+recognition2008.
+[55] L. Wolf, T. Hassner, I. Maoz, Face recognition in unconstrained videos with matched background similarity,  
+CVPR 2011, IEEE2011, pp. 529-534.
+[56] T. Zheng, W. Deng, J. Hu, Cross-age lfw: A database for studying cross-age face recognition in unconstrained 
+environments, arXiv preprint arXiv:1708.08197, (2017).
+[57] T. Zheng, W. Deng, Cross-pose lfw: A database for studying cross-pose face recognition in unconstrained 
+environments, Beijing University of Posts and Telecommunications, Tech. Rep, 5 (2018).
+[58] S. Moschoglou, A. Papaioannou, C. Sagonas, J. Deng, I. Kotsia, S. Zafeiriou, Agedb: the first manually 
+collected, in-the-wild age database,  proceedings of the IEEE conference on computer vision and pattern 
+recognition workshops2017, pp. 51-59.
+[59] S. Sengupta, J.-C. Chen, C. Castillo, V.M. Patel, R. Chellappa, D.W. Jacobs, Frontal to profile face verification 
+in the wild,  2016 IEEE winter conference on applications of computer vision (WACV), IEEE2016, pp. 1-9.
+[60] K. Cong, M. Zhou, Face Dataset Augmentation with Generative Adversarial Network,  Journal of Physics: 
+Conference Series, IOP Publishing2022, pp. 012035.
+[61] A. Kammoun, R. Slama, H. Tabia, T. Ouni, M. Abid, Generative Adversarial Networks for face generation: A 
+survey, ACM Computing Surveys, 55 (2022) 1-37.
+[62] G. Bradski, The openCV library, Dr. Dobb's Journal: Software Tools for the Professional Programmer, 25 
+(2000) 120-123.
+
+29
+29
+[63] D.E. Rumelhart, G.E. Hinton, R.J. Williams, Learning internal representations by error propagation, California 
+Univ San Diego La Jolla Inst for Cognitive Science1985.
+[64] D. Bank, N. Koenigstein, R. Giryes, Autoencoders, arXiv preprint arXiv:2003.05991, (2020).
+[65] Q. Meng, X. Xu, X. Wang, Y. Qian, Y. Qin, Z. Wang, C. Zhao, F. Zhou, Z. Lei, PoseFace: Pose-invariant 
+features and pose-adaptive loss for face recognition, arXiv preprint arXiv:2107.11721, (2021).
+[66] T. Lin, Y. Wang, X. Liu, X. Qiu, A survey of transformers, AI Open, (2022).
+[67] N. Carion, F. Massa, G. Synnaeve, N. Usunier, A. Kirillov, S. Zagoruyko, End-to-end object detection with 
+transformers,  Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, 
+Proceedings, Part I 16, Springer2020, pp. 213-229.
+[68] H. Touvron, M. Cord, M. Douze, F. Massa, A. Sablayrolles, H. Jégou, Training data-efficient image 
+transformers & distillation through attention,  International conference on machine learning, PMLR2021, pp. 
+10347-10357.
+[69] F. Yang, H. Yang, J. Fu, H. Lu, B. Guo, Learning texture transformer network for image super-resolution,  
+Proceedings of the IEEE/CVF conference on computer vision and pattern recognition2020, pp. 5791-5800.
+[70] L. Ye, M. Rochan, Z. Liu, Y. Wang, Cross-modal self-attention network for referring image segmentation,  
+Proceedings of the IEEE/CVF conference on computer vision and pattern recognition2019, pp. 10502-10511.
+[71] A.M. Hafiz, S.A. Parah, R.U.A. Bhat, Attention mechanisms and deep learning for machine vision: A survey of 
+the state of the art, arXiv preprint arXiv:2106.07550, (2021).
+[72] Z. Niu, G. Zhong, H. Yu, A review on the attention mechanism of deep learning, Neurocomputing, 452 (2021) 
+48-62.
+[73] F. Chollet, Deep learning with Python, Simon and Schuster2021.
+[74] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A.N. Gomez, Ł. Kaiser, I. Polosukhin, Attention is 
+all you need, Advances in neural information processing systems, 30 (2017).
+[75] J.-B. Cordonnier, A. Loukas, M. Jaggi, On the relationship between self-attention and convolutional layers, 
+arXiv preprint arXiv:1911.03584, (2019).
+[76] N. Park, S. Kim, How do vision transformers work?, arXiv preprint arXiv:2202.06709, (2022).
+[77] N. Park, S. Kim, Blurs behave like ensembles: Spatial smoothings to improve accuracy, uncertainty, and 
+robustness,  International Conference on Machine Learning, PMLR2022, pp. 17390-17419.
+[78] I. Goodfellow, Y. Bengio, A. Courville, Deep learning, MIT press2016.
+[79] K. Sohn, Improved deep metric learning with multi-class n-pair loss objective, Advances in neural information 
+processing systems, 29 (2016).
+[80] C. Cortes, V. Vapnik, Support vector machine, Machine learning, 20 (1995) 273-297.
+[81] Z. He, W. Zuo, M. Kan, S. Shan, X. Chen, Attgan: Facial attribute editing by only changing what you want, 
+IEEE transactions on image processing, 28 (2019) 5464-5478.
+
diff --git a/AtFLT4oBgHgl3EQfFC_E/content/tmp_files/load_file.txt b/AtFLT4oBgHgl3EQfFC_E/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7853a82a9f2b1ee891f3c7c91ed5fd5a4c98b462
--- /dev/null
+++ b/AtFLT4oBgHgl3EQfFC_E/content/tmp_files/load_file.txt
@@ -0,0 +1,2303 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf,len=2302
+page_content='1  1  FRA: A novel Face Representation Augmentation algorithm for face recognition  Soroush Hashemifar1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Abdolreza Marefat2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Javad Hassannataj Joloudari3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='*,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Hamid Hassanpour4  1School of Computer Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Iran University of Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Tehran,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Iran  2Department of Artificial Intelligence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Technical and Engineering Faculty,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' South Tehran Branch,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Islamic  Azad University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Tehran,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Irans  3Department of Computer Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Faculty of Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' University of Birjand,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Birjand  9717434765,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Iran  4Faculty of Computer Engineering & Information Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shahrood University of Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Box 316, Shahrood, Iran  Corresponding author*: javad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='hassannataj@birjand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='ir  Abstract  A low amount of training data for many state-of-the-art deep learning-based Face Recognition (FR)  systems causes a marked deterioration in their performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Although a considerable amount of research  has addressed this issue by inventing new data augmentation techniques, using either input space  transformations or Generative Adversarial Networks (GAN) for feature space augmentations, these  techniques have yet to satisfy expectations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In this paper, we propose a novel method, named the Face  Representation Augmentation (FRA) algorithm, for augmenting face datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' To the best of our  knowledge, FRA is the first method that shifts its focus towards manipulating the face embeddings  generated by any face representation learning algorithm in order to generate new embeddings  representing the same identity and facial emotion but with an altered posture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Extensive experiments  conducted in this study convince the efficacy of our methodology and its power to provide noiseless,  completely new facial representations to improve the training procedure of any FR algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Therefore,  FRA is able to help the recent state-of-the-art FR methods by providing more data for training FR  systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The proposed method, using experiments conducted on the Karolinska Directed Emotional Faces  (KDEF) dataset, improves the identity classification accuracies by 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='52 %, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='04 %, and 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='60 %, in  comparison with the base models of MagFace, ArcFace, and CosFace, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Keywords:  Face Recognition, Face Embeddings, Face Representation Learning, Autoencoder, Vision Transformers,  Latent Space Data Augmentation, Facial Pose Reconstruction  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Introduction  Face images are one of the most popular biometric modalities which have been continuously utilized in  Face Recognition (FR) systems [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' It is used in a wide range of contexts with the aim of identity  authentication and its applications vary from daily life and finance to military and public security [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In  fact, in comparison with other biometrics, such as the fingerprint, iris, or retina which are ubiquitously  used for authorizing individuals, FR can provide us with the most convenient way to capture visual  information without the need for any extra activity from the subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In recent years, FR has been one of  2  2  the most proactively studied areas in Computer Vision [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Particularly, with the advent of deep learning  and architectures like Convolutional Neural Networks (CNNs) [4], a large number of efficient facial  recognition methods with outstanding performance have been invented to address this challenge [5-12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  These successful algorithms depend heavily on the performance of neural networks which use a cascade  of layers comprised of neurons that are able to learn different levels of abstractions and representations  from the input data [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These representations are more powerful substitutions for hand-crafted features  from facial attributes such as Scale-Invariant Feature Transform (SIFT) and Speeded Up Robust Features  (SURF) [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Their principal advantage is that they obviate the need for manually and exhaustively  searching for the best features representing one’s face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Moreover, the process of learning representations  via deep learning-based algorithms makes the generated features surprisingly discriminative in that the  inter-class diversity and intra-class compactness within the training data are all taken into account by the  network itself [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  However, there are still problematic scenarios in which FR systems fail to realize the expectations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' For  instance, in real-life situations, the imagery of a person’s face has a high chance of being in a variety of  facial expressions, occlusions, poor illumination, low resolution, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' [16-18], and all these factors cause  substantial degradation of the overall performance of the current FR algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Thus, different  approaches have been adopted to rectify the negative impact of such barriers in FR systems [19-21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Some have opted for experimenting and devising new loss functions whose capability to better feedback  to their neural network in the backpropagation step, enables the extracted deep features to be more  discriminative and clearly separable [2, 6, 9, 22-26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In addition to these works, different architectures  have been implemented to extract feature maps which are more useful in terms of facial representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Moreover, developing larger and more variant datasets has been one of the main stimuli which have been  pushing the boundaries in recent FR systems [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Nevertheless, although some of these benchmark  datasets can be found in large volumes, we often lack such a training set of images when it comes to real  use cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' A typical case would be a situation in which the goal is to train a deep learning-based method  on a private, in-house set of identities that have been chosen by a multimedia organization for video  indexing purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The data-gathering phase can be very time and labor-consuming and sometimes even  impossible, and it acts as an impediment in the way of achieving a tailored amount of training datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  These have motivated researchers to pave the way by introducing different data augmentation techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Data augmentation refers to a set of techniques that are used to increase the number of training datasets  without the loss of previously annotated data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The benefit of such methods is that it equips the trained  model with more generalizability and acts as a regularizer in the case of overfitting which is one of the  most frequent complications when dealing with a small amount of training data [28, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Overall, there  are two mainstream categories of methods for augmenting data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The first set of methods has the aim of  manipulating the data in the input space in that they simply take the input image and apply different  geometric transformations such as translations, cropping, vertical and horizontal flipping, rotation, etc  [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Even though these methods are proven to be extremely useful in some other challenges like image  classification, object detection, and image captioning in computer vision, in the case of FR they cannot be  as helpful as they expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The main reason is that in order for any FR system to capture a reliable visual  representation of a face crop image, the content should be aligned in terms of facial landmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This  means that any geometric alteration on these which conspicuously happens when one uses these classical  methods, can perturb the overall performance of FR pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These challenges have motivated the  researchers to shift their studies’ direction toward more modern and domain-specific solutions [31-33],  leading to the second set of methods, which are known to be Generative Adversarial Networks (GANs)  3  3  [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These methods are the well-known type of generative models which are used with the objective of  transforming the input data in feature space with the aim of generating new augmented image data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This  group of models is capable of adjusting the facial attributes existent in a face image such as hair style,  expression, posture, skin color, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' to a target style.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' However, in most cases, these generative models  cannot create realistic outputs and these models deal with the high complexities of reconstructing the  feature space to input space, without having any considerable improvement on the downstream task,  which in our case, is classification on the identity of the samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  In order to address these difficulties, in this paper we propose the Face Representation Augmentation  (FRA) algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This algorithm augments the posture of a given face image in the latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This  means that, given a set of embeddings representing a specific person, the proposed approach alters the  embedding to sustain the identity-related features with a transformed pose feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The FRA algorithm  can help the existing facial recognition systems especially when the number of training samples is  imbalanced or less than expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Our main contributions in this paper are itemized in the following:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' A novel algorithm for facial posture augmentation inside the latent space to reduce the complexity of  the image augmentation problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Generating noiseless, non-duplicated embeddings which are proved to be linearly separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Extensive experiments were conducted on the Karolinska Directed Emotional Faces (KDEF) [35]  dataset and improved the identity classification accuracies in comparison with the base models of  MagFace, ArcFace, and CosFace, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  The rest of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In Section 2, we briefly review the related works on face-  specific data augmentation and representation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Then, in Section 4, we present the details of our  proposed methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In Section 4, we demonstrate the results of our experiments in comparison with  other related state-of-the-art approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Finally, the conclusion will be drawn in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Related works  In this section, we present an overview of face-specific data augmentation techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These are  categorized into two groups classical and generative-based methods in 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Additionally, we review the  related literature of FR algorithms in 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Face-Specific Data Augmentation  To begin with, five data augmentation techniques for face photos were reported by Lv et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These  techniques were landmark perturbation, hairdo synthesis, glasses synthesis, postures synthesis, and  lighting synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Vincent et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' [36] tried to synthesize more data by applying different types of noise  such as Gaussian and Salt-and-pepper with the objective of training Stacked Denoising Autoencoders on  more complicated samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' [37] addressed the issue of data augmentation in picture  classification using conventional transformation techniques and GANs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' They also suggested a technique  for learning network-based augmentations that better enhance the classifier in the setting of generic  photos rather than face images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Moreover, although the hair is not an intrinsic part of the human face, it interferes with facial recognition  since it obscures the face and changes its appearance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Using DiscoGAN, which was developed to find  cross-domain relationships using unpaired data, Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' altered hair color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In addition to the color, Kim  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' in [38], suggested changing the bang by transferring an unsupervised visual characteristic using a  reconfigurable GAN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' An online compositing technique was used in the face synthesis system proposed by  Kemelmacher-Shlizerman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=" The system might produce a series of fresh photographs with the  4  4  input person's identification and the questioned look using one or more photos of their face and a text  query like curly hair." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=', in [40], proposed Pose and expression resilient Spatial aware GAN  (PSGAN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=" It starts by using Makeup Distill Network to separate the reference image's makeup into two  spatially aware makeup matrices." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=" After that, a module called Attentive Makeup Morphing is developed to  let users describe how a pixel's appearance in the source picture is altered based on the reference image." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  In order to ease applications in the real-world setting, PSGAN is the first to concurrently accomplish  partial, shade tunable, and pose/expression robust makeup transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In order to separate the makeup from  the reference picture as two makeup matrices, an MDNet is also included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The flexible partial and shade  adjustable transfer is made possible by the spatially aware makeup matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' To learn all cosmetics  attributes [41], including color, form, texture, and position, it comprises an enhanced color transfer branch  and a new pattern transfer branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' They present makeup in this work as a combination of color  transformation and pattern addition, and they create a thorough makeup transfer technique that works for  both delicate and dramatic looks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' They suggest using warped faces in the Ultraviolet (UV) space while  training two network branches to eliminate the disagreement between input faces in terms of form, head  posture, and expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' They also create a new architecture with two branches for color and pattern  transfer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' They present brand-new cosmetics transfer datasets with extreme fashions that were not taken  into account in the earlier datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Representation Learning for Face Recognition  Representation learning refers to a set of algorithms that are designed to solve a variety of challenges like  image retrieval [42-44], the person [45, 46] and vehicle [47, 48] re-identification, landmark detection, and  fine-grained object recognition [49, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The task of face recognition in computer vision is heavily  dependent on learning representations that have fine intra-class and large inter-class distances [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Previous works [6, 22, 25, 52, 53] have mainly adopted different, more robust loss functions with the aim  of learning representations that satisfy the aforementioned requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  In [52], a deep convolutional neural network, named FaceNet, was proposed which learns facial  representations with the help of triplet loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The main objective of this work is to achieve an embedding  f(x) from an image x into a d-dimensional Euclidean space Rd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The obtained embedding is generated in a  way that the squared distance among the embeddings from one class is small and that of the embeddings  from different classes is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This algorithm achieves 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='63% and 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='12% accuracy in LFW [54] and  YouTube Faces Database [55] respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' [53] have proposed a new look at the loss functions  which are based on the Euclidean margin between the produced embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' For CNNs to learn  discriminative facial characteristics with clear and innovative geometric interpretation, they suggest the  A-Softmax loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=" The assumption that faces also lie on a manifold is fundamentally compatible with the  learnt features' discriminative spread on a hypersphere manifold." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In order to approximate the learning  problem that minimal inter-class distance is greater than maximum intra-class distance, they develop  lower the margin set between such classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  In [22], the authors have proposed ArcFace, a major modification of the Softmax loss to further improve  the robustness of the learned deep features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' By utilizing the arc-cosine function to calculate the angle  between the current feature and the target weight and adding an additive angular margin to the target  angle, the target logit can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Then, these logits are rescaled by a fixed feature norm followed by  exactly the same steps in the Softmax loss function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Their approach has the following advantages over the  others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' (1) Directly optimizing the geodesic distance margin (2) State-of-the-art performance in several  5  5  benchmark datasets: achieving 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='53% accuracy (3) Easiness in terms of implementation (4) Efficiency in  terms of computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  In [25], the authors reformulated the Softmax loss as a cosine loss with the aim of introducing a novel  loss function, named Large Margin Cosine Loss (LMCL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Their improvement is to further maximize the  decision margin in the angular space by introducing and training a deep model called CosFace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In this  deep model, LMCL guides the convolutional layers to learn features with huge cosine margins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Their  results demonstrate that they have achieved 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='96% accuracy in face verification on the MegaFace  benchmark, which has been a major improvement in comparison to previous works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Meng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' [6] proposed a new set of losses that enable the network to learn embeddings whose  magnitude represents the quality of the given face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' By extending ArcFace [22] and introducing the  MagFace loss function, they demonstrate that the more likely the subject is to be recognized, the bigger  the magnitude of the generated embedding becomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' MagFace learns to generate these universal  embeddings by pulling the easier samples within a class of identities to the class center and pushing them  away from the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This makes the embeddings robust to ambiguity and the absence of high  discriminative features which prevalently exist in unconstrained face images in real scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' They have  achieved 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='83% verification accuracy in the LFW benchmark dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In Table 1, a comparison of these  works is depicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Verification accuracy of MagFace, CosFace, ArcFace, and SphereFace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These models are  evaluated on CALFW, CPLFW, AgeDB, LFW, and CFP-FP datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Method  CALFW [56]  CPLFW [57]  AgeDB [58]  LFW [54]  CFP-FP [59]  MagFace [6]  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='15  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='87  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='17  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='83  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='46  CosFace [25]  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='18  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='18  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='17  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='78  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='26  ArcFace [22]  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='96  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='72  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='05  9981  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='40  SphereFace [53]  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='58  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='27  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='05  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='67  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='84  Moreover, although these approaches have significant performance, directly applying GAN approaches  appears to have a few disadvantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Models collapse, difficulty in training and convergence problems,  and poor image generation effect, along with the unreliable results of the generator for unconstrained  input images, cause the generated image examples to be incapable of being utilized for industrial data  augmentation tasks ]60 ,61[.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Proposed approach  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Overview  This section presents the proposed FRA algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As can be inferred from Figure 1, our method includes  four steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These are as follows: face detection and alignment, input preparation: facial landmark and  representation extraction, pose feature extraction, and representation augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Steps 1 and 2  comprise our data preprocessing pipeline which is explained in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Steps 3 and 4 represent our  main contribution to this paper and are explained in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  6  6  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The overall procedure of FRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' FRA is composed of four steps to generate a new representation  vector with identity i, emotion e, and posture p, by applying a target posture p on a base image with  identity i and emotion e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Dataset preprocessing and preparation  Our data preprocessing step includes three main phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These three phases are depicted in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As is  seen in the first phase, we feed the raw face images to the Multi-task Cascaded Convolutional Networks  (MTCNN) algorithm [53] which is a robust face and landmark detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' MTCNN provides us with 5  landmark points, including the center of both eyes, the tip of the nose, and the left and right corners of the  lips, and a bounding box that perfectly encloses the face area within the image without any padding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In  this phase, we also align the face images by feeding the acquired facial landmarks along with the face  image itself to the method of warp affine which exists in OpenCV [62], a famous library with ready-to-  use computer vision-related algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  In the second phase, we feed the aligned face images to MLXTEND1 so as to determine more facial  landmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As is shown in Figure 1, MLXTEND outputs 68 facial key points which we use to construct  binarized images with pixel value 0 (completely black) for the background and 1 (completely white) for  facial landmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' On the other hand, we need to have fixed-size embeddings for each sample within the  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These embeddings are in fact the training data for the combiner module which will be explained  in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In our case, we use two of the most reliable and robust face representation learning  algorithms, namely MagFace [6] and FaceNet [52], for obtaining embeddings for each image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' MagFace’s  learning procedure is for a universal embedding that is quality aware, meaning that the easier the sample  is for the recognition task, the closer its feature vector becomes to the center of the class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Furthermore,  FaceNet is an algorithm that directly learns a mapping from the samples to a compact Euclidean space  and the distances correlate to the similarity degree of a given pair of face images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In Phase 3, the  binarized images generated in Phase 2 are fed to the AE model in order to generate an embedding vector  1http://rasbt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content="io/mlxtend/  Faciallandmarkextraction  1  Face lancmark  detector  Encoder  (MLXTEND)  1 68facial  1  targetface withposturep'  landmarks  512Dposefeatures  Combiner  1  Facialrepresentationextraction  1 1 512D augmented face  Face  Face for identity i," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' emotion e,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content="  representation  detector  representation  detector  andposturep'  (MTCNN)  (FRL)  1  1  sourceface  with identity i," metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  512Dfacial  emotione,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  representation  andposturep  1  1 1  1  a)alignandcrop  b)inputspreparation  c)posefeaturesextraction  d)augmentedrepresentation7  7  representing posture features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Finally, in Phase 4, pose and face representation vectors are fed into the  combiner module to generate an augmented face representation vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Facial Landmark Restoration using Autoencoders  Autoencoders (AE)  are a particular type of neural networks whose main functionality is to encode the  input into a meaningfully compacted representation and decode this into the input space afterwards [63,  64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Following this paradigm, in this paper, we have been inspired by  the work done by Meng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' [65]  and decided to use an AE-based model for encoding our input space (binarized images of landmarks  explained in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2) into the latent space (embeddings), as shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Given Si as a sample  of facial landmarks image, the output of F(Si) is a reconstructed image S’i, where F(Si) is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' After the AE  model’s convergence, we can discard B (decoder) and take only A which has learned to encode the input  into an optimized and meaningful latent space representation denoted by Vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' It is worth mentioning that Vi  plays a vital role in our proposed method which is the latent representation of the posture of the face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Figure 2 illustrates the proposed AE-based model and its architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' A general architecture of an autoencoder-based model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' FRA utilizes a typical convolutional  autoencoder with a bottleneck of size 512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This bottleneck vector is used in further steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Combining Feature Vectors and Feature Extraction using Vision Transformers  Vision Transformers (ViT) are deep learning models whose versatility in various fields such as natural  language processing, speech recognition and computer vision has made them a prominent choice for  researchers [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In comparison with the conventional CNNs, ViT models have achieved competitive  superior results in vision tasks like object detection [67], image recognition [68], image super-resolution  [69], and segmentation [70, 71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  At the core of ViT models, there is a mechanism of attention that has been probably one of the most  significant concepts in the domain of deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Its inspiration is the biological attributes of human  beings in that, to recognize an object, we tend to focus on the most distinctive parts of that entity instead  of paying attention to all parts of it as a whole [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In terms of deep neural networks, this can be  interpreted as assigning importance scores for a given set of features where the higher scores are for more  relevant features and the lower ones for the features with less saliency [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As can be observed from  Figure 3, the model learns to have more focus on the parts which represent the target object in the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  20  5  112x112x1  56  1@112x112  112x112x1  @  4@  Convolution  Convoluton  +Max-Pool  S  Encoder (A)  Decoder (B)8  8  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The paradigm of combining two representation vectors using ViT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The combiner takes two  representation vectors with a size of 512 and combines them into a 32x32 matrix to be processed by a  vision-transformer component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Moreover, transformers [74] refer to a set of neural networks which use the mechanism of attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  These models consist of multiple encoders and decoders whose architectures are identical to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  In these models, a multi-head self-attention (MSA) mechanism is used for encoding the input, followed  by decoders which include an extra attention layer in order to process the encoder’s output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Self-attention  is a function denoted in Equation (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  (1)  where , , and  are weight matrices used in linear transformations on inputs x to produce Q, K, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The  attention score is then calculated by  as the dot product of the query and each key, scaled by the  dimension dk of the key K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Put x = "x1, x2, x3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' , xn" to calculate an answer based on a collection of  queries Q, keys K, and values V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In MSA, Q, K, and V are projected linearly and this is done for h  consecutive times with different learned weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Then, by applying the self-attention mechanism on each  of the outputs in the previous step simultaneously, we obtain h outputs which are heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Then, these  heads are concatenated to achieve the final output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The following demonstrates these computations in  mathematical terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  (2)  MSAs, compared with CNNs, transform feature maps with huge data-specific kernels and this makes  them as expressive as the CNN-based architectures [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The key difference exists where convolutions  diversify feature maps whereas MSAs combine them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' According to [76], the Fourier analysis of feature  maps demonstrates that convolutions boost high-frequency components whereas MSAs, on the other  hand, attenuate them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Furthermore, finding elements that are more pertinent for the depiction of the altered posture is made  easier by the multi-head attention layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In order to do this, the scaled dot product attention gives greater  weight to the characteristics of the input facial representation and encoded posture that is more pertinent  while providing less weight to the features that are less relevant [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The procedure chooses features  512Dpose  Concatination and Reshape  representation  Normalization Layer  512DAugmented  Vision  representation  Transformer  (ViT)  512Dface  representation9  9  from various input regions and aids in improving representation performance since there are several heads  in the attention layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  In this paper, we have opted for using a ViT-based architecture for extracting features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As stated before,  this policy ensures that the model is trained to attend to the most salient feature values within the identity  and posture-related feature vectors simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Considering E of size  as the embedding obtained  from a pre-trained facial representation learning algorithm and Vi of shape  as the bottleneck vector  generated by the autoencoder part of FRA, we concatenate and reshape the produced feature vector to  make it of shape .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Generating Pose-Aware Face Embeddings  After the ViT module in our proposed model, the output is normalized, making it into the range of 0-1,  after which it is fed to a fully connected layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This layer helps us produce an output of a 1-d shape which  is also considered the embedding generated by our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Multi-Task Loss Function  In the training procedure, we utilized a Multi-part Loss Function (MLF) as the learning objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This  MLF comprises a Binary Cross-Entropy (BCE) loss function, which is used to train the autoencoder, so it  can reconstruct the posed style better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Since the activation function of the last layer of our autoencoder is  Sigmoid, it can lead to loss of saturation (plateau) [78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This saturation could prevent gradient-based  learning algorithms from convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In order to avoid this issue, it would be better to have a logarithm  function in the objective function to undo the exponential function within the Sigmoid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This is why BCE is  preferred, because it uses a logarithm function, unlike Mean Squared Error (MSE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  The second part of our loss function is a type of N-pair Loss [79].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' N-pair loss generalizes triplet loss [52]  to include comparison with multiple negative samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The objective of this function is to keep the  distance between the anchor and positive smaller than the distance between the anchor and negative  representations, as shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Effect of the proposed loss function during the learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The N-pair loss allows the  model to distinguish between pose-variant representation vectors with the same identity and emotion, as  well as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  The proposed multi-task loss function is defined as follows,  10  10  (3)  in which, yi and pi denote the reconstructed pose style and the original pose style, respectively, and also is  defined as  (4)  where m is a margin applied to impose the separability between genuine and imposter pairs, and f denotes  the proposed architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' d is the euclidean distance applied on normalized features and it is given by  Equation (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  (5)  In Equation (6), a and p denote the anchor (generated) representation and the positive (real)  representation, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Additionally, , , and  denote the negative representation w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='t pose, identity,  and emotion of the anchor face, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Specifically, negative pose representations have the same  identity as the anchor, but with different poses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The same holds for negative emotion representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' But,  for negative identity representation, the representation of another person is chosen randomly, regardless  of what pose or emotion it has.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The goal of the triplet loss is to achieve,  (6)  The optimal state for each single triplet loss is achieved when is equal to zero and  is greater than the  predefined margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Results and Discussion  In this section we first introduce the benchmark dataset that we have used for evaluating our proposed  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Then, we elaborate the details of our implementation and introduce the metrics used in this  paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Finally, we demonstrate our experimental results and discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Datasets  With the object of benchmarking our results, we have used the KDEF dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' It is a publicly available  dataset of 4900 face images, covering 140 unique identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The images demonstrate face images with  varying pose and emotion styles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Some samples of these datasets are shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  11  11  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' A few samples of the KDEF dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The KDEF dataset provides face images of 140 different  people in various postures and emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Implementation details  We carried out our experiments on a machine with a Core i7-1165G7 @ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='80GHz CPU with 64  Gigabytes of RAM and a GeForce RTX 2060 12 GB GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' All models were implemented and trained  using the Pytorch framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Table 2 shows the hyperparameter setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Details of the training procedure and the utilized FRLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The hyperparameter settings are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  FRL arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  # epochs  Init.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' learning rate  Dropout  rate  Triplet  margin  ViT  Embedding dim  FC dim  # Heads  # Layers  Patch  size  MagFace  255  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  256  256  4  4  8  ArcFace  320  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  CosFace  157  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='001  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='05  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  Furthermore, with the object of fairly evaluating the proposed FRA, we divided KDEF datasets based  on identities with the following distributions: We randomly selected all samples from 99 identities which nearly comprise 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='7 % of all  identities in KDEF as our training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  12  12 We randomly selected all samples from 11 identities which nearly comprise 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8 % of all identities  in KDEF as our validation data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' We randomly selected all samples from 30 identities which nearly comprise 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5 % of all  identities in KDEF as our testing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Experimental Results  This section details our comprehensive experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Table 3 shows the achieved  accuracy of the Support Vector Machine (SVM) [80] classifier on the embeddings generated in  three different experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These experiments are:  (1) Pre-augmentation accuracy: In this experiment, the training happens on the embeddings extracted  using three different FRLs, namely MagFace, ArcFace, and CosFace, and the testing accuracy is  achieved on the testing partition of these embeddings (Train/Test split ratio is set 80/20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In this  experiment, we used no augmentation technique at all and this is done to find a baseline for the  quality of the original data in the chosen benchmark dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  (2) Generated embeddings’ accuracy: In this experiment, we first augmented the original  embeddings to obtain the transformed embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Then, we trained the SVM on the original data  and tested its performance on the generated embeddings by the proposed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This is done to  demonstrate how much the proposed model is able to sustain the identity, posture, and emotion-  related features without any degradation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  (3) Post-augmentation accuracy: In this experiment, we have augmented the embeddings of the  training split using FRA, where the test split is the same as (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Then, we trained the SVM classifier  on the training part and tested it on the testing one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Table3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Evaluation results of FRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Pre-augmentation and post-augmentation accuracies show the  effectiveness of FRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Generated embeddings’ accuracy denotes the sustainability of FRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  FRL  Target  (1) Pre-  augmentation  Accuracy (%)  (2) Generated  embeddings’  Accuracy  (%)  (3) Post-  augmentation  Accuracy (%)  MagFace  Posture  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='38  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='12  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='66  Identity  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='19  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='61  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='71  Emotion  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='76  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='43  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='04  ArcFace  Posture  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='12  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9  Identity  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='61  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='65  Emotion  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='55  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='98  100  CosFace  Posture  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='12  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='91  99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='12  Identity  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='91  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='11  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='50  Emotion  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='14  87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='61  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='37  13  13  Based on Table 3, it is observed that our proposed algorithm improves the classification accuracy, not  only identity-wise but also in terms of emotion and posture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' For instance, SVM outputs 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='19% accuracy  on the MagFace embeddings but after the augmentation, this score goes up to 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='71% in Post-  augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' For the same data, the generated embeddings are much more representative which  improves the classification accuracy on the identity of the SVM outputs by 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='61%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This enhancement  can also be validated for ArcFace and CosFace since our algorithm increases the accuracy in all three  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In addition, FRA can improve the accuracy of SVM embeddings remarkably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In addition to  improving the classification accuracy with respect to the identities of the embeddings, FRA improves that  pose and emotion-wise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Based on Table 5, the accuracy of the SVM classifier is increased from 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='19%  for MagFace embeddings to 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='71% after augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This improvement for ArcFace and Cosface is  from 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='61% to 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='65% and from 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='91% to 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='37%, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Furthermore, our generated embeddings should ensure the fact that they are linearly separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This  means that the embeddings can be classified using a linear classifier such as SVM with a linear kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In  our experiments we used an SVM classifier with a linear kernel and based on Table 5, we can deduce that  FRA is able to improve the accuracy in Phase 2 and Phase 3 by a large margin, effectively enhancing the  performance of SVM with a linear kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Moreover, in order to show the independence of FRA from any FR algorithms, we adopted three such  approaches, namely MagFace, ArcFace, and CosFace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Based on Table 5, after augmenting the  embeddings generated by each of these algorithms, the classification accuracy of the SVM classifier is  increased significantly and this proves the fact that FRA is not dependent on any specific FR algorithm as  its requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  In addition, for our algorithms’ performance to be verified thoroughly, the reconstructed binary images  which are created by the AE part of the proposed approach are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These images are illustrated in  Figure 6, showing the original image, and the AE’s output when dealing with MagFace embeddings,  ArcFace embeddings, and CosFace embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Also, the training and validation loss in the training  procedure of our proposed pipeline is shown in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  14  14  Original landmarks  AE-generated landmarks  for Magface FRL  AE-generated landmarks  for Arcface FRL  AE-generated landmarks  for Cosface FRL  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Some instances of reconstructed binarized facial landmark images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' These reconstructed images  denote how good the AE is performing for each FRL model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The CosFace model reconstructs the most  landmarks more precisely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  15  15  Total Loss Magface  BCE Loss Magface  Npair Loss Magface  Total Loss Arcface  BCE Loss Arcface  Npair Loss Arcface  Total Loss Cosface  BCE Loss Cosface  Npair Loss Cosface  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Total loss, BCE loss and Npair loss curves achieved by various FRL methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  The curves of Precision-Recall (PRC), Receiver Operating Characteristic (ROC), and confusion matrices  of all experiments for MagFace, ArcFace, and CosFace are shown in Figures 8-16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Train loss  Validation loss  20  15  Loss Error  10  5  0  0  50  100  150  200  250  Epoch0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='22  Train BCE losS  ValidationBCEloss  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='16  rror  E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='14  Loss  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='06  0  50  100  150  200  250  EpochTrain Npair loss  Validation Npair loss  20  15  Loss Error  10  5  0  0  50  100  150  200  250  EpochTrain loss  Validation loss  20  15  Error  Loss  10  5  0  0  50  100  150  200  250  300  EpochTrain BCE losS  Validation BCE loss  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5  rror  E  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  LosS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1  0  50  100  150  200  250  300  EpochTrain Npair loss  Validation Npair loss  20  15  Loss Error  10  5  0  0  50  100  150  200  250  300  EpochTrain loss  14  Validation loss  12  10  Error  8  Loss  6  4  2  0  0  20  40  60  80  100  120  140  160  EpochTrain BCE losS  Validation BCE loss  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='14  Loss Error  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='04  0  20  40  60  80  100  120  140  160  EpochTrain Npair loss  14  Validation Npair loss  12  10  Error  8  Loss  6  4  2  0  0  20  40  60  80  100  120  140  160  Epoch16  16  a)  Pre-augmentation PRC (pose)  b)  Pre-augmentation PRC (id)  c)  Pre-augmentation PRC  (emotion)  d)  Post-augmentation PRC  (pose)  e)  Post-augmentation PRC (id)  f)  Post-augmentation PRC  (emotion)  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' PRC curves for MagFace FRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As the curves indicate, post-augmentation PRC curves (d, e, and f) have  significant improvements in comparison to pre-augmentation PRC curves (a, b, and c) for pose, identity, and  emotion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  precision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (pose)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  precision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class FL  class HL  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class HR  class S  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' recall curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9  class AF05  class BF04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  clasS AM31  classBM13  class BF11  class AF01  class AM15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='7  class AF03  class BM16  precision  class AF10  class AM22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class AM13  class BMo5  class BM23  class AM34  class BF12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5  class AF07  class AM05  class AF27  class BF14  class BM29  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AMo1  class AF16  class AF32  class AF26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  class BM07  class AF29  class BF16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  precision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AF  class AN  class DI  class HA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class NE  class SA  class SU  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (pose  class FL  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class HL  class HR  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  precision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='95  class AF05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='90  class BF04  class AM31  class BM13  class BF11  class AF01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='85  class AM15  class AF03  precision  class BM16  class AF10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='80  class AM22  class AM13  class BM05  class BM23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='75  class AM34  class BF12  class AF07  class AM05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='70  class AF27  class BF14  class BM29  class AM01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='65  class AF16  class AF32  class AF26  class BM07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='60  class AF29  class BF16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='98  precision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='97  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='95  class AF  class AN  class DI  class HA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='94  class NE  class SA  class SU  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recall17  17  a)  Pre-augmentation ROC (pose)  b)  Pre-augmentation ROC (id)  c)  Pre-augmentation ROC  (emotion)  d)  Post-augmentation ROC  (pose)  e)  Post-augmentation ROC (id)  f)  Post-augmentation ROC  (emotion)  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' ROC curves for MagFace FRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As the curves indicate, post-augmentation ROC curves (d, e, and f) have  significant improvements in comparison to pre-augmentation ROC curves (a, b, and c) for pose, identity, and  emotion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  RoCcurve(pose)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  truepositive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class FL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9609)  class FR (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='999)  class HL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9991)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class HR (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROC curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class AM23 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8 -  class AF05 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM13 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  classAF13(AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9892)  class BF28 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM08 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF31 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class BM35 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  true positive rate  class BF33 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM18 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF13 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF19 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9918)  class AM26 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9904)  class BM12 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AF16 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF23 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM01 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM03 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9938)  class BF10 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM19 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF04 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class BF32 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM08 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9939)  class BF01 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM06 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM14 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM07 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BF15 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9949)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROCcurve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class AF (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9948)  classAN (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9921)  class DI (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9972)  class HA (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9959)  class NE (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9894)  class SA (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9939)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  classSU (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9916)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateRoC curve (pose)  class FL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='459)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class FR (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4088)  class HL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0797)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROC curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class AM23 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8 -  class AF05 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM13 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF13 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9951)  class BF28 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM08 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF31 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class BM35 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  true positive rate  class BF33 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM18 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF13 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF19 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9961)  class AM26 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9961)  class BM12 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AF16 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF23 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM01 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM03 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9951)  class BF10 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM19 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF04 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class BF32 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM08 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9989)  class BF01 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM06 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM14 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM07 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BF15 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='999)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateRoCcurve(emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class AF (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AN (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class DI (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class HA (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class NE (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class SA (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9996)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class SU (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rate18  18  a) Pre-augmentation Confusion (pose)  b) Pre-augmentation Confusion (id)  c) Pre-augmentation Confusion  (emotion)  d) Post-augmentation Confusion (pose)  e) Post-augmentation Confusion (id)  f) Post-augmentation Confusion  (emotion)  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Confusion matrices for MagFace FRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As the confusion matrices indicate, post-augmentation matrices  (d, e, and f) have significant improvements in comparison to pre-augmentation matrices (a, b, and c) for pose,  identity, and emotion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Confusionmatrix(pose  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='FL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SConfusionmatrix(id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF04  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF03  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='800  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='600  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM34 -  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF04  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF03  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF16Confusionmatrix(emo)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SU  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='DI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='NE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SUConfusionmatrix(pose)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='S  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SConfusionmatrix(id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF04  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF03  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF04  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF03  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM34  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF27  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF16Confusionmatrix(emo)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SU  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='DI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='NE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='sU19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Pre-augmentation PRC (pose)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='b)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Pre-augmentation PRC (id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='c)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Pre-augmentation PRC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='(emotion)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='d)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Post-augmentation PRC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='(pose)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='e)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Post-augmentation PRC (id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='f)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Post-augmentation PRC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='(emotion)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' PRC curves for ArcFace FRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As the curves indicate, post-augmentation PRC curves (d, e, and f) have  significant improvements in comparison to pre-augmentation PRC curves (a, b, and c) for pose, identity, and  emotion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  precision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (pose  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class FL  precision  class FR  class HL  class HR  class S  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  class BM15  class BF09  class BM14  class BF07  class AM22  class AM23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class BM18  class BM26  precision  class AF14  class BM11  class AF10  class BM16  class AF33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class BF10  class AF20  class BF02  class BM08  class BF28  class AM35  class AM07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class BF03  class BM31  class BF17  class AM10  class AF02  class BM06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BM23  class BM13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  precision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AF  class AN  class DI  class HA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class NE  class SA  class SU  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (pose)  class FL  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class FR  class HL  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  precision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BM15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9  class BF09  class BM14  class BF07  class AM22  class AM23  class BM18  class BM26  precision  class AF14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  class BM11  class AF10  class BM16  class AF33  class BF10  class AF20  class BF02  class BM08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='7  class BF28  class AM35  class AM07  class BF03  class BM31  class BF17  class AM10  class AF02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class BM06  class BM23  class BM13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  precision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class AN  class DI  class HA  class NE  class SA  class SU  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recall20  20  a)  Pre-augmentation ROC (pose)  b)  Pre-augmentation ROC (id)  c)  Pre-augmentation ROC  (emotion)  d)  Post-augmentation ROC  (pose)  e)  Post-augmentation ROC (id)  f)  Post-augmentation ROC  (emotion)  Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' ROC curves for ArcFace FRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As the curves indicate, post-augmentation ROC curves (d, e, and f) have  significant improvements in comparison to pre-augmentation ROC curves (a, b, and c) for pose, identity, and  emotion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  RoCcurve(pose)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class FL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9978)  class FR (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2198)  class HL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9953)  class HR (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9998)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  classS (AUC=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9981)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROC curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BM15 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8 -  class BF09 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM14 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF07 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM22 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM23 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9782)  class BM18 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class BM26 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  true positive rate  class AF14 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM11 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF10 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9838)  class BM16 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF33 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF10 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9841)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AF20 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF02 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9916)  class BM08 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF28 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM35 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM07 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF03 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class BM31 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF17 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM10 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF02 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9875)  class BM06 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  classBM23(AUC=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9827)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BM13 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROCcurve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  classAF(AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9885)  clasS AN (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9983)  class DI (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9975)  class HA (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9998)  class NE (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9901)  class SA (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9947)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class SU (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9968)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateRoCcurve(pose)  class FL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1322)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class FR (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='7495)  class HL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3596)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positiverateROC curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BM15 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8 -  class BF09 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM14 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF07 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM22 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM23 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9952)  class BM18 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class BM26 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  true positive rate  class AF14 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM11 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF10 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9987)  class BM16 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF33 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF10 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9979)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AF20 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF02 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM08 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF28 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM35 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM07 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF03 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  claSs BM31 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF17 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM10 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF02 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM06 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM23 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='994)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BM13 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateRoCcurve(emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  truepositive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class AF (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AN (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class DI (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class HA (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class NE (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class SA (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class SU (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rate21  21  a)  Pre-augmentation Confusion  (pose)  b)  Pre-augmentation Confusion  (id)  c)  Pre-augmentation Confusion  (emotion)  d)  Post-augmentation Confusion  (pose)  e)  Post-augmentation Confusion  (id)  f)  Post-augmentation Confusion  (emotion)  Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Confusion matrices for ArcFace FRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As the confusion matrices indicate, post-augmentation matrices (d,  e, and f) have significant improvements in comparison to pre-augmentation matrices (a, b, and c) for pose, identity,  and emotion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Confusionmatrix(pose)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='L  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='R  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='主  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='S  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='FL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='FR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='sConfusionmatrix(id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF09  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='800  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='600  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF02  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM08  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF03  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF02  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF09  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF02  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM08  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF03  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF02  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13Confusionmatrix(emo)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='NE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SU  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='DI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='NE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='sUConfusion matrix(pose)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='70  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='S  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SConfusionmatrix(id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF09  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF02  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM08  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF03  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF02  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF09  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF02  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM08  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM07  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF03  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM31  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF02  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13Confusionmatrix(emo)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='DI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='NE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='sU22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='a)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Pre-augmentation PRC (pose)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='b)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Pre-augmentation PRC (id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='c)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Pre-augmentation PRC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='(emotion)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='d)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Post-augmentation PRC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='(pose)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='e)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Post-augmentation PRC (id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='f)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Post-augmentation PRC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='(emotion)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' PRC curves for CosFace FRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As the curves indicate, post-augmentation PRC curves (d, e, and f) have  significant improvements in comparison to pre-augmentation PRC curves (a, b, and c) for pose, identity, and  emotion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  precision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (pose)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class FL  precision  class FR  class HL  class HR  class S  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  class BF25  class AM30  classBM13  class AM33  class BM21  class BF14  class BM19  class BM17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  precision  class BF15  class BF06  class AM18  class AF35  class BF13  class BM22  class BM23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class BM25  class AF08  class AF26  class BM33  class AM21  class AMo1  class AF14  class AF32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class BM28  class AM10  class BM29  class BM05  class AM06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='7  precision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AF  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  class AN  class DI  class HA  class NE  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class SA  class SU  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (pose  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class FL  class FR  class HL  class HR  class S  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  precision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class E  BF25  class AM30  class E  BM13  class AM33  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9  class BM21  class BF14  class BM19  class BM17  class BF15  class BF06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  class AM18  class AF35  precision  class BF13  class BM22  class BM23  class BM25  class AF08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='7  class AF26  class BM33  class AM21  class AMol  class AF14  class AF32  class BM28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class AM10  class BM29  class BM05  class AM06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recallprecision vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='recall curve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='7  recision  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class AF  class AN  class DI  class HA  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  class NE  class SA  class SU  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  recall23  23  a)  Pre-augmentation ROC (pose)  b)  Pre-augmentation ROC (id)  c)  Pre-augmentation ROC  (emotion)  d) Post-augmentation ROC (pose)  e) Post-augmentation ROC (id)  f) Post-augmentation ROC (emotion)  Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' ROC curves for CosFace FRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As the curves indicate, post-augmentation ROC curves (d, e, and f) have  significant improvements in comparison to pre-augmentation ROC curves (a, b, and c) for pose, identity, and  emotion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  RoC curve (pose)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class FL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5661)  class FR (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='7062)  class HL (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9998)  class HR (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9997)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class S (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROC curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BF25 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9997)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  class AM30 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM13 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9996)  class AM33 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9969)  class BM21 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9795)  class BF14 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9894)  class BM19 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9983)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class BM17 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9998)  truepositive rate  classBF15(AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9907)  class BF06 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='994)  class AM18 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9926)  class AF35 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9998)  class BF13 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9998)  class BM22 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9999)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class BM23 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9999)  class BM25 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9997)  class AF08 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9986)  class AF26 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9952)  class BM33 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9912)  class AM21 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9817)  class AM01 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9994)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class AF14 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9908)  class AF32 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9996)  class BM28 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9996)  class AM10 (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9999)  class BM29(AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9985)  class BM05 (AUC =1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class AM06 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9988)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROCcurve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  claSSAF (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9749)  class AN (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9835)  class DI (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9897)  class HA (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9994)  class NE (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9949)  class SA (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9814)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class SU (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9931)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROCcurve(pose)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  class FL (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class FR (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class HL (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class HR (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class S (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROC curve (id)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class BF25 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8 -  class AM30 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM13 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM33 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM21 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF14 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9932)  class BM19 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  class BM17 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  true positive rate  class BF15 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF06 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM18 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF35 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BF13 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM22 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  class BM23 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM25 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF08 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AF26 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM33 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM21 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM01 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  clasS AF14 (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9943)  class AF32 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM28 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class AM10 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM29 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class BM05 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class AM06 (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rateROCcurve (emo)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  true positive rate  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  classAF (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9853)  class AN (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9996)  class DI (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9965)  class HA (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  class NE (AUC =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9932)  class SA (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='9998)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  class SU (AUC = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0)  No skill  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  false positive rate24  24  a)  Pre-augmentation Confusion  (pose)  b)  Pre-augmentation Confusion  (id)  c)  Pre-augmentation Confusion  (emotion)  d)  Post-augmentation Confusion  (pose)  e)  Post-augmentation Confusion  (id)  f)  Post-augmentation Confusion  (emotion)  Figure 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Confusion matrices for CosFace FRL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' As the confusion matrices indicate, post-augmentation matrices  (d, e, and f) have significant improvements in comparison to pre-augmentation matrices (a, b, and c) for the pose,  identity, and emotion, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Discussion  FR has long been a popular field of study among specialists and academics in the field of biometric  recognition and it has the advantages of being non-contact, amiable, and simple to accept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Although  remarkable performance has been shown by some state-of-the-art approaches presented in the literature,  in real-world scenarios, there still exists the demand to improve such algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' For better handling such  uncontrolled contexts especially when we face a lack of data, DA techniques are introduced to increase  the number of training samples by applying different manipulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Classical techniques for image  transformations such as rotation, skewing, flipping, blurring, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=', and also GAN-based ones which utilize  deep generative models and disentangled features to create more realistically transformed face images  have well been studied for DA in the domain of FR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' However, these techniques have their drawbacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Classical techniques mostly manipulate face images in a way that distorts their alignment causing FR  algorithms’ performance when generating distinct representative embeddings dramatically decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' To  prove this, we have experimented with four different transformations, namely, horizontal flip, skewing,  blurring, and notifying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' We augmented samples in the KDEF dataset and increased the training dataset  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='size to be 4 times more than the original dataset and used different FR algorithms for generating  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Confusion matrix (pose)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='8000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='R  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='S  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='FL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='FR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HRConfusionmatrix(id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='800  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='600  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF08  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='M23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF08  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM06Confusionmatrix(emo)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='NE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='1000  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SU  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='DI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='NE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SUConfusion matrix (pose)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='70  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='50  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='FL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='FR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HR  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SConfusionmatrix(id)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF08  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM19  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM17  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF06  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM18  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BF13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM22  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM23  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF08  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF26  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM33  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM21  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM01  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM28  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM29  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='BM05  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AM06Confusionmatrix(emo)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AF  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='AN  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='DI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='HA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='NE  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='SU25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Then we classified the embeddings using SVM with respect to their identities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Table 6  details the results achieved by this experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Evaluation of MagFace, ArcFace, and CosFace using traditional augmentation techniques on the  KDEF dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Post-augmentation accuracy scores achieved denote the ineffectiveness of these techniques  for FR tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  FR Algorithm  Accuracy Score  Pre-augmentation  Post-augmentation  MagFace  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='49%  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='54%  ArcFace  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='12%  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='01%  CosFace  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='19%  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='33%  Table 4 shows that augmenting the face images using the classical approaches does not result in any  improvement and they, in fact, degrade the quality of embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' For instance, for the MagFace  algorithm, the accuracy obtained by SVM is decreased by 2% after applying DA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Moreover, we conducted another experiment using three state-of-the-art generative-based algorithms  namely, CPM [41], AttGAN [81], and PSGAN [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Following the previous experiments, we augmented  the face images and obtained the classification accuracy before and after augmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Table 7 shows the  results achieved by this experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Evaluation of augmentation techniques using GANs on the KDEF dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In the best case, the  post-augmentation accuracy has increased a little and in some cases, it has caused a degradation in  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  Algorithm  Accuracy Score  Pre-augmentation  Post-augmentation  CPM [40]  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='49 %  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='82 %  AttGAN  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='49 %  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='70 %  PSGAN [39]  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='49 %  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='40 %  Based on Table 5, it can be claimed that these generative models do not contribute to classification  accuracy improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Therefore, in order to address this issue, in this paper, we propose a new  algorithm, named FRA, which effectively augments the training data for FR algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' FRA functions  with original embeddings and manipulates them in a way to be representative of the same identity of the  embedding and also a differed postural information existent in these representational embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Results  achieved by our extensive experiments indicate the efficacy of FRA in augmenting samples in the FR  domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='Conclusion  26  26  Since data scarcity is a common problem in deep learning-based solutions, it can be very challenging to  build up FR systems that are robust enough to recognize face images with extreme diversity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' In this paper,  we proposed a novel method that augments the face data in latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The proposed method utilizes  two major components, one of which is an autoencoder and the other is a ViT-based model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The former is  used to encode the binarized input images consisting of sparse facial landmarks into a latent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' The  latter is used for extracting features from the combined embeddings coming from a pre-trained FRL  algorithm and the autoencoder part of our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lastly, the output of the proposed model is an  embedding representing the main identity with the same emotion but with a different posture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' This way,  we managed to improve the classification accuracy by 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='52, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='04, and 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='60, in comparison with the  based models of MagFace, ArcFace, and CosFace, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  References  [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Terhorst, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kolf, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Damer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kirchbuchner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kuijper, SER-FIQ: Unsupervised estimation of face image  quality based on stochastic embedding robustness,  Proceedings of the IEEE/CVF conference on computer  vision and pattern recognition2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 5651-5660.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Deng, Deep face recognition: A survey, Neurocomputing, 429 (2021) 215-244.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [3] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Ali, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Tian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Din, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Iradukunda, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Khan, Classical and modern face recognition approaches: a  complete review, Multimedia tools and applications, 80 (2021) 4825-4880.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Krizhevsky, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sutskever, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Hinton, Imagenet classification with deep convolutional neural networks,  Communications of the ACM, 60 (2017) 84-90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [5] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Taigman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Ranzato, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wolf, Deepface: Closing the gap to human-level performance in face  verification,  Proceedings of the IEEE conference on computer vision and pattern recognition2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 1701-  1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [6] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Meng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Huang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhou, Magface: A universal representation for face recognition and quality  assessment,  Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  14225-14234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [7] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Cao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Xie, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Parkhi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zisserman, Vggface2: A dataset for recognising faces across pose and  age,  2018 13th IEEE international conference on automatic face & gesture recognition (FG 2018), IEEE2018,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 67-74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [8] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Meng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sun, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zheng, Age-invariant face recognition  by multi-feature fusionand decomposition with self-attention, ACM Transactions on Multimedia Computing,  Communications, and Applications (TOMM), 18 (2022) 1-18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [9] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zheng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Pal, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Savvides, Ring loss: Convex feature normalization for face recognition,  Proceedings of  the IEEE conference on computer vision and pattern recognition2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 5089-5097.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [10] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Fang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Qiao, Range loss for deep face recognition with long-tailed training data,  Proceedings of the IEEE International Conference on Computer Vision2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 5409-5418.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [11] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Peng, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gao, DLFace: Deep local descriptor for cross-modality face recognition, Pattern  Recognition, 90 (2019) 161-171.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Bhattacharyya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Chatterjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sinitca, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kaplun, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sarkar, A deep learning model for classifying  human facial expressions from infrared thermal images, Scientific Reports, 11 (2021) 20696.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gupta, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Thakur, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kumar, 2D-human face recognition using SIFT and SURF descriptors of face’s feature  regions, The Visual Computer, 37 (2021) 447-456.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [14] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kortli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jridi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Al Falou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Atri, A comparative study of CFs, LBP, HOG, SIFT, SURF, and BRIEF for  security and face recognition,  Advanced Secure Optical Image Processing for Communications, IOP  Publishing2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [15] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Duan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhou, Uniformface: Learning deep equidistributed representation for face recognition,  Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 3415-3424.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  27  27  [16] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lahasan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lutfi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' San-Segundo, A survey on techniques to handle face recognition challenges:  occlusion, single sample per subject and expression, Artificial Intelligence Review, 52 (2019) 949-979.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [17] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, Cropping and attention based approach for masked face recognition, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=',  51 (2021) 3012-3025.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Prieto, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Mery, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Flynn, On low-resolution face recognition in the wild: Comparisons and new  techniques, IEEE Transactions on Information Forensics and Security, 14 (2019) 2000-2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [19] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Song, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gong, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, Occlusion robust face recognition based on mask learning with  pairwise differential siamese network,  Proceedings of the IEEE/CVF International Conference on Computer  Vision2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 773-782.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [20] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jiang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kot, Deep coupled resnet for low-resolution face recognition, IEEE Signal Processing  Letters, 25 (2018) 526-530.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Deng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zafeririou, Arcface for disguised face recognition,  Proceedings of the IEEE/CVF International  Conference on Computer Vision Workshops2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 0-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Deng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Guo, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Xue, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zafeiriou, Arcface: Additive angular margin loss for deep face recognition,  Proceedings of the IEEE/CVF conference on computer vision and pattern recognition2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 4690-4699.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [23] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Srivastava, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Murali, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Dubey, A performance evaluation of loss functions for deep face recognition,  Computer Vision, Pattern Recognition, Image Processing, and Graphics: 7th National Conference,  NCVPRIPG 2019, Hubballi, India, December 22–24, 2019, Revised Selected Papers 7, Springer2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 322-  332.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [24] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Tai, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Huang, Curricularface: adaptive curriculum  learning loss for deep face recognition,  proceedings of the IEEE/CVF conference on computer vision and  pattern recognition2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 5901-5910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [25] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Ji, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, Cosface: Large margin cosine loss for  deep face recognition,  Proceedings of the IEEE conference on computer vision and pattern recognition2018,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 5265-5274.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [26] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Mei, Co-mining: Deep face recognition with noisy labels,  Proceedings  of the IEEE/CVF International Conference on Computer Vision2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 9358-9367.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [27] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Luo, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Tang, Deep learning face attributes in the wild,  Proceedings of the IEEE  international conference on computer vision2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 3730-3738.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [28] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wong, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gatt, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Stamatescu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' McDonnell, Understanding data augmentation for classification:  when to warp?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=',  2016 international conference on digital image computing: techniques and applications  (DICTA), IEEE2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 1-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lv, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Huang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhou, Data augmentation for face recognition,  Neurocomputing, 230 (2017) 184-196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [30] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Masi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Trần, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Hassner, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sahin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Medioni, Face-specific data augmentation for unconstrained face  recognition, International Journal of Computer Vision, 127 (2019) 642-667.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [31] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jiang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Hu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gao, Efficient 3D reconstruction for face recognition, Pattern  Recognition, 38 (2005) 787-798.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [32] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Mohammadzade, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Hatzinakos, Projection into expression subspaces for face recognition from single  sample per person, IEEE Transactions on Affective Computing, 4 (2012) 69-82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [33] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Luo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Tang, Faceid-gan: Learning a symmetry three-player gan for identity-  preserving face synthesis,  Proceedings of the IEEE conference on computer vision and pattern  recognition2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 821-830.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [34] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Goodfellow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Pouget-Abadie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Mirza, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Xu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Warde-Farley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Ozair, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Courville, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Bengio,  Generative adversarial networks, Communications of the ACM, 63 (2020) 139-144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [35] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lundqvist, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Flykt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Öhman, Karolinska directed emotional faces, Cognition and Emotion, (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [36] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Vincent, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Larochelle, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lajoie, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Bengio, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Manzagol, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Bottou, Stacked denoising autoencoders:  Learning useful representations in a deep network with a local denoising criterion, Journal of machine learning  research, 11 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [37] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Perez, The effectiveness of data augmentation in image classification using deep learning,  Convolutional Neural Networks Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Recognit, 11 (2017) 1-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [38] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Cha, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kim, Learning to discover cross-domain relations with generative  adversarial networks,  International conference on machine learning, PMLR2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 1857-1865.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [39] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kemelmacher-Shlizerman, Transfiguring portraits, ACM Transactions on Graphics (TOG), 35 (2016) 1-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  28  28  [40] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jiang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Cao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' He, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Feng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yan, Psgan: Pose and expression robust spatial-aware gan  for customizable makeup transfer,  Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern  Recognition2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 5194-5202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [41] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Nguyen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Tran, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=" Hoai, Lipstick ain't enough: beyond color matching for in-the-wild makeup transfer,  Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition2021, pp." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 13305-  13314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [42] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Manmatha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Smola, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Krahenbuhl, Sampling matters in deep embedding learning,  Proceedings of the IEEE international conference on computer vision2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 2840-2848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [43] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Movshovitz-Attias, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Toshev, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Leung, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Ioffe, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Singh, No fuss distance metric learning using  proxies,  Proceedings of the IEEE international conference on computer vision2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 360-368.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [44] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Ustinova, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lempitsky, Learning deep embeddings with histogram loss, Advances in Neural Information  Processing Systems, 29 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [45] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Xiao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Luo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhang, Margin sample mining loss: A deep learning based method for person re-  identification, arXiv preprint arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='00478, (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [46] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Huang, Beyond triplet loss: a deep quadruplet network for person re-  identification,  Proceedings of the IEEE conference on computer vision and pattern recognition2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 403-  412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [47] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sanakoyeu, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Tschernezki, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Buchler, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Ommer, Divide and conquer the embedding space for metric  learning,  Proceedings of the ieee/cvf conference on computer vision and pattern recognition2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 471-  480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [48] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Bai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lou, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Duan, Group-sensitive triplet embedding for vehicle  reidentification, IEEE Transactions on Multimedia, 20 (2018) 2385-2399.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [49] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Em, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gag, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Huang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Duan, Incorporating intra-class variance to fine-grained  visual recognition,  2017 IEEE International Conference on Multimedia and Expo (ICME), IEEE2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  1452-1457.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [50] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Smirnov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Oleinik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lavrentev, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shulga, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Galyuk, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Garaev, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zakuanova, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Melnikov, Face  representation learning using composite mini-batches,  Proceedings of the IEEE/CVF International Conference  on Computer Vision Workshops2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 0-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [51] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sohn, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Chandraker, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jain, Towards universal representation learning for deep face  recognition,  Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  6817-6826.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [52] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Schroff, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kalenichenko, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Philbin, Facenet: A unified embedding for face recognition and clustering,  Proceedings of the IEEE conference on computer vision and pattern recognition2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 815-823.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [53] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Raj, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Song, Sphereface: Deep hypersphere embedding for face recognition,  Proceedings of the IEEE conference on computer vision and pattern recognition2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 212-220.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [54] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Mattar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Berg, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=" Learned-Miller, Labeled faces in the wild: A database forstudying face  recognition in unconstrained environments,  Workshop on faces in'Real-Life'Images: detection, alignment, and  recognition2008." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [55] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wolf, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Hassner, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Maoz, Face recognition in unconstrained videos with matched background similarity,  CVPR 2011, IEEE2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 529-534.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [56] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zheng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Deng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Hu, Cross-age lfw: A database for studying cross-age face recognition in unconstrained  environments, arXiv preprint arXiv:1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='08197, (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [57] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zheng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Deng, Cross-pose lfw: A database for studying cross-pose face recognition in unconstrained  environments, Beijing University of Posts and Telecommunications, Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Rep, 5 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [58] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Moschoglou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Papaioannou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sagonas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Deng, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kotsia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zafeiriou, Agedb: the first manually  collected, in-the-wild age database,  proceedings of the IEEE conference on computer vision and pattern  recognition workshops2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 51-59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [59] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sengupta, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Castillo, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Patel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Chellappa, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jacobs, Frontal to profile face verification  in the wild,  2016 IEEE winter conference on applications of computer vision (WACV), IEEE2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 1-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [60] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Cong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhou, Face Dataset Augmentation with Generative Adversarial Network,  Journal of Physics:  Conference Series, IOP Publishing2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 012035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [61] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kammoun, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Slama, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Tabia, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Ouni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Abid, Generative Adversarial Networks for face generation: A  survey, ACM Computing Surveys, 55 (2022) 1-37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [62] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Bradski, The openCV library, Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=" Dobb's Journal: Software Tools for the Professional Programmer, 25  (2000) 120-123." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  29  29  [63] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Rumelhart, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Hinton, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Williams, Learning internal representations by error propagation, California  Univ San Diego La Jolla Inst for Cognitive Science1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [64] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Bank, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Koenigstein, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Giryes, Autoencoders, arXiv preprint arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='05991, (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [65] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Meng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Xu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Qian, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Qin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lei, PoseFace: Pose-invariant  features and pose-adaptive loss for face recognition, arXiv preprint arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='11721, (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [66] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Qiu, A survey of transformers, AI Open, (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [67] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Carion, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Massa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Synnaeve, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Usunier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kirillov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zagoruyko, End-to-end object detection with  transformers,  Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020,  Proceedings, Part I 16, Springer2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 213-229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [68] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Touvron, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Cord, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Douze, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Massa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sablayrolles, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jégou, Training data-efficient image  transformers & distillation through attention,  International conference on machine learning, PMLR2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  10347-10357.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [69] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Fu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Lu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Guo, Learning texture transformer network for image super-resolution,  Proceedings of the IEEE/CVF conference on computer vision and pattern recognition2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 5791-5800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [70] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Ye, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Rochan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Wang, Cross-modal self-attention network for referring image segmentation,  Proceedings of the IEEE/CVF conference on computer vision and pattern recognition2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 10502-10511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [71] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Hafiz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Parah, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Bhat, Attention mechanisms and deep learning for machine vision: A survey of  the state of the art, arXiv preprint arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='07550, (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [72] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Niu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zhong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Yu, A review on the attention mechanism of deep learning, Neurocomputing, 452 (2021)  48-62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [73] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Chollet, Deep learning with Python, Simon and Schuster2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [74] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Vaswani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shazeer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Parmar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Uszkoreit, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jones, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Gomez, Ł.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kaiser, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Polosukhin, Attention is  all you need, Advances in neural information processing systems, 30 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [75] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Cordonnier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Loukas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Jaggi, On the relationship between self-attention and convolutional layers,  arXiv preprint arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='03584, (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [76] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kim, How do vision transformers work?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=', arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='06709, (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [77] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kim, Blurs behave like ensembles: Spatial smoothings to improve accuracy, uncertainty, and  robustness,  International Conference on Machine Learning, PMLR2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' 17390-17419.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [78] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Goodfellow, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Bengio, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Courville, Deep learning, MIT press2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [79] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Sohn, Improved deep metric learning with multi-class n-pair loss objective, Advances in neural information  processing systems, 29 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [80] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Cortes, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Vapnik, Support vector machine, Machine learning, 20 (1995) 273-297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content='  [81] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Zuo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Kan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Shan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
+page_content=' Chen, Attgan: Facial attribute editing by only changing what you want,  IEEE transactions on image processing, 28 (2019) 5464-5478.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/AtFLT4oBgHgl3EQfFC_E/content/2301.11986v1.pdf'}
diff --git a/CtAyT4oBgHgl3EQfR_f1/vector_store/index.pkl b/CtAyT4oBgHgl3EQfR_f1/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..df8a310de4cb30c82ba5e385248f37d03acd585b
--- /dev/null
+++ b/CtAyT4oBgHgl3EQfR_f1/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9a999d37283c8cae3fd30c1764c85c50c46f2101ef950685b990d01c3d5481a8
+size 337509
diff --git a/D9AzT4oBgHgl3EQfif2Z/content/tmp_files/2301.01501v1.pdf.txt b/D9AzT4oBgHgl3EQfif2Z/content/tmp_files/2301.01501v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..97fea4c53d8af7ca9d4c25955806dbe5462fa8ba
--- /dev/null
+++ b/D9AzT4oBgHgl3EQfif2Z/content/tmp_files/2301.01501v1.pdf.txt
@@ -0,0 +1,741 @@
+Towards Edge-Cloud Architectures for Personal
+Protective Equipment Detection
+Jarosław Legierski
+jaroslaw.legierski@orange.com
+Orange Innovation, Orange
+Polska S.A.
+Warsaw, Poland
+Kajetan Rachwał
+Piotr Sowinski
+kajetan.rachwal@ibspan.waw.pl
+piotr.sowinski@ibspan.waw.pl
+Systems Research Institute Polish
+Academy of Sciences
+Poland
+Warsaw Univesity of Technology
+Warsaw, Poland
+Wojciech Niewolski
+wojciech.niewolski@orange.com
+Orange Innovation, Orange
+Polska S.A.
+Poland
+Warsaw Univesity of Technology
+Warsaw, Poland
+Przemysław Ratuszek
+Zbigniew Kopertowski
+przemyslaw.ratuszek@orange.com
+zbigniew.kopertowski@orange.com
+Orange Innovation, Orange
+Polska S.A.
+Warsaw, Poland
+Marcin Paprzycki
+Maria Ganzha
+marcin.paprzycki@ibspan.waw.pl
+maria.ganzha@ibspan.waw.pl
+Systems Research Institute Polish
+Academy of Sciences
+Warsaw, Poland
+Abstract
+Detecting Personal Protective Equipment in images and video
+streams is a relevant problem in ensuring the safety of con-
+struction workers. In this contribution, an architecture en-
+abling live image recognition of such equipment is proposed.
+The solution is deployable in two settings – edge-cloud and
+edge-only. The system was tested on an active construction
+site, as a part of a larger scenario, within the scope of the
+ASSIST-IoT H2020 project. To determine the feasibility of
+the edge-only variant, a model for counting people wearing
+safety helmets was developed using the YOLOX method. It
+was found that an edge-only deployment is possible for this
+use case, given the hardware infrastructure available on site.
+In the preliminary evaluation, several important observations
+were made, that are crucial to the further development and de-
+ployment of the system. Future work will include an in-depth
+investigation of performance aspects of the two architecture
+variants.
+Keywords: edge-cloud continuum architectures, PPE detec-
+tion, image recognition, worker safety
+1
+Introduction
+Nowadays, the demand for intelligent video analytics is grow-
+ing across a wide spectrum of application areas [17]. The
+key part of such systems is usually an image recognition (IR)
+component. However, as of today, the IR subsystem is, most
+commonly, deployed in the cloud. This approach offers mul-
+tiple benefits, such as availability of large and scalable com-
+putational resources, reliable APIs, and shifting the burden
+of system maintenance to the cloud service provider. How-
+ever, this comes at a cost. Sending data to the cloud raises
+both security and privacy concerns. Moreover, communicat-
+ing with the cloud always induces network latency, which
+may be significant in time-critical applications. To address
+issues brought about by cloud-centric solutions, edge com-
+puting has been proposed. Here, the core of the approach is
+processing the data as close to the source as possible. This
+allows for latency reduction, and helps ensure the security
+and privacy of data, which remains within the local network.
+However, edge computing has its own set of issues. Typically,
+the computational resources, which are available at the edge
+are considerably smaller. A possible solution to addressing
+the downsides of both these options is a combined approach –
+an edge-cloud continuum, where data is partially processed
+on the edge and partially in the cloud. However, this raises
+the obvious question: at which point(s), within the continuum,
+individual parts of the system should be deployed.
+Here, this question is considered within a real-world sce-
+nario of monitoring the entrance to an active construction
+site. Specifically, the system is tasked with ensuring that (1)
+no unauthorized people enter the worksite, and (2) every-
+body is wearing appropriate Personal Protective Equipment
+(PPE), i.e. helmets and safety vests. The scenario is evalu-
+ated as part of the ASSIST-IoT project, on a construction site
+in Warsaw, Poland, managed by the construction company
+Mostostal Warszawa. Here, the edge versus cloud discussion
+becomes particularly relevant. On the one hand, the privacy
+of workers is of paramount importance, while latencies must
+be minimized, to ensure a quick reaction, which hints at an
+arXiv:2301.01501v1  [cs.CV]  4 Jan 2023
+
+Legierski and Rachwał et al.
+edge deployment. On the other hand, given the limited hard-
+ware resources available on the edge, and the extremely harsh
+conditions of the construction site, a cloud deployment seems
+attractive.
+Given the possible benefits of both solutions, in this contri-
+bution, a solution is proposed for an edge-cloud continuum
+video analytics architecture. The architecture can be deployed
+in two variants (edge-only, and edge-cloud), described in the
+Architecture section. Moreover, to determine the viability of
+the solution, an initial experimental study was performed.
+Here, an IR model was developed and integrated with the
+edge-only variant of the architecture. Next, it was tasked with
+detecting when personnel wearing PPE entered and exited the
+work site.
+2
+Background
+To provide a context for this study, the state of the art of (1)
+IR system architectures and (2) machine learning models for
+PPE detection is summarized.
+System architectures. The most obvious benefit of deploy-
+ing IR systems on the edge is the decreased latency. This was
+demonstrated in [20], where facial recognition models were
+deployed on the edge. The authors found that deploying the
+models on the edge resulted in significantly better response
+speeds, as compared to a cloud deployment. In other stud-
+ies [8, 9], the viability of deploying deep convolutional neural
+networks (CNNs) in the edge-only scenario was investigated.
+CNNs are characterized by high resource utilization, and thus
+are typically deployed in the cloud. The studies found that
+deploying CNNs is viable on mobile devices, when parts of
+the computation can be offloaded to other edge devices. Edge
+deployment allowed to achieve a consistently low latency
+of 2.24 ms while using CNNs to perform real-time object
+tracking in augmented reality [8]. Both studies showed that
+the edge deployment distributing the workload increased the
+inference capabilities of the system, as the models could not
+be run on the disconnected mobile devices alone.
+One study [5] investigated an edge-cloud architecture, where
+data preprocessing servers were deployed close to the data
+source. The preprocessed data was then sent to a cloud-based
+deep-learning platform. This resulted in decreasing network
+latency and traffic. It also increased the security and privacy
+of the raw data.
+On the other hand, edge deployments are more limited
+in terms of the available hardware. Low computational re-
+sources naturally limit the size of models and inference speed.
+A study compared different implementations (based on Ten-
+sorFlow, TensorRT, and TFLite) of the same video processing
+model [6], and found them to differ in their resource utiliza-
+tion. The choice of implementation influenced the energy
+consumption of the model, as well as its inference speed.
+Interestingly, the slowest implementation (TFLite) was the
+most energy efficient. It was also found that TFLite managed
+to remain on par with the other implementations in terms of
+speed, when processing low-resolution video. In the case of
+high-resolution video, more resource-intensive models were
+needed to maintain the speed, suggesting that a cloud deploy-
+ment could be more beneficial in low-resource settings. Nev-
+ertheless, some resource-intensive models can be deployed
+on the edge, if resources available there are sufficient. The
+deployment proposed in a different study required all nodes
+to be equipped with a GPU [9]. This allowed the authors to
+use CNNs on the edge. A similar result was reported in [13],
+were IR models deployed on a Raspberry Pi 4B, equipped
+with a camera, and an Intel Neural Compute Stick 2 (a USB
+device for deep learning inference on the edge) were studied.
+These devices were chosen for their low power consumption
+and good computing capabilities. Overall, a model tasked
+with detecting PPE in the form of helmets and safety vests
+achieved precision on the order of 99.5%.
+Models for PPE detection. Effective video analytics-based
+methods for detecting the presence of protective helmets,
+worn by workers, due to its health and safety importance, is
+currently a hot research topic.
+The usage of existing, unmodified machine learning models
+for detecting protective head covers does not provide suffi-
+cient detection accuracy, as proven in a recent study [19].
+In said article, several versions of the popular YOLO algo-
+rithm [1] were compared. It was shown that the most effective
+version of YOLO for helmet detection is the v4. After improv-
+ing the loss function, it achieved more than 93% accuracy
+during tests. A similar study [10] focused on improving the
+YOLOv5 algorithm. The system achieved results close to 97%
+accuracy, thanks to the improvement of the structure of the
+neural network. Another study [18], also investigated improv-
+ing YOLOv5. However, instead of the algorithm itself, work
+was focused on processing of input data by applying filters
+on the input image. This allowed to improve the accuracy to
+above 95%. Yet another study [15] presented an approach for
+improving the detection speed and accuracy by designing a
+multi-level pyramidal feature fusion network based on the
+ConCaNet attention mechanism. Here, YOLOv3 was applied
+and a dataset with 6000 images was used. The results demon-
+strate the effectiveness of this approach, which managed to
+reduce the number of necessary parameters.
+Helmet detection can also be done using the SSD-MobileNet
+algorithm [4], which is based on yet another variant of CNN.
+An analysis of this method, reported in [7], tested its effec-
+tiveness and managed to reach 80% accuracy during tests.
+In a wider comparison of algorithm types [11], the authors
+proposed a helmet detection method based on a dynamically
+changing neural network – SHDDM (Safety Helmet Detec-
+tion Dynamic Model). The developed model analyzes the
+human posture and defines the area where the helmet should
+be located, to eliminate the detection of the helmet outside
+the head area and thus reduce the false positive rate. There are
+
+Towards Edge-Cloud Architectures for Personal Protective Equipment Detection
+also other approaches to helmet detection, such as methods
+based on color and shape used to to locate the face, and the
+proper wearing of a helmet [16]. Another solution used low-
+resolution images, captured from a video stream, using the
+Local Binary Pattern (LBP) and gray-level co-occurrence ma-
+trix (GLCM) methods along with a back-propagation neural
+network [14].
+Another study [2] investigated the usefulness of artificially
+created images in the training of CNNs for PPE detection. The
+paper presented the results achieved with YOLOv3, trained on
+artificial images generated by the Rockstar Advanced Game
+Engine (RAGE) from the Grand Theft Auto V video game.
+This approach achieved a mean average precision (mAP) of
+only 55.11% on a test dataset consisting of real-world images.
+The mAP for synthetic images was much higher at 87.24%.
+It should be noted that the poor results for the real-world
+images are most likely caused by the RAGE engine being
+unable to generate a sufficient amount of head, welding mask,
+ear protection, and chest object variations.
+As can be seen, there are many possibilities for detecting
+protective helmets. Here, the SHDDM is particularly note-
+worthy, as it has an important feature of checking whether the
+helmet is worn properly, and not only detecting its presence.
+This, in turn, is particularly relevant in real-world applica-
+tions.
+3
+Proposed Architecture
+The proposed video analytics system can be deployed in
+two architecture variants: edge-cloud (Fig. 1) and edge-only
+(Fig. 2). As outlined above, there are reasons to believe that
+both variants may be appropriate for the considered scenario.
+Both architectures share a common core deployed on the edge,
+consisting of: a camera, the Image Processor (IP) component,
+and the OSH (Occupational Safety and Health) manager’s
+mobile device.
+The camera (in the reported experiments the Dahua IPC-
+HFW5449T-ASE-LED was used) provides a live RTSP video
+stream, which is directed to the Image Processor. The IP is
+a service written in Python, which can optionally perform
+preliminary image analysis. Using configurable methods such
+as motion detection and brightness thresholding, the IP is able
+to discard image frames that do not contain moving people,
+reducing network traffic to components involved in actual im-
+age analysis. It is also responsible for communicating with the
+rest of the system, designed in accordance with the ASSIST-
+IoT reference architecture [3]. IP communicates with the rest
+of the system publishing alerts to an MQTT topic. This de-
+sign allows other components and devices in the ASSIST-IoT
+deployment to be notified in a streaming manner of any OSH
+violations, such as workers not wearing protective helmets.
+In the first version of the architecture – the edge-cloud
+deployment – the IP is configured to use the cloud-based
+AWS Rekognition platform, with its PPE detection service.
+ASSIST-IoT deployment 
+AWS
+Rekognition
+Video stream
+OSH alert
+Image Processor
+Camera
+OSH manager's
+mobile device
+Edge
+Filtered 
+video stream
+Inference 
+results
+AWS Cloud
+Figure 1. Edge-cloud deployment
+Video stream
+OSH alert
+Image Processor
+Camera
+OSH manager's
+mobile device
+Edge
+Orange AI&ML Platform
+Video stream
+Processing pipeline
+AI-X
+AI-2
+AI-1
+...
+Result adaptation
+Inference 
+results
+External platform connector
+ASSIST-IoT deployment 
+Figure 2. Edge deployment
+In the edge-only variant, the video analysis is performed by
+the Orange AI&ML Platform, which is deployed on a server
+on the construction site. This edge deployment allows for
+maintaining lower network latency, and ensures the privacy
+of worker data. The AI&ML Platform’s services are written
+as Python runnable modules that provide their own APIs and
+GUIs. The services can reuse the APIs and GUIs provided
+by the platform, or build them from scratch. A service col-
+lects frames from a video source, processes them in an ML
+pipeline specific to the service, and adapts or interprets the
+results. The inference results from the Platform are forwarded
+to external services, with the use of provided connectors. As
+the Orange AI&ML Platform operates on the edge, all video
+
+Legierski and Rachwał et al.
+processing takes place on the client’s site, ensuring full secu-
+rity of customer data (video) and compliance with appropriate
+regulations, such as GDPR.
+4
+Methodology
+As part of this study, a preliminary version of the edge-only
+variant of the architecture was deployed on an active construc-
+tion site. Using the Orange AI&ML Platform, a model was
+trained to count people wearing helmets entering and exiting a
+specific area. The system counts people in helmets in defined
+recognition areas (bounding boxes), crossing the yellow and
+green lines visible in Figs. 3 and 4. People entering the con-
+struction site are counted after crossing the green line, while
+people leaving are counted after crossing the yellow line. The
+machine learning pipeline consists of a YOLOX object detec-
+tion model, trained for detecting heads in helmets, and a Deep-
+SORT [12] multi-object tracking algorithm. The YOLOX
+model was trained using a dataset provided by the Northeast-
+ern University of China (https://public.roboflow.com/object-
+detection/hard-hat-workers).
+The system’s results were compared to those obtained
+from an algorithm built into the Dahua camera. It should
+be noted that the camera counted all people entering and leav-
+ing, including those without protective helmets. However, this
+should not impact the results much, as the safety regulations
+on this particular site forbid entering it without a helmet and
+the rule is strictly enforced before workers reach the counting
+location.
+The measurements were performed in two series – each
+using a different bounding box definition. A single series
+spanned the length of one workday on the construction site.
+The number of entering and leaving people was counted in
+hourly intervals (between 5 AM and 7 PM).
+5
+Results
+The Tables 1 and 2 present the results of the performed exper-
+iments. The Table 1 contains measurements made on 22nd
+November 2022, with the bounding box set as presented in
+Fig. 3. The average difference between the number of people
+entering, as measured by the camera and the model was equal
+to −6.21, with the standard deviation of σ = 5.08, whereas
+for people exiting it was 1.35 and σ = 2.73 respectively. The
+correlation between entrances detected by the camera and the
+model deployed on the AI&ML platform, expressed by the
+Pearson coefficient is 0.988, whereas for exits 0.995. The cor-
+relations were found to be statistically significant (p ≤ 0.05).
+Table 2 contains measurements from 24th November 2022
+(for modified detection areas, depicted in Fig. 4). On that day,
+the average difference for entering was −4.93 with σ = 4.25
+and for exiting 3.92 with σ = 4.92. For these measurements
+the Pearson coefficient for people entering is equal to 0.993
+and exiting 0.989. The correlations were found to be statisti-
+cally significant (p ≤ 0.05).
+Figure 3. Bounding boxes location on November 22 (before
+modification)
+Figure 4. Bounding boxes location on November 24 (after
+modification)
+The tables also present differences in the number of people
+detected by the camera and the AI&ML platform and the sum
+of these differences calculated for both movement directions:
+entries and exits.
+During the experiments, several unexpected events took
+place, which had a significant impact on the reported results.
+Workers were observed acting in an unexpected manner –
+lingering or walking around the detection area (Fig. 5). It
+was also noticed that sometimes the workers put on their
+helmets after having passed the detection area (Fig. 6). These
+behaviors present a challenge to the future system, as they
+significantly affect its accuracy.
+
+Inferen
+POlnferen
+me
+POTowards Edge-Cloud Architectures for Personal Protective Equipment Detection
+Hour
+05:00
+06:00
+07:00
+08:00
+09:00
+10:00
+11:00
+12:00
+13:00
+14:00
+15:00
+16:00
+17:00
+18:00
+Total
+Dahua In
+12
+65
+84
+47
+26
+84
+50
+51
+28
+70
+28
+8
+9
+0
+562
+Dahua Out
+2
+15
+21
+35
+81
+44
+61
+31
+63
+32
+59
+66
+26
+8
+544
+AI&ML In
+11
+78
+87
+52
+28
+96
+60
+58
+43
+75
+33
+18
+10
+0
+649
+AI&ML Out
+2
+13
+23
+33
+73
+44
+63
+31
+58
+31
+59
+62
+25
+8
+525
+Diff. In
+1
+-13
+-3
+-5
+-2
+-12
+-10
+-7
+-15
+-5
+-5
+-10
+-1
+0
+-87
+Diff. Out
+0
+2
+-2
+2
+8
+0
+-2
+0
+5
+1
+0
+4
+1
+0
+19
+Table 1. Entries and exits to the construction site, 22 November 2022.
+Hour
+05:00
+06:00
+07:00
+08:00
+09:00
+10:00
+11:00
+12:00
+13:00
+14:00
+15:00
+16:00
+17:00
+18:00
+Total
+Dahua In
+4
+57
+113
+62
+34
+73
+75
+65
+56
+93
+27
+10
+9
+0
+678
+Dahua Out
+0
+10
+29
+57
+80
+53
+74
+41
+82
+52
+49
+84
+20
+8
+639
+AI&ML In
+3
+61
+113
+68
+43
+76
+79
+73
+69
+98
+33
+21
+10
+0
+747
+AI&ML Out
+0
+11
+26
+46
+64
+48
+72
+38
+73
+49
+47
+82
+22
+6
+584
+Diff. In
+1
+-4
+0
+-6
+-9
+-3
+-4
+-8
+-13
+-5
+-6
+-11
+-1
+0
+-69
+Diff. Out
+0
+-1
+3
+11
+16
+5
+2
+3
+9
+3
+2
+2
+-2
+2
+55
+Table 2. Entries and exits to the construction site, 24 November 2022.
+6
+Concluding remarks
+The tested model demonstrated relatively good performance
+in the investigated scenario. Its accuracy when tasked with
+counting people wearing protective helmets was found to be
+sufficient, and was validated against a different system. A
+number of discrepancies between the counts of the model and
+the camera can be attributed to unexpected situations (Figs. 5
+and 6) and the fact that the Dahua camera did not differentiate
+people wearing and not wearing helmets. The high correla-
+tion coefficient between the camera and the Orange AI&ML
+Platform’s model allows to conclude that the two solutions
+perform comparably well.
+It should be noted that there were changes in the correla-
+tion between the days of experiments. These differences are
+explained by the changes to the bounding box. This is one of
+the parameters that have to be investigated further.
+Both variants of the proposed architecture can be used
+in the investigated scenario of PPE detection on a construc-
+tion site. The feasibility of using an edge-deployment was
+confirmed – the server’s computational capabilities were suf-
+ficient to maintain satisfactory inference accuracy. Therefore,
+it can be concluded that the construction site is equipped with
+sufficient hardware to warrant further experiments with the
+deployment.
+In the future, the two proposed architecture variants will be
+compared in terms of network latencies, resource utilization,
+and their accuracy. The presented model will also be tested
+further, which will include manually annotating the videos to
+obtain a ground truth for comparison. This will allow for de-
+termining the actual accuracy of the developed model. Further
+optimization of bounding box locations is also planned.
+Acknowledgments
+Work supported by ASSIST-IoT project funded from the Eu-
+ropean Union’s H2020 RIA program under grant 957258.
+References
+[1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao.
+2020. YOLOv4: Optimal speed and accuracy of object detection. arXiv
+preprint arXiv:2004.10934 (2020).
+[2] Marco di Benedetto, Enrico Meloni, Giuseppe Amato, Fabrizio Falchi,
+and Claudio Gennaro. 2019. Learning Safety Equipment Detection
+using Virtual Worlds. In 2019 International Conference on Content-
+Based Multimedia Indexing (CBMI). 1–6.
+https://doi.org/10.1109/
+CBMI.2019.8877466
+[3] Alejandro Fornés-Leal, Ignacio Lacalle, Carlos E Palau, Paweł Szmeja,
+Maria Ganzha, Marcin Paprzycki, Eduardo Garro, and Francisco Blan-
+quer. 2022. ASSIST-IoT: A reference architecture for next generation
+Internet of Things. In New Trends in Intelligent Software Methodologies,
+Tools and Techniques. IOS Press, 109–128.
+[4] Andrew G. Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko,
+Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam.
+2017. MobileNets: Efficient Convolutional Neural Networks for Mobile
+Vision Applications. https://doi.org/10.48550/ARXIV.1704.04861
+[5] Yutao Huang, Xiaoqiang Ma, Xiaoyi Fan, Jiangchuan Liu, and Wei
+Gong. 2017. When deep learning meets edge computing. In 2017
+IEEE 25th International Conference on Network Protocols (ICNP).
+1–2. https://doi.org/10.1109/ICNP.2017.8117585
+[6] Anis Koubaa, Adel Ammar, Anas Kanhouch, and Yasser AlHabashi.
+2022. Cloud Versus Edge Deployment Strategies of Real-Time Face
+Recognition Inference. IEEE Transactions on Network Science and
+Engineering 9, 1 (2022), 143–160. https://doi.org/10.1109/TNSE.2021.
+3055835
+[7] Yange Li, Han Wei, Zheng Han, Jianling Huang, and Wei-Dong Wang.
+2020. Deep Learning-Based Safety Helmet Detection in Engineering
+Management Based on Convolutional Neural Networks. Advances in
+Civil Engineering 2020 (09 2020), 1–10. https://doi.org/10.1155/2020/
+9703560
+[8] Luyang Liu, Hongyu Li, and Marco Gruteser. 2019. Edge Assisted
+Real-Time Object Detection for Mobile Augmented Reality. In The
+25th Annual International Conference on Mobile Computing and
+
+Legierski and Rachwał et al.
+Figure 5. Unexpected worker behavior – staying in the detec-
+tion area for longer
+Figure 6. Unexpected worker behavior – putting the helmet
+on behind the detection line
+Networking (Los Cabos, Mexico) (MobiCom ’19). Association for
+Computing Machinery, New York, NY, USA, Article 25, 16 pages.
+https://doi.org/10.1145/3300061.3300116
+[9] Peng Liu, Bozhao Qi, and Suman Banerjee. 2018. EdgeEye: An Edge
+Service Framework for Real-time Intelligent Video Analytics. 1–6.
+https://doi.org/10.1145/3213344.3213345
+[10] Weiran Liu, Yi Hu, and Dawei Fan. 2022. Safety Helmet Wearing
+Recognition Based on Improved YOLOv5. In 2022 11th International
+Conference of Information and Communication Technology (ICTech)).
+466–470. https://doi.org/10.1109/ICTech55460.2022.00099
+[11] Yao Nan, Qin Jian-Hua, Wang Zhen, and Wang Hong-Chang. 2022.
+Safety Helmet Detection Dynamic Model Based on the Critical Area
+Attention Mechanism. In 2022 7th Asia Conference on Power and
+Electrical Engineering (ACPEE). 1296–1303. https://doi.org/10.1109/
+ACPEE53904.2022.9783764
+[12] Nicolai Wojke, Alex Bewley, and Dietrich Paulus. 2017. Simple Online
+and Realtime Tracking with a Deep Association Metric. https://doi.
+org/10.48550/ARXIV.1703.07402
+[13] Pei-Shao Wu, Chun-Yi Lin, Tang-Yu Cheng, and Wu-Sung Yao. 2021.
+Analysis and design of industrial safety automatic identification sys-
+tem based on Tiny-YOLOv3. In 2021 IEEE International Future En-
+ergy Electronics Conference (IFEEC). 1–6. https://doi.org/10.1109/
+IFEEC53238.2021.9661778
+[14] JIANG Xinhua, XUE Heru, ZHANG Lina, and ZHOU Yanqing. 2021.
+A Study of Low-resolution Safety Helmet Image Recognition Combin-
+ing Statistical Features with Artificial Neural Network. In International
+Journal of Simulation: Systems, Science and Technology (IJSSST). 1–6.
+https://doi.org/10.5013/IJSSST.a.17.37.11
+[15] Chang Xu, Jinyu Tian, and Zhiqiang Zeng. 2022. Lightweight Fusion
+Channel Attention Convolutional Neural Network for Helmet Recogni-
+tion. In WSPC Proceedings. 1–8.
+[16] Geng Zhang, Lei Lv, Li Dan, and Min Zhu. 2017. The Method for
+Recognizing Recognition Helmet Based On Color and Shape. In 5th
+International Conference on Machinery, Materials and Computing
+Technology (ICMMCT). 1–5.
+[17] Qingyang Zhang, Hui Sun, Xiaopei Wu, and Hong Zhong. 2019. Edge
+video analytics for public safety: A review. Proc. IEEE 107, 8 (2019),
+1675–1696.
+[18] Fangbo Zhou, Huailin Zhao, and Zhen Nie. 2021. Safety Helmet
+Detection Based on YOLOv5. In 2021 IEEE International Conference
+on Power Electronics, Computer Applications (ICPECA). 6–11. https:
+//doi.org/10.1109/ICPECA51329.2021.9362711
+[19] Mudi Zhou, Zhuli Fang, Bin Zhao, and Pengfei Li. 2021. Safety Helmet
+Wearing Detection and Recognition Based on YOLOv4. In 2021 3rd
+International Academic Exchange Conference on Science and Technol-
+ogy Innovation (IAECST). https://doi.org/10.1109/IAECST54258.2021.
+9695790
+[20] Xihao Zhou and Sye Loong Keoh. 2020. Deployment of Facial Recogni-
+tion Models at the Edge: A Feasibility Study. In 2020 21st Asia-Pacific
+Network Operations and Management Symposium (APNOMS). 214–
+219. https://doi.org/10.23919/APNOMS50412.2020.9236972
+
+RC
\ No newline at end of file
diff --git a/D9AzT4oBgHgl3EQfif2Z/content/tmp_files/load_file.txt b/D9AzT4oBgHgl3EQfif2Z/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ab0fc144e0bc62fb4d7473e10c74beda49dcc1ea
--- /dev/null
+++ b/D9AzT4oBgHgl3EQfif2Z/content/tmp_files/load_file.txt
@@ -0,0 +1,376 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf,len=375
+page_content='Towards Edge-Cloud Architectures for Personal  Protective Equipment Detection  Jarosław Legierski  jaroslaw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='legierski@orange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='com  Orange Innovation, Orange  Polska S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Warsaw, Poland  Kajetan Rachwał  Piotr Sowinski  kajetan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='rachwal@ibspan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='waw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='pl  piotr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='sowinski@ibspan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='waw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='pl  Systems Research Institute Polish  Academy of Sciences  Poland  Warsaw Univesity of Technology  Warsaw, Poland  Wojciech Niewolski  wojciech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='niewolski@orange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='com  Orange Innovation, Orange  Polska S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Poland  Warsaw Univesity of Technology  Warsaw, Poland  Przemysław Ratuszek  Zbigniew Kopertowski  przemyslaw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='ratuszek@orange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='com  zbigniew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='kopertowski@orange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='com  Orange Innovation, Orange  Polska S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Warsaw, Poland  Marcin Paprzycki  Maria Ganzha  marcin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='paprzycki@ibspan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='waw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='pl  maria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='ganzha@ibspan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='waw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='pl  Systems Research Institute Polish  Academy of Sciences  Warsaw, Poland  Abstract  Detecting Personal Protective Equipment in images and video  streams is a relevant problem in ensuring the safety of con-  struction workers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In this contribution, an architecture en-  abling live image recognition of such equipment is proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  The solution is deployable in two settings – edge-cloud and  edge-only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The system was tested on an active construction  site, as a part of a larger scenario, within the scope of the  ASSIST-IoT H2020 project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' To determine the feasibility of  the edge-only variant, a model for counting people wearing  safety helmets was developed using the YOLOX method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' It  was found that an edge-only deployment is possible for this  use case, given the hardware infrastructure available on site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  In the preliminary evaluation, several important observations  were made, that are crucial to the further development and de-  ployment of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Future work will include an in-depth  investigation of performance aspects of the two architecture  variants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Keywords: edge-cloud continuum architectures, PPE detec-  tion, image recognition, worker safety  1  Introduction  Nowadays, the demand for intelligent video analytics is grow-  ing across a wide spectrum of application areas [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The  key part of such systems is usually an image recognition (IR)  component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' However, as of today, the IR subsystem is, most  commonly, deployed in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This approach offers mul-  tiple benefits, such as availability of large and scalable com-  putational resources, reliable APIs, and shifting the burden  of system maintenance to the cloud service provider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' How-  ever, this comes at a cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Sending data to the cloud raises  both security and privacy concerns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Moreover, communicat-  ing with the cloud always induces network latency, which  may be significant in time-critical applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' To address  issues brought about by cloud-centric solutions, edge com-  puting has been proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Here, the core of the approach is  processing the data as close to the source as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This  allows for latency reduction, and helps ensure the security  and privacy of data, which remains within the local network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  However, edge computing has its own set of issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Typically,  the computational resources, which are available at the edge  are considerably smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' A possible solution to addressing  the downsides of both these options is a combined approach –  an edge-cloud continuum, where data is partially processed  on the edge and partially in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' However, this raises  the obvious question: at which point(s), within the continuum,  individual parts of the system should be deployed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Here, this question is considered within a real-world sce-  nario of monitoring the entrance to an active construction  site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Specifically, the system is tasked with ensuring that (1)  no unauthorized people enter the worksite, and (2) every-  body is wearing appropriate Personal Protective Equipment  (PPE), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' helmets and safety vests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The scenario is evalu-  ated as part of the ASSIST-IoT project, on a construction site  in Warsaw, Poland, managed by the construction company  Mostostal Warszawa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Here, the edge versus cloud discussion  becomes particularly relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' On the one hand, the privacy  of workers is of paramount importance, while latencies must  be minimized, to ensure a quick reaction, which hints at an  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='01501v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='CV]  4 Jan 2023  Legierski and Rachwał et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  edge deployment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' On the other hand, given the limited hard-  ware resources available on the edge, and the extremely harsh  conditions of the construction site, a cloud deployment seems  attractive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Given the possible benefits of both solutions, in this contri-  bution, a solution is proposed for an edge-cloud continuum  video analytics architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The architecture can be deployed  in two variants (edge-only, and edge-cloud), described in the  Architecture section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Moreover, to determine the viability of  the solution, an initial experimental study was performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Here, an IR model was developed and integrated with the  edge-only variant of the architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Next, it was tasked with  detecting when personnel wearing PPE entered and exited the  work site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  2  Background  To provide a context for this study, the state of the art of (1)  IR system architectures and (2) machine learning models for  PPE detection is summarized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  System architectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The most obvious benefit of deploy-  ing IR systems on the edge is the decreased latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This was  demonstrated in [20], where facial recognition models were  deployed on the edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The authors found that deploying the  models on the edge resulted in significantly better response  speeds, as compared to a cloud deployment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In other stud-  ies [8, 9], the viability of deploying deep convolutional neural  networks (CNNs) in the edge-only scenario was investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  CNNs are characterized by high resource utilization, and thus  are typically deployed in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The studies found that  deploying CNNs is viable on mobile devices, when parts of  the computation can be offloaded to other edge devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Edge  deployment allowed to achieve a consistently low latency  of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='24 ms while using CNNs to perform real-time object  tracking in augmented reality [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Both studies showed that  the edge deployment distributing the workload increased the  inference capabilities of the system, as the models could not  be run on the disconnected mobile devices alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  One study [5] investigated an edge-cloud architecture, where  data preprocessing servers were deployed close to the data  source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The preprocessed data was then sent to a cloud-based  deep-learning platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This resulted in decreasing network  latency and traffic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' It also increased the security and privacy  of the raw data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  On the other hand, edge deployments are more limited  in terms of the available hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Low computational re-  sources naturally limit the size of models and inference speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  A study compared different implementations (based on Ten-  sorFlow, TensorRT, and TFLite) of the same video processing  model [6], and found them to differ in their resource utiliza-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The choice of implementation influenced the energy  consumption of the model, as well as its inference speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Interestingly, the slowest implementation (TFLite) was the  most energy efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' It was also found that TFLite managed  to remain on par with the other implementations in terms of  speed, when processing low-resolution video.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In the case of  high-resolution video, more resource-intensive models were  needed to maintain the speed, suggesting that a cloud deploy-  ment could be more beneficial in low-resource settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Nev-  ertheless, some resource-intensive models can be deployed  on the edge, if resources available there are sufficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The  deployment proposed in a different study required all nodes  to be equipped with a GPU [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This allowed the authors to  use CNNs on the edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' A similar result was reported in [13],  were IR models deployed on a Raspberry Pi 4B, equipped  with a camera, and an Intel Neural Compute Stick 2 (a USB  device for deep learning inference on the edge) were studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  These devices were chosen for their low power consumption  and good computing capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Overall, a model tasked  with detecting PPE in the form of helmets and safety vests  achieved precision on the order of 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Models for PPE detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Effective video analytics-based  methods for detecting the presence of protective helmets,  worn by workers, due to its health and safety importance, is  currently a hot research topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  The usage of existing, unmodified machine learning models  for detecting protective head covers does not provide suffi-  cient detection accuracy, as proven in a recent study [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  In said article, several versions of the popular YOLO algo-  rithm [1] were compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' It was shown that the most effective  version of YOLO for helmet detection is the v4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' After improv-  ing the loss function, it achieved more than 93% accuracy  during tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' A similar study [10] focused on improving the  YOLOv5 algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The system achieved results close to 97%  accuracy, thanks to the improvement of the structure of the  neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Another study [18], also investigated improv-  ing YOLOv5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' However, instead of the algorithm itself, work  was focused on processing of input data by applying filters  on the input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This allowed to improve the accuracy to  above 95%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Yet another study [15] presented an approach for  improving the detection speed and accuracy by designing a  multi-level pyramidal feature fusion network based on the  ConCaNet attention mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Here, YOLOv3 was applied  and a dataset with 6000 images was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The results demon-  strate the effectiveness of this approach, which managed to  reduce the number of necessary parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Helmet detection can also be done using the SSD-MobileNet  algorithm [4], which is based on yet another variant of CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  An analysis of this method, reported in [7], tested its effec-  tiveness and managed to reach 80% accuracy during tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  In a wider comparison of algorithm types [11], the authors  proposed a helmet detection method based on a dynamically  changing neural network – SHDDM (Safety Helmet Detec-  tion Dynamic Model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The developed model analyzes the  human posture and defines the area where the helmet should  be located, to eliminate the detection of the helmet outside  the head area and thus reduce the false positive rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' There are  Towards Edge-Cloud Architectures for Personal Protective Equipment Detection  also other approaches to helmet detection, such as methods  based on color and shape used to to locate the face, and the  proper wearing of a helmet [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Another solution used low-  resolution images, captured from a video stream, using the  Local Binary Pattern (LBP) and gray-level co-occurrence ma-  trix (GLCM) methods along with a back-propagation neural  network [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Another study [2] investigated the usefulness of artificially  created images in the training of CNNs for PPE detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The  paper presented the results achieved with YOLOv3, trained on  artificial images generated by the Rockstar Advanced Game  Engine (RAGE) from the Grand Theft Auto V video game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  This approach achieved a mean average precision (mAP) of  only 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='11% on a test dataset consisting of real-world images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  The mAP for synthetic images was much higher at 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='24%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  It should be noted that the poor results for the real-world  images are most likely caused by the RAGE engine being  unable to generate a sufficient amount of head, welding mask,  ear protection, and chest object variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  As can be seen, there are many possibilities for detecting  protective helmets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Here, the SHDDM is particularly note-  worthy, as it has an important feature of checking whether the  helmet is worn properly, and not only detecting its presence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  This, in turn, is particularly relevant in real-world applica-  tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  3  Proposed Architecture  The proposed video analytics system can be deployed in  two architecture variants: edge-cloud (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 1) and edge-only  (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' As outlined above, there are reasons to believe that  both variants may be appropriate for the considered scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Both architectures share a common core deployed on the edge,  consisting of: a camera, the Image Processor (IP) component,  and the OSH (Occupational Safety and Health) manager’s  mobile device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  The camera (in the reported experiments the Dahua IPC-  HFW5449T-ASE-LED was used) provides a live RTSP video  stream, which is directed to the Image Processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The IP is  a service written in Python, which can optionally perform  preliminary image analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Using configurable methods such  as motion detection and brightness thresholding, the IP is able  to discard image frames that do not contain moving people,  reducing network traffic to components involved in actual im-  age analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' It is also responsible for communicating with the  rest of the system, designed in accordance with the ASSIST-  IoT reference architecture [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' IP communicates with the rest  of the system publishing alerts to an MQTT topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This de-  sign allows other components and devices in the ASSIST-IoT  deployment to be notified in a streaming manner of any OSH  violations, such as workers not wearing protective helmets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  In the first version of the architecture – the edge-cloud  deployment – the IP is configured to use the cloud-based  AWS Rekognition platform, with its PPE detection service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content="  ASSIST-IoT deployment  AWS  Rekognition  Video stream  OSH alert  Image Processor  Camera  OSH manager's  mobile device  Edge  Filtered  video stream  Inference  results  AWS Cloud  Figure 1." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=" Edge-cloud deployment  Video stream  OSH alert  Image Processor  Camera  OSH manager's  mobile device  Edge  Orange AI&ML Platform  Video stream  Processing pipeline  AI-X  AI-2  AI-1  ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Result adaptation  Inference  results  External platform connector  ASSIST-IoT deployment  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Edge deployment  In the edge-only variant, the video analysis is performed by  the Orange AI&ML Platform, which is deployed on a server  on the construction site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This edge deployment allows for  maintaining lower network latency, and ensures the privacy  of worker data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The AI&ML Platform’s services are written  as Python runnable modules that provide their own APIs and  GUIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The services can reuse the APIs and GUIs provided  by the platform, or build them from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' A service col-  lects frames from a video source, processes them in an ML  pipeline specific to the service, and adapts or interprets the  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The inference results from the Platform are forwarded  to external services, with the use of provided connectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' As  the Orange AI&ML Platform operates on the edge, all video  Legierski and Rachwał et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  processing takes place on the client’s site, ensuring full secu-  rity of customer data (video) and compliance with appropriate  regulations, such as GDPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  4  Methodology  As part of this study, a preliminary version of the edge-only  variant of the architecture was deployed on an active construc-  tion site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Using the Orange AI&ML Platform, a model was  trained to count people wearing helmets entering and exiting a  specific area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The system counts people in helmets in defined  recognition areas (bounding boxes), crossing the yellow and  green lines visible in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' People entering the con-  struction site are counted after crossing the green line, while  people leaving are counted after crossing the yellow line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The  machine learning pipeline consists of a YOLOX object detec-  tion model, trained for detecting heads in helmets, and a Deep-  SORT [12] multi-object tracking algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The YOLOX  model was trained using a dataset provided by the Northeast-  ern University of China (https://public.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='roboflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='com/object-  detection/hard-hat-workers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  The system’s results were compared to those obtained  from an algorithm built into the Dahua camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' It should  be noted that the camera counted all people entering and leav-  ing, including those without protective helmets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' However, this  should not impact the results much, as the safety regulations  on this particular site forbid entering it without a helmet and  the rule is strictly enforced before workers reach the counting  location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  The measurements were performed in two series – each  using a different bounding box definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' A single series  spanned the length of one workday on the construction site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  The number of entering and leaving people was counted in  hourly intervals (between 5 AM and 7 PM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  5  Results  The Tables 1 and 2 present the results of the performed exper-  iments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The Table 1 contains measurements made on 22nd  November 2022, with the bounding box set as presented in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The average difference between the number of people  entering, as measured by the camera and the model was equal  to −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='21, with the standard deviation of σ = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='08, whereas  for people exiting it was 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='35 and σ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='73 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The  correlation between entrances detected by the camera and the  model deployed on the AI&ML platform, expressed by the  Pearson coefficient is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='988, whereas for exits 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The cor-  relations were found to be statistically significant (p ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Table 2 contains measurements from 24th November 2022  (for modified detection areas, depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' On that day,  the average difference for entering was −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='93 with σ = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='25  and for exiting 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='92 with σ = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' For these measurements  the Pearson coefficient for people entering is equal to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='993  and exiting 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The correlations were found to be statisti-  cally significant (p ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Bounding boxes location on November 22 (before  modification)  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Bounding boxes location on November 24 (after  modification)  The tables also present differences in the number of people  detected by the camera and the AI&ML platform and the sum  of these differences calculated for both movement directions:  entries and exits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  During the experiments, several unexpected events took  place, which had a significant impact on the reported results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Workers were observed acting in an unexpected manner –  lingering or walking around the detection area (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' It  was also noticed that sometimes the workers put on their  helmets after having passed the detection area (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' These  behaviors present a challenge to the future system, as they  significantly affect its accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Inferen  POlnferen  me  POTowards Edge-Cloud Architectures for Personal Protective Equipment Detection  Hour  05:00  06:00  07:00  08:00  09:00  10:00  11:00  12:00  13:00  14:00  15:00  16:00  17:00  18:00  Total  Dahua In  12  65  84  47  26  84  50  51  28  70  28  8  9  0  562  Dahua Out  2  15  21  35  81  44  61  31  63  32  59  66  26  8  544  AI&ML In  11  78  87  52  28  96  60  58  43  75  33  18  10  0  649  AI&ML Out  2  13  23  33  73  44  63  31  58  31  59  62  25  8  525  Diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In  1  13  3  5  2  12  10  7  15  5  5  10  1  0  87  Diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Out  0  2  2  2  8  0  2  0  5  1  0  4  1  0  19  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Entries and exits to the construction site, 22 November 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Hour  05:00  06:00  07:00  08:00  09:00  10:00  11:00  12:00  13:00  14:00  15:00  16:00  17:00  18:00  Total  Dahua In  4  57  113  62  34  73  75  65  56  93  27  10  9  0  678  Dahua Out  0  10  29  57  80  53  74  41  82  52  49  84  20  8  639  AI&ML In  3  61  113  68  43  76  79  73  69  98  33  21  10  0  747  AI&ML Out  0  11  26  46  64  48  72  38  73  49  47  82  22  6  584  Diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In  1  4  0  6  9  3  4  8  13  5  6  11  1  0  69  Diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Out  0  1  3  11  16  5  2  3  9  3  2  2  2  2  55  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Entries and exits to the construction site, 24 November 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  6  Concluding remarks  The tested model demonstrated relatively good performance  in the investigated scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Its accuracy when tasked with  counting people wearing protective helmets was found to be  sufficient, and was validated against a different system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' A  number of discrepancies between the counts of the model and  the camera can be attributed to unexpected situations (Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 5  and 6) and the fact that the Dahua camera did not differentiate  people wearing and not wearing helmets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The high correla-  tion coefficient between the camera and the Orange AI&ML  Platform’s model allows to conclude that the two solutions  perform comparably well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  It should be noted that there were changes in the correla-  tion between the days of experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' These differences are  explained by the changes to the bounding box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This is one of  the parameters that have to be investigated further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Both variants of the proposed architecture can be used  in the investigated scenario of PPE detection on a construc-  tion site.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The feasibility of using an edge-deployment was  confirmed – the server’s computational capabilities were suf-  ficient to maintain satisfactory inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Therefore,  it can be concluded that the construction site is equipped with  sufficient hardware to warrant further experiments with the  deployment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  In the future, the two proposed architecture variants will be  compared in terms of network latencies, resource utilization,  and their accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The presented model will also be tested  further, which will include manually annotating the videos to  obtain a ground truth for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' This will allow for de-  termining the actual accuracy of the developed model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Further  optimization of bounding box locations is also planned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Acknowledgments  Work supported by ASSIST-IoT project funded from the Eu-  ropean Union’s H2020 RIA program under grant 957258.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  References  [1] Alexey Bochkovskiy, Chien-Yao Wang, and Hong-Yuan Mark Liao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' YOLOv4: Optimal speed and accuracy of object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' arXiv  preprint arXiv:2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='10934 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  [2] Marco di Benedetto, Enrico Meloni, Giuseppe Amato, Fabrizio Falchi,  and Claudio Gennaro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Learning Safety Equipment Detection  using Virtual Worlds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In 2019 International Conference on Content-  Based Multimedia Indexing (CBMI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1109/  CBMI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='8877466  [3] Alejandro Fornés-Leal, Ignacio Lacalle, Carlos E Palau, Paweł Szmeja,  Maria Ganzha, Marcin Paprzycki, Eduardo Garro, and Francisco Blan-  quer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' ASSIST-IoT: A reference architecture for next generation  Internet of Things.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In New Trends in Intelligent Software Methodologies,  Tools and Techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' IOS Press, 109–128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  [4] Andrew G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko,  Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' MobileNets: Efficient Convolutional Neural Networks for Mobile  Vision Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='04861  [5] Yutao Huang, Xiaoqiang Ma, Xiaoyi Fan, Jiangchuan Liu, and Wei  Gong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' When deep learning meets edge computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In 2017  IEEE 25th International Conference on Network Protocols (ICNP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  1–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1109/ICNP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='8117585  [6] Anis Koubaa, Adel Ammar, Anas Kanhouch, and Yasser AlHabashi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Cloud Versus Edge Deployment Strategies of Real-Time Face  Recognition Inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' IEEE Transactions on Network Science and  Engineering 9, 1 (2022), 143–160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1109/TNSE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  3055835  [7] Yange Li, Han Wei, Zheng Han, Jianling Huang, and Wei-Dong Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Deep Learning-Based Safety Helmet Detection in Engineering  Management Based on Convolutional Neural Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Advances in  Civil Engineering 2020 (09 2020), 1–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1155/2020/  9703560  [8] Luyang Liu, Hongyu Li, and Marco Gruteser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Edge Assisted  Real-Time Object Detection for Mobile Augmented Reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In The  25th Annual International Conference on Mobile Computing and  Legierski and Rachwał et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Unexpected worker behavior – staying in the detec-  tion area for longer  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Unexpected worker behavior – putting the helmet  on behind the detection line  Networking (Los Cabos, Mexico) (MobiCom ’19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Association for  Computing Machinery, New York, NY, USA, Article 25, 16 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1145/3300061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='3300116  [9] Peng Liu, Bozhao Qi, and Suman Banerjee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' EdgeEye: An Edge  Service Framework for Real-time Intelligent Video Analytics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1145/3213344.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='3213345  [10] Weiran Liu, Yi Hu, and Dawei Fan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Safety Helmet Wearing  Recognition Based on Improved YOLOv5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In 2022 11th International  Conference of Information and Communication Technology (ICTech)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  466–470.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1109/ICTech55460.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='00099  [11] Yao Nan, Qin Jian-Hua, Wang Zhen, and Wang Hong-Chang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Safety Helmet Detection Dynamic Model Based on the Critical Area  Attention Mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In 2022 7th Asia Conference on Power and  Electrical Engineering (ACPEE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 1296–1303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1109/  ACPEE53904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='9783764  [12] Nicolai Wojke, Alex Bewley, and Dietrich Paulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Simple Online  and Realtime Tracking with a Deep Association Metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='07402  [13] Pei-Shao Wu, Chun-Yi Lin, Tang-Yu Cheng, and Wu-Sung Yao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  Analysis and design of industrial safety automatic identification sys-  tem based on Tiny-YOLOv3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In 2021 IEEE International Future En-  ergy Electronics Conference (IFEEC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1109/  IFEEC53238.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='9661778  [14] JIANG Xinhua, XUE Heru, ZHANG Lina, and ZHOU Yanqing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  A Study of Low-resolution Safety Helmet Image Recognition Combin-  ing Statistical Features with Artificial Neural Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In International  Journal of Simulation: Systems, Science and Technology (IJSSST).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='5013/IJSSST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='11  [15] Chang Xu, Jinyu Tian, and Zhiqiang Zeng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Lightweight Fusion  Channel Attention Convolutional Neural Network for Helmet Recogni-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In WSPC Proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 1–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  [16] Geng Zhang, Lei Lv, Li Dan, and Min Zhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' The Method for  Recognizing Recognition Helmet Based On Color and Shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In 5th  International Conference on Machinery, Materials and Computing  Technology (ICMMCT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 1–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  [17] Qingyang Zhang, Hui Sun, Xiaopei Wu, and Hong Zhong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Edge  video analytics for public safety: A review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' IEEE 107, 8 (2019),  1675–1696.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  [18] Fangbo Zhou, Huailin Zhao, and Zhen Nie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Safety Helmet  Detection Based on YOLOv5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In 2021 IEEE International Conference  on Power Electronics, Computer Applications (ICPECA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 6–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https:  //doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1109/ICPECA51329.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='9362711  [19] Mudi Zhou, Zhuli Fang, Bin Zhao, and Pengfei Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Safety Helmet  Wearing Detection and Recognition Based on YOLOv4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In 2021 3rd  International Academic Exchange Conference on Science and Technol-  ogy Innovation (IAECST).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='1109/IAECST54258.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='  9695790  [20] Xihao Zhou and Sye Loong Keoh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' Deployment of Facial Recogni-  tion Models at the Edge: A Feasibility Study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' In 2020 21st Asia-Pacific  Network Operations and Management Symposium (APNOMS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' 214–  219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='23919/APNOMS50412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
+page_content='9236972  RC' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/D9AzT4oBgHgl3EQfif2Z/content/2301.01501v1.pdf'}
diff --git a/EdA0T4oBgHgl3EQfA_-G/content/tmp_files/2301.01970v1.pdf.txt b/EdA0T4oBgHgl3EQfA_-G/content/tmp_files/2301.01970v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..441c5313496795691bf8a3029f60dfe1bd88bd22
--- /dev/null
+++ b/EdA0T4oBgHgl3EQfA_-G/content/tmp_files/2301.01970v1.pdf.txt
@@ -0,0 +1,2269 @@
+CAT: LoCalization and IdentificAtion Cascade Detection Transformer
+for Open-World Object Detection
+Shuailei Ma 1* Yuefeng Wang1† Jiaqi Fan1 Ying Wei1‡
+Thomas H. Li3 Hongli Liu2 Fanbing Lv2
+1Northeast University, 2Changsha Hisense Intelligent System Research Institute Co., Ltd.
+3Information Technology R&D Innovation Center of Peking University,
+Abstract
+Open-world object detection (OWOD), as a more gen-
+eral and challenging goal, requires the model trained from
+data on known objects to detect both known and unknown
+objects and incrementally learn to identify these unknown
+objects.
+The existing works which employ standard de-
+tection framework and fixed pseudo-labelling mechanism
+(PLM) have the following problems: (𝑖) The inclusion of de-
+tecting unknown objects substantially reduces the model’s
+ability to detect known ones. (𝑖𝑖) The PLM does not ade-
+quately utilize the priori knowledge of inputs. (𝑖𝑖𝑖) The fixed
+selection manner of PLM cannot guarantee that the model
+is trained in the right direction. We observe that humans
+subconsciously prefer to focus on all foreground objects and
+then identify each one in detail, rather than localize and
+identify a single object simultaneously, for alleviating the
+confusion. This motivates us to propose a novel solution
+called CAT: LoCalization and IdentificAtion Cascade De-
+tection Transformer which decouples the detection process
+via the shared decoder in the cascade decoding way. In the
+meanwhile, we propose the self-adaptive pseudo-labelling
+mechanism which combines the model-driven with input-
+driven PLM and self-adaptively generates robust pseudo-
+labels for unknown objects, significantly improving the abil-
+ity of CAT to retrieve unknown objects. Comprehensive ex-
+periments on two benchmark datasets, 𝑖.𝑒., MS-COCO and
+PASCAL VOC, show that our model outperforms the state-
+of-the-art in terms of all metrics in the task of OWOD, in-
+cremental object detection (IOD) and open-set detection.
+1. Introduction
+Open-world object detection (OWOD) is a more prac-
+tical detection problem in computer vision, making artifi-
+*First author. Email: xiaomabufei@gmail.com
+†Code url: https://github.com/xiaomabufei/CAT
+‡Corresponding author. Email: weiying@ise.neu.edu.cn
+Bear
+Frog
+Flower
+Squirrel
+Unknown
+Cat
+BeeUnknown
+Unknown
+Unknown
+Unknown
+Figure 1. When faced with new scenes in open world, humans sub-
+consciously focus on all foreground objects and then identify them
+in detail in order to alleviate the confusion between the known and
+unknown objects and get a clear view. Motivated by this, our CAT
+utilizes the shared decoder to decouple the localization and iden-
+tification process in the cascade decoding way, where the former
+decoding process is used for localization and the latter for identi-
+fication.
+cial intelligence (AI) smarter to face more difficulties in real
+scenes. Within the OWOD paradigm, the model’s life-span
+is pushed by iterative learning process. At each episode, the
+model trained only by known objects needs to detect known
+objects while simultaneously localizing unknown objects
+and identifying them into the unknown class. Human an-
+notators then label a few of these tagged unknown classes
+of interest gradually. The model given these newly-added
+annotations will continue to incrementally update its knowl-
+edge without retraining from scratch.
+Recently, the work [17] proposed an open-world ob-
+ject detector, ORE, based on the two-stage Faster R-CNN
+[33] pipeline. ORE utilizes an auto-labelling step to obtain
+pseudo-unknowns for training model to detect unknown ob-
+jects and learns an energy-based binary classifier to distin-
+guish the unknown class from known classes. However,
+its success largely relies on a held-out validation set which
+1
+arXiv:2301.01970v1  [cs.CV]  5 Jan 2023
+
+is leveraged to estimate the distribution of unknown ob-
+jects in the energy-based classifier. To alleviate the prob-
+lems in ORE, OW-DETR [13] proposes to use the detection
+transformer [3, 38] for OWOD in a justifiable way and di-
+rectly leverages the framework of DDETR [38]. In addi-
+tion, OW-DETR proposes an attention-driven PLM which
+selects pseudo labels for unknown objects according to the
+attention scores.
+For the existing works, we find the following hindering
+problems. (𝑖) Owing to the inclusion of detecting unknown
+objects, the model’s ability to detect known objects substan-
+tially drops. To alleviate the confusion between known and
+unknown objects, humans prefer to dismantle the process of
+open-world object detection rather than parallelly localize
+and identify open-world objects like most standard detec-
+tion models. (𝑖𝑖) To the best of our knowledge, in the exist-
+ing OWOD PLM, models leverage the learning process for
+known objects to guide the generation of pseudo labels for
+unknown objects, without leveraging the prior conditions of
+the inputs (𝑡𝑒𝑥𝑡𝑢𝑟𝑒,𝑙𝑖𝑔ℎ𝑡 𝑓 𝑙𝑜𝑤,𝑒𝑡𝑐). As a result, the model
+cannot learn knowledge beyond the data annotation. (𝑖𝑖𝑖)
+The fixed selection manner of PLM cannot guarantee that
+the model learns to detect unknown objects in the right di-
+rection, due to the uncertain quality of the pseudo labels.
+The models may be worse for detecting unknown objects.
+When faced with a new scene, humans prefer focusing
+on all foreground objects and then analyse them in detail,
+as shown in Figure.1. Motivated by this and the aforemen-
+tioned observations, we propose a novel LoCalization and
+IdentificAtion Cascade Detection Transformer. CAT com-
+prises three dedicated components namely, self-adaptive
+pseudo-labelling mechanism, shared transformer de-
+coder and cascade decoupled decoding structure. The
+self-adaptive PLM maintains the ability of CAT to ex-
+plore the knowledge beyond the known objects and self-
+adaptively adjusts the pseudo-label generation according to
+the model training process. Via the cascade decoupled de-
+coding structure, the shared transformer decoder decouples
+the localization and identification process for alleviating the
+influence of detecting unknown objects on the detection of
+known objects, where the former decoding process is used
+for localization and the latter for identification. In the mean-
+while, we observe the structure substantially improves the
+model’s ability for incremental object detection according
+to the experiments. In addition, we explore the decoupled
+structures for detection transformer. Our contributions can
+be summarized fourfold:
+• We propose a novel localization and identification cas-
+cade detection transformer (CAT), which decouples
+the localization and identification process of detection
+and alleviates the influence of detecting unknown ob-
+jects on the detection of known ones.
+• We introduce a novel pseudo-labelling mechanism
+which self-adaptively combines the model-driven and
+input-driven pseudo-labelling during the training pro-
+cess for generating robust pseudo-labels and exploring
+knowledge beyond known objects.
+• We explore the decoupled decoding methods of the de-
+tection transformer, 𝑖.𝑒., the fully decoupled decoding
+structure and the cascade decoupled decoding struc-
+ture.
+• Our extensive experiments on two popular bench-
+marks demonstrate the effectiveness of the proposed
+CAT. CAT outperforms the recently introduced ORE
+and OW-DETR for OWOD, IOD and open-set detec-
+tion. For OWOD, CAT achieves absolute gains ranging
+from 11.8% to 18.3% in terms of unknown recall over
+OW-DETR.
+2. Problem Formulation
+At time 𝑡, let K𝑡 = {1,2,...,𝐶} denote the set of known
+object classes and U𝑡 = {𝐶 + 1,...} denote the unknown
+classes which might be encountered at the test time. The
+known object categories K𝑡 are labeled in the dataset
+D𝑡 = {J 𝑡,L𝑡} where J 𝑡 denotes the input images and
+L𝑡 denotes the corresponding labels at time 𝑡. The train-
+ing image set consists of 𝑀 images J 𝑡 = {𝑖1,𝑖2,...,𝑖𝑀 }
+and corresponding labels L𝑡 = {ℓ1,ℓ2,...,ℓ𝑀 }. Each ℓ𝑖 =
+{T1,T2,...,T𝑁 } denotes a set of 𝑁 object instances with
+their class labels 𝑐𝑛 ⊂ K𝑡 and locations, 𝑥𝑛, 𝑦𝑛,𝑤𝑛, ℎ𝑛
+denote the bounding box center coordinates, width and
+height respectively. The Open-World Object Detection re-
+moves the artificial assumptions and restrictions in tradi-
+tional object detection and makes object detection tasks
+more aligned with real life. It requires the trained model
+M𝑡 not only to detect the previously encountered known
+classes 𝐶 but also to identify an unseen class instance as
+belonging to the unknown class. In addition, it requires the
+object detector to be capable of incremental update for new
+knowledge and this cycle continues over the detector’s lifes-
+pan. In incremental updating phase, the unknown instances
+identified by M𝑡 are annotated manually, and along with
+their corresponding training examples, update D𝑡 to D𝑡+1
+and K𝑡 to K𝑡+1 = {1,2,...,𝐶,...,𝐶 +n}, the model adds the
+𝑛 new classes to known classes and updates itself to M𝑡+1
+without retraining from scratch on the whole dataset D𝑡+1.
+3. Proposed method
+This section elaborates the proposed CAT in details. In
+Sec.3.1, the overall architecture of CAT is described in de-
+tail. A novel self-adaptive adjustment strategy for pseudo-
+labelling is proposed in Sec.3.2. We explore to decouple
+the decoding process of the detection transformer and pro-
+pose the localization and identification cascade decoupled
+2
+
+Figure 2. Overall Architecture of proposed CAT framework. The proposed CAT consists of a multi-scale feature extractor, the shared trans-
+former decoder, the regression prediction branch, and the self-adaptive pseudo-labelling. The multi-scale feature extractor comprises the
+mainstream feature extraction backbone and a deformable transformer encoder, for extracting multi-scale features. The shared transformer
+decoder is a deformable transformer decoder and decouples the localization and identification process in the cascade decoding way. The
+regression prediction branch contains the bounding box regression branch 𝐹𝑟𝑒𝑔, novelty objectness branch 𝐹𝑜𝑏 𝑗, and novelty classification
+branch 𝐹𝑐𝑙𝑠. While the novelty classification and objectness branches are single-layer feed-forward networks (FFN) and the regression
+branch is a 3-layer FFN.
+decoding structure in Sec.3.3. In Sec.3.4, we illustrate the
+end-to-end training strategy of CAT.
+3.1. Overall Architecture
+As shown in Figure.2, for a given image J ∈ R𝐻×𝑊 ×3,
+CAT uses a hierarchical feature extraction backbone to
+extract multi-scale features Z𝑖 ∈ R
+H
+4×𝑖2 ×
+𝑤
+4×2𝑖 ×2𝑖𝐶𝑠,𝑖 = 1,2,3.
+The feature maps 𝑍𝑖 are projected from dimension 𝐶𝑠
+to dimension 𝐶𝑑 by using 1×1 convolution and concate-
+nated to 𝑁𝑠 vectors with 𝐶𝑑 dimensions after flattening
+out.Afterwards, along with supplement positional encod-
+ing 𝑃𝑛 ∈ R𝑁𝑠×𝐶𝑑, the multi-scale features are sent into the
+deformable transformer encoder to encode semantic fea-
+tures. The encoded semantic features 𝑀 ∈ R𝑁𝑠×𝑐𝑑 are ac-
+quired and sent into the shared decoder together with a
+set of 𝑁 learnable location queries and positional embed-
+dings 𝑃𝑚 ∈ R𝑁𝑠×𝐶𝑑. Aided by interleaved cross-attention
+and self-attention modules, the shared decoder transforms
+the location queries Q location ∈ R𝑁 ×𝐷 to a set of N loca-
+tion query embeddings E location ∈ R𝑁 ×𝐷. The Elocation are
+then input to the regression branch to locate N foreground
+bounding boxes containing the known classes and unknown
+classes. Meanwhile, the E location are used as class queries
+and sent into the shared decoder together with the 𝑀 and
+𝑃𝑚 again. The shared decoder transforms the class queries
+to 𝑁 class query embeddings Eclass that are corresponding to
+the location query embeddings. The Eclass are then sent into
+the objectness and novelty classification branch to predict
+the objectness and category respectively. After selecting the
+unique queries that best match the known instances by a bi-
+partite matching loss, the remaining queries are utilized to
+select the unknown category instances and generate pseudo
+labels by self-adaptive pseudo-labelling mechanism.
+3.2. Self-Adaptive Pseudo-labelling
+Pseudo labels play an important role in guiding mod-
+els to detect unknown object instances, determining the up-
+per learning limitation of the model. The existing meth-
+ods [13,17] only use model-driven pseudo-labelling and do
+not take full advantage of the inputs’ priori knowledge (light
+flow, textures, 𝑒𝑡𝑐).
+The model-driven pseudo-labelling
+[13] makes the model’s learning get caught up in the knowl-
+edge of known objects, for the reason that the only source
+of knowledge for the model is known object instances.
+In addition, their fixed selection manner cannot guarantee
+the right learning direction for unknown objects. We pro-
+pose to combine model-driven with input-driven pseudo-
+labelling [31, 36, 39] for expanding the knowledge sources
+of the model. In the meanwhile, the pseudo-labels selec-
+tion scheme should not be fixed, but be adapted as train-
+ing and able to adjust itself when facing the unexpected
+problems. In this paper, a novel pseudo-labelling mech-
+anism is proposed for self-adaptively combining model-
+driven and input-driven pseudo-labelling according to the
+situation faced by the model, where the attention-driven
+pseudo-labelling [13] is used as the model-driven pseudo-
+3
+
+Shared Decoder
+Multi-Scale Feature
+Decoder
+Decoder
+Decoder
+Freg
+Layer 1
+Layer 2
+Layer N
+Deformable
+Transformer
+Encoder
+Fobj
+Decoder
+Decoder
+Decoder
+Layer 1
+Layer 2
+Layer N
+Fcls
+Shared Decoder
+human
+cup
+unknown
+Positional Encoding
+Self-Adaptive Pseudo-Labelling
+Pseudo labels
+Model-driven
+Positional Embeddings
+Pseudo-labelling
+Self-Adaptive
+Location Queries
+Adjustment Strategy
+Location Embeddings
+Input-driven
+Class Queries
+Pseudo-labelling
+Class Embeddingslabelling and selective search [36] is selected as the input-
+driven pseudo-labelling. In self-adaptive pseudo-labelling
+mechanism, the model-driven pseudo-labelling generates
+pseudo-labels’ candidate boxes 𝑃𝑚 and the corresponding
+confidence 𝑠𝑜, and the input-driven pseudo-labelling gen-
+erates pseudo-label candidate boxes 𝑃𝐼 . The object confi-
+dence of generated pseudo labels is formulated as follows:
+S𝑖 = (𝑛𝑜𝑟𝑚 (𝑠𝑜))W𝑚 ·
+�
+max
+1≤ 𝑗 ≤|P𝐼 |
+�
+IOU
+�
+𝑃𝐼
+𝑗, 𝑃𝑚
+𝑖
+��� W𝐼
+, (1)
+where IOU(·) (Intersection-over-union [34]) is the most
+commonly used metric for comparing the similarity be-
+tween two arbitrary shapes, 𝑖 denotes the index of the
+pseudo labels. W𝑚 and W𝐼 are the self-adaptive weights,
+which are controlled by the 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑟, 𝑆𝑒𝑛𝑠𝑜𝑟 and
+𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑟, as formulated below:
+W𝑡 = 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑟(W𝑡−1, 𝑆𝑒𝑛𝑠𝑜𝑟(𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑟(𝐿𝑚))), (2)
+where 𝐿𝑚 represents the loss memory which is stored and
+updated in real time during model training. The formulation
+is illustrated in Equation.3:
+𝐿𝑚 = DEQUE(𝑙𝑜𝑠𝑠𝑡−1,𝑙𝑜𝑠𝑠𝑡−2,··· ,𝑙𝑜𝑠𝑠𝑡−𝑛),
+(3)
+where 𝑡 is the current iteration. Considering the sensitivity
+of the model and the uneven quality of the data, we leverage
+𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑟 to obtain the trend of the losses Δ𝑙 for replacing
+the single loss. The formula is as follows:
+𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑟(𝐿𝑚) =
+�𝑛
+𝑖=1 𝛼𝑖 · 𝑙𝑜𝑠𝑠𝑡−𝑖
+�𝑁
+𝑗=𝑛+1 𝛽 𝑗 · 𝑙𝑜𝑠𝑠𝑡− 𝑗
+,
+𝑛 < 𝑁 < 𝑇,
+(4)
+where 𝛼 and 𝛽 denote the weighted average weights and
+�𝑛
+𝑖=1 𝛼𝑖 = �𝑁
+𝑗=𝑛+1 𝛽 𝑗 = 𝛼𝑖−𝛼𝑖−1
+𝛼𝑖+1−𝛼𝑖 = 𝛽𝑗−𝛽𝑗−1
+𝛽𝑗+1−𝛽𝑗 = 1. In the 𝑆𝑒𝑛𝑠𝑜𝑟,
+the variable of the weight Δ𝑤 is acquired as follows:
+𝑆𝑒𝑛𝑠𝑜𝑟(Δ𝑙) =
+� 𝜋𝑛𝑚𝑎 · 𝑆𝑖𝑔𝑚𝑜𝑖𝑑(Δ𝑙 −1),Δ𝑙 > 1,
+−𝜋𝑝𝑚𝑎 ·Δ𝑙,Δ𝑙 ≤ 1,
+(5)
+where 𝜋𝑝𝑚𝑎 and 𝜋𝑛𝑚𝑎 represents the positive and negative
+momentum amplitude, respectively. In the 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑟, we
+use Equation.6 to update the self-adaptive weight via a in-
+cremental way [5,14,17], for memory storage and enhanc-
+ing the robustness (more explanations in Appendix A.1).
+���
+���
+W 𝑡
+𝑚 = W 𝑡−1
+𝑚
++Δ𝑤 ×W 𝑡−1
+𝑚
+,
+W 𝑡
+𝐼 = W 𝑡−1
+𝐼
+−Δ𝑤 ×W 𝑡−1
+𝐼
+,
+W 𝑡
+𝑚,W 𝑡
+𝐼 = 𝑛𝑜𝑟𝑚 �W 𝑡
+𝑚,W 𝑡
+𝐼
+� ,
+(6)
+where 𝑛𝑜𝑟𝑚(·) is the normalization operation. The update
+strategy for the weights during training is shown in Algo-
+rithm.1.
+Algorithm 1 COMPUTINGADAPTIVEWEIGHTS
+Input: Loss Memory: 𝐿𝑚; Current Interation: 𝑡; Positive
+Momentum Amplitude: 𝜋𝑝𝑚𝑎; Negative Momentum
+Amplitude: 𝜋𝑛𝑚𝑎; 𝑇𝑠𝑡𝑎𝑟𝑡: Start iteration; 𝑇𝑏: Weight
+updating cycle; Loss← Compute using Equation.11
+Output: self-adaptive weights 𝑊𝑚𝑡 and 𝑊𝐼 𝑡
+1: while 𝑡𝑟𝑎𝑖𝑛 do
+2:
+if 𝑡 ≤ 𝑇𝑠𝑡𝑎𝑟𝑡 then
+3:
+Initialise 𝑊𝑚0 ← 0.8 and 𝑊𝐼 0 ← 0.2
+4:
+Initialise 𝐿𝑚 using Equation.3
+5:
+else
+6:
+Update 𝐿𝑚 using Equation.3
+7:
+if 𝑡%𝑇𝑏 == 0 then
+8:
+Compute Δ𝑙 using 𝐿𝑚 and Equation.4
+9:
+Compute Δ𝑤 using Δ𝑙 and Equation.5
+10:
+Update W𝑚𝑡 and W𝐼 𝑡 using Equation.6
+11:
+end if
+12:
+end if
+13: end while
+3.3. Exploration of Decoupled Decoding Structure
+Detection transformer [2, 3, 7, 21, 27, 38] leverages the
+object queries to detect object instances, where each ob-
+ject query represents an object instance.
+In the decod-
+ing stage, the object queries are updated to query embed-
+dings by connecting object queries with semantic informa-
+tion from the encoded semantic features. The generated
+query embeddings couple the location and category infor-
+mation for both object localization and identification pro-
+cess simultaneously. For open-world object detection, the
+model requires to detect the known objects, localize the un-
+known objects and identify them as the unknown class. For
+the parallel decoding structure, we observe that the inclu-
+sion of detecting unknown reduces the model’s ability to
+detect known objects.
+Inspired by how humans subcon-
+sciously confront new scenarios, we propose to decouple
+the decoding process of DETR for mitigating the impact of
+unknown object detection on detecting known objects. In
+this paper, we explore two decoupled decoding ways, 𝑖.𝑒.,
+the fully decoupled decoding structure and the cascade de-
+coupled decoding structure.
+3.3.1
+Fully Decoupled Decoding Structure
+For decoupling the location and category information, an
+intuitive way is to carry out the localization and identifi-
+cation process independently. Motivated by this, the fully
+decoupled decoding structure (FD) is proposed. In the fully
+decoupled decoding structure, location and class queries are
+two sets of mutually independent queries sent to the shared
+decoder. This operation of FD is shown in Figure 3 (a),
+4
+
+Figure 3. (a) The fully decoupled decoding structure has two independent decoding processes for localization and identification. (b) In
+the cascade decoupled decoding structure, the location embeddings are used as class queries for knowledge retention. (c) For the coupled
+decoding structure, the same query is put into the decoder for localization and identification.
+which is formulated as follows:
+ELocation = F𝑠 (F𝑒(∅(J), 𝑃𝑛), 𝑃𝑚,Q Location,R) ,
+(7)
+EClass = F𝑠 (F𝑒(∅(J), 𝑃𝑛), 𝑃𝑚,Q Class ,R) ,
+(8)
+where F𝑠(·) denotes the shared decoder. F𝑒(·) is the en-
+coder and ∅(·) is the backbone. 𝑃𝑛 and 𝑃𝑚 stands for the
+positional encoding and embeddings, respectively. R repre-
+sents the reference points and J denotes the input image.
+Q Class stands for the class queries.
+3.3.2
+Cascade Decoupled Decoding Structure
+Inspired by how people react to new scenarios, a cascade
+decoupled decoding structure is proposed to decode the en-
+coded features in a cascade way so that the localization pro-
+cess is not restricted by the category information, while the
+identification process can get help from the location knowl-
+edge in the cascade structure. The operation of localization
+and identification cascade decoding structure is expressed
+as follows:
+ELocation = F𝑠 (F𝑒(∅(J), 𝑃𝑛), 𝑃𝑚,Q Location,R) ,
+(9)
+EClass = F𝑠 (F𝑒(∅(J), 𝑃𝑛), 𝑃𝑚,ELocation ,R) .
+(10)
+As shown in Figure.3 (b), the location embeddings are used
+as class queries to generate class embeddings.
+3.4. Training and Inference
+Our CAT is trained end-to-end using the following joint
+loss formulation:
+𝐿 = 𝐿𝑙𝑜𝑐𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 + 𝐿𝑖𝑑𝑒𝑛𝑡𝑖 𝑓 𝑖𝑐𝑎𝑡𝑖𝑜𝑛 + 𝐿𝑜𝑏 𝑗𝑒𝑐𝑡𝑛𝑒𝑠𝑠,
+(11)
+where 𝐿𝑙𝑜𝑐𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛, 𝐿𝑖𝑑𝑒𝑛𝑡𝑖 𝑓 𝑖𝑐𝑎𝑡𝑖𝑜𝑛 and 𝐿𝑜𝑏 𝑗𝑒𝑐𝑡𝑛𝑒𝑠𝑠 de-
+notes the loss terms for foreground localization, novelty
+identification and object scoring, respectively. When a set
+of new categories are introduced at each episode, we em-
+ploy an exemplar replay based finetuning to alleviate catas-
+trophic forgetting of learned classes and then finetune the
+model using a balanced set of exemplars stored for each
+known class. The bounding boxes and categories predic-
+tions of the known and 𝑡𝑜𝑝-k unknown objects are simulta-
+neous used during evaluation.
+4. Experiments
+4.1. Datasets and Metrics
+The experiments are implemented on two mainstream
+splits of MS-COCO [23] and Pascal VOC [10] dataset.
+We group the classes into a set of nonoverlapping tasks
+�
+𝑇1,...,𝑇𝑡,...
+�
+. The class in task 𝑇 𝑐 only appears in tasks
+where 𝑡 ≥ 𝑐. In task 𝑇 𝑐, classes encountered in {𝑇 𝑐 : 𝑐 ≤ 𝑡}
+and {𝑇 𝑐 : 𝑐 > 𝑡} are considered as known and unknown
+classes, respectively.
+OWOD SPLIT [17] spilts the 80 classes of MS-COCO into
+4 tasks and selects training set for each task from the MS-
+COCO and Pascal VOC training set images. Pascal VOC
+testing and MS-COCO validation set are used for evalua-
+tion. See more details in Appendix A.2.
+MS-COCO SPLIT [13] mitigates data leakage across tasks
+in [17] and is more challenging. The training and testing
+data are selected from MS-COCO.
+Metrics: Following the most commonly used evaluation
+metric for object detection, we use mean average preci-
+sion (mAP) to evaluate the known objects.
+Inspired by
+[1,9,13,17,25], U-Recall, Wilderness Impact (WI, see de-
+tailed in Appendix A.3) and Absolute Open-Set Error (A-
+OSE) are used as main metric for unknown objects. U-
+Recall measures the ability of the model to retrieve un-
+5
+
+Location Queries
+Location Queries
+Encoded Semantic Features
+Location
+Encoded Semantic Features
+Location
+I Semantic Features
+Object Queries
+Embeddings
+Shared
+Embeddings
+Shared
+Location
+Decoder
+Decoder
+Embeddings
+Class Queries
+Decoder
+Class Queries
+Shared
+Class Embeddings
+Shared
+Decoder
+Decoder
+Class Embeddings
+Class Embeddings
+(a) Fully Decoupled Decoding
+(b) Cascade Decoupled Decoding
+(c) Coupled DecodingTable 1. State-of-the-art comparison on OWOD split. The comparison is shown in terms of U-Recall, WI, A-OSE and known class mAP.
+U-Recall measures the ability of the model to retrieve unknown object instances for OWOD problem. Both WI and A-OSE implicitly
+quantify the effevtiveness of the model in handling unknown objects. For a fair comparison, we compare with the recently introduced
+OW-DETR [13] and ORE [17] not employing EBUI (the results are reproduced by the same GPUs as our model). The CAT achieves
+improved all metrics over the existing works across all tasks, demonstrating our model’s effectiveness for OWOD problem. U-Recall, WI
+and A-OSE cannot be computed in Task 4 due to the absence of unknown test annotations, for the reason that all 80 classes are known.
+Task IDs →
+Task 1
+Task 2
+Task 3
+Task 4
+U-Recall
+WI
+A-OSE
+mAP(↑)
+U-Recall
+WI
+A-OSE
+mAP(↑)
+U-Recall
+WI
+A-OSE
+mAP(↑)
+mAP(↑)
+(↑)
+(↓)
+(↓)
+Current
+known
+(↑)
+(↓)
+(↓)
+Previously
+known
+Current
+known
+Both
+(↑)
+(↓)
+(↓)
+Previously
+known
+Current
+known
+Both
+Previously
+known
+Current
+known
+Both
+Faster-RCNN [33]
+-
+0.0699
+13396
+56.4
+-
+0.0371
+12291
+3.7
+26.7
+15.2
+-
+0.0213
+9174
+2.5
+15.2
+6.7
+0.8
+14.5
+4.2
+Faster-RCNN
++ Finetuning
+Not applicable in Task 1
+-
+0.0375
+12497
+51.0
+25.0
+38.0
+-
+0.0279
+9622
+38.2
+13.6
+30.0
+29.7
+13.0
+25.6
+DDETR [38]
+-
+0.0608
+33270
+60.3
+-
+0.0368
+18115
+4.5
+31.3
+17.9
+-
+0.0197
+9392
+3.3
+22.5
+8.5
+2.5
+16.4
+6.0
+DDETR
++ Finetuning
+Not applicable in Task 1
+-
+0.0337
+17834
+54.5
+34.4
+44.8
+-
+0.0195
+10095
+40.0
+17.8
+33.3
+32.5
+20.0
+29.4
+Cascade
+-
+0.0476
+42083
+60.5
+-
+0.0308
+21928
+5.0
+33.7
+19.2
+-
+0.0189
+12189
+4.2
+24.9
+10.2
+3.6
+18.2
+7.6
+Cascade
++ Finetuning
+Not applicable in Task 1
+-
+0.0296
+20587
+55.4
+35.0
+46.0
+-
+0.0184
+12854
+42.4
+19.2
+35.2
+34.6
+21.8
+31.6
+ORE-EBUI [17]
+4.9
+0.0621
+10459
+56.0
+2.9
+0.0282
+10445
+52.7
+26.0
+39.4
+3.9
+0.0211
+7990
+38.2
+12.7
+29.7
+29.6
+12.4
+25.3
+OW-DETR [13]
+7.1
+0.0590
+10248
+58.9
+6.8
+0.0279
+8540
+52.9
+29.1
+41.0
+7.8
+0.0191
+6840
+38.1
+14.7
+30.3
+30.8
+13.3
+26.4
+Ours:CAT
+21.8
+0.0581
+7070
+59.9
+18.6
+0.0263
+5902
+54.0
+33.6
+43.8
+23.9
+0.0177
+5189
+42.1
+19.8
+34.7
+35.1
+17.1
+30.6
+(+14.7)
+(-0.0009)
+(-3178)
+(+1.0)
+(+11.8)
+(-0.0016)
+(-2638)
+(+1.1)
+(+4.5)
+(+2.8)
+(+16.1)
+(-0.0014)
+(-1651)
+(+4.0)
+(+5.1)
+(+4.4)
+(+4.3)
+(+3.8)
+(+4.2)
+Table 2. State-of-the-art comparison on MS-COCO split. The
+comparison is shown in terms of U-Recall and mAP. Although
+the MS-COCO split is more challenging, our model gets a more
+significant improvement on this in comparison to ORE and OW-
+DETR. The significant metric improvements demonstrate that our
+CAT has the ability to retrieve new knowledge beyond the range
+of closed set and would not be limited by category knowledge of
+existing objects. See Sec.4.3 for more details.
+Task IDs ↓
+Metrics
+ORE
+OW-DETR
+Our:CAT
+U-Recall(↑)
+1.5
+5.7
+24.0 (+18.3)
+Task1
+mAP(↑)
+Current known
+61.4
+71.5
+74.2 (+2.7)
+U-Recall(↑)
+3.9
+6.2
+23.0 (+16.8)
+Previously known
+56.5
+62.8
+67.6 (+4.8)
+Current known
+26.1
+27.5
+35.5 (+8.0)
+Task2
+mAP(↑)
+Both
+40.6
+43.8
+50.7 (+6.9)
+U-Recall(↑)
+3.6
+6.9
+24.6 (+17.7)
+Previously known
+38.7
+45.2
+51.2 (+6.0)
+Current known
+23.7
+24.9
+32.6 (+7.7)
+Task3
+mAP(↑)
+Both
+33.7
+38.5
+45.0 (+6.5)
+Previously known
+33.6
+38.2
+45.4 (+7.2)
+Current known
+26.3
+28.1
+35.1 (+7.0)
+Task4
+mAP(↑)
+Both
+31.8
+33.1
+42.8 (+9.7)
+known object instances for OWOD problem. Both WI and
+A-OSE implicitly quantify the effevtiveness of the model in
+handling unknown objects.
+4.2. Implementation Details
+The multi-scale feature extractor consists of a Resnet-
+50 [16] pretrained on ImageNet [8] in a self-supervised [4]
+manner and a deformable transformer encoder whose num-
+ber of layer is set to 6. For the shared decoder, we use a
+deformable transformer decoder and the numbder of layer
+is set to 6, too. We set the number of queries 𝑀 = 100, the
+dimension of the embeddings 𝐷 = 256 and the number of
+pseudo-labels 𝑘 = 5. During inference, 𝑡𝑜𝑝-50 high scor-
+ing detections are used for evaluation for per image. More
+details are described in the Appendix A.4.
+4.3. Comparison With State-of-the-art Methods
+For a fair comparison, we compare CAT with ORE [17]
+without the energy-based unknown identifier (EBUI) that
+relies on held-out validation data with weak unknown object
+supervision and OW-DETR [13] to demonstrate the effec-
+tiveness of our method for OWOD problem. We present the
+comparison in terms of known class mAP, unknown class
+recall, WI, and A-OSE, where U-Recall, WI and A-OSE
+cannot be computed in Task 4 due to the absence of un-
+known test annotations, for the reason that all 80 classes are
+known. Furthermore, we demonstrate the effectiveness of
+our model for incremental object detection in comparison
+to [13,17,30,35].
+OWOD SPLIT: The results compared with the state-of-
+the-art methods on OWOD split for OWOD problem are
+shown in Table.1. The performance of proposed standard
+cascade detection transformer is also reported to be com-
+pared with Faster R-CNN [33] and the standard Deformable
+DETR [38] frameworks, for demonstrating the power of
+localization identification cascade structure.
+These three
+can only identify known objects, and so U-Recall cannot
+be computed for them. Benefiting from the self-adaptive
+pseudo-labelling, the ability of CAT to detect unknown ob-
+jects goes substantially beyond the existing models. Com-
+pared with OW-DETR’s U-Recall of 7.1, 6.8 and 7.8 on
+Task 1, 2 and 3, our CAT achieves 21.8, 18.6 and 23.9 in the
+6
+
+corresponding tasks, achieving significant absolute gains up
+to 16.1%. In terms of WI and A-OSE, CAT also exceeds
+them in all tasks. The ability to detect known objects and al-
+leviate catastrophic forgetting of previous knowledge gains
+an improved performance with significant gains, achieving
+significant absolute gains up to 4.4%. This demonstrates the
+significant performance of the cascade decoding structure.
+In addition, we report qualitative results in Figure.4, along
+with failure case analysis. See more detailed qualitative re-
+sults in Appendix B.2.
+MS-COCO SPLIT: We report the results on MS-COCO
+split in Table.2.
+MS-COCO split mitigates data leakage
+across tasks and assign more data to each Task, while CAT
+receives a more significant boost compared with OWOD
+split. Compared with OW-DETR’s U-Recall of 5.7, 6.2 and
+6.9 on Task 1, 2 and 3, our CAT achieves 24.0, 23.0 and
+24.6 in the corresponding tasks, achieving significant abso-
+lute gains up to 18.3%. Furthermore, the performance on
+detecting known objects achieves significant absolute gains
+up to 9.7%. This demonstrates that our CAT has the more
+powerful ability to retrieve new knowledge and detect the
+known objects when faced with more difficult tasks.
+Figure 4. Predictions from CAT after being trained on Task 1.
+The results show that the model not only detects other categories
+in the total category that have not yet been learned, such as ‘key-
+board’, ‘kite’ and ‘dining table’, but also accurately detects cate-
+gories outside the total category, such as ‘calendar’, ‘table lamp’
+and ‘rubbish bins’. The approach misclassifies two of the ‘bird’
+as ‘aeroplane’ and ‘unknown’, showing the limitation of CAT. See
+more detailed qualitative results and analysis in Appendix B.2.
+Incremental Object Detection: To intuitively present our
+CAT’s ability for detecting object instances, we compare it
+to [13,17,30,35] on the incremental object detection (IOD)
+task. We evaluate the experiments on three standard set-
+tings, where a group of classes (10, 5 and last class) are in-
+troduced incrementally to a detector trained on the remain-
+ing classes (10, 15 and 19), based on PASCAL VOC 2007
+dataset [10]. As the results shown in Table.3, CAT outper-
+forms the existing method in a great migration on all three
+settings, indicating the power of localization and identifica-
+tion cascade detection transformer for IOD.
+Table 3. State-of-the-art comparison for incremental object detec-
+tion for three different settings on PASCAL VOC dataset. The
+comparison is shown in terms of overall mAP. Our CAT achieves
+significant performance in comparison to existing works on all the
+three settings. See more details in Sec.4.3 and Appedix B.1.
+Method
+10+10 settings
+15+5 settings
+19+1 settings
+ILOD [35]
+63.2
+65.8
+68.2
+Faster ILOD [30]
+62.1
+67.9
+68.5
+ORE [17]
+64.5
+68.5
+68.8
+OW-DETR [13]
+65.7
+69.4
+70.2
+Ours: CAT
+67.7 (+2.0)
+72.2 (+2.8)
+73.8 (+3.6)
+4.4. Ablation Study
+We conduct abundant ablative experiments to verify the
+effectiveness of CAT’s components on the OWOD split
+[17].
+Cascade Decoupled Decoding Structure: We compare
+between OW-DETR, fully decoupled decoding structure
+and CAT in Table.4. The results illustrate that the decoupled
+decoding structure improves the performance of detecting
+known objects and does mitigate the influence of unknown
+objects on the detection of known objects to some extent.
+Because it reduces the difficulty of parameter learning and
+mitigates the risk of confusion for known and unknown ob-
+jects by disassembling the localization and identification
+process of detection. Compared with the fully decoupled
+decoding structure, the cascade decoupled decoding struc-
+ture is able to allow the identification process to draw on
+location information while the localization process is not
+limited by category knowledge and outperforms it.
+Self-Adaptive Pseudo-labelling: As shown in Figure.5 (a)
+and (b), we performed a number of ablation experiments
+on Task 1 for different update cycles, positive and nega-
+tive momentum amplitudes. The results demonstrate that
+the self-adaptive pseudo-labelling makes the training pro-
+cess of CAT robust, as we analyzed earlier. Especially for
+the pink line, even if there are unexpected situations in the
+training process, CAT can still self-adjust and develop in
+a good direction. In addition, we compare the attention-
+driven (AD) and self-adaptive (SA) paeudo-labelling mech-
+anism in Table.5 and Figure.5 (c). The results demonstrate
+that our self-adaptive pseudo-labelling mechanism signifi-
+cantly improves the model’s ability to retrieve unknown ob-
+jects. During training, CAT requires double decoding pro-
+cesses so that it is affected by generated pseudo-labels twice
+as often as OW-DETR. Thus, for the high quality pseudo-
+7
+
+person:76%
+unknown:29%
+unkn0wn:35%
+tvmonitor:93%
+unknown:29%
+aeroplane:79%
+2
+bird:45%
+unkn0wn:29%
+unkn0wn:31%
+unkn0wn:26%
+unknunkn0wh:26%
+unknown:27%
+unkn0wn:26%
+unkn0wn:28%
+person:94%
+chair:82%
+chair:91%
+pottedplant:81%
+unknown:25%
+unkn0wn:30%Figure 5. (a) and (b) illustrate performance comparison between different update cycles, positive and negative momentum amplitude on
+A-OSE and U-Recall. Where the cycle is set to 150 and 300, the positive momentum amplitude is set to 25%, 33% and 50%, the negative
+momentum amplitude is set to 50%, respectively. The lighter coloured lines are the real data and the corresponding darker coloured lines
+are the data after smoothing. (c) shows performance comparison between AD and SA. See detail in Sec.4.4.
+Table 4. Performance comparison between different decoupled de-
+coding structures and OW-DETR. ‘FD’ refers to the fully decou-
+pled decoding structure. See more details in Sec.4.4.
+Task IDs ↓
+Metrics
+OW-DETR
+FD
+CAT
+Task1
+mAP(↑)
+Current known
+59.3
+57.9
+59.9
+Previously known
+53.0
+49.5
+54.0
+Current known
+29.4
+29.4
+33.6
+Task2
+mAP(↑)
+Both
+41.3
+39.4
+43.8
+Previously known
+38.1
+41.2
+42.1
+Current known
+15.0
+18.5
+19.8
+Task3
+mAP(↑)
+Both
+30.5
+33.5
+34.7
+Previously known
+30.6
+33.3
+35.1
+Current known
+14.0
+15.8
+17.1
+Task4
+mAP(↑)
+Both
+26.8
+28.9
+30.6
+labels, CAT could learn better to detect unknown objects
+than OW-DETR. For the low quality pseudo-labels, CAT
+would also be affected to a greater extent. The results in Ta-
+ble.5 further demonstrate this investigation and the robust-
+ness of our pseudo-labelling mechanism to generate pseudo
+labels.
+Open-set Detection Comparison: To further demonstrate
+CAT’s ability to handle unknown instances in open-set data,
+we follow the same evaluation protocol as [13, 17, 26] and
+report the performance in Table.6. CAT achieves promising
+performance in comparison to the existing methods.
+5. Relation to Prior Works
+The issue of standard object detection [3,6,12,15,22,24,
+29,32,33,38,40] has been raised for several years, number-
+ous works have investigated this problem and push the field
+to certain heights. Whereas the strong assumption that the
+label space of object categories to be encountered during the
+life-span of the model is the same as during its training re-
+sults that these methods cannot meet real-world needs. The
+success of [11,18–20,28,33] demonstrates the feasibility of
+Table 5. Performance comparison AD and SA pseudo-labelling
+mechanism.
+The results demonstrate that SA substantially en-
+hances the model’s ability to retrieve unknown objects
+Method
+Task IDs ↓
+AD
+SA
+U-Recall
+WI
+A-OSE
+
+
+7.1
+0.0590
+10248
+Task1
+
+
+19.8
+0.0578
+8360
+
+
+6.8
+0.0279
+8540
+Task2
+
+
+16.8
+0.0268
+6452
+
+
+7.8
+0.0191
+6840
+OW-DETR
+Task3
+
+
+21.8
+0.0175
+5310
+
+
+5.4
+0.0533
+41474
+Task1
+
+
+21.8
+0.0581
+7070
+
+
+4.9
+0.0271
+20410
+Task2
+
+
+18.6
+0.0263
+5902
+
+
+6.0
+0.0186
+11078
+CAT
+Task3
+
+
+23.9
+0.0177
+5189
+Table 6. Performance comparison on open-set object detection
+task. Our CAT achieves significant performance in comparison to
+existing works. See more details in Sec.4.4.
+Evaluated on →
+VOC
+WR1
+Standard Faster R-CNN [35]
+81.8
+77.1
+Standard RetinaNet
+79.2
+73.8
+Dropout Sampling [26]
+78.1
+71.1
+ORE [17]
+81.3
+78.2
+OW-DETR [13]
+82.1
+78.6
+Ours: CAT
+83.2 (+1.1)
+79.5 (+0.9)
+foreground localization based on the position and appear-
+ance of objects. ORE [17] and OW-DETR [13] leverage
+the models of standard object detection and pseudo labels
+to detect objects in open world. In this paper, we propose a
+novel transformer [37] based framework, CAT, for OWOD.
+CAT decouples the localization and identification process
+and connects them in a cascade approach. In CAT, the fore-
+ground localization process is not limited by the category
+8
+
+24
+24
+3e+4
+20
+20
+2.6e+4
+16
+2.2e+4
+I
+12
+1.8e+4
+Tp=150, Tpma=25%,Tnma=50%
+Tp=150, Tpma=33%,Tnma=50%
+1.4e+4
+Tp=150, Tpma=50%,Tnma=50%
+Tp=300, Tpma=25%,Tnma=50%
+CAT + Self_Adaptive
+le+z
+CAT + Attention_Driven
+Tp=300, Tpma=33%,Tnma=50%
+OW-DETR + Self_Adaptive
+be+s
+Tp=300, Tpma=50%,Tnma=50%
+OW-DETR + Attention_Drive
+5
+20
+25
+30
+35
+40
+45
+0
+15
+20
+25
+30
+35
+40
+45
+50
+10
+15
+20
+25
+30
+35
+40
+45
+50of known objects, whereas the process of foreground iden-
+tification can use information from the localization process.
+Along with self-adaptive pseudo-labelling, CAT can gain
+information beyond the data annotation and maintain a sta-
+ble learning process according to self-regulation.
+6. Conclusions
+In this paper, we analyze the drawbacks of the paral-
+lel decoding structure for open-world object detection and
+explore the decoupled decoding structures of the detection
+transformer. Motivated by the subconscious reactions of
+humans when facing new scenes, we propose a novel lo-
+calization and identification cascade detection transformer
+(CAT), which decouples the localization and identification
+process via the cascade decoding structure. The cascade
+decoding structure alleviates the influence of detecting un-
+known objects on the detection of known objects.
+With
+the self-adaptive pseudo-labelling mechanism, CAT gains
+knowledge beyond the data annotation, generates pseudo
+labels with robustness and maintains a stable training pro-
+cess via self-adjustment. The extensive experiments on two
+popular benchmarks, 𝑖.𝑒., PASCAL VOC and MS COCO
+demonstrate that CAT consistently outperforms the existing
+works for all task settings on all splits and achieves state-of-
+the-art performance in the incremental object detection and
+open-set detection.
+Acknowledgment
+This work is supported by National Natural Science
+Foundation of China (grant No.61871106 and No.6137015
+2), Key R&D projects of Liaoning Province, China (grant
+No.2020JH2/10100029), and the Open Project Program Fo-
+undation of the Key Laboratory of Opto-Electronics Infor-
+mation Processing, Chinese Academy of Sciences (OEIP-
+O-202002).
+A. Additional Experiments Material
+A.1. Theory For Self-Adaptive Pseudo-labelling
+For 0 < 𝑤2 < 𝑤1 < 1, we find the potential relationship
+as follows:
+� 𝑥𝑤1 > 𝑥𝑤2,𝑖 𝑓 𝑥 > 1
+𝑥𝑤1 < 𝑥𝑤2,𝑖 𝑓 𝑥 < 1
+(12)
+Thus, for 𝑥𝑤1 ·𝑦𝑤2 and 𝑤1 > 𝑤2, if 𝑥 > 1 and 𝑦 > 1, 𝑥 weights
+more and 𝑦 weights more if 𝑥 < 1 and 𝑦 < 1.
+For the self-adaptive pseudo-labelling, we first normal-
+ize 𝑠𝑜 to the range 0 to 1. Considering that the model it-
+self has little knowledge in the early stages of model train-
+ing, the model-driven pseudo-labelling should weight less
+than the input-deiven pseudo-labelling. As the training time
+of the model increasing, the knowledge base of the model
+grows and the weight of the model-driven pseudo-labelling
+gets bigger. Combining this with the patterns above, we set
+W𝑚0 to 0.8, W𝐼 0 to 0.2 and update them as follows:
+���
+���
+W 𝑡
+𝑚 = W 𝑡−1
+𝑚
++Δ𝑤 ×W 𝑡−1
+𝑚
+,
+W 𝑡
+𝐼 = W 𝑡−1
+𝐼
+−Δ𝑤 ×W 𝑡−1
+𝐼
+,
+W 𝑡
+𝑚,W 𝑡
+𝐼 = 𝑛𝑜𝑟𝑚 �W 𝑡
+𝑚,W 𝑡
+𝐼
+� ,
+(13)
+A.2. Additional Illustration For Data Split
+As shown in Table.7, the OWOD split proposed in ORE
+groups all VOC classes and data as 𝑇𝑎𝑠𝑘 1. The remaining
+60 classes of MS-COCO are grouped into three successive
+tasks (𝑇𝑎𝑠𝑘 2, 3, 4) with semantic drifts. However, it leads
+data leakage across tasks since different classes which be-
+long to a super-categories are introduced in different tasks.
+The MS-COCO split proposed in OW-DETR is a stricter
+split, where all the classes of a super-categories are intro-
+duced at a time in a task.
+Table 7. The table shows task composition in the OWOD and MS-
+COCO split for Open-world evaluation protocol. The semantics of
+each task and the number of images and instances(objects) across
+splits are shown.
+Task ID
+Task 1
+Task 2
+Task 3
+Task 4
+OWOD split
+Semantic split
+VOC
+Classes
+Outdoor, Accessories,
+Appliances, Truck
+Sports,
+Food
+Electronic, Indoor,
+Kitchen, Furniture
+# training images
+16551
+45520
+39402
+40260
+# test images
+4952
+1914
+1642
+1738
+# train instances
+47223
+113741
+114452
+138996
+# test instances
+14976
+4966
+4826
+6039
+MS-COCO split
+Semantic split
+Animals,Person,
+Vehicles
+Appliances, Accessories,
+Outdoor, Furniture
+Sports,
+Food
+Electronic, Indoor,
+Kitchen
+# training images
+89490
+55870
+39402
+38903
+# test images
+3793
+2351
+1642
+1691
+# train instances
+421243
+163512
+114452
+160794
+# test instances
+17786
+7159
+4826
+7010
+A.3. WI, A-OSE and U-Recall Metrics
+In this paper, we mainly illustrate the state-of-the-art
+comparison in terms of wilderness impact (WI), absolute
+open-set error (A-OSE), unknown recall (U-Recall) and
+mean average precision (mAP). WI measures the model’s
+confusion in predicting an unknown instance as known
+class. The calculation formula is as follows:
+WI =
+𝑃K
+𝑃K∪U
+−1
+(14)
+Where 𝑃K is the prediction on known classes and 𝑃K∪U
+is the prediction on known and unknown classes. A-OSE
+devotes the total number of unknown instances detected as
+known classes. Both WI and A-OSE indicate the degree of
+confusion in predicting the known classes in the presence
+9
+
+of unknown instances. Furthermore, U-Recall directly mea-
+sures the model’s ability to retrieve the unknown instances.
+A.4. Additional Implementation Details
+For selective search, we use the 𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑣𝑒 𝑠𝑒𝑎𝑟𝑐ℎ
+function in Selectivesearch library and the scale, sigma,
+min size of parameter is set to 500, 0.9 and 200, respec-
+tively. In addition, we eliminate candidate boxes with less
+than 2000 pixel points. The multi-scale feature maps ex-
+tracted from the backbone are projected to feature maps
+with 256-channels using 1 × 1 convolution filters and used
+as multi-scale input to deformable transformer encoder. The
+PyTorch library and eight NVIDIA RTX 3090 GPUs are
+used to train our CAT framework with a batch size of 3 im-
+ages per GPUs. In each task, the CAT framework is trained
+for 50 epochs and finetuned for 20 epochs during the in-
+cremental learning step. We train our CAT using the Adam
+optimizer with a base learning rate of 2 × 10−4, 𝛽1 = 0.9,
+𝛽2 = 0.999, and weight decay of 10−4. For finetuning dur-
+ing incremental step, the learning rate is reduced by a factor
+of 10 and trained using a set of 50 stored exemplars per
+known class.
+B. Additional Results
+B.1. Incremental Object Detection
+Table.8 shows a detailed comparison of CAT with exist-
+ing approaches on PASCAL VOC. Evaluation is performed
+on three standard settings, where a group of classes (10, 5
+and last class) are introduced incrementally to a detector
+trained on the remaining classes (10,15 and 19). Our CAT
+performs favorably against existing approaches on all three
+settings, illustrating the power of localization identification
+cascade detection transformer for incremental objection de-
+tection.
+B.2. Additional Qualitative Results
+Figure.6 illustrates the visualization results comparison
+between OW-DETR and our CAT. We use OW-DETR and
+CAT which are both trained on Task 1, the known classes
+are ‘aeroplane’, ‘bicycle’, ‘bird’, ‘boat’, ‘bottle’, ‘bus’,
+‘car’, ‘cat’, ‘chair’, ‘cow’, ‘diningtable’, ‘dog’, ‘horse’,
+‘motorbike’, ‘person’, ‘pottedplant’, ‘sheep’, ‘sofa’, ‘train’
+and ‘tvmonitor’. The results show that our CAT substan-
+tially outperforms OW-DETR in terms of the ability to ex-
+plore unknown objects and the accuracy of detection due to
+the clever cascade decoupled decoding structure and self-
+adaptive pseudo-labelling. As shown in the first row, OW-
+DETR identifies the background and known objects as un-
+knowns and the real unknown object (carton) as the back-
+ground, and our model accurately identifies the carton as
+the unknown object. In the second row, OW-DETR iden-
+tifies the two calendars as the chair and the background,
+respectively, and the keyboard as the background, and our
+CAT accurately identifies them as unknown objects. The
+third row shows that OW-DETR fails to detect the true
+unknown object (frame) and identifies two known objects
+(sofa) as one. Our model accurately identifies the frame as
+an unknown object and also accurately identifies the two
+sofas.
+Figure.7 describes the visualization results comparison
+between CAT and Oracle. We visualize the detection results
+of our model for known and unknown objects, as well as the
+ground truth on the tasks corresponding to the weights, in-
+cluding the labels of known and unknown categories, where
+the objects of unknown categories are the objects of other
+categories that have not yet appeared in the total categories
+of the dataset.
+Our model can accurately detect known
+objects and unknown objects outside the total class of the
+dataset, such as the electric plug and sound switch in the
+first row, the camera in the second row and the kitten toy
+in the third row. It is also worth noting that although our
+model detects the audio, it does not identify it as an un-
+known object, but as a remote, showing the limitations of
+our model.
+Figure.8 exhibits the visualization performance on in-
+cremental object detection. We visualize the detection re-
+sults of the weights corresponding to different tasks for the
+same scenario. The results show that our CAT can identify
+unknown kinds of objects as the unknown class and accu-
+rately identify their classes after incrementally learning the
+unknown classes, such as sports ball and tennis racket in
+the first row, surfboard in the second row and traffic light in
+the third row.
+C. Societal Impact and Limitations
+Open-world object detection makes artificial intelligence
+smarter to face more problems in real life. It takes object de-
+tection to a cognitive level, as the model requires more than
+simply remembering the objects learned, it requires deeper
+thinking about the scene.
+Although our results demonstrate significant improve-
+ments over ORE and OW-DETR in terms of WI, A-OSE,
+U-Recall and mAP, the performances are still on the lower
+side due to the challenging nature of the open-world de-
+tection problem.
+In this paper, we are mainly commit-
+ted to enhance the model’s ability to explore unknown
+classes. However, the confidence level of our model for
+the detection of unknown objects still needs to be im-
+proved, and this is what we will strive for in the fu-
+ture.
+References
+[1] Ankan Bansal, Karan Sikka, Gaurav Sharma, Rama Chel-
+lappa, and Ajay Divakaran. Zero-shot object detection. In
+10
+
+Figure 6. Visualization results comparison between OW-DETR and our CAT. We use OW-DETR and CAT which are both trained on Task
+1, the known classes are ‘aeroplane’, ‘bicycle’, ‘bird’, ‘boat’, ‘bottle’, ‘bus’, ‘car’, ‘cat’, ‘chair’, ‘cow’, ‘diningtable’, ‘dog’, ‘horse’,
+‘motorbike’, ‘person’, ‘pottedplant’, ‘sheep’, ‘sofa’, ‘train’ and ‘tvmonitor’. The results show that our CAT substantially outperforms
+OW-DETR in terms of the ability to explore unknown objects and the accuracy of detection due to the clever cascade decoupled decoding
+structure and self-adaptive pseudo-labelling mechanism. As shown in the first row, OW-DETR identifies the background and known objects
+as unknowns and the real unknown object (carton) as the background, and our model accurately identifies the carton as the unknown
+object. In the second row, OW-DETR identifies the two calendars as the chair and the background, respectively, and the keyboard as the
+background, and our CAT accurately identifies them as unknown objects. The third row shows that OW-DETR not only does not detect the
+true unknown object (frame), but also identifies two known objects (sofa) as one. Our model accurately identifies the frame as an unknown
+object and also accurately identifies the two sofas.
+11
+
+OW-DETR
+Ours:CAT
+i0g:29%
+unkn0wn:41%
+d0g:57%
+d0g:66%
+dog:68%
+unknown:60
+unknown:25%
+unkn0wn:29%
+unknown:35%
+pers0n:85%
+person:76%
+unknown:29%
+chair:25%
+unkn0wn:27%
+unkn0wn:38%
+unkn0wn:26%
+:68
+person:
+unknown:34%Table 8. The detailed comparison of CAT with existing approaches on PASCAL VOC. Evaluation is performed on three standard settings,
+where a group of classes (10, 5 and last class) are introduced incrementally to a detector trained on the remaining classes (10,15 and 19).
+Our CAT performs favorably against existing approaches on all three settings, illustrating the power of localization identification cascade
+detection transformer for incremental objection detection.
+10 + 10 setting
+aero
+cycle
+bird
+boat
+bottle
+bus
+car
+cat
+chair
+cow
+table
+dog
+horse
+bike
+person
+plant
+sheep
+sofa
+train
+tv
+mAP
+ILOD
+69.9
+70.4
+69.4
+54.3
+48
+68.7
+78.9
+68.4
+45.5
+58.1
+59.7
+72.7
+73.5
+73.2
+66.3
+29.5
+63.4
+61.6
+69.3
+62.2
+63.2
+Faster ILOD
+72.8
+75.7
+71.2
+60.5
+61.7
+70.4
+83.3
+76.6
+53.1
+72.3
+36.7
+70.9
+66.8
+67.6
+66.1
+24.7
+63.1
+48.1
+57.1
+43.6
+62.1
+ORE - (CC + EBUI)
+53.3
+69.2
+62.4
+51.8
+52.9
+73.6
+83.7
+71.7
+42.8
+66.8
+46.8
+59.9
+65.5
+66.1
+68.6
+29.8
+55.1
+51.6
+65.3
+51.5
+59.4
+ORE - EBUI
+63.5
+70.9
+58.9
+42.9
+34.1
+76.2
+80.7
+76.3
+34.1
+66.1
+56.1
+70.4
+80.2
+72.3
+81.8
+42.7
+71.6
+68.1
+77
+67.7
+64.5
+OW - DETR
+75.4
+63.9
+57.9
+50.0
+52.0
+70.9
+79.5
+72.4
+44.3
+57.9
+59.7
+73.5
+77.7
+75.2
+76.2
+44.9
+68.8
+65.4
+79.3
+69.0
+65.7
+Ours: CAT
+76.5
+75.7
+67.0
+51.0
+62.4
+73.2
+82.3
+83.7
+42.7
+64.4
+56.8
+74.1
+75.8
+79.2
+78.1
+39.9
+65.1
+59.6
+78.4
+67.4
+67.7
+15 + 5 setting
+aero
+cycle
+bird
+boat
+bottle
+bus
+car
+cat
+chair
+cow
+table
+dog
+horse
+bike
+person
+plant
+sheep
+sofa
+train
+tv
+mAP
+ILOD
+70.5
+79.2
+68.8
+59.1
+53.2
+75.4
+79.4
+78.8
+46.6
+59.4
+59
+75.8
+71.8
+78.6
+69.6
+33.7
+61.5
+63.1
+71.7
+62.2
+65.8
+Faster ILOD
+66.5
+78.1
+71.8
+54.6
+61.4
+68.4
+82.6
+82.7
+52.1
+74.3
+63.1
+78.6
+80.5
+78.4
+80.4
+36.7
+61.7
+59.3
+67.9
+59.1
+67.9
+ORE - (CC + EBUI)
+65.1
+74.6
+57.9
+39.5
+36.7
+75.1
+80
+73.3
+37.1
+69.8
+48.8
+69
+77.5
+72.8
+76.5
+34.4
+62.6
+56.5
+80.3
+65.7
+62.6
+ORE - EBUI
+75.4
+81
+67.1
+51.9
+55.7
+77.2
+85.6
+81.7
+46.1
+76.2
+55.4
+76.7
+86.2
+78.5
+82.1
+32.8
+63.6
+54.7
+77.7
+64.6
+68.5
+OW - DETR
+78.0
+80.7
+79.4
+70.4
+58.8
+65.1
+84.0
+86.2
+56.5
+76.7
+62.4
+84.8
+85.0
+81.8
+81.0
+34.3
+48.2
+57.9
+62.0
+57.0
+69.4
+Ours: CAT
+75.3
+81.0
+84.4
+64.5
+56.6
+74.4
+84.1
+86.6
+53.0
+70.1
+72.4
+83.4
+85.5
+81.6
+81.0
+32.0
+58.6
+60.7
+81.6
+63.5
+72.2
+19 + 1 setting
+aero
+cycle
+bird
+boat
+bottle
+bus
+car
+cat
+chair
+cow
+table
+dog
+horse
+bike
+person
+plant
+sheep
+sofa
+train
+tv
+mAP
+ILOD
+69.4
+79.3
+69.5
+57.4
+45.4
+78.4
+79.1
+80.5
+45.7
+76.3
+64.8
+77.2
+80.8
+77.5
+70.1
+42.3
+67.5
+64.4
+76.7
+62.7
+68.2
+Faster ILOD
+64.2
+74.7
+73.2
+55.5
+53.7
+70.8
+82.9
+82.6
+51.6
+79.7
+58.7
+78.8
+81.8
+75.3
+77.4
+43.1
+73.8
+61.7
+69.8
+61.1
+68.5
+ORE - (CC + EBUI)
+60.7
+78.6
+61.8
+45
+43.2
+75.1
+82.5
+75.5
+42.4
+75.1
+56.7
+72.9
+80.8
+75.4
+77.7
+37.8
+72.3
+64.5
+70.7
+49.9
+64.9
+ORE - EBUI
+67.3
+76.8
+60
+48.4
+58.8
+81.1
+86.5
+75.8
+41.5
+79.6
+54.6
+72.8
+85.9
+81.7
+82.4
+44.8
+75.8
+68.2
+75.7
+60.1
+68.8
+OW - DETR
+82.2
+80.7
+73.9
+56.0
+58.6
+72.1
+82.4
+79.6
+48.0
+72.8
+64.2
+83.3
+83.1
+82.3
+78.6
+42.1
+65.5
+55.4
+82.9
+60.1
+70.2
+Ours: CAT
+86.0
+85.8
+78.8
+65.3
+61.3
+71.4
+84.8
+84.8
+52.9
+78.4
+71.6
+82.7
+83.8
+81.2
+80.7
+43.7
+75.9
+58.5
+85.2
+61.1
+73.8
+Proceedings of the European Conference on Computer Vi-
+sion (ECCV), pages 384–400, 2018. 5
+[2] Josh Beal, Eric Kim, Eric Tzeng, Dong Huk Park, Andrew
+Zhai, and Dmitry Kislyuk. Toward transformer-based object
+detection. arXiv preprint arXiv:2012.09958, 2020. 4
+[3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas
+Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-
+end object detection with transformers. In European confer-
+ence on computer vision, pages 213–229. Springer, 2020. 2,
+4, 8
+[4] Mathilde Caron, Hugo Touvron, Ishan Misra, Herv´e J´egou,
+Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerg-
+ing properties in self-supervised vision transformers.
+In
+Proceedings of the IEEE/CVF International Conference on
+Computer Vision, pages 9650–9660, 2021. 6
+[5] Xinlei Chen, Haoqi Fan, Ross Girshick, and Kaiming He.
+Improved baselines with momentum contrastive learning.
+arXiv preprint arXiv:2003.04297, 2020. 4
+[6] Xingyu Chen, Junzhi Yu, Shihan Kong, Zhengxing Wu,
+and Li Wen. Joint anchor-feature refinement for real-time
+accurate object detection in images and videos.
+IEEE
+Transactions on Circuits and Systems for Video Technology,
+31(2):594–607, 2020. 8
+[7] Xiyang Dai, Yinpeng Chen, Jianwei Yang, Pengchuan
+Zhang, Lu Yuan, and Lei Zhang. Dynamic detr: End-to-
+end object detection with dynamic attention. In Proceedings
+of the IEEE/CVF International Conference on Computer Vi-
+sion, pages 2988–2997, 2021. 4
+[8] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li,
+and Li Fei-Fei. Imagenet: A large-scale hierarchical image
+database. In 2009 IEEE conference on computer vision and
+pattern recognition, pages 248–255. Ieee, 2009. 6
+[9] Akshay Dhamija, Manuel Gunther, Jonathan Ventura, and
+Terrance Boult. The overlooked elephant of object detection:
+Open set. In Proceedings of the IEEE/CVF Winter Confer-
+ence on Applications of Computer Vision, pages 1021–1030,
+2020. 5
+[10] Mark Everingham, Luc Van Gool, Christopher KI Williams,
+John Winn, and Andrew Zisserman. The pascal visual object
+classes (voc) challenge. International journal of computer
+vision, 88(2):303–338, 2010. 5, 7
+[11] Spyros Gidaris and Nikos Komodakis. Attend refine repeat:
+Active box proposal generation via in-out localization. arXiv
+preprint arXiv:1606.04446, 2016. 8
+[12] Ross Girshick. Fast r-cnn. In Proceedings of the IEEE inter-
+national conference on computer vision, pages 1440–1448,
+2015. 8
+[13] Akshita Gupta, Sanath Narayan, KJ Joseph, Salman Khan,
+Fahad Shahbaz Khan, and Mubarak Shah. Ow-detr: Open-
+world detection transformer. In CVPR, 2022. 2, 3, 5, 6, 7,
+8
+[14] Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross
+Girshick. Momentum contrast for unsupervised visual rep-
+resentation learning. In Proceedings of the IEEE/CVF con-
+ference on computer vision and pattern recognition, pages
+9729–9738, 2020. 4
+[15] Kaiming He, Georgia Gkioxari, Piotr Doll´ar, and Ross Gir-
+shick. Mask r-cnn. In Proceedings of the IEEE international
+conference on computer vision, pages 2961–2969, 2017. 8
+12
+
+Figure 7. Visualization results comparison between CAT and Oracle. We visualize the detection results of our model for known and
+unknown objects, as well as the ground truth on the tasks corresponding to the weights, including the labels of known categories and the
+labels of unknown categories, where the objects of unknown categories are the objects of other categories that have not yet appeared in the
+total categories of the dataset. Our model can accurately detect known objects and unknown objects outside the total class of the dataset,
+such as the electric plug and sound switch in the first row, the camera in the second row and the kitten toy in the third row. It is also worth
+noting that although our model detects the audio, it does not identify it as an unknown object, but as a remote, showing the limitations of
+our model.
+13
+
+Oracle
+Ours:CAT
+tvmonitor
+tvmonitor:79%
+remote:28%
+mote:35
+O
+unknown:3
+unknown:38%
+1kn0wn:34%
+unkn0wn:26%%
+keyboard
+keyboard:42
+mouse
+mouse
+person
+tvmonitor:88%
+unkn0wn:36%
+sofa:43%
+cat:80%
+cat
+unknown:26%
+unknown:43
+unknown:35%
+inknov
+unknown:25%Figure 8. Visualization performance on incremental object detection. We visualize the detection results of the weights corresponding to
+different tasks for the same scenario. The results show that our CAT can identify unknown kinds of objects as the unknown class and
+accurately identify their classes after incrementally learning the unknown classes, such as sports ball and tennis racket in the first row,
+surfboard in the second row and traffic light in the third row.
+[16] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.
+Deep residual learning for image recognition. In Proceed-
+14
+
+Before Learning
+After Learning
+tennis racket:84%
+erson:89%
+unk
+sports
+ball:80%
+erson:87%
+surfb0ard:60%
+unkn0wn:30%
+raffic light:60%3%
+unknowi
+traffic
+1ght:78%
+ight:6
+car:88%
+car:68%
+unknown
+ar:58
+car
+23%
+:21%ings of the IEEE conference on computer vision and pattern
+recognition, pages 770–778, 2016. 6
+[17] K J Joseph, Salman Khan, Fahad Shahbaz Khan, and Vi-
+neeth N Balasubramanian. Towards open world object de-
+tection. In 2021 IEEE/CVF Conference on Computer Vision
+and Pattern Recognition (CVPR), pages 5826–5836, 2021.
+1, 3, 4, 5, 6, 7, 8
+[18] Bingyi Kang, Zhuang Liu, Xin Wang, Fisher Yu, Jiashi Feng,
+and Trevor Darrell.
+Few-shot object detection via feature
+reweighting. In Proceedings of the IEEE/CVF International
+Conference on Computer Vision, pages 8420–8429, 2019. 8
+[19] Dahun Kim, Tsung-Yi Lin, Anelia Angelova, In So Kweon,
+and Weicheng Kuo. Learning open-world object proposals
+without learning to classify. IEEE Robotics and Automation
+Letters, 7(2):5453–5460, 2022. 8
+[20] Hongyang Li, Yu Liu, Wanli Ouyang, and Xiaogang Wang.
+Zoom out-and-in network with map attention decision for re-
+gion proposal and object detection. International Journal of
+Computer Vision, 127(3):225–238, 2019. 8
+[21] Yanghao Li, Hanzi Mao, Ross Girshick, and Kaiming He.
+Exploring plain vision transformer backbones for object de-
+tection. arXiv preprint arXiv:2203.16527, 2022. 4
+[22] Tsung-Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and
+Piotr Doll´ar. Focal loss for dense object detection. In Pro-
+ceedings of the IEEE international conference on computer
+vision, pages 2980–2988, 2017. 8
+[23] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays,
+Pietro Perona, Deva Ramanan, Piotr Doll´ar, and C Lawrence
+Zitnick. Microsoft coco: Common objects in context. In
+European conference on computer vision, pages 740–755.
+Springer, 2014. 5
+[24] Yue Lu, Xingyu Chen, Zhengxing Wu, and Junzhi Yu. De-
+coupled metric network for single-stage few-shot object de-
+tection. IEEE Transactions on Cybernetics, 2022. 8
+[25] Dimity Miller, Lachlan Nicholson, Feras Dayoub, and Niko
+S¨underhauf. Dropout sampling for robust object detection
+in open-set conditions. In 2018 IEEE International Confer-
+ence on Robotics and Automation (ICRA), pages 3243–3249.
+IEEE, 2018. 5
+[26] Dimity Miller, Lachlan Nicholson, Feras Dayoub, and Niko
+S¨underhauf. Dropout sampling for robust object detection
+in open-set conditions. In 2018 IEEE International Confer-
+ence on Robotics and Automation (ICRA), pages 3243–3249.
+IEEE, 2018. 8
+[27] Ishan Misra, Rohit Girdhar, and Armand Joulin. An end-to-
+end transformer model for 3d object detection. In Proceed-
+ings of the IEEE/CVF International Conference on Com-
+puter Vision, pages 2906–2917, 2021. 4
+[28] Pedro O O Pinheiro, Ronan Collobert, and Piotr Doll´ar.
+Learning to segment object candidates. Advances in neural
+information processing systems, 28, 2015. 8
+[29] Yanwei Pang, Tiancai Wang, Rao Muhammad Anwer, Fa-
+had Shahbaz Khan, and Ling Shao. Efficient featurized im-
+age pyramid network for single shot detector. In Proceedings
+of the IEEE/CVF Conference on Computer Vision and Pat-
+tern Recognition, pages 7336–7344, 2019. 8
+[30] Can Peng, Kun Zhao, and Brian C Lovell. Faster ilod: In-
+cremental learning for object detectors based on faster rcnn.
+Pattern recognition letters, 140:109–115, 2020. 6, 7
+[31] Jordi Pont-Tuset, Pablo Arbel´aez, Jonathan T. Barron, Fer-
+ran Marques, and Jitendra Malik. Multiscale combinatorial
+grouping for image segmentation and object proposal gener-
+ation. IEEE Transactions on Pattern Analysis and Machine
+Intelligence, 39(1):128–140, 2017. 3
+[32] Joseph Redmon, Santosh Divvala, Ross Girshick, and Ali
+Farhadi. You only look once: Unified, real-time object de-
+tection. In Proceedings of the IEEE conference on computer
+vision and pattern recognition, pages 779–788, 2016. 8
+[33] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun.
+Faster r-cnn: Towards real-time object detection with region
+proposal networks. Advances in neural information process-
+ing systems, 28, 2015. 1, 6, 8
+[34] Adrian Rosebrock.
+Intersection over union (iou) for ob-
+ject detection.
+Diambil kembali dari PYImageSearch
+https//www. pyimagesearch. com/2016/11/07/intersection-
+over-union-iou-for-object-detection, 2016. 4
+[35] Konstantin Shmelkov, Cordelia Schmid, and Karteek Ala-
+hari. Incremental learning of object detectors without catas-
+trophic forgetting. In Proceedings of the IEEE international
+conference on computer vision, pages 3400–3409, 2017. 6,
+7, 8
+[36] Jasper RR Uijlings, Koen EA Van De Sande, Theo Gev-
+ers, and Arnold WM Smeulders. Selective search for ob-
+ject recognition. International journal of computer vision,
+104(2):154–171, 2013. 3, 4
+[37] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszko-
+reit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia
+Polosukhin. Attention is all you need. Advances in neural
+information processing systems, 30, 2017. 8
+[38] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang
+Wang, and Jifeng Dai. Deformable detr: Deformable trans-
+formers for end-to-end object detection.
+arXiv preprint
+arXiv:2010.04159, 2020. 2, 4, 6, 8
+[39] C Lawrence Zitnick and Piotr Doll´ar. Edge boxes: Locat-
+ing object proposals from edges. In European conference on
+computer vision, pages 391–405. Springer, 2014. 3
+[40] Zhengxia Zou, Zhenwei Shi, Yuhong Guo, and Jieping Ye.
+Object detection in 20 years: A survey.
+arXiv preprint
+arXiv:1905.05055, 2019. 8
+15
+
diff --git a/EdA0T4oBgHgl3EQfA_-G/content/tmp_files/load_file.txt b/EdA0T4oBgHgl3EQfA_-G/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3b524d0a21fd7c5ac119ed94ad99cf232f781773
--- /dev/null
+++ b/EdA0T4oBgHgl3EQfA_-G/content/tmp_files/load_file.txt
@@ -0,0 +1,1328 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf,len=1327
+page_content='CAT: LoCalization and IdentificAtion Cascade Detection Transformer  for Open-World Object Detection  Shuailei Ma 1* Yuefeng Wang1† Jiaqi Fan1 Ying Wei1‡  Thomas H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Li3 Hongli Liu2 Fanbing Lv2  1Northeast University, 2Changsha Hisense Intelligent System Research Institute Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=', Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  3Information Technology R&D Innovation Center of Peking University,  Abstract  Open-world object detection (OWOD), as a more gen-  eral and challenging goal, requires the model trained from  data on known objects to detect both known and unknown  objects and incrementally learn to identify these unknown  objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  The existing works which employ standard de-  tection framework and fixed pseudo-labelling mechanism  (PLM) have the following problems: (𝑖) The inclusion of de-  tecting unknown objects substantially reduces the model’s  ability to detect known ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (𝑖𝑖) The PLM does not ade-  quately utilize the priori knowledge of inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (𝑖𝑖𝑖) The fixed  selection manner of PLM cannot guarantee that the model  is trained in the right direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We observe that humans  subconsciously prefer to focus on all foreground objects and  then identify each one in detail, rather than localize and  identify a single object simultaneously, for alleviating the  confusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' This motivates us to propose a novel solution  called CAT: LoCalization and IdentificAtion Cascade De-  tection Transformer which decouples the detection process  via the shared decoder in the cascade decoding way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In the  meanwhile, we propose the self-adaptive pseudo-labelling  mechanism which combines the model-driven with input-  driven PLM and self-adaptively generates robust pseudo-  labels for unknown objects, significantly improving the abil-  ity of CAT to retrieve unknown objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Comprehensive ex-  periments on two benchmark datasets, 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=', MS-COCO and  PASCAL VOC, show that our model outperforms the state-  of-the-art in terms of all metrics in the task of OWOD, in-  cremental object detection (IOD) and open-set detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Introduction  Open-world object detection (OWOD) is a more prac-  tical detection problem in computer vision, making artifi-  First author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Email: xiaomabufei@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='com  †Code url: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='com/xiaomabufei/CAT  ‡Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Email: weiying@ise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='neu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='cn  Bear  Frog  Flower  Squirrel  Unknown  Cat  BeeUnknown  Unknown  Unknown  Unknown  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' When faced with new scenes in open world, humans sub-  consciously focus on all foreground objects and then identify them  in detail in order to alleviate the confusion between the known and  unknown objects and get a clear view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Motivated by this, our CAT  utilizes the shared decoder to decouple the localization and iden-  tification process in the cascade decoding way, where the former  decoding process is used for localization and the latter for identi-  fication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  cial intelligence (AI) smarter to face more difficulties in real  scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Within the OWOD paradigm, the model’s life-span  is pushed by iterative learning process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' At each episode, the  model trained only by known objects needs to detect known  objects while simultaneously localizing unknown objects  and identifying them into the unknown class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Human an-  notators then label a few of these tagged unknown classes  of interest gradually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The model given these newly-added  annotations will continue to incrementally update its knowl-  edge without retraining from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Recently, the work [17] proposed an open-world ob-  ject detector, ORE, based on the two-stage Faster R-CNN  [33] pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' ORE utilizes an auto-labelling step to obtain  pseudo-unknowns for training model to detect unknown ob-  jects and learns an energy-based binary classifier to distin-  guish the unknown class from known classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' However,  its success largely relies on a held-out validation set which  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='01970v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='CV]  5 Jan 2023  is leveraged to estimate the distribution of unknown ob-  jects in the energy-based classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' To alleviate the prob-  lems in ORE, OW-DETR [13] proposes to use the detection  transformer [3, 38] for OWOD in a justifiable way and di-  rectly leverages the framework of DDETR [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In addi-  tion, OW-DETR proposes an attention-driven PLM which  selects pseudo labels for unknown objects according to the  attention scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  For the existing works, we find the following hindering  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (𝑖) Owing to the inclusion of detecting unknown  objects, the model’s ability to detect known objects substan-  tially drops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' To alleviate the confusion between known and  unknown objects, humans prefer to dismantle the process of  open-world object detection rather than parallelly localize  and identify open-world objects like most standard detec-  tion models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (𝑖𝑖) To the best of our knowledge, in the exist-  ing OWOD PLM, models leverage the learning process for  known objects to guide the generation of pseudo labels for  unknown objects, without leveraging the prior conditions of  the inputs (𝑡𝑒𝑥𝑡𝑢𝑟𝑒,𝑙𝑖𝑔ℎ𝑡 𝑓 𝑙𝑜𝑤,𝑒𝑡𝑐).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' As a result, the model  cannot learn knowledge beyond the data annotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (𝑖𝑖𝑖)  The fixed selection manner of PLM cannot guarantee that  the model learns to detect unknown objects in the right di-  rection, due to the uncertain quality of the pseudo labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  The models may be worse for detecting unknown objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  When faced with a new scene, humans prefer focusing  on all foreground objects and then analyse them in detail,  as shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Motivated by this and the aforemen-  tioned observations, we propose a novel LoCalization and  IdentificAtion Cascade Detection Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' CAT com-  prises three dedicated components namely, self-adaptive  pseudo-labelling mechanism, shared transformer de-  coder and cascade decoupled decoding structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The  self-adaptive PLM maintains the ability of CAT to ex-  plore the knowledge beyond the known objects and self-  adaptively adjusts the pseudo-label generation according to  the model training process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Via the cascade decoupled de-  coding structure, the shared transformer decoder decouples  the localization and identification process for alleviating the  influence of detecting unknown objects on the detection of  known objects, where the former decoding process is used  for localization and the latter for identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In the mean-  while, we observe the structure substantially improves the  model’s ability for incremental object detection according  to the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In addition, we explore the decoupled  structures for detection transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Our contributions can  be summarized fourfold:  We propose a novel localization and identification cas-  cade detection transformer (CAT), which decouples  the localization and identification process of detection  and alleviates the influence of detecting unknown ob-  jects on the detection of known ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  We introduce a novel pseudo-labelling mechanism  which self-adaptively combines the model-driven and  input-driven pseudo-labelling during the training pro-  cess for generating robust pseudo-labels and exploring  knowledge beyond known objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  We explore the decoupled decoding methods of the de-  tection transformer, 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=', the fully decoupled decoding  structure and the cascade decoupled decoding struc-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Our extensive experiments on two popular bench-  marks demonstrate the effectiveness of the proposed  CAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' CAT outperforms the recently introduced ORE  and OW-DETR for OWOD, IOD and open-set detec-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' For OWOD, CAT achieves absolute gains ranging  from 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8% to 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3% in terms of unknown recall over  OW-DETR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Problem Formulation  At time 𝑡, let K𝑡 = {1,2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=',𝐶} denote the set of known  object classes and U𝑡 = {𝐶 + 1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='} denote the unknown  classes which might be encountered at the test time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The  known object categories K𝑡 are labeled in the dataset  D𝑡 = {J 𝑡,L𝑡} where J 𝑡 denotes the input images and  L𝑡 denotes the corresponding labels at time 𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The train-  ing image set consists of 𝑀 images J 𝑡 = {𝑖1,𝑖2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=',𝑖𝑀 }  and corresponding labels L𝑡 = {ℓ1,ℓ2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=',ℓ𝑀 }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Each ℓ𝑖 =  {T1,T2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=',T𝑁 } denotes a set of 𝑁 object instances with  their class labels 𝑐𝑛 ⊂ K𝑡 and locations, 𝑥𝑛, 𝑦𝑛,𝑤𝑛, ℎ𝑛  denote the bounding box center coordinates, width and  height respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The Open-World Object Detection re-  moves the artificial assumptions and restrictions in tradi-  tional object detection and makes object detection tasks  more aligned with real life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' It requires the trained model  M𝑡 not only to detect the previously encountered known  classes 𝐶 but also to identify an unseen class instance as  belonging to the unknown class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In addition, it requires the  object detector to be capable of incremental update for new  knowledge and this cycle continues over the detector’s lifes-  pan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In incremental updating phase, the unknown instances  identified by M𝑡 are annotated manually, and along with  their corresponding training examples, update D𝑡 to D𝑡+1  and K𝑡 to K𝑡+1 = {1,2,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=',𝐶,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=',𝐶 +n}, the model adds the  𝑛 new classes to known classes and updates itself to M𝑡+1  without retraining from scratch on the whole dataset D𝑡+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Proposed method  This section elaborates the proposed CAT in details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In  Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1, the overall architecture of CAT is described in de-  tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' A novel self-adaptive adjustment strategy for pseudo-  labelling is proposed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We explore to decouple  the decoding process of the detection transformer and pro-  pose the localization and identification cascade decoupled  2  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Overall Architecture of proposed CAT framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The proposed CAT consists of a multi-scale feature extractor, the shared trans-  former decoder, the regression prediction branch, and the self-adaptive pseudo-labelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The multi-scale feature extractor comprises the  mainstream feature extraction backbone and a deformable transformer encoder, for extracting multi-scale features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The shared transformer  decoder is a deformable transformer decoder and decouples the localization and identification process in the cascade decoding way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The  regression prediction branch contains the bounding box regression branch 𝐹𝑟𝑒𝑔, novelty objectness branch 𝐹𝑜𝑏 𝑗, and novelty classification  branch 𝐹𝑐𝑙𝑠.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' While the novelty classification and objectness branches are single-layer feed-forward networks (FFN) and the regression  branch is a 3-layer FFN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  decoding structure in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4, we illustrate the  end-to-end training strategy of CAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Overall Architecture  As shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2, for a given image J ∈ R𝐻×𝑊 ×3,  CAT uses a hierarchical feature extraction backbone to  extract multi-scale features Z𝑖 ∈ R  H  4×𝑖2 ×  𝑤  4×2𝑖 ×2𝑖𝐶𝑠,𝑖 = 1,2,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  The feature maps 𝑍𝑖 are projected from dimension 𝐶𝑠  to dimension 𝐶𝑑 by using 1×1 convolution and concate-  nated to 𝑁𝑠 vectors with 𝐶𝑑 dimensions after flattening  out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Afterwards, along with supplement positional encod-  ing 𝑃𝑛 ∈ R𝑁𝑠×𝐶𝑑, the multi-scale features are sent into the  deformable transformer encoder to encode semantic fea-  tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The encoded semantic features 𝑀 ∈ R𝑁𝑠×𝑐𝑑 are ac-  quired and sent into the shared decoder together with a  set of 𝑁 learnable location queries and positional embed-  dings 𝑃𝑚 ∈ R𝑁𝑠×𝐶𝑑.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Aided by interleaved cross-attention  and self-attention modules, the shared decoder transforms  the location queries Q location ∈ R𝑁 ×𝐷 to a set of N loca-  tion query embeddings E location ∈ R𝑁 ×𝐷.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The Elocation are  then input to the regression branch to locate N foreground  bounding boxes containing the known classes and unknown  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Meanwhile, the E location are used as class queries  and sent into the shared decoder together with the 𝑀 and  𝑃𝑚 again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The shared decoder transforms the class queries  to 𝑁 class query embeddings Eclass that are corresponding to  the location query embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The Eclass are then sent into  the objectness and novelty classification branch to predict  the objectness and category respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' After selecting the  unique queries that best match the known instances by a bi-  partite matching loss, the remaining queries are utilized to  select the unknown category instances and generate pseudo  labels by self-adaptive pseudo-labelling mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Self-Adaptive Pseudo-labelling  Pseudo labels play an important role in guiding mod-  els to detect unknown object instances, determining the up-  per learning limitation of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The existing meth-  ods [13,17] only use model-driven pseudo-labelling and do  not take full advantage of the inputs’ priori knowledge (light  flow, textures, 𝑒𝑡𝑐).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  The model-driven pseudo-labelling  [13] makes the model’s learning get caught up in the knowl-  edge of known objects, for the reason that the only source  of knowledge for the model is known object instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  In addition, their fixed selection manner cannot guarantee  the right learning direction for unknown objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We pro-  pose to combine model-driven with input-driven pseudo-  labelling [31, 36, 39] for expanding the knowledge sources  of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In the meanwhile, the pseudo-labels selec-  tion scheme should not be fixed, but be adapted as train-  ing and able to adjust itself when facing the unexpected  problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In this paper,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' a novel pseudo-labelling mech-  anism is proposed for self-adaptively combining model-  driven and input-driven pseudo-labelling according to the  situation faced by the model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' where the attention-driven  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='pseudo-labelling [13] is used as the model-driven pseudo-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Shared Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Multi-Scale Feature  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Freg  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Layer 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Layer 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Layer N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Deformable  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Transformer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Encoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Fobj  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Layer 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Layer 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Layer N  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Fcls  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Shared Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='human  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='cup  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='unknown  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Positional Encoding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Self-Adaptive Pseudo-Labelling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Pseudo labels  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Model-driven  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Positional Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Pseudo-labelling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Self-Adaptive  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Location Queries  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Adjustment Strategy  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Location Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Input-driven  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Class Queries  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Pseudo-labelling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Class Embeddingslabelling and selective search [36] is selected as the input-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='driven pseudo-labelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In self-adaptive pseudo-labelling  mechanism, the model-driven pseudo-labelling generates  pseudo-labels’ candidate boxes 𝑃𝑚 and the corresponding  confidence 𝑠𝑜, and the input-driven pseudo-labelling gen-  erates pseudo-label candidate boxes 𝑃𝐼 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The object confi-  dence of generated pseudo labels is formulated as follows:  S𝑖 = (𝑛𝑜𝑟𝑚 (𝑠𝑜))W𝑚 ·  �  max  1≤ 𝑗 ≤|P𝐼 |  �  IOU  �  𝑃𝐼  𝑗, 𝑃𝑚  𝑖  ��� W𝐼  , (1)  where IOU(·) (Intersection-over-union [34]) is the most  commonly used metric for comparing the similarity be-  tween two arbitrary shapes, 𝑖 denotes the index of the  pseudo labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' W𝑚 and W𝐼 are the self-adaptive weights,  which are controlled by the 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑟, 𝑆𝑒𝑛𝑠𝑜𝑟 and  𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑟, as formulated below:  W𝑡 = 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑟(W𝑡−1, 𝑆𝑒𝑛𝑠𝑜𝑟(𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑟(𝐿𝑚))), (2)  where 𝐿𝑚 represents the loss memory which is stored and  updated in real time during model training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The formulation  is illustrated in Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3:  𝐿𝑚 = DEQUE(𝑙𝑜𝑠𝑠𝑡−1,𝑙𝑜𝑠𝑠𝑡−2,··· ,𝑙𝑜𝑠𝑠𝑡−𝑛),  (3)  where 𝑡 is the current iteration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Considering the sensitivity  of the model and the uneven quality of the data, we leverage  𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑟 to obtain the trend of the losses Δ𝑙 for replacing  the single loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The formula is as follows:  𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑟(𝐿𝑚) =  �𝑛  𝑖=1 𝛼𝑖 · 𝑙𝑜𝑠𝑠𝑡−𝑖  �𝑁  𝑗=𝑛+1 𝛽 𝑗 · 𝑙𝑜𝑠𝑠𝑡− 𝑗  ,  𝑛 < 𝑁 < 𝑇,  (4)  where 𝛼 and 𝛽 denote the weighted average weights and  �𝑛  𝑖=1 𝛼𝑖 = �𝑁  𝑗=𝑛+1 𝛽 𝑗 = 𝛼𝑖−𝛼𝑖−1  𝛼𝑖+1−𝛼𝑖 = 𝛽𝑗−𝛽𝑗−1  𝛽𝑗+1−𝛽𝑗 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In the 𝑆𝑒𝑛𝑠𝑜𝑟,  the variable of the weight Δ𝑤 is acquired as follows:  𝑆𝑒𝑛𝑠𝑜𝑟(Δ𝑙) =  � 𝜋𝑛𝑚𝑎 · 𝑆𝑖𝑔𝑚𝑜𝑖𝑑(Δ𝑙 −1),Δ𝑙 > 1,  −𝜋𝑝𝑚𝑎 ·Δ𝑙,Δ𝑙 ≤ 1,  (5)  where 𝜋𝑝𝑚𝑎 and 𝜋𝑛𝑚𝑎 represents the positive and negative  momentum amplitude, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In the 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑟, we  use Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6 to update the self-adaptive weight via a in-  cremental way [5,14,17], for memory storage and enhanc-  ing the robustness (more explanations in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  ���  ���  W 𝑡  𝑚 = W 𝑡−1  𝑚  +Δ𝑤 ×W 𝑡−1  𝑚  ,  W 𝑡  𝐼 = W 𝑡−1  𝐼  −Δ𝑤 ×W 𝑡−1  𝐼  ,  W 𝑡  𝑚,W 𝑡  𝐼 = 𝑛𝑜𝑟𝑚 �W 𝑡  𝑚,W 𝑡  𝐼  � ,  (6)  where 𝑛𝑜𝑟𝑚(·) is the normalization operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The update  strategy for the weights during training is shown in Algo-  rithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Algorithm 1 COMPUTINGADAPTIVEWEIGHTS  Input: Loss Memory: 𝐿𝑚;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Current Interation: 𝑡;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Positive  Momentum Amplitude: 𝜋𝑝𝑚𝑎;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Negative Momentum  Amplitude: 𝜋𝑛𝑚𝑎;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 𝑇𝑠𝑡𝑎𝑟𝑡: Start iteration;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 𝑇𝑏: Weight  updating cycle;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Loss← Compute using Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='11  Output: self-adaptive weights 𝑊𝑚𝑡 and 𝑊𝐼 𝑡  1: while 𝑡𝑟𝑎𝑖𝑛 do  2:  if 𝑡 ≤ 𝑇𝑠𝑡𝑎𝑟𝑡 then  3:  Initialise 𝑊𝑚0 ← 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8 and 𝑊𝐼 0 ← 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  4:  Initialise 𝐿𝑚 using Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  5:  else  6:  Update 𝐿𝑚 using Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  7:  if 𝑡%𝑇𝑏 == 0 then  8:  Compute Δ𝑙 using 𝐿𝑚 and Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  9:  Compute Δ𝑤 using Δ𝑙 and Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  10:  Update W𝑚𝑡 and W𝐼 𝑡 using Equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  11:  end if  12:  end if  13: end while  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Exploration of Decoupled Decoding Structure  Detection transformer [2, 3, 7, 21, 27, 38] leverages the  object queries to detect object instances, where each ob-  ject query represents an object instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  In the decod-  ing stage, the object queries are updated to query embed-  dings by connecting object queries with semantic informa-  tion from the encoded semantic features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The generated  query embeddings couple the location and category infor-  mation for both object localization and identification pro-  cess simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' For open-world object detection, the  model requires to detect the known objects, localize the un-  known objects and identify them as the unknown class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' For  the parallel decoding structure, we observe that the inclu-  sion of detecting unknown reduces the model’s ability to  detect known objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Inspired by how humans subcon-  sciously confront new scenarios, we propose to decouple  the decoding process of DETR for mitigating the impact of  unknown object detection on detecting known objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In  this paper, we explore two decoupled decoding ways, 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=',  the fully decoupled decoding structure and the cascade de-  coupled decoding structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  Fully Decoupled Decoding Structure  For decoupling the location and category information, an  intuitive way is to carry out the localization and identifi-  cation process independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Motivated by this, the fully  decoupled decoding structure (FD) is proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In the fully  decoupled decoding structure, location and class queries are  two sets of mutually independent queries sent to the shared  decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' This operation of FD is shown in Figure 3 (a),  4  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (a) The fully decoupled decoding structure has two independent decoding processes for localization and identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (b) In  the cascade decoupled decoding structure, the location embeddings are used as class queries for knowledge retention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (c) For the coupled  decoding structure, the same query is put into the decoder for localization and identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  which is formulated as follows:  ELocation = F𝑠 (F𝑒(∅(J), 𝑃𝑛), 𝑃𝑚,Q Location,R) ,  (7)  EClass = F𝑠 (F𝑒(∅(J), 𝑃𝑛), 𝑃𝑚,Q Class ,R) ,  (8)  where F𝑠(·) denotes the shared decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' F𝑒(·) is the en-  coder and ∅(·) is the backbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 𝑃𝑛 and 𝑃𝑚 stands for the  positional encoding and embeddings, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' R repre-  sents the reference points and J denotes the input image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Q Class stands for the class queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  Cascade Decoupled Decoding Structure  Inspired by how people react to new scenarios, a cascade  decoupled decoding structure is proposed to decode the en-  coded features in a cascade way so that the localization pro-  cess is not restricted by the category information, while the  identification process can get help from the location knowl-  edge in the cascade structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The operation of localization  and identification cascade decoding structure is expressed  as follows:  ELocation = F𝑠 (F𝑒(∅(J), 𝑃𝑛), 𝑃𝑚,Q Location,R) ,  (9)  EClass = F𝑠 (F𝑒(∅(J), 𝑃𝑛), 𝑃𝑚,ELocation ,R) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  (10)  As shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3 (b), the location embeddings are used  as class queries to generate class embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Training and Inference  Our CAT is trained end-to-end using the following joint  loss formulation:  𝐿 = 𝐿𝑙𝑜𝑐𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 + 𝐿𝑖𝑑𝑒𝑛𝑡𝑖 𝑓 𝑖𝑐𝑎𝑡𝑖𝑜𝑛 + 𝐿𝑜𝑏 𝑗𝑒𝑐𝑡𝑛𝑒𝑠𝑠,  (11)  where 𝐿𝑙𝑜𝑐𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛, 𝐿𝑖𝑑𝑒𝑛𝑡𝑖 𝑓 𝑖𝑐𝑎𝑡𝑖𝑜𝑛 and 𝐿𝑜𝑏 𝑗𝑒𝑐𝑡𝑛𝑒𝑠𝑠 de-  notes the loss terms for foreground localization, novelty  identification and object scoring, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' When a set  of new categories are introduced at each episode, we em-  ploy an exemplar replay based finetuning to alleviate catas-  trophic forgetting of learned classes and then finetune the  model using a balanced set of exemplars stored for each  known class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The bounding boxes and categories predic-  tions of the known and 𝑡𝑜𝑝-k unknown objects are simulta-  neous used during evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Experiments  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Datasets and Metrics  The experiments are implemented on two mainstream  splits of MS-COCO [23] and Pascal VOC [10] dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  We group the classes into a set of nonoverlapping tasks  �  𝑇1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=',𝑇𝑡,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The class in task 𝑇 𝑐 only appears in tasks  where 𝑡 ≥ 𝑐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In task 𝑇 𝑐, classes encountered in {𝑇 𝑐 : 𝑐 ≤ 𝑡}  and {𝑇 𝑐 : 𝑐 > 𝑡} are considered as known and unknown  classes, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  OWOD SPLIT [17] spilts the 80 classes of MS-COCO into  4 tasks and selects training set for each task from the MS-  COCO and Pascal VOC training set images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Pascal VOC  testing and MS-COCO validation set are used for evalua-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' See more details in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  MS-COCO SPLIT [13] mitigates data leakage across tasks  in [17] and is more challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The training and testing  data are selected from MS-COCO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Metrics: Following the most commonly used evaluation  metric for object detection, we use mean average preci-  sion (mAP) to evaluate the known objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Inspired by  [1,9,13,17,25], U-Recall, Wilderness Impact (WI, see de-  tailed in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3) and Absolute Open-Set Error (A-  OSE) are used as main metric for unknown objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' U-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Recall measures the ability of the model to retrieve un-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Location Queries  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Location Queries  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Encoded Semantic Features  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Location  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Encoded Semantic Features  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Location  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='I Semantic Features  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Object Queries  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Shared  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Shared  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Location  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Class Queries  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Class Queries  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Shared  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Class Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Shared  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Class Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Class Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='(a) Fully Decoupled Decoding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='(b) Cascade Decoupled Decoding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='(c) Coupled DecodingTable 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' State-of-the-art comparison on OWOD split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The comparison is shown in terms of U-Recall, WI, A-OSE and known class mAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  U-Recall measures the ability of the model to retrieve unknown object instances for OWOD problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Both WI and A-OSE implicitly  quantify the effevtiveness of the model in handling unknown objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' For a fair comparison, we compare with the recently introduced  OW-DETR [13] and ORE [17] not employing EBUI (the results are reproduced by the same GPUs as our model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The CAT achieves  improved all metrics over the existing works across all tasks, demonstrating our model’s effectiveness for OWOD problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' U-Recall, WI  and A-OSE cannot be computed in Task 4 due to the absence of unknown test annotations, for the reason that all 80 classes are known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Task IDs →  Task 1  Task 2  Task 3  Task 4  U-Recall  WI  A-OSE  mAP(↑)  U-Recall  WI  A-OSE  mAP(↑)  U-Recall  WI  A-OSE  mAP(↑)  mAP(↑)  (↑)  (↓)  (↓)  Current  known  (↑)  (↓)  (↓)  Previously  known  Current  known  Both  (↑)  (↓)  (↓)  Previously  known  Current  known  Both  Previously  known  Current  known  Both  Faster-RCNN [33] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0699  13396  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0371  12291  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0213  9174  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  Faster-RCNN  + Finetuning  Not applicable in Task 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0375  12497  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0279  9622  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  DDETR [38] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0608  33270  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0368  18115  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0197  9392  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  DDETR  + Finetuning  Not applicable in Task 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0337  17834  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0195  10095  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  Cascade 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0476  42083  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0308  21928  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0189  12189  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  Cascade  + Finetuning  Not applicable in Task 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0296  20587  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0184  12854  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  ORE-EBUI [17]  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0621  10459  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0282  10445  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0211  7990  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  OW-DETR [13]  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0590  10248  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0279  8540  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0191  6840  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  Ours:CAT  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0581  7070  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0263  5902  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0177  5189  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  (+14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7)  (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0009)  (-3178)  (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0)  (+11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8)  (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0016)  (-2638)  (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1)  (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5)  (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8)  (+16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1)  (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0014)  (-1651)  (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0)  (+5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1)  (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4)  (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3)  (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8)  (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2)  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' State-of-the-art comparison on MS-COCO split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The  comparison is shown in terms of U-Recall and mAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Although  the MS-COCO split is more challenging, our model gets a more  significant improvement on this in comparison to ORE and OW-  DETR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The significant metric improvements demonstrate that our  CAT has the ability to retrieve new knowledge beyond the range  of closed set and would not be limited by category knowledge of  existing objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' See Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Task IDs ↓  Metrics  ORE  OW-DETR  Our:CAT  U-Recall(↑)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0 (+18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3)  Task1  mAP(↑)  Current known  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7)  U-Recall(↑)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0 (+16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8)  Previously known  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6 (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8)  Current known  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5 (+8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0)  Task2  mAP(↑)  Both  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7 (+6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9)  U-Recall(↑)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6 (+17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7)  Previously known  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2 (+6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0)  Current known  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6 (+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7)  Task3  mAP(↑)  Both  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0 (+6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5)  Previously known  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4 (+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2)  Current known  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1 (+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0)  Task4  mAP(↑)  Both  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8 (+9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7)  known object instances for OWOD problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Both WI and  A-OSE implicitly quantify the effevtiveness of the model in  handling unknown objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Implementation Details  The multi-scale feature extractor consists of a Resnet-  50 [16] pretrained on ImageNet [8] in a self-supervised [4]  manner and a deformable transformer encoder whose num-  ber of layer is set to 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' For the shared decoder, we use a  deformable transformer decoder and the numbder of layer  is set to 6, too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We set the number of queries 𝑀 = 100, the  dimension of the embeddings 𝐷 = 256 and the number of  pseudo-labels 𝑘 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' During inference, 𝑡𝑜𝑝-50 high scor-  ing detections are used for evaluation for per image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' More  details are described in the Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Comparison With State-of-the-art Methods  For a fair comparison, we compare CAT with ORE [17]  without the energy-based unknown identifier (EBUI) that  relies on held-out validation data with weak unknown object  supervision and OW-DETR [13] to demonstrate the effec-  tiveness of our method for OWOD problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We present the  comparison in terms of known class mAP, unknown class  recall, WI, and A-OSE, where U-Recall, WI and A-OSE  cannot be computed in Task 4 due to the absence of un-  known test annotations, for the reason that all 80 classes are  known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Furthermore, we demonstrate the effectiveness of  our model for incremental object detection in comparison  to [13,17,30,35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  OWOD SPLIT: The results compared with the state-of-  the-art methods on OWOD split for OWOD problem are  shown in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The performance of proposed standard  cascade detection transformer is also reported to be com-  pared with Faster R-CNN [33] and the standard Deformable  DETR [38] frameworks, for demonstrating the power of  localization identification cascade structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  These three  can only identify known objects, and so U-Recall cannot  be computed for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Benefiting from the self-adaptive  pseudo-labelling, the ability of CAT to detect unknown ob-  jects goes substantially beyond the existing models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Com-  pared with OW-DETR’s U-Recall of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8 on  Task 1, 2 and 3, our CAT achieves 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8, 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6 and 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9 in the  6  corresponding tasks, achieving significant absolute gains up  to 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In terms of WI and A-OSE, CAT also exceeds  them in all tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The ability to detect known objects and al-  leviate catastrophic forgetting of previous knowledge gains  an improved performance with significant gains, achieving  significant absolute gains up to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' This demonstrates the  significant performance of the cascade decoding structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  In addition, we report qualitative results in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4, along  with failure case analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' See more detailed qualitative re-  sults in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  MS-COCO SPLIT: We report the results on MS-COCO  split in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  MS-COCO split mitigates data leakage  across tasks and assign more data to each Task, while CAT  receives a more significant boost compared with OWOD  split.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Compared with OW-DETR’s U-Recall of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2 and  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9 on Task 1, 2 and 3, our CAT achieves 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0, 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0 and  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6 in the corresponding tasks, achieving significant abso-  lute gains up to 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Furthermore, the performance on  detecting known objects achieves significant absolute gains  up to 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' This demonstrates that our CAT has the more  powerful ability to retrieve new knowledge and detect the  known objects when faced with more difficult tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Predictions from CAT after being trained on Task 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  The results show that the model not only detects other categories  in the total category that have not yet been learned, such as ‘key-  board’, ‘kite’ and ‘dining table’, but also accurately detects cate-  gories outside the total category, such as ‘calendar’, ‘table lamp’  and ‘rubbish bins’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The approach misclassifies two of the ‘bird’  as ‘aeroplane’ and ‘unknown’, showing the limitation of CAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' See  more detailed qualitative results and analysis in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Incremental Object Detection: To intuitively present our  CAT’s ability for detecting object instances, we compare it  to [13,17,30,35] on the incremental object detection (IOD)  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We evaluate the experiments on three standard set-  tings, where a group of classes (10, 5 and last class) are in-  troduced incrementally to a detector trained on the remain-  ing classes (10, 15 and 19), based on PASCAL VOC 2007  dataset [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' As the results shown in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3, CAT outper-  forms the existing method in a great migration on all three  settings, indicating the power of localization and identifica-  tion cascade detection transformer for IOD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' State-of-the-art comparison for incremental object detec-  tion for three different settings on PASCAL VOC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The  comparison is shown in terms of overall mAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Our CAT achieves  significant performance in comparison to existing works on all the  three settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' See more details in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3 and Appedix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Method  10+10 settings  15+5 settings  19+1 settings  ILOD [35]  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  Faster ILOD [30]  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  ORE [17]  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  OW-DETR [13]  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  Ours: CAT  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0)  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8)  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Ablation Study  We conduct abundant ablative experiments to verify the  effectiveness of CAT’s components on the OWOD split  [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Cascade Decoupled Decoding Structure: We compare  between OW-DETR, fully decoupled decoding structure  and CAT in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The results illustrate that the decoupled  decoding structure improves the performance of detecting  known objects and does mitigate the influence of unknown  objects on the detection of known objects to some extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Because it reduces the difficulty of parameter learning and  mitigates the risk of confusion for known and unknown ob-  jects by disassembling the localization and identification  process of detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Compared with the fully decoupled  decoding structure, the cascade decoupled decoding struc-  ture is able to allow the identification process to draw on  location information while the localization process is not  limited by category knowledge and outperforms it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Self-Adaptive Pseudo-labelling: As shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5 (a)  and (b), we performed a number of ablation experiments  on Task 1 for different update cycles, positive and nega-  tive momentum amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The results demonstrate that  the self-adaptive pseudo-labelling makes the training pro-  cess of CAT robust, as we analyzed earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Especially for  the pink line, even if there are unexpected situations in the  training process, CAT can still self-adjust and develop in  a good direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In addition, we compare the attention-  driven (AD) and self-adaptive (SA) paeudo-labelling mech-  anism in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5 and Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5 (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The results demonstrate  that our self-adaptive pseudo-labelling mechanism signifi-  cantly improves the model’s ability to retrieve unknown ob-  jects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' During training, CAT requires double decoding pro-  cesses so that it is affected by generated pseudo-labels twice  as often as OW-DETR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Thus, for the high quality pseudo-  7  person:76%  unknown:29%  unkn0wn:35%  tvmonitor:93%  unknown:29%  aeroplane:79%  2  bird:45%  unkn0wn:29%  unkn0wn:31%  unkn0wn:26%  unknunkn0wh:26%  unknown:27%  unkn0wn:26%  unkn0wn:28%  person:94%  chair:82%  chair:91%  pottedplant:81%  unknown:25%  unkn0wn:30%Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (a) and (b) illustrate performance comparison between different update cycles, positive and negative momentum amplitude on  A-OSE and U-Recall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Where the cycle is set to 150 and 300, the positive momentum amplitude is set to 25%, 33% and 50%, the negative  momentum amplitude is set to 50%, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The lighter coloured lines are the real data and the corresponding darker coloured lines  are the data after smoothing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' (c) shows performance comparison between AD and SA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' See detail in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Performance comparison between different decoupled de-  coding structures and OW-DETR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' ‘FD’ refers to the fully decou-  pled decoding structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' See more details in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Task IDs ↓  Metrics  OW-DETR  FD  CAT  Task1  mAP(↑)  Current known  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  Previously known  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  Current known  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  Task2  mAP(↑)  Both  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  Previously known  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  Current known  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  Task3  mAP(↑)  Both  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  Previously known  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  Current known  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  Task4  mAP(↑)  Both  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  labels, CAT could learn better to detect unknown objects  than OW-DETR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' For the low quality pseudo-labels, CAT  would also be affected to a greater extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The results in Ta-  ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5 further demonstrate this investigation and the robust-  ness of our pseudo-labelling mechanism to generate pseudo  labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Open-set Detection Comparison: To further demonstrate  CAT’s ability to handle unknown instances in open-set data,  we follow the same evaluation protocol as [13, 17, 26] and  report the performance in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' CAT achieves promising  performance in comparison to the existing methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Relation to Prior Works  The issue of standard object detection [3,6,12,15,22,24,  29,32,33,38,40] has been raised for several years, number-  ous works have investigated this problem and push the field  to certain heights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Whereas the strong assumption that the  label space of object categories to be encountered during the  life-span of the model is the same as during its training re-  sults that these methods cannot meet real-world needs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The  success of [11,18–20,28,33] demonstrates the feasibility of  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Performance comparison AD and SA pseudo-labelling  mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  The results demonstrate that SA substantially en-  hances the model’s ability to retrieve unknown objects  Method  Task IDs ↓  AD  SA  U-Recall  WI  A-OSE  \x14  \x17  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0590  10248  Task1  \x17  \x14  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0578  8360  \x14  \x17  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0279  8540  Task2  \x17  \x14  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0268  6452  \x14  \x17  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0191  6840  OW-DETR  Task3  \x17  \x14  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0175  5310  \x14  \x17  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0533  41474  Task1  \x17  \x14  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0581  7070  \x14  \x17  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0271  20410  Task2  \x17  \x14  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0263  5902  \x14  \x17  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0186  11078  CAT  Task3  \x17  \x14  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0177  5189  Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Performance comparison on open-set object detection  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Our CAT achieves significant performance in comparison to  existing works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' See more details in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Evaluated on →  VOC  WR1  Standard Faster R-CNN [35]  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  Standard RetinaNet  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  Dropout Sampling [26]  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  ORE [17]  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  OW-DETR [13]  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  Ours: CAT  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2 (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1)  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9)  foreground localization based on the position and appear-  ance of objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' ORE [17] and OW-DETR [13] leverage  the models of standard object detection and pseudo labels  to detect objects in open world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In this paper, we propose a  novel transformer [37] based framework, CAT, for OWOD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  CAT decouples the localization and identification process  and connects them in a cascade approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In CAT, the fore-  ground localization process is not limited by the category  8  24  24  3e+4  20  20  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6e+4  16  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2e+4  I  12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8e+4  Tp=150, Tpma=25%,Tnma=50%  Tp=150, Tpma=33%,Tnma=50%  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4e+4  Tp=150, Tpma=50%,Tnma=50%  Tp=300, Tpma=25%,Tnma=50%  CAT + Self_Adaptive  le+z  CAT + Attention_Driven  Tp=300, Tpma=33%,Tnma=50%  OW-DETR + Self_Adaptive  be+s  Tp=300, Tpma=50%,Tnma=50%  OW-DETR + Attention_Drive  5  20  25  30  35  40  45  0  15  20  25  30  35  40  45  50  10  15  20  25  30  35  40  45  50of known objects, whereas the process of foreground iden-  tification can use information from the localization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Along with self-adaptive pseudo-labelling, CAT can gain  information beyond the data annotation and maintain a sta-  ble learning process according to self-regulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Conclusions  In this paper, we analyze the drawbacks of the paral-  lel decoding structure for open-world object detection and  explore the decoupled decoding structures of the detection  transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Motivated by the subconscious reactions of  humans when facing new scenes, we propose a novel lo-  calization and identification cascade detection transformer  (CAT), which decouples the localization and identification  process via the cascade decoding structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The cascade  decoding structure alleviates the influence of detecting un-  known objects on the detection of known objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  With  the self-adaptive pseudo-labelling mechanism, CAT gains  knowledge beyond the data annotation, generates pseudo  labels with robustness and maintains a stable training pro-  cess via self-adjustment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The extensive experiments on two  popular benchmarks, 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='𝑒.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=', PASCAL VOC and MS COCO  demonstrate that CAT consistently outperforms the existing  works for all task settings on all splits and achieves state-of-  the-art performance in the incremental object detection and  open-set detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Acknowledgment  This work is supported by National Natural Science  Foundation of China (grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='61871106 and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6137015  2), Key R&D projects of Liaoning Province, China (grant  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2020JH2/10100029), and the Open Project Program Fo-  undation of the Key Laboratory of Opto-Electronics Infor-  mation Processing, Chinese Academy of Sciences (OEIP-  O-202002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Additional Experiments Material  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Theory For Self-Adaptive Pseudo-labelling  For 0 < 𝑤2 < 𝑤1 < 1, we find the potential relationship  as follows:  � 𝑥𝑤1 > 𝑥𝑤2,𝑖 𝑓 𝑥 > 1  𝑥𝑤1 < 𝑥𝑤2,𝑖 𝑓 𝑥 < 1  (12)  Thus, for 𝑥𝑤1 ·𝑦𝑤2 and 𝑤1 > 𝑤2, if 𝑥 > 1 and 𝑦 > 1, 𝑥 weights  more and 𝑦 weights more if 𝑥 < 1 and 𝑦 < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  For the self-adaptive pseudo-labelling, we first normal-  ize 𝑠𝑜 to the range 0 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Considering that the model it-  self has little knowledge in the early stages of model train-  ing, the model-driven pseudo-labelling should weight less  than the input-deiven pseudo-labelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' As the training time  of the model increasing, the knowledge base of the model  grows and the weight of the model-driven pseudo-labelling  gets bigger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Combining this with the patterns above, we set  W𝑚0 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8, W𝐼 0 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2 and update them as follows:  ���  ���  W 𝑡  𝑚 = W 𝑡−1  𝑚  +Δ𝑤 ×W 𝑡−1  𝑚  ,  W 𝑡  𝐼 = W 𝑡−1  𝐼  −Δ𝑤 ×W 𝑡−1  𝐼  ,  W 𝑡  𝑚,W 𝑡  𝐼 = 𝑛𝑜𝑟𝑚 �W 𝑡  𝑚,W 𝑡  𝐼  � ,  (13)  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Additional Illustration For Data Split  As shown in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7, the OWOD split proposed in ORE  groups all VOC classes and data as 𝑇𝑎𝑠𝑘 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The remaining  60 classes of MS-COCO are grouped into three successive  tasks (𝑇𝑎𝑠𝑘 2, 3, 4) with semantic drifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' However, it leads  data leakage across tasks since different classes which be-  long to a super-categories are introduced in different tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  The MS-COCO split proposed in OW-DETR is a stricter  split, where all the classes of a super-categories are intro-  duced at a time in a task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The table shows task composition in the OWOD and MS-  COCO split for Open-world evaluation protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The semantics of  each task and the number of images and instances(objects) across  splits are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Task ID  Task 1  Task 2  Task 3  Task 4  OWOD split  Semantic split  VOC  Classes  Outdoor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Accessories,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Appliances,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Truck  Sports,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Food  Electronic,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Indoor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Kitchen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Furniture  # training images  16551  45520  39402  40260  # test images  4952  1914  1642  1738  # train instances  47223  113741  114452  138996  # test instances  14976  4966  4826  6039  MS-COCO split  Semantic split  Animals,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='Person,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Vehicles  Appliances,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Accessories,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Outdoor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Furniture  Sports,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Food  Electronic,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Indoor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Kitchen  # training images  89490  55870  39402  38903  # test images  3793  2351  1642  1691  # train instances  421243  163512  114452  160794  # test instances  17786  7159  4826  7010  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' WI, A-OSE and U-Recall Metrics  In this paper, we mainly illustrate the state-of-the-art  comparison in terms of wilderness impact (WI), absolute  open-set error (A-OSE), unknown recall (U-Recall) and  mean average precision (mAP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' WI measures the model’s  confusion in predicting an unknown instance as known  class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The calculation formula is as follows:  WI =  𝑃K  𝑃K∪U  −1  (14)  Where 𝑃K is the prediction on known classes and 𝑃K∪U  is the prediction on known and unknown classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' A-OSE  devotes the total number of unknown instances detected as  known classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Both WI and A-OSE indicate the degree of  confusion in predicting the known classes in the presence  9  of unknown instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Furthermore, U-Recall directly mea-  sures the model’s ability to retrieve the unknown instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Additional Implementation Details  For selective search, we use the 𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑣𝑒 𝑠𝑒𝑎𝑟𝑐ℎ  function in Selectivesearch library and the scale, sigma,  min size of parameter is set to 500, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9 and 200, respec-  tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In addition, we eliminate candidate boxes with less  than 2000 pixel points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The multi-scale feature maps ex-  tracted from the backbone are projected to feature maps  with 256-channels using 1 × 1 convolution filters and used  as multi-scale input to deformable transformer encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The  PyTorch library and eight NVIDIA RTX 3090 GPUs are  used to train our CAT framework with a batch size of 3 im-  ages per GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In each task, the CAT framework is trained  for 50 epochs and finetuned for 20 epochs during the in-  cremental learning step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We train our CAT using the Adam  optimizer with a base learning rate of 2 × 10−4, 𝛽1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9,  𝛽2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='999, and weight decay of 10−4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' For finetuning dur-  ing incremental step, the learning rate is reduced by a factor  of 10 and trained using a set of 50 stored exemplars per  known class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Additional Results  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Incremental Object Detection  Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8 shows a detailed comparison of CAT with exist-  ing approaches on PASCAL VOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Evaluation is performed  on three standard settings, where a group of classes (10, 5  and last class) are introduced incrementally to a detector  trained on the remaining classes (10,15 and 19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Our CAT  performs favorably against existing approaches on all three  settings, illustrating the power of localization identification  cascade detection transformer for incremental objection de-  tection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Additional Qualitative Results  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6 illustrates the visualization results comparison  between OW-DETR and our CAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We use OW-DETR and  CAT which are both trained on Task 1, the known classes  are ‘aeroplane’, ‘bicycle’, ‘bird’, ‘boat’, ‘bottle’, ‘bus’,  ‘car’, ‘cat’, ‘chair’, ‘cow’, ‘diningtable’, ‘dog’, ‘horse’,  ‘motorbike’, ‘person’, ‘pottedplant’, ‘sheep’, ‘sofa’, ‘train’  and ‘tvmonitor’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The results show that our CAT substan-  tially outperforms OW-DETR in terms of the ability to ex-  plore unknown objects and the accuracy of detection due to  the clever cascade decoupled decoding structure and self-  adaptive pseudo-labelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' As shown in the first row, OW-  DETR identifies the background and known objects as un-  knowns and the real unknown object (carton) as the back-  ground, and our model accurately identifies the carton as  the unknown object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In the second row, OW-DETR iden-  tifies the two calendars as the chair and the background,  respectively, and the keyboard as the background, and our  CAT accurately identifies them as unknown objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The  third row shows that OW-DETR fails to detect the true  unknown object (frame) and identifies two known objects  (sofa) as one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Our model accurately identifies the frame as  an unknown object and also accurately identifies the two  sofas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7 describes the visualization results comparison  between CAT and Oracle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We visualize the detection results  of our model for known and unknown objects, as well as the  ground truth on the tasks corresponding to the weights, in-  cluding the labels of known and unknown categories, where  the objects of unknown categories are the objects of other  categories that have not yet appeared in the total categories  of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Our model can accurately detect known  objects and unknown objects outside the total class of the  dataset, such as the electric plug and sound switch in the  first row, the camera in the second row and the kitten toy  in the third row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' It is also worth noting that although our  model detects the audio, it does not identify it as an un-  known object, but as a remote, showing the limitations of  our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8 exhibits the visualization performance on in-  cremental object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We visualize the detection re-  sults of the weights corresponding to different tasks for the  same scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The results show that our CAT can identify  unknown kinds of objects as the unknown class and accu-  rately identify their classes after incrementally learning the  unknown classes, such as sports ball and tennis racket in  the first row, surfboard in the second row and traffic light in  the third row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Societal Impact and Limitations  Open-world object detection makes artificial intelligence  smarter to face more problems in real life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' It takes object de-  tection to a cognitive level, as the model requires more than  simply remembering the objects learned, it requires deeper  thinking about the scene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Although our results demonstrate significant improve-  ments over ORE and OW-DETR in terms of WI, A-OSE,  U-Recall and mAP, the performances are still on the lower  side due to the challenging nature of the open-world de-  tection problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  In this paper, we are mainly commit-  ted to enhance the model’s ability to explore unknown  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' However, the confidence level of our model for  the detection of unknown objects still needs to be im-  proved, and this is what we will strive for in the fu-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  References  [1] Ankan Bansal, Karan Sikka, Gaurav Sharma, Rama Chel-  lappa, and Ajay Divakaran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Zero-shot object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In  10  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Visualization results comparison between OW-DETR and our CAT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We use OW-DETR and CAT which are both trained on Task  1, the known classes are ‘aeroplane’, ‘bicycle’, ‘bird’, ‘boat’, ‘bottle’, ‘bus’, ‘car’, ‘cat’, ‘chair’, ‘cow’, ‘diningtable’, ‘dog’, ‘horse’,  ‘motorbike’, ‘person’, ‘pottedplant’, ‘sheep’, ‘sofa’, ‘train’ and ‘tvmonitor’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The results show that our CAT substantially outperforms  OW-DETR in terms of the ability to explore unknown objects and the accuracy of detection due to the clever cascade decoupled decoding  structure and self-adaptive pseudo-labelling mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' As shown in the first row, OW-DETR identifies the background and known objects  as unknowns and the real unknown object (carton) as the background, and our model accurately identifies the carton as the unknown  object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In the second row, OW-DETR identifies the two calendars as the chair and the background, respectively, and the keyboard as the  background, and our CAT accurately identifies them as unknown objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The third row shows that OW-DETR not only does not detect the  true unknown object (frame), but also identifies two known objects (sofa) as one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Our model accurately identifies the frame as an unknown  object and also accurately identifies the two sofas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  11  OW-DETR  Ours:CAT  i0g:29%  unkn0wn:41%  d0g:57%  d0g:66%  dog:68%  unknown:60  unknown:25%  unkn0wn:29%  unknown:35%  pers0n:85%  person:76%  unknown:29%  chair:25%  unkn0wn:27%  unkn0wn:38%  unkn0wn:26%  :68  person:  unknown:34%Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The detailed comparison of CAT with existing approaches on PASCAL VOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Evaluation is performed on three standard settings,  where a group of classes (10, 5 and last class) are introduced incrementally to a detector trained on the remaining classes (10,15 and 19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Our CAT performs favorably against existing approaches on all three settings, illustrating the power of localization identification cascade  detection transformer for incremental objection detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  10 + 10 setting  aero  cycle  bird  boat  bottle  bus  car  cat  chair  cow  table  dog  horse  bike  person  plant  sheep  sofa  train  tv  mAP  ILOD  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  48  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  Faster ILOD  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  ORE - (CC + EBUI)  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  ORE - EBUI  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  77  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  OW - DETR  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  Ours: CAT  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  15 + 5 setting  aero  cycle  bird  boat  bottle  bus  car  cat  chair  cow  table  dog  horse  bike  person  plant  sheep  sofa  train  tv  mAP  ILOD  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  59  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  Faster ILOD  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  ORE - (CC + EBUI)  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  80  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  69  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  ORE - EBUI  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  81  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  OW - DETR  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  Ours: CAT  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  19 + 1 setting  aero  cycle  bird  boat  bottle  bus  car  cat  chair  cow  table  dog  horse  bike  person  plant  sheep  sofa  train  tv  mAP  ILOD  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  Faster ILOD  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  ORE - (CC + EBUI)  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  45  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  ORE - EBUI  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  60  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  OW - DETR  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  Ours: CAT  86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='0  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='3  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='4  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='6  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='7  75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='9  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='5  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='2  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='1  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='8  Proceedings of the European Conference on Computer Vi-  sion (ECCV), pages 384–400, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 5  [2] Josh Beal, Eric Kim, Eric Tzeng, Dong Huk Park, Andrew  Zhai, and Dmitry Kislyuk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Toward transformer-based object  detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' arXiv preprint arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='09958, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 4  [3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas  Usunier, Alexander Kirillov, and Sergey Zagoruyko.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' End-to-  end object detection with transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In European confer-  ence on computer vision, pages 213–229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Springer, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 2,  4, 8  [4] Mathilde Caron, Hugo Touvron, Ishan Misra, Herv´e J´egou,  Julien Mairal, Piotr Bojanowski, and Armand Joulin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Emerg-  ing properties in self-supervised vision transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  In  Proceedings of the IEEE/CVF International Conference on  Computer Vision, pages 9650–9660, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 6  [5] Xinlei Chen, Haoqi Fan, Ross Girshick, and Kaiming He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Improved baselines with momentum contrastive learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  arXiv preprint arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='04297, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 4  [6] Xingyu Chen, Junzhi Yu, Shihan Kong, Zhengxing Wu,  and Li Wen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Joint anchor-feature refinement for real-time  accurate object detection in images and videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  IEEE  Transactions on Circuits and Systems for Video Technology,  31(2):594–607, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [7] Xiyang Dai, Yinpeng Chen, Jianwei Yang, Pengchuan  Zhang, Lu Yuan, and Lei Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Dynamic detr: End-to-  end object detection with dynamic attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceedings  of the IEEE/CVF International Conference on Computer Vi-  sion, pages 2988–2997, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 4  [8] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li,  and Li Fei-Fei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Imagenet: A large-scale hierarchical image  database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In 2009 IEEE conference on computer vision and  pattern recognition, pages 248–255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Ieee, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 6  [9] Akshay Dhamija, Manuel Gunther, Jonathan Ventura, and  Terrance Boult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The overlooked elephant of object detection:  Open set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF Winter Confer-  ence on Applications of Computer Vision, pages 1021–1030,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 5  [10] Mark Everingham, Luc Van Gool, Christopher KI Williams,  John Winn, and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The pascal visual object  classes (voc) challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' International journal of computer  vision, 88(2):303–338, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 5, 7  [11] Spyros Gidaris and Nikos Komodakis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Attend refine repeat:  Active box proposal generation via in-out localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' arXiv  preprint arXiv:1606.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='04446, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [12] Ross Girshick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Fast r-cnn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceedings of the IEEE inter-  national conference on computer vision, pages 1440–1448,  2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [13] Akshita Gupta, Sanath Narayan, KJ Joseph, Salman Khan,  Fahad Shahbaz Khan, and Mubarak Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Ow-detr: Open-  world detection transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In CVPR, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 2, 3, 5, 6, 7,  8  [14] Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross  Girshick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Momentum contrast for unsupervised visual rep-  resentation learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF con-  ference on computer vision and pattern recognition, pages  9729–9738, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 4  [15] Kaiming He, Georgia Gkioxari, Piotr Doll´ar, and Ross Gir-  shick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Mask r-cnn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceedings of the IEEE international  conference on computer vision, pages 2961–2969, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  12  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Visualization results comparison between CAT and Oracle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We visualize the detection results of our model for known and  unknown objects, as well as the ground truth on the tasks corresponding to the weights, including the labels of known categories and the  labels of unknown categories, where the objects of unknown categories are the objects of other categories that have not yet appeared in the  total categories of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Our model can accurately detect known objects and unknown objects outside the total class of the dataset,  such as the electric plug and sound switch in the first row, the camera in the second row and the kitten toy in the third row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' It is also worth  noting that although our model detects the audio, it does not identify it as an unknown object, but as a remote, showing the limitations of  our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  13  Oracle  Ours:CAT  tvmonitor  tvmonitor:79%  remote:28%  mote:35  O  unknown:3  unknown:38%  1kn0wn:34%  unkn0wn:26%%  keyboard  keyboard:42  mouse  mouse  person  tvmonitor:88%  unkn0wn:36%  sofa:43%  cat:80%  cat  unknown:26%  unknown:43  unknown:35%  inknov  unknown:25%Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Visualization performance on incremental object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' We visualize the detection results of the weights corresponding to  different tasks for the same scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' The results show that our CAT can identify unknown kinds of objects as the unknown class and  accurately identify their classes after incrementally learning the unknown classes, such as sports ball and tennis racket in the first row,  surfboard in the second row and traffic light in the third row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  [16] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Deep residual learning for image recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceed-  14  Before Learning  After Learning  tennis racket:84%  erson:89%  unk  sports  ball:80%  erson:87%  surfb0ard:60%  unkn0wn:30%  raffic light:60%3%  unknowi  traffic  1ght:78%  ight:6  car:88%  car:68%  unknown  ar:58  car  23%  :21%ings of the IEEE conference on computer vision and pattern  recognition, pages 770–778, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 6  [17] K J Joseph, Salman Khan, Fahad Shahbaz Khan, and Vi-  neeth N Balasubramanian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Towards open world object de-  tection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In 2021 IEEE/CVF Conference on Computer Vision  and Pattern Recognition (CVPR), pages 5826–5836, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  1, 3, 4, 5, 6, 7, 8  [18] Bingyi Kang, Zhuang Liu, Xin Wang, Fisher Yu, Jiashi Feng,  and Trevor Darrell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Few-shot object detection via feature  reweighting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceedings of the IEEE/CVF International  Conference on Computer Vision, pages 8420–8429, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [19] Dahun Kim, Tsung-Yi Lin, Anelia Angelova, In So Kweon,  and Weicheng Kuo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Learning open-world object proposals  without learning to classify.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' IEEE Robotics and Automation  Letters, 7(2):5453–5460, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [20] Hongyang Li, Yu Liu, Wanli Ouyang, and Xiaogang Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Zoom out-and-in network with map attention decision for re-  gion proposal and object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' International Journal of  Computer Vision, 127(3):225–238, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [21] Yanghao Li, Hanzi Mao, Ross Girshick, and Kaiming He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Exploring plain vision transformer backbones for object de-  tection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' arXiv preprint arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='16527, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 4  [22] Tsung-Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and  Piotr Doll´ar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Focal loss for dense object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Pro-  ceedings of the IEEE international conference on computer  vision, pages 2980–2988, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [23] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays,  Pietro Perona, Deva Ramanan, Piotr Doll´ar, and C Lawrence  Zitnick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Microsoft coco: Common objects in context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In  European conference on computer vision, pages 740–755.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Springer, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 5  [24] Yue Lu, Xingyu Chen, Zhengxing Wu, and Junzhi Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' De-  coupled metric network for single-stage few-shot object de-  tection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' IEEE Transactions on Cybernetics, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [25] Dimity Miller, Lachlan Nicholson, Feras Dayoub, and Niko  S¨underhauf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Dropout sampling for robust object detection  in open-set conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In 2018 IEEE International Confer-  ence on Robotics and Automation (ICRA), pages 3243–3249.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 5  [26] Dimity Miller, Lachlan Nicholson, Feras Dayoub, and Niko  S¨underhauf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Dropout sampling for robust object detection  in open-set conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In 2018 IEEE International Confer-  ence on Robotics and Automation (ICRA), pages 3243–3249.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [27] Ishan Misra, Rohit Girdhar, and Armand Joulin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' An end-to-  end transformer model for 3d object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceed-  ings of the IEEE/CVF International Conference on Com-  puter Vision, pages 2906–2917, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 4  [28] Pedro O O Pinheiro, Ronan Collobert, and Piotr Doll´ar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Learning to segment object candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Advances in neural  information processing systems, 28, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [29] Yanwei Pang, Tiancai Wang, Rao Muhammad Anwer, Fa-  had Shahbaz Khan, and Ling Shao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Efficient featurized im-  age pyramid network for single shot detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceedings  of the IEEE/CVF Conference on Computer Vision and Pat-  tern Recognition, pages 7336–7344, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [30] Can Peng, Kun Zhao, and Brian C Lovell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Faster ilod: In-  cremental learning for object detectors based on faster rcnn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Pattern recognition letters, 140:109–115, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 6, 7  [31] Jordi Pont-Tuset, Pablo Arbel´aez, Jonathan T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Barron, Fer-  ran Marques, and Jitendra Malik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Multiscale combinatorial  grouping for image segmentation and object proposal gener-  ation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' IEEE Transactions on Pattern Analysis and Machine  Intelligence, 39(1):128–140, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 3  [32] Joseph Redmon, Santosh Divvala, Ross Girshick, and Ali  Farhadi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' You only look once: Unified, real-time object de-  tection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceedings of the IEEE conference on computer  vision and pattern recognition, pages 779–788, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [33] Shaoqing Ren, Kaiming He, Ross Girshick, and Jian Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Faster r-cnn: Towards real-time object detection with region  proposal networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Advances in neural information process-  ing systems, 28, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 1, 6, 8  [34] Adrian Rosebrock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Intersection over union (iou) for ob-  ject detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Diambil kembali dari PYImageSearch  https//www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' pyimagesearch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' com/2016/11/07/intersection-  over-union-iou-for-object-detection, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 4  [35] Konstantin Shmelkov, Cordelia Schmid, and Karteek Ala-  hari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Incremental learning of object detectors without catas-  trophic forgetting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In Proceedings of the IEEE international  conference on computer vision, pages 3400–3409, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 6,  7, 8  [36] Jasper RR Uijlings, Koen EA Van De Sande, Theo Gev-  ers, and Arnold WM Smeulders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Selective search for ob-  ject recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' International journal of computer vision,  104(2):154–171, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 3, 4  [37] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszko-  reit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia  Polosukhin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Attention is all you need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Advances in neural  information processing systems, 30, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  [38] Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang  Wang, and Jifeng Dai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Deformable detr: Deformable trans-  formers for end-to-end object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  arXiv preprint  arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='04159, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 2, 4, 6, 8  [39] C Lawrence Zitnick and Piotr Doll´ar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Edge boxes: Locat-  ing object proposals from edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' In European conference on  computer vision, pages 391–405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' Springer, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 3  [40] Zhengxia Zou, Zhenwei Shi, Yuhong Guo, and Jieping Ye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  Object detection in 20 years: A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='  arXiv preprint  arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content='05055, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
+page_content=' 8  15' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/EdA0T4oBgHgl3EQfA_-G/content/2301.01970v1.pdf'}
diff --git a/GtE4T4oBgHgl3EQfgQ2M/content/tmp_files/2301.05115v1.pdf.txt b/GtE4T4oBgHgl3EQfgQ2M/content/tmp_files/2301.05115v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..359f09e672b4daa090f4d273b2a8aeaf7d2c747a
--- /dev/null
+++ b/GtE4T4oBgHgl3EQfgQ2M/content/tmp_files/2301.05115v1.pdf.txt
@@ -0,0 +1,4198 @@
+MNRAS 00, 1–31 (2023)
+Preprint 13 January 2023
+Compiled using MNRAS LATEX style file v3.0
+QUIJOTE scientific results – VI. The Haze as seen by QUIJOTE
+F. Guidi,1,2,3★ R. T. Génova-Santos,1,2† J. A. Rubiño-Martín,1,2 M. W. Peel,1,2
+M. Fernández-Torreiro,1,2 C. H. López-Caraballo,1,2 R. Vignaga,1,2 E. de la Hoz,4,5
+P. Vielva,4 R. A. Watson,6 M. Ashdown,7,8 C. Dickinson,6 E. Artal,9 R. B. Barreiro,4
+F. J. Casas,4 D. Herranz,4 R. J. Hoyland,1,2 A. N. Lasenby,7,8 E. Martinez-Gonzalez,4
+L. Piccirillo,6 F. Poidevin,1,2 R. Rebolo,1,2,10 B. Ruiz-Granados,1,2,11 D. Tramonte,12,13,1,2
+F. Vansyngel1,2
+1Instituto de Astrofísica de Canarias, E-38200 La Laguna, Tenerife, Spain
+2Departamento de Astrofísica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain
+3Institut d’Astrophysique de Paris, UMR 7095, CNRS & Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
+4Instituto de Fisica de Cantabria (IFCA), CSIC-Univ. de Cantabria, Avda. los Castros, s/n, E-39005 Santander, Spain
+5Dpto. de Física Moderna, Universidad de Cantabria, Avda. los Castros s/n, E-39005 Santander, Spain
+6Jodrell Bank Centre for Astrophysics, Alan Turing Building, Department of Physics and Astronomy, School of Nature Sciences, University of Manchester,
+Oxford Road, Manchester M13 9PL, U.K
+7Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK
+8Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA
+9Departamento de Ingenieria de COMunicaciones (DICOM), Edificio Ingenieria de Telecomunicacion, Plaza de la Ciencia s/n, E-39005 Santander, Spain
+10Consejo Superior de Investigaciones Cientificas, E-28006 Madrid, Spain
+11Departamento de Física. Facultad de Ciencias. Universidad de Córdoba. Campus de Rabanales, Edif. C2. Planta Baja. E-14071 Córdoba, Spain
+12Purple Mountain Observatory, CAS, No.10 Yuanhua Road, Qixia District, Nanjing 210034, China
+13NAOC-UKZN Computational Astrophysics Center (NUCAC), University of Kwazulu-Natal, Durban 4000, South Africa
+Accepted XXX. Received YYY; in original form ZZZ
+ABSTRACT
+The Haze is an excess of microwave intensity emission surrounding the Galactic centre. It
+is spatially correlated with the 𝛾-ray Fermi bubbles, and with the S-PASS radio polarization
+plumes, suggesting a possible common provenance. The models proposed to explain the origin
+of the Haze, including energetic events at the Galactic centre and dark matter decay in the
+Galactic halo, do not yet provide a clear physical interpretation. In this paper we present a re-
+analysis of the Haze including new observations from the Multi-Frequency Instrument (MFI)
+of the Q-U-I Joint TEnerife (QUIJOTE) experiment, at 11 and 13 GHz. We analyze the Haze in
+intensity and polarization, characterizing its spectrum. We detect an excess of diffuse intensity
+signal ascribed to the Haze. The spectrum at frequencies 11 ≤ 𝜈 ≤ 70 GHz is a power-law with
+spectral index 𝛽H = −2.79 ± 0.08, which is flatter than the Galactic synchrotron in the same
+region (𝛽S = −2.98 ± 0.04), but steeper than that obtained from previous works (𝛽H ∼ −2.5 at
+23 ≤ 𝜈 ≤ 70 GHz). We also observe an excess of polarized signal in the QUIJOTE-MFI maps
+in the Haze area. This is a first hint detection of polarized Haze, or a consequence of curvature
+of the synchrotron spectrum in that area. Finally, we show that the spectrum of polarized
+structures associated with Galactic centre activity is steep at low frequencies (𝛽 ∼ −3.2 at
+2.3 ≤ 𝜈 ≤ 23 GHz), and becomes flatter above 11 GHz.
+Key words: diffuse radiation – Galaxy: centre – ISM: bubbles – cosmology: observations
+1
+INTRODUCTION
+During the last decades multiple high sensitivity surveys have been
+carried out in order to provide an accurate characterization of the
+★ E-mail: federica.guidi@iap.fr
+† E-mail: rgs@iac.es
+Galactic foregrounds at radio and microwave wavelengths, with
+the final goal of doing cosmology with the Cosmic Microwave
+Background (CMB; see e.g., Planck Collaboration et al. 2020b).
+The main target of the two satellite missions Wilkinson Microwave
+Anisotropy Probe (WMAP; e.g., Bennett et al. 2003) and Planck
+(e.g., Planck Collaboration et al. 2020a) was the CMB, which im-
+© 2023 The Authors
+arXiv:2301.05115v1  [astro-ph.HE]  12 Jan 2023
+
+2
+F. Guidi et al.
+plied the generation of full sky images of the Galactic emission at
+multiple frequencies, between 23 and 857 GHz. These data provided
+an accurate picture of the emission of our own Galaxy, and enabled
+a number of discoveries, among them that of the microwave Haze.
+The Haze was discovered in the process of disentangling the
+Galactic emission from the cosmological CMB signal using WMAP
+data between 23 and 60 GHz by Finkbeiner (2004), and it was con-
+firmed by further studies (Dobler & Finkbeiner 2008; Dobler 2012;
+Pietrobon et al. 2012; Planck Collaboration et al. 2013). During this
+process, a diffuse and extended signal became evident in the residu-
+als after removing all the already known emission mechanisms from
+the WMAP frequency maps. The microwave (or sometimes WMAP)
+Haze is indeed an excess of diffuse emission with an elliptically
+symmetric shape centred on the Galactic centre, extending towards
+the north and the south of the Galactic plane and reaching high
+Galactic latitudes |𝑏| ≈ 35◦. The Haze has been measured to have a
+relatively flat spectrum (𝛽 ≈ −2.5) at the lowest WMAP frequencies
+compared to that of typical Galactic synchrotron emission at high
+Galactic latitudes (𝛽 ≈ −3.0).
+The Planck Collaboration also detected the Haze excess
+(Planck Collaboration et al. 2013) with an independent dataset be-
+tween 30 and 70 GHz. They measured the spectrum of the South
+Haze bubble using Planck and WMAP data, showing a synchrotron-
+like power-law with a spectral index 𝛽 = −2.56 ± 0.05. This spec-
+trum is in agreement with what had been previously observed with
+WMAP data alone.
+The microwave Haze has a 𝛾-ray counterpart, the so-called
+Fermi bubbles, which were discovered in the Fermi-LAT data at
+energies 2–50 GeV (Dobler et al. 2010; Su et al. 2010). The Fermi
+bubbles are two extended 𝛾-ray lobes located at a position coin-
+cident to that of the WMAP Haze, but with a larger extension in
+Galactic latitude, reaching |𝑏| ≈ 50◦, and with a flat spectrum. This
+multi-wavelength correspondence confirmed the interpretation of
+the microwave Haze as a real sky component and it was ascribed
+to synchrotron emission of a young population of cosmic-ray elec-
+trons (Dobler et al. 2010). Cosmic-ray electrons with energies 10–
+100 GeV produce microwave synchrotron during their interaction
+with a magnetic field, but also 𝛾-ray photons through Inverse Comp-
+ton scattering (IC) with the Interstellar Radiation Field (ISRF).
+In addition, recent observations of the eRosita X-ray space tele-
+scope (Merloni et al. 2012) detected a distinct but possibly related
+structure: two circular and symmetric soft-X-ray (0.3–2.3 keV) bub-
+bles, which extended up to high Galactic latitude |𝑏| ≈ 85◦ (Predehl
+et al. 2020). The eRosita bubbles enclose the Fermi bubbles, and the
+northern one partially overlaps with the North Polar Spur (NPS), a
+large and polarized filament that emerges from the Galactic centre
+and goes toward the north. This spatial correlation points towards a
+possible connection between the NPS and the Haze, which could be
+generated by an explosive event in the Galactic centre (Sofue 1977,
+1994). Several works support this hypothesis by locating the NPS
+at a distance of ∼10 kpc, which is comparable to the distance to the
+Galactic centre (e.g., Sofue 2015; Predehl et al. 2020; Kataoka et al.
+2021). However this aspect is still controversial. According with dif-
+ferent works (e.g., Planck Collaboration et al. 2016c; Panopoulou
+et al. 2021) the distance to the NPS is smaller than to the Galactic
+centre, being of the order of ∼ 100–200 pc, identifying therefore the
+NPS and the Haze as two different components, with respectively a
+local and a Galactic centre origin.
+The Haze, moreover, is not peculiar to our own Galaxy. Li
+et al. (2019) reported the first detection of a Haze-like structure
+in an external galaxy, using radio (C-band) and X-ray (0.8–8 keV)
+data. The spectral index of this extra-galactic Haze is 𝛽 ≈ −3.1 at
+radio wavelengths, which is typical for synchrotron emission, and
+takes the slightly flatter value 𝛽 ≈ −2.8 in the joint fit of radio and
+X-ray data.
+It is well known that the synchrotron emission is polarized,
+and to confirm that the Haze has a synchrotron origin it should
+be possible to observe an associated polarized component. Such a
+component was identified for the first time by the S-PASS southern
+sky survey at 2.3 GHz, which detected two giant radio polarized
+plumes extending from the centre of our Galaxy (Carretti et al.
+2013). The plumes spatially correlate with the Fermi bubbles, with
+the microwave Haze, and with X-ray structures observed by ROSAT
+(Almy et al. 2000; Carretti et al. 2013) that connect the plumes
+with the centre of the Galaxy. Interestingly, the radio polarized
+plumes appear to be more extended than the Fermi bubbles, reaching
+|𝑏| ≈ 60◦.
+The radio polarized plumes can also be roughly identified in the
+low frequency maps of Planck and WMAP, although the signal-to-
+noise is not as good as in S-PASS. The combination of S-PASS and
+WMAP data allowed the measurement of the spectral index of the
+polarized emission between 2.3 GHz and 23 GHz, which is 𝛽 = −3.2
+(Carretti et al. 2013). It should be noted that the spectral index is
+significantly flatter in intensity than in polarization, making the in-
+terpretation of the Haze/bubbles to be very puzzling. The difference
+in the spectral index might suggest that the cosmic-ray electrons
+that generate the intensity of the Haze and the polarization of the
+plumes belong to two different electron populations. Alternatively,
+the superposition of different components along the line-of-sight
+could explain the different spectral index in polarization.
+A variety of scenarios have been proposed in order to explain
+the possible origin of the Haze signal. One intriguing proposal is
+that it is generated by secondary emission of dark matter particles
+(Hooper et al. 2007; Cholis et al. 2009; Dobler et al. 2010; Delahaye
+et al. 2012; Gaskins 2016; Egorov et al. 2016). However the exis-
+tence of 𝛾-ray bubbles with sharp edges (Su et al. 2010) and radio
+polarized sharp filaments and plumes (Biermann et al. 2010; Jones
+et al. 2012; Crocker & Aharonian 2011; Carretti et al. 2013; Planck
+Collaboration et al. 2016c) contradict the dark matter hypothesis as
+a complete explanation of this phenomenon, while energetic events
+in the Galactic centre provide a much more likely scenario. Still, it
+cannot be excluded that a small fraction of the Haze emission could
+have a dark matter origin (Egorov et al. 2016).
+Other proposed progenitors for the Haze emission demand
+energetic events in the Galactic centre. AGN activity of the super-
+massive black hole in the centre of the Milky Way (SgrA*) (Zubovas
+& Nayakshin 2012; Guo et al. 2012; Guo & Mathews 2012; Ack-
+ermann et al. 2014; Fox et al. 2015; Zhang & Guo 2020, 2021;
+Pillepich et al. 2021; Yang et al. 2022), nuclear activity in the
+central Galactic region such as star-formation, star-bursts, or su-
+pernovae explosions, which could power outflows of hot and mag-
+netized plasma and accelerate cosmic rays (Crocker & Aharonian
+2011; Crocker 2012; Lacki 2014; Carretti et al. 2013; Zhang et al.
+2021), or more complex scenarios (Ashley et al. 2022).
+A study from Crocker et al. (2015) proposed a unified model for
+the microwave Haze, radio plumes, and Fermi bubbles, as generated
+by outflows powered by nuclear activity. For the first time, this
+model provided an explanation for the change of the spectral index
+in the outer and inner part of the bubbles at microwave or radio
+wavelengths, as suggested by observations (Carretti et al. 2013).
+However, even if the scenarios proposed in the literature par-
+tially explain some of the Haze characteristics, none of them provide
+a complete description. New observations are crucial for the under-
+standing of the origin of the Haze, and independent determinations
+MNRAS 00, 1–31 (2023)
+
+The Haze as seen by QUIJOTE
+3
+Survey
+Freq.
+FWHM
+𝜎c
+Reference
+[GHz]
+[deg]
+[%]
+S-PASS
+2.3
+0.15
+5
+Carretti et al. (2019)
+QUIJOTE
+11.1
+0.93
+5
+Rubiño-Martín et al. (2023)
+QUIJOTE
+12.9
+0.92
+5
+Rubiño-Martín et al. (2023)
+WMAP K-band
+22.8
+0.88
+3
+Bennett et al. (2013)
+Planck-LFI
+28.4
+0.54
+3
+Planck Collaboration et al. (2020c)
+WMAP Ka-band
+33.0
+0.66
+3
+Bennett et al. (2013)
+WMAP Q-band
+40.6
+0.51
+3
+Bennett et al. (2013)
+Planck-LFI
+44.1
+0.45
+3
+Planck Collaboration et al. (2020c)
+WMAP V-band
+60.8
+0.35
+3
+Bennett et al. (2013)
+Planck-LFI
+70.4
+0.22
+3
+Planck Collaboration et al. (2020c)
+Table 1. Summary of the data that are used in this work. We show central
+frequencies, beam FWHMs and adopted calibration uncertainties (𝜎c) of
+each survey.
+of the spectral index of the emission across the Haze area, as well
+as polarization measurements, can yield a clearer picture of this
+complex region.
+In this paper we provide new observational constraints on the
+Haze microwave emission using data from the Multi-Frequency In-
+strument of the Q-U-I Joint TEnerife experiment (Rubiño-Martín
+et al. 2012b; Hoyland et al. 2012). We performed a full reanalysis
+of the Haze bubbles and filaments first reproducing, in an inde-
+pendent manner, previous results obtained with WMAP (Dobler &
+Finkbeiner 2008), Planck-LFI (Planck Collaboration et al. 2013),
+and S-PASS (Carretti et al. 2013) data. Afterwards we included in
+the analysis microwave data from QUIJOTE-MFI at 11 and 13 GHz.
+In particular, we performed for the first time a component separa-
+tion in polarization, searching for a polarized Haze component at
+the QUIJOTE frequencies. Note that there is a gap of available
+data between 2.3 GHz and 23 GHz, and 2.3 GHz data are affected
+by Faraday rotation and depolarization (Carretti et al. 2019). QUI-
+JOTE effectively extends the frequency coverage of WMAP and
+Planck down to 11 GHz, where the signal is relatively strong and
+not significantly affected by Faraday effects, providing robust spec-
+tral measurements in intensity and polarization.
+The paper is organized as follows: we present the new QUI-
+JOTE maps of the Haze and the ancillary data used for the analysis
+in Sect. 2, we then describe the methodologies applied for this work
+in Sect. 3, consisting of a template fitting component separation
+described in Sec 3.1, and a correlation T-T plots analysis in polar-
+ization, as described in Sect. 3.2. Afterwards, in Sect. 4 we present
+the results of the template fitting (Sect. 4.1 in intensity and 4.2 in
+polarization), and of the T-T plots in polarization (Sect. 4.3). Finally,
+we summarize and we conclude in Sect. 5 and 6.
+2
+DATA
+We describe here the dataset that is used in this work, which is com-
+posed of the QUIJOTE-MFI data at 11 and 13 GHz (see Sect. 2.1),
+in combination with ancillary data (see Sect. 2.2) from S-PASS
+at 2.3 GHz (Carretti et al. 2019), WMAP at ∼23, 33, 41, 61 GHz
+(Bennett et al. 2013), and Planck-LFI at ∼30, 44, 70 GHz (Planck
+Collaboration et al. 2020c). A summary of the dataset can be found
+in Table. 1.
+2.1
+QUIJOTE-MFI data
+QUIJOTE is a polarimetric ground-based CMB experiment located
+at the Teide observatory (Tenerife, Spain), at 2400 m above sea level
+(Rubiño-Martín et al. 2012b). The MFI instrument of QUIJOTE
+observes the sky of the Northern hemisphere at four frequency
+bands in the range 10–20 GHz, and with an angular resolution of
+≈ 1◦ (Hoyland et al. 2012).
+The reference dataset for this paper is the survey of the full
+northern sky performed with QUIJOTE-MFI (hereafter the wide-
+survey). This survey provides an average sensitivity in polarization
+of ∼ 40–55 𝜇K deg−1 in the four bands centred around 11, 13, 17
+and 19 GHz (see Sect. 4.3 in Rubiño-Martín et al. 2023). This paper
+is part of the release that describes the survey and the associated
+scientific results, concerning principally the characterization of dif-
+fuse synchrotron radiation and Anomalous Microwave Emission
+(AME). A complete description of the wide survey can be found in
+Rubiño-Martín et al. (2023).
+The QUIJOTE-MFI maps used in this work are a combination
+of this wide-survey data with additional raster-scan observations
+that were performed specifically around the Haze region in order
+to improve the signal-to-noise ratio. These raster scan observations
+consisted of back-and-forth constant elevation scans of the telescope
+performed with a scanning speed of 1 deg/s on the sky in the period
+June 2013 – August 2018. In particular, four sky fields have been ob-
+served, which we call the "HAZE", "HAZE2" and "HAZE3" fields,
+as well as a sky patch enclosing the 𝜌-Ophiuchi cloud complex,1
+covering, in total, a sky fraction 𝑓sky ∼ 5%. The approximate cen-
+tral coordinates of each raster scan field are indicated in Fig. 2 and
+in Table 2, where also their total observing time is reported.
+Although we have produced the maps for all the QUIJOTE-
+MFI channels, here we use only the 11 and 13 GHz frequency
+maps from horn 3 (central frequencies 11.1 and 12.9 GHz), which
+have sufficiently good signal-to-noise for this analysis. Note that
+there are some difficulties inherent to the observations, which are:
+(1) the contamination of Radio Frequency Interference (RFI) from
+geostationary satellites that requires the flagging of a declination
+band with −10◦ ≲ 𝛿 ≲ −1◦; (2) the fact that elevation of the Haze
+area from the Teide Observatory (geographical latitude +28◦) is very
+low (𝑒𝑙 ≲ 35◦), so all the observations are taken looking through a
+large air-mass. Point (2) is the main reason why the two additional
+QUIJOTE maps at 17 and 19 GHz are not used here.
+The maps are shown in Fig. 1, where we present the I, Q, and U
+maps at the original angular resolution and pixel size (𝑁side = 512 in
+the HEALPix2 pixelization scheme; Górski et al. 2005). The maps
+have been generated with the PICASSO map-making code, which
+was implemented for the construction of maps from the QUIJOTE-
+MFI data (Guidi et al. 2021). The maps have been obtained with a
+single run of PICASSO, combining simultaneously the wide-survey
+data and the additional raster observations with an efficient sub-
+traction of the correlated 1/ 𝑓 noise. The parameters adopted for
+this run (priors on noise properties, baseline length, etc) are iden-
+tical to those used for the wide survey (see details in Sect. 2.3 of
+Rubiño-Martín et al. 2023).
+In Fig. 2 we show the statistical white noise level (𝜎) of the
+11 GHz map in intensity, computed from the propagation of the
+weights in the TOD through the map-making procedure, and with
+pixel resolution 𝑁side = 512. The location of the raster observa-
+tions can be seen as the bluish regions at the center of these maps,
+corresponding to a decrease of 𝜎. The raster scan data result in
+1 𝜌-Ophiuchi observations had a different scientific goal, specifically the
+study of this specific cloud complex. However, since they lie nearby the
+Haze fields, we included them in this analysis.
+2 https://sourceforge.net/projects/healpix/
+MNRAS 00, 1–31 (2023)
+
+4
+F. Guidi et al.
+Figure 1. I, Q, and U maps from QUIJOTE-MFI at 11 GHz (top) and 13 GHz (bottom) at the original angular resolution and pixel size (𝑁side = 512). The
+maps are mollweide projections and in Galactic coordinates, with the centre of the projection at (𝑙, 𝑏) = (0◦, 0◦), and with longitude increasing to the left.
+Colour scales are linear and grey represents missing data or regions contaminated by RFI. The data used to generate these maps combine the wide-survey and
+the dedicated raster scan observations described in the text.
+Figure 2. Uncertainty (𝜎) of the Intensity map from QUIJOTE at 11 GHz,
+at the original angular resolution and pixel size (𝑁side = 512; the uncertainty
+distribution is similar for Q and U, and at 13 GHz). The location of the three
+fields observed with raster-scans are indicated in the maps (see Table 2), as
+well as the position of “a” and “b” where noise estimates are provided (see
+Table 3).
+an improvement of the noise level with respect to the wide-survey
+data alone in two specific areas: in the Galactic centre region (with
+“HAZE” and “HAZE2”, around the location identified by “a” in
+Fig. 2), and in the proximity of the NPS (with “HAZE3”, around
+“b” in Fig. 2). We report in Table 3 the typical noise levels of the
+new QUIJOTE maps in a 1◦ FWHM beam, including wide-survey
+and raster data, and we compare these values with the noise lev-
+els achieved with wide-survey data alone. The numbers have been
+obtained by computing the median value of the uncertainty maps
+within circles with a radius of 5◦, centred in two different positions:
+close to the Galactic centre at (𝑙, 𝑏) = (5◦, 0◦) (a), and in the
+proximity of the NPS at (𝑙, 𝑏) = (40◦, 20◦) (b). We observe that
+the raster scan data improve the noise level, both in intensity and
+polarization, by a factor ∼ 3 in the Galactic centre, and by ∼ 1.2–1.5
+in the NPS region. The 𝜎-maps are scaled-up by a multiplicative
+factor obtained from the QUIJOTE weight maps (𝜎 = 1/√𝑤) that
+accounts for the 1/ 𝑓 noise contribution, which is characterized by
+the half-mission wide-survey null-test, as described in Sect. 4.1 of
+Rubiño-Martín et al. (2023). The factors are: 𝑓 = 5.214 (I), 1.333
+(Q), 1.335 (U) at 11 GHz, and 𝑓 = 4.682 (I), 1.320 (Q), 1.321 (U)
+at 13 GHz. Finally, given the integration time in the same area,
+we found that the estimated global noise level correspond to an
+instantaneous sensitivity of ∼ 0.42–0.44 mK√s in intensity, and
+∼ 0.13–0.14 mK√s in polarization.
+In the analysis presented in this paper, we use the QUIJOTE-
+MFI maps convolved to 1◦ angular resolution with the window
+function of QUIJOTE-MFI (Génova-Santos et al., in preparation),
+and degraded to 𝑁side = 64 (pixel resolution ∼ 0.9◦). In order to
+obtain uncertainty maps at this resolution, we performed 100 white
+noise realizations, whose amplitude is given by the 𝜎 maps pre-
+sented above. We applied the same smoothing and degradation of
+the data to the noise simulations, and we computed the standard de-
+viation of the noise realizations to obtain a smoothed and degraded
+variance map. We also tested different methodologies to determine
+the variance maps, accounting for 1/ 𝑓 noise correlation at large an-
+gular scales, and we obtained no significant differences in the final
+results. Finally, the noise of the 11 GHz and 13 GHz maps of QUI-
+JOTE is partially correlated between the frequency channels. The
+correlation of the noise in intensity is 𝜌 = 0.76 and in polarization
+it is 𝜌 = 0.35 (see Sect. 4.3.3 in Rubiño-Martín et al. 2023). We ac-
+count for this correlation in this work, and for an overall calibration
+uncertainty of 5 % (for more details see Sect. 5 of Rubiño-Martín
+et al. 2023 and Génova-Santos et al., in preparation).
+2.2
+Ancillary data
+We use as ancillary data the WMAP 9-year maps (Bennett et al.
+2013) in the K, Ka, Q and V bands (central frequencies 22.8, 33.0,
+40.7 and 60.7 GHz) and the NPIPE Planck-LFI maps (Planck Col-
+laboration et al. 2020c), at 30, 44 and 70 GHz (central frequencies
+28.4, 44.1, and 70.4 GHz). In addition, for the analysis in polariza-
+MNRAS 00, 1–31 (2023)
+
+11 GHz ()
+mKcMB
+2011GHz (Q)
+mKcMB
+211GHz (U)
+mKcMB
+213GHz (D
+mKcMB
+2013 GHz (Q)
+mKcMB
+213 GHz (U)
+mKcMB
+2o11GHz(
+HAZE2
+d
+HAZE3
+-Oph
+a
+HAZE
+mKcMB
+0
+2.5The Haze as seen by QUIJOTE
+5
+HAZE
+HAZE 2
+HAZE 3
+𝜌-Ophiuchi
+(𝑙, 𝑏)
+(16◦, 2◦)
+(352◦, 22◦)
+(37◦, 13◦)
+(352◦, 16◦)
+Δ𝑎𝑧
+47◦
+33◦
+86◦
+18◦
+𝑒𝑙
+30◦– 40◦
+32.5◦, 36◦, 37◦
+39◦, 62◦
+32◦, 33◦, 37◦
+Time [h]
+742.5
+98.8
+494.4
+258.7
+Table 2. General characteristics of the raster scan observations for the four
+fields used in this work. We report the central coordinates of the fields (in
+Galactic coordinates), the typical length of the azimuth rasters, the approx-
+imate elevation at which they were taken, and the total number of hours of
+the observations.
+Map
+Area
+11 GHz [𝜇𝐾CMB/1◦]
+13 GHz [𝜇𝐾CMB/1◦]
+𝐼
+𝑄
+𝑈
+𝐼
+𝑄
+𝑈
+Rasters +
+wide-survey
+a
+47.0
+19.6
+19.7
+37.2
+18.4
+18.7
+b
+82.3
+28.5
+28.4
+57.1
+24.8
+24.8
+wide-survey
+a
+145.5
+57.7
+57.9
+140.6
+57.4
+57.6
+b
+94.7
+44.0
+44.4
+80.7
+38.5
+38.7
+Table 3. Noise level of the QUIJOTE maps of the rasters plus wide-survey
+data (top two lines), and of the wide-survey data alone (bottom two lines), in
+a 1◦-FWHM beam. This is obtained as the median of the uncertainty maps
+(shown in Fig. 2), computed within a 5◦ radius circle centred in two different
+positions: close to the Galactic centre (a) at (𝑙, 𝑏) = (5◦, 0◦), and in the
+proximity of the NPS (b) at (𝑙, 𝑏) = (40◦, 20◦).
+tion, we include the S-PASS data (Carretti et al. 2019) at 2.3 GHz.
+As in previous works (Planck Collaboration et al. 2011, 2014a), in
+order to take into account the uncertainty due to, for example, beam
+asymmetries and colour corrections, we adopt a calibration uncer-
+tainty of 3% in WMAP and in Planck-LFI, and of 5% in S-PASS
+(Carretti et al. 2019). We summarize the main data parameters in
+Table 1.
+All the maps are smoothed to the common angular resolution
+of 1◦, and degraded to 𝑁side = 64, which corresponds to a pixel
+size of ∼ 0.9◦ and prevents noise pixel-to-pixel correlation. For
+the computation of spectral indices we apply colour corrections by
+using the python code fastcc presented in Peel et al. (2022), which
+includes colour correction models for different datasets including
+QUIJOTE-MFI, Planck, and WMAP. No colour correction for S-
+PASS data is applied.3
+A collection of figures representing the full dataset is shown
+in appendix A (Fig. A1, A2 and A3 for, respectively, 𝐼, 𝑄 and 𝑈).
+In Fig. A4 we also show the debiased polarization amplitude maps
+(𝑃MAS, given by Eq. 14) at some selected frequencies: S-PASS at
+2.3 GHz, QUIJOTE 11 GHz, WMAP K-band and Planck 30 GHz.
+From a quick visual inspection of the polarization amplitude and
+polarization angle maps in Fig. A4, we can see that, while the QUI-
+JOTE, WMAP and Planck maps show very high similarity in the
+synchrotron polarized structures and angles, at the S-PASS fre-
+quency there is evident depolarization in the Galactic plane, up to
+|𝑏| ≈ 15 deg. We can also see a rotation of the polarization angle
+up to high Galactic latitudes, which is produced by Faraday rotation
+along the line-of-sight (Carretti et al. 2019; Iacobelli et al. 2014).
+Faraday rotation is important at 2.3 GHz in some of the regions that
+are studied in this work. We therefore correct the S-PASS maps for
+Faraday rotation as described in appendix B, and shown in Fig. A5.
+QUIJOTE, WMAP and Planck data are not corrected for Faraday
+rotation, since the effect in the regions we are studying is expected
+3 S-PASS uses a spectral back-end which allows to flatten the bandpass and
+to reduce the necessary colour correction.
+Figure 3. Selected regions for the analysis overlaid on the WMAP K-band
+polarization amplitude map. The regions are listed and described in Tab. 4.
+to be negligible at these frequencies, i.e., within the uncertainty of
+the calibration angle (see e.g., Hutschenreuter et al. 2022 and Vidal
+et al. 2015, where Faraday rotation is shown to be lower than 1◦ in
+WMAP, everywhere except in the Galactic centre).
+For the subsequent analysis, in order to assign uncertainties to
+the data, we use uncertainty maps at the same angular and pixel res-
+olution as for the maps (𝑁side = 64 and 1◦ resolution). The variance
+maps are generated with Monte Carlo realizations, as described in
+more detail in Peel et al. (in preparation).
+2.3
+Selection of the regions
+We identified thirteen regions of particular interest for the study of
+the Haze. Six of them are within the footprint of our QUIJOTE map.
+They are shown in Fig. 3 and are listed and described in Tab. 4. We
+use the numbering in the table to identify specific regions throughout
+this work.
+Regions 7 and 8 have been selected in order to reproduce the
+analysis of the diffuse Haze in intensity presented in Dobler &
+Finkbeiner (2008); Planck Collaboration et al. (2013). We extend
+the same analysis including QUIJOTE data, using for the first time
+also polarization data.
+Region 3 has been used in order to reproduce the result by
+Planck Collaboration et al. (2016c), who measured the polarization
+spectral index of the filament. We repeated here the analysis also
+using QUIJOTE data. We also define as regions 2 and 4 two features
+of diffuse emission extending, respectively, outside and inside the
+border of region 3.
+Regions 5, 9 and 10 have been defined to identify the polarized
+radio plumes observed by S-PASS (Carretti et al. 2013), in order to
+carry out a spectral index analysis using QUIJOTE and ancillary
+data.
+Region 6 is the Galactic Centre Spur (GCS, Vidal et al. 2015),
+which is a very bright polarized feature connected to the Galactic
+Center. Its relation with the Haze is still unclear.
+Regions 11 and 13 have been identified as the borders of the
+eROSITA bubbles (Predehl et al. 2020), and have been used for a
+spectral index analysis using QUIJOTE and ancillary data.
+Region 12 is defined as an area with some faint diffuse po-
+larized emission with unknown origin. It was identified during the
+analysis of the polarization template fitting residuals (see Fig. 9).
+Finally, region 0 is the sky observed by each survey, after
+MNRAS 00, 1–31 (2023)
+
+G353-34
+Tb [mKr]]
+0
+0.086
+F. Guidi et al.
+Region
+Description
+Coordinates
+Reference
+0
+High-latitudes sky observed by each survey
+1
+North Polar Spur (NPS)
+(𝑙, 𝑏) ∼ (30◦, 45◦)
+Large et al. (1962)
+2
+Bright polarized feature between the NPS and the Haze filament
+(𝑙, 𝑏) ∼ (30◦, 35◦)
+Defined in this work
+3
+Filament surrounding the northern Fermi bubble in 𝛾-rays
+(𝑙, 𝑏) ∼ (7◦, 47◦)
+Vidal et al. (2015) (region IX)
+Planck Collaboration et al. (2016c)
+4
+Polarized structure below the Haze filament
+(𝑙, 𝑏) ∼ (20◦, 27◦)
+Defined in this work
+5
+North Haze Bubble
+(𝑙, 𝑏) ∼ (−4◦, 31◦)
+Carretti et al. (2013)
+6
+The Galactic Centre Spur (GCS)
+(𝑙, 𝑏) ∼ (5◦, 16◦)
+(e.g.,) Vidal et al. (2015)
+7
+Rectangle enclosing the South Haze Bubble
+|𝑙| < 35◦
+−35◦ < 𝑏 < −10◦
+Planck Collaboration et al. 2013
+8
+Same as region 7, restricted to the QUIJOTE map area
+|𝑙| < 35◦
+−35◦ < 𝑏 < −10◦
+−32◦ ≲ 𝛿 ≲ −10◦
+Defined in this work
+9
+South Haze Bubble
+(𝑙, 𝑏) ∼ (−1◦, −30◦)
+Carretti et al. (2013)
+10
+Region 9 excluding Faraday depolarized regions:
+"A" and G353.34
+(𝑙, 𝑏) ∼ (−1◦, −30◦)
+Carretti et al. (2013)
+Iacobelli et al. (2014)
+"A": (𝑙, 𝑏) ∼ (20◦, −52◦)
+G353.34: (𝑙, 𝑏) ∼ (30◦, −62◦)
+11
+Western eRosita bubble or South Polar Spur (SPS)
+(𝑙, 𝑏) ∼ (58◦, −45◦)
+Predehl et al. (2020)
+Vidal et al. (2015) (region VIIb)
+Planck Collaboration et al. (2016c)
+12
+Faint polarized spur with unknown origin
+(𝑙, 𝑏) ∼ (53◦, −35◦)
+Defined in this work
+13
+Eastern eRosita bubble
+(𝑙, 𝑏) ∼ (−29◦, −26◦)
+Predehl et al. (2020)
+Table 4. List and description of the regions selected for this work. See Fig. 3 for visualisation.
+excluding the Galactic plane with the mask described in 3.1.1, and
+region 1 corresponds to the North Polar Spur (NPS, Large et al.
+1962). These two regions are used for comparison purposes.
+3
+METHODOLOGY
+In this section, we describe the two methodologies that are applied
+in this work: the template fitting procedure, both in intensity and in
+polarization, and the correlation T-T plots analysis in polarization.
+3.1
+Template fitting
+In order to isolate the diffuse emission of the Haze from the other
+Galactic foregrounds, we apply a template fitting technique, fol-
+lowing the same formalism as in Finkbeiner (2004); Dobler &
+Finkbeiner (2008); Planck Collaboration et al. (2013). This method-
+ology relies on the assumption that each frequency map is a linear
+combination of several templates, which spatially trace the Galactic
+emission of different mechanisms, such as the synchrotron, free-
+free, thermal dust and AME. This can be represented analytically
+as:
+𝑑𝜈 = 𝑎𝜈 · P𝜈,
+(1)
+where 𝑑𝜈 is the map at frequency 𝜈, P𝜈 is a the template matrix
+that contains one template map per column, estimated at frequency
+𝜈, and 𝑎𝜈 is a vector of coefficients indicating the amplitude of
+the templates. The template fitting problem consists in determining
+the amplitudes 𝑎𝜈 that provide the best description of the data
+with the templates in P𝜈. We solve the problem with a maximum
+likelihood approach, by applying an extended formalism to include
+the correlation between different templates.4 The logarithm of the
+posterior of this problem, including priors for the fitted amplitudes
+𝑎𝜈 is given by:
+ln P ∝ (𝑑 − 𝑎 · P)𝑇 𝐶−1
+w (𝑑 − 𝑎 · P) + (𝑎 − 𝑎0)𝑇 𝐶−1
+a (𝑎 − 𝑎0) + 𝑐, (2)
+where we neglect the frequency subscript 𝜈 for brevity. Here, 𝐶w
+is the noise covariance matrix of the data, 𝑎0 is the central value
+of the amplitude priors, 𝐶a is the covariance matrix of the template
+amplitudes, and 𝑐 is a global constant. The solution of equation 2
+is:
+𝑎 = (P𝑇 𝐶−1
+w P + 𝐶−1
+a )−1 · (𝑃𝑇 𝐶−1
+w 𝑑 + 𝐶−1
+a 𝑎0).
+(3)
+By means of the term 𝐶−1
+a 𝑎0, we can apply priors on the fitting of
+the foreground templates. In particular, the off-diagonal elements
+of 𝐶a allow us to introduce in the fitting the degree of correlation
+between the templates, which is measured for synchrotron and dust
+to be at the order of 20–40 %, with some evident spatial variation
+(Peel et al. 2012; Choi & Page 2015; Krachmalnicoff et al. 2018).
+This improved template fitting technique has been tested with
+simulations based on the foreground templates and frequency scal-
+ing used in this work (see Sect. 3.1.1). We observed that a more
+precise separation of the foregrounds is achieved by applying priors
+that account for their spatial correlation. In particular we noticed
+that, at low frequencies, where the dust component is subdominant
+but spatially correlated with the synchrotron, the separation of syn-
+chrotron and dust is significantly improved by applying priors as in
+Eq. 3. Simulations have also been used to check for biases in the
+results, when including or excluding priors in the fitting procedure.
+We observed that the results on the spectrum of the Haze are not
+4 This formalism was developed and applied for the radio/microwaves map-
+making problem. See for example Keihänen et al. (2010), or Guidi et al.
+(2021)
+MNRAS 00, 1–31 (2023)
+
+The Haze as seen by QUIJOTE
+7
+significantly different in the two cases, while the spectra of the fore-
+grounds components, especially that of the synchrotron, is affected
+by significant biases if priors are not adopted. We concluded that
+the use of priors allows us to have better control on the fitting of the
+foreground components, while not significantly affecting the results
+on the spectrum of the Haze.
+3.1.1
+Templates
+The fitting is performed in intensity and polarization, using inde-
+pendently the 𝐼 map, and the 𝑄 and 𝑈 Stokes parameters maps
+simultaneously for polarization, assuming a negligible Q and U
+correlation. All the templates are convolved to 1◦ angular resolu-
+tion and degraded to 𝑁side = 64 in order to avoid pixel-to-pixel
+correlation, as we did for the data (see Sect. 2). The intensity and
+polarization templates are shown, respectively, in Figs. 4 and 5. A
+detailed description follows in this section.
+Synchrotron. The full-sky intensity map by Haslam et al. (1982),
+at 408 MHz, is dominated by synchrotron emission, and it is only
+marginally contaminated by free-free along the Galactic plane and in
+bright free-free sources (e.g., M42). This makes the 408 MHz map
+a good tracer of diffuse synchrotron emission in intensity. We use
+the reprocessed version of this map by Remazeilles et al. (2015) as a
+template, and we scale5 it in frequency using a power-law spectrum
+assuming a spatially-constant spectral index 𝛽s = −3.1 across the
+full sky. In addition, as indicated by Dobler (2012), the cosmic
+ray propagation length is energy dependent, and this results in a
+synchrotron radiation that is more extended around the Galactic disk
+at 408 MHz compared with the higher frequencies (like QUIJOTE,
+Planck and WMAP). In order to trace this excess at low frequency,
+and following Dobler (2012) and Planck Collaboration et al. (2013),
+we adopt an elliptic Gaussian template centred in the Galactic centre,
+with extension (𝜎𝑙, 𝜎𝑏) = (±20◦, ±5◦). The diffuse synchrotron
+and the disk-like synchrotron excess are fitted independently with
+two separate templates.
+In polarization, we use the 2018 Stokes Q and U Commander6
+synchrotron solution (Planck Collaboration et al. 2018), scaled to
+each central frequency with a power-law with a spectral index
+𝛽 = −3.1, which is assumed to be constant across the sky.
+Thermal dust and AME Thermal and AME are two distinct fore-
+ground components produced by dust grains. The thermal dust fol-
+lows a modified black body spectrum that shows up mainly at high
+frequencies (𝜈>100 GHz), while the spinning dust is significant at
+intermediate frequencies (10 GHz ≲ 𝜈 ≲ 60 GHz). The carriers of
+the AME have not been unequivocally identified yet, but the most
+accredited hypothesis to date is that AME is produced by the rotation
+of small dust grains (for a review see Dickinson et al. 2018).
+We could use two independent templates to fit thermal dust and
+AME, using the Commander solution (Planck Collaboration et al.
+5 The frequency scaling of a template map is usually irrelevant for tem-
+plate fitting. Indeed, given the spatial morphology of the template, we fit
+for a global amplitude. However, in order to assign priors as explained in
+Sect. 3.1.2, frequency scaling is needed.
+6 Commander is a software developed for the component separation of
+Planck data. It consists of a pixel based Bayesian parametric method (MCMC
+Gibbs sampling algorithm), aimed to fit the parameters describing different
+Galactic foreground components. See Eriksen et al. (2004, 2008) for more
+details.
+2016b) for the two components. However, AME and thermal dust
+are highly correlated, and a simultaneous fit of the two components
+could be affected by strong degeneracy. In addition, we noticed that
+the Commander AME map presents an excess of emission with a
+shape similar to that of the Haze. There is the possibility that a frac-
+tion of the Haze emission leaked into this map. Moreover, Planck
+Collaboration et al. (2016c) reported that the degeneracy between
+the AME and free-free components could affect the stability of the
+Commander AME solution, due to the lack of low-frequency infor-
+mation. Therefore, in order to perform a blind and unbiased fit of the
+foregrounds we decided not to use the Commander AME map, fitting
+the combination of thermal dust and AME with a single template.
+We adopt the 2015 Commander solution for thermal dust, scaled at
+each central frequency with the modified black body spectrum of
+thermal dust reported in Planck Collaboration et al. (2016b). Due to
+the dust and AME correlation, this template will capture, in addition
+to the thermal dust component, the AME emission at intermediate
+frequencies (∼20–60 GHz). Note also that, thanks to the fact that
+the AME (𝜈 ≲ 60 GHz) and the thermal dust (𝜈 ≳ 800 GHz; Planck
+Collaboration et al. 2016b) emissions do not overlap in frequency,
+even if we use a single template to fit the two components, they are
+easily distinguishable in the frequency spectrum.
+In this work we assume no polarized AME, which is well
+justified given the observational constraints that set the AME polar-
+ization to be ≲1% (e.g., Rubiño-Martín et al. 2012a; Génova-Santos
+et al. 2017; Dickinson et al. 2018). Therefore no AME is fitted in
+polarization. Thermal dust instead is typically 5–10 % polarized
+(Dickinson et al. 2011; Planck Collaboration et al. 2016b,a). We
+fit therefore the polarized dust emission using the 𝑄 and 𝑈 2018
+Commander thermal dust maps (Planck Collaboration et al. 2018)
+as templates, after scaling to each central frequency as indicated in
+Planck Collaboration et al. (2016b).
+Free-free. We construct the free-free intensity template using the
+H𝛼 map by Finkbeiner (2003). We correct the H𝛼 map for dust
+absorption by applying the methodology of Dickinson et al. (2003),
+and using the reddening 𝐸(𝐵 − 𝑉) map7 of Planck (Planck Col-
+laboration et al. 2014b). We assume uniform mixing between gas
+and dust by setting an effective dust fraction along the line of sight8
+𝑓𝑑 = 0.5, an average electron temperature 𝑇𝑒 = 7000 K across the
+full sky, and we scale the corrected H𝛼 map from Rayleigh (R) to
+𝜇K, at each central frequency, by computing the conversion factor
+with Eq. (11) in Dickinson et al. (2003). Despite these approxima-
+tions, what is important here is to construct a good enough tracer
+of the spatial distribution of free-free emission, independently from
+the absolute scale. With this aim, applying a good correction of dust
+absorption is important.
+This template provides a sufficiently good approximation of the
+free-free in the sky, except for the regions with high dust absorption.
+Furthermore, we expect large fluctuations of the gas temperature in
+the brightest H𝛼 regions, which can produce some inaccuracies in
+the template (Dickinson et al. 2003; Planck Collaboration et al.
+2013). In order to avoid such problematic regions, we mask the
+pixels with absorption larger than one magnitude (2.51·𝐸(𝐵−𝑉) >
+7 https://irsa.ipac.caltech.edu/data/Planck/release_1/
+all-sky-maps/previews/HFI_CompMap_DustOpacity_2048_R1.
+10/
+8 We also tried 𝑓d = 0.33, but this change did not affect the resulting Haze
+morphology and spectrum.
+MNRAS 00, 1–31 (2023)
+
+8
+F. Guidi et al.
+Figure 4. Intensity template maps at 11 GHz at 𝑁side = 64. They are: a simple model of the Haze as described in Sect. 3.1.1 (top left), a disk template
+for the Galactic plane diffuse synchrotron emission (multiplied by 10 for display purposes; top centre), free-free (multiplied by 10 for display purposes; top
+right), synchrotron (bottom left), dust (multiplied by 103 for display purposes; bottom centre), which is used to fit both thermal dust and AME, and the CMB
+anisotropies (bottom right). The maps are in units of mK Rayleigh-Jeans, and have had the mean subtracted. The grey area represents the mask that is used for
+the analysis, which is a combination of the QUIJOTE sky coverage with the free-free and CMB mask, as described in Sect. 3.1.1.
+Figure 5. Polarization template maps at 11 GHz, of Stokes 𝑄 (top) and 𝑈 (bottom). They are, from left to right: synchrotron, thermal dust (multiplied by 104
+for display purposes) and the CMB. The maps are in units of mK Rayleigh-Jeans, and are mean corrected. The grey area represents the mask that is used for
+the analysis, which is a combination of the QUIJOTE sky coverage with the free-free and CMB mask, as described in Sect. 3.1.1.
+1 mag), or with H𝛼 intensity greater than 10 R. The free-free has
+negligible polarization, therefore it is fitted only in intensity.
+CMB. The 2018 SMICA9 CMB map (Planck Collaboration et al.
+2018) is subtracted from each frequency map, both in intensity and
+in polarization, at 1◦ angular resolution. As discussed in Dobler
+9 Spectral Matching Independent Component Analysis (SMICA) is one of
+the methods that was implemented for the component-separation of Planck
+data. It is based on a linear combination between the Planck frequency
+channels, using weights that depend on the multipole. See Cardoso et al.
+(2008) for more details.
+(2012), the foreground contamination of the CMB map could pro-
+duce a bias in the determination of the Haze spectrum. However,
+the last version of maps produced with the Planck data provide now
+a high quality CMB map. We assume therefore that the CMB bias
+mentioned above is negligible as compared with other sources on
+uncertainty. In order to confirm that, we repeated the analysis us-
+ing the Commander CMB map, obtaining compatible results on the
+Haze separation.
+The Haze. Following Dobler & Finkbeiner (2008) and Planck Col-
+laboration et al. (2013), we include a template that approximately
+traces the emission of the Haze in the fitting of the intensity. Even
+MNRAS 00, 1–31 (2023)
+
+Disk Template 11.oGHz
+-0.80
+Tb [mKr/] · 10
+1.50Free-Free 11.0GHz
+-0.80
+Tb [mKr/] · 10
+1.50Synchrotron 11.oGHz
+-0.80
+Tb [mKR]]
+1.50LhermalDustIt.oGHz
+-0.80
+T, [mKr] · 103
+1.50CMB Smica
+-0.23
+T,[mKcMB]
+0.25-0.50
+Tb [mKR]]
+0.50LhermalDuststokes-ot.oGHz
+-0.50
+T, [mKr] · 104
+0.50Q CMB Smica
+-0.003
+T,[mKcMB]
+0.003Synchrotron Stokes-U 11.oGHz
+-0.50
+Tb [mKR]]
+0.50LhermalDuststokes-ul.oGHz
+-0.50
+T, [mKrj] · 104
+0.50UCMBSmica
+-0.003
+T,[mKcMB]
+0.003Haze Template 11.0GHz
+-0.80
+T,[mKRj]
+1.50The Haze as seen by QUIJOTE
+9
+if we do not have a precise characterization of the spatial distri-
+bution of the Haze, an approximated template is needed in order
+to avoid a bias in the fit of other foreground templates. We use a
+Gaussian ellipse in Galactic coordinates, centred in the Galactic
+centre, and with major axes perpendicular to the Galactic plane line
+(𝑏 = 0◦). The minor and major axes are, respectively, 𝜎𝑙 = 15◦ and
+𝜎𝑏 = 25◦. The template has the same unitary amplitude at different
+frequencies.
+Monopole and dipole. In order to overcome any possible issue
+related with zero levels, we subtract the average value of the un-
+masked pixels from the maps and from the templates. In addition,
+we fit a monopole component at each frequency in order to ad-
+just any residual zero level mismatch. Finally, from the residual
+maps at frequencies 𝜈 > 40 GHz, we noticed a residual dipole pat-
+tern. For this reason, before applying the template fitting to these
+maps, we remove the residual dipole with the HEALPix routine
+remove_dipole, after masking pixels with |𝑏| < 20◦ to avoid
+Galactic contamination.
+Mask. Following Dobler & Finkbeiner (2008) and Planck Collab-
+oration et al. (2013), we mask all the regions where the templates
+can deviate from the real foreground emission. The mask includes,
+as described above for the free-free, the regions where the H𝛼 emis-
+sion exceeds 10 R, or where the dust extinction is larger than 1
+magnitude. In addition, we mask the point sources from the Planck
+LFI catalog (Planck Collaboration et al. 2016d). We used the mask
+excluding the LFI compact sources that is available in the Planck
+Legacy Archive10 (PLA). Finally, in order to avoid any possible bias
+from foreground residuals in the CMB map, we mask the pixels that
+are outside the confidence region11 of the CMB map that we are
+using.
+3.1.2
+Priors
+Our implementation of the template fitting procedure, which is
+described in Sect. 3.1, allows us to apply priors on the amplitudes
+of the foreground templates. The priors are introduced by the vector
+𝑎0, which contains the central values of the prior at frequency12 𝜈,
+and by the covariance matrix 𝐶a. The elements of the covariance
+matrix are defined as:
+𝐶a,𝑖 𝑗 = 𝑐𝑜𝑣(𝑎𝑖, 𝑎 𝑗) = 𝐸
+�
+(𝑎𝑖 − 𝑎0𝑖)(𝑎 𝑗 − 𝑎0 𝑗)
+�
+,
+(4)
+where 𝐸[·] denotes the expected value operator, 𝑎0 the expected
+amplitude, and the indices 𝑖 and 𝑗 indicate the foreground maps at
+the frequency 𝜈 (e.g., 𝑖=thermal dust, 𝑗=synchrotron, at 11 GHz).
+The diagonal elements of 𝐶a are:
+𝐶a,𝑖𝑖 = 𝑐𝑜𝑣(𝑎𝑖, 𝑎𝑖) = 𝜎2
+𝑖 ,
+(5)
+10 The
+mask
+used
+in
+this
+work
+can
+be
+found
+in
+the
+PLA:
+http://pla.esac.esa.int/pla/aio/product-action?MAP.MAP_
+ID=LFI_Mask_PointSrc_2048_R2.00.fits.
+Relevant
+information
+about the mask can be found in the PLA Explanatory Supplement at
+https://wiki.cosmos.esa.int/planck-legacy-archive/index.
+php/Frequency_maps#Masks.
+11 The CMB mask used in this work is taken from the fits file containing
+the CMB map (SMICA, PR3-2018), downloaded from the PLA (http:
+//pla.esac.esa.int/pla). Relevant information about the mask can be
+found in the PLA Explanatory Supplement at https://wiki.cosmos.
+esa.int/planck-legacy-archive/index.php/CMB_maps#SMICA.
+12 For brevity in the notation, the subscript 𝜈 is not explicit, keeping in
+mind that the fitting is always performed at a given frequency.
+where 𝜎𝑖 is our choice for the width of the Gaussian prior for the
+amplitude of the template 𝑖. We assign to the width of the priors the
+analytic uncertainty on 𝑎𝑖 that is obtained by the second derivative
+of the logarithm of the posterior in Eq. 2, neglecting the priors term
+(𝐶−1
+a
+= 0). It is:
+𝜎2
+𝑖 = (P𝑇
+𝑖 𝐶−1
+w P𝑖)−1,
+(6)
+where P𝑖 is the 𝑖𝑡ℎ column of the templates matrix P, so it is simply
+the map of the 𝑖𝑡ℎ template (e.g., 𝑖=thermal dust). The off diagonal
+elements of 𝐶a are:
+𝐶a,𝑖 𝑗 = 𝑐𝑜𝑣(𝑎𝑖, 𝑎 𝑗) = 𝜌𝑖 𝑗 · 𝜎𝑖𝜎𝑗,
+(7)
+where 𝜌𝑖 𝑗 is the correlation between the templates 𝑖 and 𝑗. It is
+known that different foreground mechanisms are spatially correlated
+(e.g., Choi & Page 2015), therefore 𝜌𝑖 𝑗 ≠ 0 and 𝐶a is not diagonal.
+In this work, we assign average values of correlation between the
+intensity templates of the foregrounds, by computing 𝜌𝑖 𝑗 as:
+𝜌𝑖 𝑗 =
+�
+𝐶P𝑖×P 𝑗
+ℓ
+√︃
+𝐶P𝑖
+ℓ · 𝐶P 𝑗
+ℓ )
+�
+2<ℓ<100
+,
+(8)
+where 𝐶P𝑖×P𝑗
+ℓ
+is the cross power spectrum between the template
+maps 𝑖 and 𝑗 (e.g., 𝑖=thermal dust, 𝑗=synchrotron, at 11 GHz), while
+𝐶P𝑖
+ℓ
+and 𝐶P𝑗
+ℓ
+are their auto power spectra. The level of correlation
+between templates is not the same at large and small angular scales.
+As 𝜌𝑖 𝑗 is a function of the multipole ℓ, in order to provide an average
+level of correlation, we compute the mean value of 𝜌𝑖 𝑗 (ℓ) in the
+multipole range 2 < ℓ < 100.
+We computed the power spectra of Eq. 8 with the publicly
+available code Xpol13 (Tristram et al. 2005), and we used a mask
+of the full sky, excluding a band in Galactic latitude |𝑏| < 5◦ to
+mask the brightest Galactic plane emission. The averages in the
+multipole range 2 < ℓ < 200, are 𝜌𝑠,𝑑 = 0.30 for synchrotron
+and thermal dust, 𝜌𝑠, 𝑓 = 0.14 for synchrotron and free-free, and
+𝜌𝑑, 𝑓
+= 0.26 for thermal dust and free-free. In polarization we
+have 𝜌𝑠,𝑑 = 0.20 for synchrotron and thermal dust, in agreement
+with Choi & Page (2015), who measured a correlation 𝜌 = 0.2
+between Planck 353 GHz and WMAP 23 GHz in the multipole range
+30 < ℓ < 200.
+Finally we define the central values of the priors. For syn-
+chrotron and free-free we use 𝑎0,𝑠 = 𝑎0, 𝑓 = 1, since the template
+maps are specifically computed at each central frequency, and the
+expected emission by synchrotron and free-free are the template map
+themselves. For the fitting of the thermal dust and the AME we use
+a single template, which is the thermal dust of Commander, scaled
+at the corresponding central frequency, as described in Sect. 3.1.1.
+Here we assume that AME and the thermal dust are totally corre-
+lated, and that we can capture these two components with the same
+template, with an expected amplitude 𝑎0,𝑑 = 1 + 𝑟, where 𝑟 is an
+average AME to thermal dust ratio. We define 𝑟 as a representative
+value of the ratio between the Commander AME and the thermal
+dust maps, computed (following Planck Collaboration et al. 2016b)
+at the same central frequency 𝜈:
+𝑟(𝜈) =
+� AME(𝜈)
+th-dust(𝜈)
+�
+,
+(9)
+where <> indicates the median over the pixels enclosed in the
+mask described in Sect. 3.1.1. We impose a prior on the total dust
+13 https://gitlab.in2p3.fr/tristram/Xpol
+MNRAS 00, 1–31 (2023)
+
+10
+F. Guidi et al.
+amplitude which is centred in 𝑎0,𝑑 = 1 + 𝑟. For the rest of the
+templates, which are the Galactic ellipse of diffuse synchrotron, the
+monopole and the Haze, we do not want to impose any stringent
+prior. Therefore we assign to them 𝑎0 = 0 and 𝜎 ≈ ∞.
+In polarization, we fit a synchrotron and a thermal dust tem-
+plate, separately in 𝑄 and 𝑈. Similarly to intensity, the templates
+are computed to match the emission of the foreground at the corre-
+sponding central frequency, therefore we assign the expected central
+value with the prior 𝑎𝑄,𝑈
+0,𝑠
+= 𝑎𝑄,𝑈
+0,𝑑
+= 1. The width of the priors are
+computed with Eq. 6. The off-diagonal elements of the covariance
+matrix are computed as in Eq. 7 and 8, giving 𝜌𝑄,𝑈
+𝑠,𝑑
+= 0.2.
+3.2
+Polarization T-T plots
+In order to analyze the polarization data with a different and inde-
+pendent technique, we use correlation plots, commonly called T-T
+plots. This methodology is widely used in the literature (e.g., Planck
+Collaboration et al. 2016c; Fuskeland et al. 2019), therefore we ap-
+plied it in order to reproduce results presented in previous works
+(Planck Collaboration et al. 2016c; Carretti et al. 2013), and extend
+them using the new QUIJOTE data. The specifics of the applied
+methodology are described as follows.
+3.2.1
+T-T plots of 𝑃MAS
+The low frequency polarized foregrounds are dominated by syn-
+chrotron radiation, which is described by a power-law spectrum:
+𝑑𝜈 =
+� 𝜈
+𝜈0
+�𝛽
+· 𝑑𝜈0,
+(10)
+where 𝑑𝜈 are the polarization data at frequency 𝜈, 𝑑𝜈0 are the po-
+larization data at a reference frequency 𝜈0, and 𝛽 is the synchrotron
+spectral index.
+It is possible, therefore, to derive the synchrotron spectral index
+across a coherent region with a simple correlation analysis between
+the polarized emission of two frequency maps. We can fit a linear
+dependence of 𝑑𝜈 as a function of 𝑑𝜈0:
+𝑑𝜈 = 𝑚 · 𝑑𝜈0 + 𝑞,
+(11)
+where 𝑞 is a relative offset, and the slope 𝑚 is related to the spectral
+index 𝛽 (with Eq. 10 and 11) as:
+𝛽 =
+ln(𝑚)
+ln(𝜈/𝜈0) .
+(12)
+The uncertainty on 𝛽 can be derived as the propagation of the
+uncertainty on 𝑚, 𝜎𝑚, as:
+𝜎𝛽 = 𝜎𝑚
+𝑚
+1
+ln(𝜈/𝜈0) .
+(13)
+This technique is commonly used to compute the spectral in-
+dex of the polarization amplitude 𝑃 =
+√︁
+𝑄2 + 𝑈2, in Rayleigh-Jeans
+temperature units. However, with 𝑃 being a positive definite quan-
+tity, it is affected by noise bias. Several techniques have been pro-
+posed to estimate an unbiased polarization amplitude (Plaszczynski
+et al. 2014; Vidal et al. 2016). In this paper, we use the unbiased
+polarization amplitude 𝑃MAS by applying the Modified Asymptotic
+estimator (MAS) presented in Plaszczynski et al. (2014), as:
+𝑃MAS = 𝑃 − 𝑏2 1 − 𝑒−𝑃2/𝑏2
+2𝑃
+,
+(14)
+with
+𝑏 =
+√︃
+(𝑄𝜎𝑈)2 + (𝑈𝜎𝑄)2/𝑃,
+(15)
+where 𝑃 is the noise biased polarization amplitude (as defined
+above), and 𝜎𝑄 and 𝜎𝑈 represent the uncertainties on the mea-
+sured 𝑄 and 𝑈 parameters. The uncertainty on 𝑃MAS is given by:
+𝜎𝑃MAS =
+√︃
+(𝑄𝜎𝑄)2 + (𝑈𝜎𝑈)2/𝑃.
+(16)
+This estimator is unbiased for pixels with signal-to-noise larger than
+2.
+3.2.2
+T-T plots of Q and U combined projection
+In order to overcome problems related with polarization noise bias
+in the data, due to zero-level mismatch, and also to variation of
+the spectral index with the polarization angle of the emission, we
+apply the technique that was proposed in Fuskeland et al. (2014).
+The T-T plot method described in Sect. 3.2 has been widely used in
+previous works (e.g., Planck Collaboration et al. 2016c), so we have
+also applied it for the sake of reproducing their results, however we
+believe that the Fuskeland et al. (2014) method is more reliable, and
+hence we use that by default.
+This methodology does not compute the polarization ampli-
+tude 𝑃, which is affected by noise bias, and allows to marginalize
+the result over the polarization angle. We make direct use of the Q
+and U Stokes maps that, after a projection into a rotated reference,
+are mixed to construct the data vector 𝑑(𝛼):
+𝑑(𝛼) = 𝑄 cos(2𝛼) + 𝑈 sin(2𝛼),
+(17)
+where 𝛼 is the rotation angle. We can use the data 𝑑(𝛼) and Eq. 12
+and 13 to compute the spectral index as a function of 𝛼, for a set
+of 18 angles distributed in the range 𝛼 ∈ [0◦, 85◦], in steps of 5◦.
+The resulting (strongly correlated) spectral indices 𝛽𝑖 = 𝛽(𝛼𝑖) are
+finally averaged with weights:
+𝛽 =
+�18
+𝑖=1(𝛽𝑖/𝜎2
+𝛽𝑖)
+�18
+𝑖=1(1/𝜎2
+𝛽𝑖)
+.
+(18)
+Due to correlation of the estimated 𝛽(𝛼𝑖) as a function of the angle,
+the statistical uncertainty on the final spectral index 𝛽 is taken to be
+the minimum uncertainty among the 18 measurements:
+𝜎stat
+𝛽
+=
+min
+𝑖∈[1,18]
+�𝜎𝛽𝑖
+� .
+(19)
+However, variations of the spectral index as a function of the polar-
+ization angle can induce an additional uncertainty on the determina-
+tion of 𝛽 across a wide region. We can define an intrinsic uncertainty
+due to this effect as the standard deviation of the 𝛽𝑖 estimated at
+different rotation angles, as:
+𝜎int
+𝛽 = std𝑖 (𝛽𝑖) .
+(20)
+In order to account for the effect that dominates the uncertainty of
+the spectral index in each particular region (statistical or intrinsic
+uncertainty), we adopt as a final uncertainty the maximum between
+the two estimates of the error:
+𝜎𝛽 = max
+�
+𝜎stat
+𝛽 , 𝜎int
+𝛽
+�
+.
+(21)
+In the process of estimating the spectral index with correlation
+plots of 𝑑(𝛼), we perform the linear fit considering the uncertain-
+ties of 𝑑(𝛼) in both axes, and, for each angle 𝛼, we apply colour
+MNRAS 00, 1–31 (2023)
+
+The Haze as seen by QUIJOTE
+11
+corrections (see Sect. 2.2) in an iterative way, until the spectral in-
+dex variations are lower than 0.001. The main results of this work,
+in polarization (Sect. 4.3), are obtained by applying the methodol-
+ogy described in this section. However, in a few special cases, we
+compare the resulting spectral indices with those obtained with the
+more common methodology described Sect. 3.2.1, the T-T plots of
+the polarization amplitude 𝑃MAS in order to give strength to the
+reliability of the result, and show some possible sources of error. In
+addition, in order to check the robustness of the linear regression
+of the T-T plots for each angle 𝛼𝑖, we compute the posterior distri-
+bution of the spectral index parameters. Appendix D provides the
+details and the results of this last check.
+4
+RESULTS
+Here we report first the results obtained for the Haze with the
+methodology of template fitting. The aim is to compare with the
+results from Planck Collaboration et al. (2013) in intensity (in
+Sect. 4.1), and to present our results in polarization (in Sect. 4.2),
+which is the main novelty from this work. In this part of the anal-
+ysis, after fitting the foreground templates across the full sky, we
+perform a detailed study of the residuals in regions of particular
+interest among those listed in Sect. 2.3.
+Subsequently, in Sect. 4.3 we show the results obtained with
+the correlation T-T plots in polarization, following the methodol-
+ogy described in Sect. 3.2.2. Also in this case, we concentrate the
+analysis on the regions that are presented in Sect. 2.3.
+As noted in Rubiño-Martín et al. (2023) (see Sect. 2.4.2 and
+Appendix B) and in de la Hoz et al. (2023), the filter that is applied
+to the QUIJOTE-MFI data to clean residual RFI contamination (so-
+called FDEC) removes from the maps a monopole term at constant
+declination. We have checked that the effect of the FDEC filter does
+not induce any significant bias on the results presented in this work.
+4.1
+Intensity template fitting
+We performed a template-fitting component separation using the
+intensity frequency maps of QUIJOTE, WMAP and Planck (see
+Table 1 and Sect. 2 for a more detailed description of the data).
+We show in the appendix (Fig. A1) the CMB subtracted sky maps
+within the sky area used in this analysis, which is limited by the
+QUIJOTE sky coverage and by the mask of reliable foregrounds
+description (see Sect. 3.1.1 for further details on the mask).
+The templates that are used for the component separation in
+intensity are shown in Fig. 4. They are: synchrotron, free-free, dust
+(thermal dust and AME are adjusted with the same template of
+thermal dust), a disk template14 for the Galactic plane diffuse syn-
+chrotron emission, and the Haze, as described in Sect. 3.1.1. The
+CMB is fixed and subtracted from the maps before the fitting. The
+fitted amplitudes for these templates are reported in Table 5.
+As a result of this simple component separation, we construct
+the residual map 𝑅𝜈, by subtracting the foreground templates P𝜈
+scaled by the fitted amplitudes 𝑎𝜈 from the corresponding frequency
+map 𝑑𝜈. It is:
+𝑅𝜈 = 𝑑𝜈 − 𝑎𝜈 · P𝜈.
+(22)
+14 The reconstruction of the Haze signal does not change significantly if we
+exclude the Galactic diffuse disk and Haze templates from the fit.
+Ideally, the residual 𝑅𝜈 is a map of the noise at frequency 𝜈. How-
+ever, the foreground templates may not perfectly trace the real fore-
+ground spatial structure, and some residual sky structure could leak
+in the residual map. In particular, we are interested in the Haze com-
+ponent, which we fit with an approximate Gaussian elliptic template
+centred in the Galactic centre. This template is not expected to trace
+perfectly the spatial distribution of the Haze, therefore part of it
+could remain as a residual. For this reason, following Dobler &
+Finkbeiner (2008) and Planck Collaboration et al. (2013), we con-
+struct a residual plus Haze map as:
+𝑅𝐻
+𝜈 = 𝑅𝜈 + 𝑎𝐻
+𝜈 · P𝐻
+𝜈 ,
+(23)
+where P𝐻
+𝜈 is the Haze template and 𝑎𝐻
+𝜈 is the fitted Haze amplitude.
+The residual maps can then be used to study the physical prop-
+erties of the isolated emission of the Haze as compared with the
+global synchrotron emission. With this aim we define the total syn-
+chrotron map as the residual map, plus the fitted Haze and syn-
+chrotron as:
+𝑅𝑆
+𝜈 = 𝑅𝐻
+𝜈 + 𝑎𝑠
+𝜈 · P𝑠
+𝜈,
+(24)
+where P𝑠𝜈 is the synchrotron template, 𝑎𝑠𝜈 its amplitude at frequency
+𝜈, and 𝑅𝐻
+𝜈 the residual plus Haze map (Eq. 23).
+We show the resulting maps in Fig. 6, and we study the Haze
+spectrum, which is shown in Fig. 7 and 8.
+4.1.1
+Intensity Haze maps
+In Fig. 6 we show the residual plus Haze maps (𝑅𝐻
+𝜈 ) across region 8
+(defined in Sect. 2.3), for several selected frequencies (QUIJOTE
+11 and 13 GHz, WMAP K-band and Planck 30 GHz). We observe
+that the bulk of the Haze component is detected in all the maps,
+including QUIJOTE.
+Nulltest maps of QUIJOTE (see appendix C and Fig. C1) have
+been used to validate the sky origin of the observed signal. The
+nulltest maps do not show evident residual systematics, therefore
+the structures observed in the residual maps are associated with sky
+signal.
+Beyond the Haze, we notice that the bottom part of the NPS
+(region 1), close to the Galactic centre at (𝑙, 𝑏) ∼ (31.5◦, 16.5◦),
+is visible in the residual maps of QUIJOTE. This indicates that
+our templates do not perfectly match the base of the NPS region,
+and this could be associated with a synchrotron component with a
+spectrum that is different with respect to the sky average. Note that
+the NPS residual that we observe in this work corresponds to the
+region that Panopoulou et al. (2021) identified as possibly associated
+with Galactic centre activity. In contrast, the NPS emission at high
+galactic latitudes is usually ascribed to a nearby supernova shell. A
+detailed study of the NPS with QUIJOTE data is beyond the scope
+of this work and will be presented in Watson et al. (in preparation).
+4.1.2
+Intensity Haze spectrum
+Under the hypothesis that the Haze is synchrotron emission, both
+the Haze and the total synchrotron are characterized by a power-law
+spectrum (as in Eq. 10), which is defined by two parameters: the
+amplitude and the spectral index 𝛽.
+We performed the measurement of the spectral index of the
+Haze and of the total synchrotron by fitting the SED of the signal
+within a selected area: region 8 in this case. We computed the
+average of the emission in the unmasked 𝑅𝐻 and 𝑅𝑆 pixels within
+the selected region. The zero level must be properly set at each
+MNRAS 00, 1–31 (2023)
+
+12
+F. Guidi et al.
+I
+Map
+Sync
+Free-free
+Dust
+Disk
+Mono
+Haze
+[mKRJ]
+[mKRJ]
+[mKRJ]
+QUIJOTE 11
+0.93
+1.28
+357.38
+8.85
+9.0×10−3
+0.70
+QUIJOTE 13
+0.89
+1.26
+231.44
+5.40
+6.6×10−3
+0.54
+WMAP K-band
+1.07
+0.85
+44.37
+0.39
+3.5×10−15
+0.19
+Planck 30
+1.07
+0.87
+18.02
+0.03
+−2.3×10−16
+0.10
+WMAP Ka-band
+0.98
+0.85
+9.05
+0.07
+−2.6×10−16
+0.07
+WMAP Q-band
+0.89
+0.88
+3.74
+0.07
+−8.6×10−17
+0.02
+Planck 44
+0.90
+0.90
+2.69
+0.05
+−4.3×10−17
+0.02
+WMAP V-band
+0.86
+0.83
+1.16
+0.04
+−1.5×10−16
+0.01
+Planck 70
+0.85
+0.82
+1.02
+0.01
+6.4×10−17
+0.01
+Q,U
+Sync
+Dust
+Mono
+[mKRJ]
+0.87
+-37.51
+2.8×10−3
+0.92
+-8.59
+1.6×10−3
+0.98
+3.33
+6.9×10−5
+1.04
+0.29
+8.1×10−6
+0.95
+1.59
+5.8×10−5
+1.01
+0.94
+4.7×10−5
+1.04
+0.82
+4.4×10−5
+1.01
+0.69
+6.4×10−5
+1.31
+0.72
+8.0×10−3
+Table 5. Stokes I (left) and Q,U (right) template fitting coefficients, fitted as described in Sect. 3.1.
+Figure 6. Residual plus Haze intensity maps in the southern Haze region (region 8, see Sect. 2.3), for, from left to right: QUIJOTE 11 GHz, QUIJOTE 13 GHz,
+WMAP K-band, Planck 30 GHz. The grid is centred at coordinates (𝑙, 𝑏) = (20◦, −23◦) and is spaced by 10◦ in Galactic latitude and longitude. The maps are
+in mK Rayleigh-Jeans temperature units, and the colour bar is scaled with a synchrotron-like power-law: 2 mK·(𝜈/11 GHz)𝛽, with 𝛽 = −3.0.
+frequency 𝜈. We therefore fitted a linear slope to the pixel-to-pixel
+correlation plot of 𝑅𝐻
+𝜈 against 𝑅𝐻
+22.8 (or 𝑅𝑆𝜈 against 𝑅𝑆
+22.8), given
+by:
+𝑅𝐻,𝑆
+𝜈
+= 𝑚𝜈 · 𝑅𝐻,𝑆
+22.8 + 𝑞𝜈,
+(25)
+obtaining the relative offset to WMAP K-band, 𝑞𝜈, and the slope 𝑚𝜈.
+This is done with a linear fit accounting for errors in both axes,15
+where the uncertainty is calculated as the standard deviation of the
+residual map in the selected area, propagated in quadrature with the
+uncertainty on the fitted amplitude of the templates.
+The uncertainty on the SED points is given as the standard
+deviation of the residual map, scaled by the square-root of the
+number of averaged pixels, and summed in quadrature with the
+calibration uncertainty of each frequency map. We assume a power-
+law behaviour for the spectrum of the Haze (
+�
+𝑅𝐻
+𝜈
+�
+− 𝑞𝐻
+𝜈 ) and of
+the total synchrotron (
+�
+𝑅𝑆𝜈
+�
+− 𝑞𝑆𝜈) at our frequencies, therefore we
+can write the linear relation of ln
+��
+𝑅𝐻,𝑆
+𝜈
+�
+− 𝑞𝐻,𝑆
+𝜈
+�
+against ln(𝜈),
+as:
+ln
+��
+𝑅𝐻,𝑆
+𝜈
+�
+− 𝑞𝐻,𝑆
+𝜈
+�
+= 𝛽𝐻,𝑆 · ln(𝜈) + 𝑐𝑜𝑛𝑠𝑡.,
+(26)
+whose slope provides the spectral index 𝛽.
+Here we look at the southern Haze area (region 7) that has been
+identified by previous works (Dobler & Finkbeiner 2008; Planck
+Collaboration et al. 2013). However, the sky observed by QUIJOTE
+does not cover the full area of region 7, and we restrict our analysis
+15 For this fit we used the Orthogonal Distance Regression (ODR)
+SciPy package (https://docs.scipy.org/doc/scipy/reference/
+odr.html).
+Figure 7. Intensity SED of the Haze enclosed in region 8 (see Sect. 2.3 and
+Fig. 6). The data and the fit of the residual plus Haze spectrum (multiplied
+by three for display purposes) are shown in red, while the data and the fit of
+the total synchrotron are shown in green.
+in the overlap with the QUIJOTE sky coverage (region 8), which is
+also shown on the right in Fig.6.
+The SED with the integrated spectrum in region 8 is given in
+MNRAS 00, 1–31 (2023)
+
+QlT11:TResidual+Haze
+8.5/pix,200x200pix
+(20,-23)
+Tb [mKR]
+-2.00
+2.00QlT13:TResidual+Haze
+8.5/pix,200x200pix
+(20,-23)
+Tb [mKR]
+-1.21
+1.21WMAPK:TResidual+Haze
+8.5°/pix,200x200 pix
+(20,-23)
+Tb [mKR]
+-0.22
+0.22PLA3O:TResidual+Haze
+8.5/pix,200x200pix
+(20,-23)
+Tb [mKr/]
+-0.12
+0.12I QiT Rectangle South Haze
+(RH),β= 2.79±0.08
+0.10
+(RS),β= -2.98±0.04
+[<R>-B)(v/23)2 [mKRj]
+0.01
+10
+20
+30
+40
+50
+60
+70
+freq [GHz]The Haze as seen by QUIJOTE
+13
+Figure 8. Intensity SED of the rectangle enclosing the southern Haze region (region 7), in the South Haze Bubble (region 9) and in the North Haze Bubble
+(region 5). In red is the spectrum of the residual plus Haze, and in green is the total synchrotron.
+the legend of Fig. 7. With a linear fit to these data,16 we measure
+𝛽𝐻 = −2.79 ± 0.08 and 𝛽𝑆 = −2.98 ± 0.04.
+We can observe that the spectrum of the Haze is flatter than that
+of the total synchrotron, with a difference in the spectral index of
+about Δ𝛽 = 𝛽𝐻 −𝛽𝑆 = 0.26±0.13. The difference has a significance
+of 2𝜎.
+Notice that if we remove the QUIJOTE data from the SED
+fit, the spectral indices are 𝛽𝐻 = −2.76 ± 0.12 and 𝛽𝑆 = −3.02 ±
+0.06, showing that QUIJOTE data does not significantly change the
+central value of the fit, but improves the precision with which the
+spectral indices are determined, by a factor 1.5.
+The correlation plots mentioned above, which we performed
+to set the zero level for the SED, also provided an estimate of the
+spectral index as obtained from the slope of the linear fit 𝑚𝜈 with
+Eq. 12. We obtained 𝛽𝐻 = −2.78 ± 0.19 and 𝛽𝑆 = −2.97 ± 0.05.
+This secondary measurement is consistent with the results that are
+obtained from the SED fitting, but the methodology is less precise.
+We can also discuss the effect of using, instead of region 8,
+the broader region 7, which is the subject of the studies presented
+in Planck Collaboration et al. (2013). Excluding QUIJOTE data
+and applying our methodology that uses priors to fit the various
+foregrounds, we measure the values 𝛽𝐻 = −2.70 ± 0.05 and 𝛽𝑆 =
+−3.06 ± 0.04 (see left panel in Fig. 8). We first notice that our
+measurement of the Haze spectrum in region 7 is slightly flatter
+than what we obtain in region 8 (by Δ𝛽𝐻 = 0.06), although they
+are consistent within the uncertainties.
+In region 7, Planck Collaboration et al. (2013) reports values
+of 𝛽𝐻 = −2.56 ± 0.05 and 𝛽𝑆 = −3.1. If we compare this with
+our results we can see that, in agreement with the Planck paper, the
+Haze in region 7 emits with a flatter index than that of the total syn-
+chrotron, but there is a discrepancy in the recovered Haze spectral
+index. In order to test the origin of this discrepancy, we reproduced
+the results of Planck Collaboration et al. (2013) by applying their
+same methodology, with no priors, excluding QUIJOTE data, and
+integrating the same southern Haze area (region 7). In this case,
+we obtain 𝛽𝐻 = −2.47 ± 0.06 and 𝛽𝑆 = −3.19 ± 0.04, which is
+consistent with the Planck’s results, showing that the main source of
+the observed difference is the use of priors, which results in a shift
+of the Haze spectral index towards steeper values, by Δ𝛽𝐻 = 0.23
+in region 7. The use of priors in the pipeline of this work has been
+tested with simulations (as discussed in Sec. 3.1), with which we
+noticed a clear improvement in the fitting of the foregrounds when
+16 The fit is performed with a MCMC sampling of the full posterior of the
+data, implemented with the Python emcee package (Foreman-Mackey et al.
+2013, https://emcee.readthedocs.io/en/stable/).
+compared with the case with no-priors. For this reason we finally
+applied priors in our analysis, despite the slightly different results
+in the Haze region as compared with previous works.
+4.1.3
+Spectra of regions 5, 7 and 9
+There are more regions that are interesting for the study of the
+Haze, but which are unfortunately not accessible by QUIJOTE,
+in the northern hemisphere. These are: the South Haze Bubble
+(region 9), which is located in the southern sky and can only be
+partially observed with QUIJOTE, and the North Haze Bubble
+(region 5), which is observed by QUIJOTE but coincides with a
+region with large residuals that are not fully understood. We studied
+these two regions by applying our template fitting methodology
+(with priors), using only WMAP and Planck data. We show their
+integrated spectra in the central and right panels in Fig. 8. In the
+South Haze Bubble (region 9) we obtain the spectral indices 𝛽𝐻 =
+−2.67±0.05 and 𝛽𝑆 = −2.99±0.05, which are compatible with the
+already discussed results for the rectangle enclosing the southern
+Haze (region 7; left panel in Fig. 8). In the North Haze Bubble,
+instead, we obtain a flatter Haze spectrum, with 𝛽𝐻 = −2.40±0.05,
+and also a flatter total synchrotron spectrum, it being 𝛽𝑆 = −2.51 ±
+0.05. We detect a significant difference between the spectral index
+of the North and South Haze bubbles in intensity, with the spectrum
+of the northern bubble flatter than that in the South. As in other
+regions, the Haze component is flatter than the total synchrotron,
+but in the northern bubble the total synchrotron spectrum is also
+significantly flatter than that in other regions. Interestingly, as we
+report later (Sect. 4.3), the polarization between 23 GHz and 30 GHz
+shows the same behaviour, with the northern bubble having a flatter
+spectrum than the southern one. In addition, the polarization spectral
+index of the North Haze Bubble is compatible with that of the total
+synchrotron in intensity, while the polarization spectral index of the
+South Haze Bubble is between the intensity 𝛽𝐻 and 𝛽𝑆 .
+4.2
+Polarization template fitting
+We applied the template fitting procedure in polarization, by fitting a
+synchrotron and thermal dust component to the Q and U frequency
+maps simultaneously across the full unmasked sky (see Sect. 3.1
+for a detailed description of the methodology). The CMB is fixed
+and subtracted from the maps before the fitting. The resulting fitted
+amplitudes are reported in Table 5.
+We computed the residual polarization amplitude maps as:
+𝑅P,𝜈 =
+√︃
+𝑅2
+𝑄,𝜈 + 𝑅2
+𝑈,𝜈,
+(27)
+MNRAS 00, 1–31 (2023)
+
+I Rectangle South Haze
+2 × 10-1
+(RH),β=-2.70±0.05
+(RS),β= -3.06±0.04
+0.10
+6 ×10-2
+4 × 10-2
+3× 10-2
+10
+20
+30
+40
+50
+60
+70
+freq [GHz]I South Haze Bubble
+2 ×10-1
+(RH), β = -2.67 ±0.05
+(RS),β= -2.99±0.05
+0.10
+6×10-2
+4×10-2
+3 × 10-2
+10
+20
+30
+40
+50
+60
+70
+freg[GHz]LNorthHazeBubble
+2 ×10-
+(<R>-B)·(v/23)2 [mKrj]
+0.10
+(RH),β=-2.40±0.05
+6 ×10-2
+(RS),β= -2.51±0.05
+10
+20
+30
+40
+50
+60
+70
+freg[GHz]14
+F. Guidi et al.
+with17 𝑅𝑄,𝑈 = 𝑅0
+𝑄,𝑈 − (𝑄0,𝑈0). Here, 𝑅0
+𝑄,𝑈 are the residual
+Q,U maps obtained after subtracting the fitted foregrounds from
+the original Q,U frequency maps. 𝑄0,𝑈0 are constant offsets to be
+subtracted to 𝑅0
+𝑄,𝑈 in order to adjust the zero level across frequen-
+cies. 𝑄0 and 𝑈0 are obtained with T-T plots of 𝑅0
+𝑄,𝑈 at frequency 𝜈
+with respect to the residual map at 𝜈 = 22.8 GHz (WMAP K-band),
+across the unmasked sky pixels. At this stage we do not attempt to
+debias the polarization amplitude maps, so 𝑅P could be marginally
+affected by noise bias.
+We also define the fitted polarization amplitude synchrotron
+map as:
+𝑆P,𝜈 =
+√︃
+𝑆2
+𝑄,𝜈 + 𝑆2
+𝑈,𝜈,
+(28)
+where 𝑆𝑄,𝑈 = 𝑎𝑠
+𝑄,𝑈 (𝑄𝑠,𝑈𝑠) are the fitted synchrotron maps,
+with 𝑄𝑠,𝑈𝑠 being the polarization synchrotron template maps, and
+𝑎𝑠
+𝑄,𝑎𝑠
+𝑈 the correspondent fitted amplitudes.
+Finally, we define the residual plus synchrotron map as:
+𝑅𝑆
+P,𝜈 =
+√︂�
+𝑅𝑆
+Q,𝜈
+�2
++
+�
+𝑅𝑆
+U,𝜈
+�2
+,
+(29)
+where 𝑅𝑆
+Q,U = 𝑅𝑄,𝑈 + 𝑆𝑄,𝑈 − (𝑄′
+0,𝑈′
+0) are the 𝑄,𝑈 residual plus
+synchrotron maps, with 𝑄′
+0,𝑈′
+0 adjusting the relative zero levels
+across frequencies, computed with T-T plots across the unmasked
+sky pixels with respect to WMAP K-band (22.8 GHz).
+4.2.1
+Polarization residual maps
+Fig. 9 shows maps of the residual polarization amplitude 𝑅P (left,
+see Eq. 27) and of the residual plus synchrotron 𝑅S
+P (centre, see
+Eq. 29) of QUIJOTE 11 and 13 GHz, of WMAP K-band and of
+Planck 30 GHz. Similar to Fig. 6, we also show a zoom-in of the 𝑅P
+maps across region 8 (right). We can observe that the WMAP K-band
+and Planck 30 GHz residual maps are mostly noise with potentially
+some low level systematics. In particular, the residual polarization
+map of Planck 30 GHz has very low values as compared with the
+other residual maps. This is due to the fact that for the template
+fitting procedure we use the Commander synchrotron solution (see
+Sect. 3.1.1), which strongly relies, by construction, on the 30 GHz
+Planck polarization data.
+The QUIJOTE polarization residual maps, instead, show struc-
+tures that can be associated with residual sky signal. The detection
+of similar structures was not possible in previous works based only
+on WMAP or Planck data. QUIJOTE data is now providing hints
+of a detection of a previously unknown polarized diffuse signal.
+Indeed we can observe, at 11 GHz and 13 GHz, evident structures
+across the full Haze area, towards the South in region 8, but also
+towards the North reaching high Galactic latitudes (𝑏 ∼ 85◦). We
+also detect residual signal in the lower part of the NPS, close to
+the Galactic plane (at (𝑙, 𝑏) ∼ (31.5◦, 16.5◦), bottom of region 1),
+which is seen also in the intensity residual maps (see Sect. 4.1.1).
+We refer to Watson et al. (in preparation) for a detailed study of the
+NPS using QUIJOTE data.
+In order to validate the sky origin of the observed polarization
+excesses, we analyzed noise maps of QUIJOTE obtained with null-
+tests (as shown in appendix C, Fig. C1), showing that the noise level
+can not explain the observed residuals, which are therefore ascribed
+to sky signal.
+17 We drop the specification of 𝜈 subscript for brevity.
+This kind of residuals could possibly be originated by spatial
+variations of the synchrotron spectral index, which has not been
+taken into account in the fitting procedure. We tested this hypothesis
+by repeating the analysis allowing the synchrotron spectral index
+to vary across the sky. We used for this purpose the synchrotron
+spectral index map extracted by de la Hoz et al. (2023), which is
+derived from a pixel-based component separation (B-SeCRET, de
+la Hoz et al. 2020) using data from QUIJOTE, WMAP and Planck.
+In this case we recover similar residual polarization maps as those
+shown in Fig. 9, concluding that the observed residuals are not
+attributable to spatial variations of the synchrotron index. On the
+other hand, they could be due to a curvature of the spectrum at
+low frequencies (𝜈 < 23 GHz), across the area where we observe a
+positive residual.
+4.2.2
+Polarization residual spectrum
+Following the same procedure that is applied in intensity, we com-
+puted the spectrum of maps integrated in several selected regions.
+In this case, as stated in Sect. 3.1.1, we do not perform the fit of an
+independent Haze template, because the projection of the Haze in
+the Stokes Q and U maps is unknown. Therefore, if the data contain
+a Haze component that is not identified as synchrotron with the
+sky average spectral index, or as thermal dust (even if it is a very
+minor component at these frequencies), it will be revealed in the
+residual maps 𝑅Q, 𝑅U, or 𝑅P defined in Eq. 27 and shown in Fig. 9.
+We therefore look for a polarized Haze component in the residual
+plus synchrotron spectrum (e.g., Eq. 29), by comparing it with the
+spectrum of the synchrotron alone (e.g., Eq. 28).
+We computed the spectrum of the combination of Stokes Q
+and U parameters with a sinusoidal function, as defined in Eq. 17,
+projecting them in the direction of the polarization angle 𝛼 of the
+region, and averaging the resulting signal within the selected region.
+This allows us to overcome problems related with noise bias of the
+polarization amplitude.
+The representative projection angle 𝛼 in the region is deter-
+mined by inverting the median value of sin(2𝛼), which is a con-
+tinuum function when the angle has a discontinuity (at 𝛼 ± 90◦).
+The angle is computed using the WMAP K-band data, and it is used
+for all the other frequencies. We use 𝛼 = 71.5◦ in region 8 and
+𝛼 = 36.3◦ in region 5.
+In Fig. 10 we show the spectrum of the average Q and U com-
+bination for the polarized synchrotron (𝑆, in black) and for the
+residual plus synchrotron (𝑅𝑆, in green) as a function of the fre-
+quency, within two different regions: the North Haze Bubble (region
+5) and the southern Haze area (region 8).
+The Q and U uncertainties (𝜎𝑄 , 𝜎𝑈) for the WMAP and Planck
+data points are estimates of the scatter of the residual 𝑅𝑄 and 𝑅𝑈
+maps, between pixels enclosed in the region being examined. For
+QUIJOTE, instead, the residual maps show an evident signal con-
+tribution, therefore we derive 𝜎𝑄 and 𝜎𝑈 as the standard deviation
+of the null-test 𝑄 and 𝑈 maps shown in appendix A, within the
+selected region. Finally, the Q and U uncertainties are normalized
+by the square-root of the number of unmasked pixels, are summed
+in quadrature with the corresponding calibration uncertainty, and
+are propagated through Eq. 17.
+We fit to the synchrotron and residual plus synchrotron spectra
+the amplitude 𝐴, the spectral index 𝛽, and the curvature 𝑐 of a
+modified power-law (as in e.g., Kogut 2012):
+𝑑(𝜈) = 𝐴
+� 𝜈
+𝜈0
+�𝛽+𝑐 ln 𝜈
+𝜈0 ,
+(30)
+MNRAS 00, 1–31 (2023)
+
+The Haze as seen by QUIJOTE
+15
+Figure 9. Residual (left, Eq. 27) and residual plus synchrotron (centre, Eq. 29) polarization amplitude maps of, from top to bottom, QUIJOTE 11 GHz,
+QUIJOTE 13 GHz, WMAP K-band, Planck 30 GHz. The right column figures show the residual 𝑃 maps zoomed in the southern Haze region (region 8, see
+Sect. 2.3, same grid as the right panels in Fig. 6). The maps are in mK Rayleigh-Jeans temperature units, and the colour bar is scaled with a synchrotron-like
+power-law: 0.5 mK · (𝜈/11 GHz)𝛽, with 𝛽 = −3.0.
+where 𝜈0 = 23 GHz a reference frequency. The range of frequency
+used is 11 ≲ 𝜈 ≲ 70 GHz. The fit is performed with a MCMC
+sampling of the full posterior of the data with emcee. For the fit of
+the residual plus synchrotron we applied a flat prior on the spectral
+index −4 < 𝛽 < −2, and a Gaussian prior to the curvature parameter,
+with a width 𝜎𝑐 = 1 and central values 𝜇𝑐 = 0 (dashed green line
+in Fig. 10). The synchrotron alone instead is fitted with no priors.
+For comparison we also fit the 𝐴 and 𝛽 parameters for a simple
+power-law, given by Eq. 30 with 𝑐 = 0. The fitted spectra in this
+case are shown as thick lines in Fig. 10, and the respective 𝛽 are
+reported in the legend. No priors are applied in this case.
+It can be observed in region 8 (left panel in Fig. 10) that
+the spectral index of a simple power-law for the residual plus
+synchrotron is 𝛽 = −3.07+0.37
+−0.45, and for the synchrotron it is
+𝛽 = −2.91 ± 0.11. The two spectral indices are compatible within
+the uncertainties. When including the curvature parameter in the fit,
+the estimated 𝛽 are in even better agreement, with 𝛽 = −2.97+0.48
+−0.41
+for the residual plus synchrotron and 𝛽 = −2.97+0.19
+−0.16 for the syn-
+chrotron alone. Although the residual plus synchrotron shows slight
+preference for a positive value of 𝑐, and the synchrotron alone
+MNRAS 00, 1–31 (2023)
+
+Residual P QlT11
+0.00
+Tb [mKR]]
+0.49Residual+Synchrotron P QlT1
+0.00
+Tb [mKR]]
+0.49QlT11:P Residua
+8.5/pix,200x200pix
+(20,-23)
+Tb [mKR]
+0.00
+0.49Residual P QlT13
+0.00
+T,[mKRj]
+0.31Residual+Synchrotron P QjT13
+0.00
+Tb [mKR]]
+0.31QIT13: P Residual
+8.5/pix,200x200pix
+(20,-23)
+Tb[mKR]
+0.00
+0.31ResidualPWMAPK
+0.00
+Tb [mKR]]
+0.06Residual+Synchrotron P WMAPK
+0.00
+Tb [mKR]]
+0.06WMAPK:PResidual
+8.5/pix,200x200pix
+(20,-23)
+Tb[mKR]
+0.00
+0.06ResidualPPLA30
+0.00
+Tb [mKR]]
+0.03Residual+SynchrotronPPLA3o
+0.00
+Tb [mKR]]
+0.03PLA3O: P Residua
+200x200 pix
+8.5/pix,
+(20,-23)
+Tb [mKr]]
+0.00
+0.0316
+F. Guidi et al.
+Figure 10. Polarization SED after template fitting in the rectangle enclosing the southern Haze area in the overlap with the QUIJOTE sky (region 8, left), and
+in the North Haze Bubble (region 5, right). The green points and lines represent the averaged and colour-corrected residual plus synchrotron spectrum (𝑅S,
+e.g., Eq. 29), fitted with a simple (thick green line) and modified (dashed green line) power-law. The same, in black color, is for synchrotron (𝑆, e.g., Eq. 28).
+The fitted spectra indices are reported in the legend.
+shows a preference for negative 𝑐, curvature is not detected with
+this methodology.
+In region 5 (see right panel in Fig. 10) the spectral index
+of a simple power-law for the residual plus synchrotron is 𝛽 =
+−2.87+0.62
+−0.71, and for the synchrotron alone it is 𝛽 = −2.93±0.02. The
+two spectral indices are compatible within the uncertainties. Also in
+this case, when including the curvature parameter in the fit, the esti-
+mated spectral indices are in better agreement, with 𝛽 = −2.96+0.57
+−0.54
+for the residual plus synchrotron, and 𝛽 = −2.96+0.03
+−0.03 for the syn-
+chrotron alone. Although both the residual plus synchrotron and
+the synchrotron alone show slight preference for values of 𝑐 < 0,
+curvature is not detected with this analysis.
+To summarize, no clear differences between the synchrotron
+and residual plus synchrotron spectral indices are detected. The
+curvature is obtained to be compatible with zero given the large
+error bars, especially on the spectral index of the residuals plus syn-
+chrotron. However, estimates of the curvature on these two regions
+are also presented in de la Hoz et al. (2023), where a negative curva-
+ture is detected at high significance using the parametric component
+separation method B-SeCRET (de la Hoz et al. 2020), although there
+is not enough statistical evidence to favour the curvature against the
+single power-law model.
+An independent but complementary analysis of the polariza-
+tion spectrum is shown in the next section, where we performed a
+detailed analysis with T-T plots in polarization.
+4.3
+T-T plots of Haze polarized plumes and spurs
+With the aim of studying the Haze region in polarization with a
+different approach to that presented in Sect. 4.2, we performed a
+correlation T-T plot analysis as described in Sect. 3.2.2, in the re-
+gions presented in Sect. 2.3. In this analysis, we also include the
+S-PASS data at 2.3 GHz, corrected for Faraday rotation as described
+in Appendix B. We computed the spectral indices between the fre-
+quency pairs:
+• 23–30 GHz (WMAP K-band – Planck 30 GHz)
+• 11–30 GHz (QUIJOTE 11 GHz – Planck 30 GHz)
+• 11–23 GHz (QUIJOTE 11 GHz – WMAP K-band)
+• 2.3–30 GHz (S-PASS 2.3 GHz – Planck 30 GHz)
+• 2.3–23 GHz (S-PASS 2.3 GHz – WMAP K-band)
+• 2.3–11 GHz (S-PASS 2.3 GHz – QUIJOTE 11 GHz)
+A summary of the results is reported in Table 6, and a graphical
+representation of the estimated spectral indices and uncertainties
+is shown in Fig. 11 for three selected frequency cases. In order to
+validate our results, we present a detailed analysis of the posterior
+distribution of the T-T plots in appendix D.
+By looking at Fig. 11 (or Table 6), we can notice that the Haze
+in polarization appears as two extended and slightly asymmetric
+bubbles (region 5,7–10), surrounded and connected to the Galactic
+plane with filaments and spurs (region 2, 3, 4, 6, 11, 12, 13). Our
+interpretation is that the regions 2–13 are related to the Haze, or in
+general to emission related to activity of the Galactic centre. Indeed,
+our measurements show that the spectral index of these regions is
+flat at high frequencies (23–30 GHz) and uniformly moves towards
+steeper values at lower frequencies (11–23 GHz and 2.3–23 GHz).
+The typical spectral indices of the Haze regions at 23–30 GHz are
+−2.8 ≲ 𝛽 ≲ −2.6, while at lower frequencies they became steeper,
+being −3.2 ≲ 𝛽 ≲ −3.0 at 11–23 GHz and at 2.3–23 GHz.
+We quote for comparison the average spectral indices of the
+full-sky available from each survey combined with the mask de-
+scribed in Sect. 3.1.1, and of the NPS (region 1), which is a widely
+studied region, currently modeled as synchrotron emission originat-
+ing from the expanding shell of a nearby supernova explosion (e.g.,
+Planck Collaboration et al. 2016c; Panopoulou et al. 2021 and Wat-
+son et al. (in preparation). We can notice that the spectral indices of
+the full-sky and of the NPS at 23–30 GHz are steeper than those of
+the Haze associated regions. Instead, at 11–23 GHz we observe the
+opposite behaviour: the full sky and NPS spectral indices are flatter
+than those of the Haze associated regions.
+We will extend the discussion of these results in Sec 5, where
+we provide an overview and an interpretation of the measurements
+obtained with different methodologies.
+MNRAS 00, 1–31 (2023)
+
+QTRectangleSouthHaze
+0.000
+0.001
+Qcos(2α)+Usin(2α)>
+0.002
+0.003
+0.004
+RS β= -3.07±037
+0.45
+RS β = - 2.97+0-48 c = 0.26+078
+0.005
+0.63
+Sβ= -2.91+0.11
+0.11
+0.006
+V
+0.16
+-0.29
+10
+20
+30
+40
+50
+60
+70
+freq [GHz]North Haze Bubble
+RS β = - 2.87+02
+0.050
+07
+RS βB= -2.96+057
+0.54
+6L0
+0.040
+S β= - 2.93±0.93
+-0.02
+-0.03
+0.05
+0.030
+0.020
+0.010
+0.000
+V
+10
+20
+30
+40
+50
+60
+70
+freq [GHz]The Haze as seen by QUIJOTE
+17
+Region
+Description
+𝛽 23–30
+𝛽 11–23
+𝛽 11–30
+𝛽 2.3–23
+𝛽 2.3–30
+𝛽 2.3–11
+0
+Full high-latitudes sky
+−3.06 ± 0.05
+−3.11 ± 0.06
+−3.12 ± 0.04
+−3.19 ± 0.03
+−3.19 ± 0.03
+−3.42 ± 0.12
+1
+NPS
+−3.11 ± 0.04
+−3.06 ± 0.05
+−3.08 ± 0.06
+-
+-
+-
+2
+Ext Haze Filament
+−2.99 ± 0.19
+−3.25 ± 0.06
+−3.20 ± 0.05
+-
+-
+-
+3
+Haze Filament
+−2.66 ± 0.18
+−3.10 ± 0.12
+−3.01 ± 0.12
+−3.01 ± 0.08
+−2.96 ± 0.05
+−3.09 ± 0.19
+4
+Int Haze Filament
+−2.17 ± 0.31
+−3.40 ± 0.80
+−3.10 ± 1.08
+−3.01 ± 0.21
+−2.92 ± 0.32
+-
+5
+North Haze Bubble
+−2.54 ± 0.14
+−3.24 ± 0.25
+−3.10 ± 0.18
+−3.22 ± 0.03
+−3.18 ± 0.01
+−3.24 ± 0.11
+6
+GCS
+−2.77 ± 0.25
+−3.40 ± 0.08
+−3.30 ± 0.10
+−3.09 ± 0.05
+−3.08 ± 0.06
+−2.94 ± 0.10
+7
+Rectangle South Haze
+−2.79 ± 0.06
+−3.50 ± 0.24
+−3.31 ± 0.13
+−3.12 ± 0.02
+−3.10 ± 0.02
+−3.05 ± 0.02
+8
+QJT Rectangle South Haze
+−2.77 ± 0.15
+−3.50 ± 0.36
+−3.32 ± 0.23
+−3.10 ± 0.04
+−3.11 ± 0.04
+−3.17 ± 0.07
+9
+South Haze Bubble
+−2.82 ± 0.13
+−3.50 ± 0.09
+−3.26 ± 0.15
+−3.11 ± 0.06
+−3.09 ± 0.04
+−2.97 ± 0.07
+10
+South Haze Bubble clean
+−2.81 ± 0.13
+−3.54 ± 0.09
+−3.33 ± 0.13
+−3.10 ± 0.07
+−3.09 ± 0.05
+−2.96 ± 0.07
+11
+eRosita West
+−2.16 ± 0.22
+−3.79 ± 0.13
+−3.43 ± 0.11
+−3.36 ± 0.03
+−3.24 ± 0.05
+−3.41 ± 0.26
+12
+unknown residual
+−2.74 ± 0.34
+−3.29 ± 0.16
+−3.23 ± 0.17
+−3.28 ± 0.18
+−3.31 ± 0.11
+−3.22 ± 0.15
+13
+eRosita East
+−2.83 ± 0.33
+-
+-
+−3.28 ± 0.04
+−3.28 ± 0.05
+-
+Table 6. Polarization spectral indices in the selected regions obtained with a T-T plots analysis based on data from Planck 30 GHz, WMAP K-band, QUIJOTE
+11 GHz, and S-PASS 2.3 GHz. For the determination of the spectral indices we use the methodology described in Sect. 3.2.2.
+Figure 11. Polarization spectral indices in the selected regions (top) and uncertainties (bottom), obtained with a T-T plots analysis based on data from Planck
+30 GHz (left), QUIJOTE 11 GHz (center), and S-PASS 2.3 GHz (right), with WMAP K-band as a pivot.
+5
+SUMMARY AND DISCUSSION
+We discuss here the results presented in the previous section, and
+summarize what we obtained in some specific regions, particularly
+in the southern Haze area (regions 7–10), in the North Haze Bubble
+(region 5), and in North Haze filament (region 3), in intensity and
+polarization, and with different methodologies.
+5.1
+South Haze area
+Previous studies of the Haze emission in intensity have been concen-
+trating in the area below the Galactic centre (region 7 in this work)
+because of the apparently little complexity and low foregrounds
+contamination of the intensity signal at WMAP and Planck-LFI
+frequencies. However, the S-PASS polarization data (see Fig. A4)
+provided a more detailed picture of the area, showing an extended
+polarized plume in the south (region 9), but also localized contam-
+inated areas that appear to be depolarized, and whose location is
+indicated in Fig. 3. These depolarized areas are, in particular, re-
+gion "A" identified by Iacobelli et al. (2014) and G353.34, a nearby
+supernova remnant (see Tab. 4). Moreover, S-PASS data in polar-
+ization show that almost the full southern bubble is affected by
+Faraday rotation at low frequencies. Indeed, from the polarization
+angle maps shown in Fig. A4, we can observe that the polarization
+angle across the South Haze Bubble (region 9) has a transition from
+positive to negative values when comparing the high (23 GHz and
+30 GHz) and low (2.3 GHz) frequencies. In this work, according to
+these considerations, we identified several regions in the area be-
+low the Galactic centre (region 7, 8, 9, 10 - see Sect. 2.3) and we
+studied them with different methodologies, including also the new
+QUIJOTE data, both in intensity and polarization.
+First of all, we reproduced the analysis of the Haze in intensity
+by using Planck and WMAP data in region 7, and applying a similar
+technique to that in Planck Collaboration et al. (2013). We obtained
+a spectrum of the Haze in region 7, using only Planck and WMAP
+data (Fig. 8), with 𝛽𝐻 = −2.70 ± 0.05, and of the total synchrotron
+with 𝛽𝑆 = −3.06 ± 0.04. We repeated the same analysis in region
+9, which encloses the brightest part of the South Haze Bubble,
+obtaining 𝛽𝐻 = −2.67 ± 0.05 and 𝛽𝑆 = −2.99 ± 0.05. From these
+results we can notice that the intensity Haze spectrum in region 9
+(the South Haze Bubble) is consistent with the spectrum in region
+7, although the latter is more extended.
+MNRAS 00, 1–31 (2023)
+
+β PLA 30-WMAP K
+-3.11-2.66
+-2.99.2.54
+2.79
+2
+83
+2.74
+-2.81
+16
+-3.06
+-3.4
+-2.4β QJT 11-WMAP K
+3.06 -3.10
+-3.25-3.24
+:3.50
+39
+3
+-3.11
+-3.4
+-2.4β SPASS-WMAP K
+01
+3.09
+3.10
+3
+.11
+-3.10
+36
+-3.4
+-2.4Oβ PLA 30-WMAP K
+0.04
+0.18
+0.190.14
+0.31
+0.25
+0.15
+0.13
+0.34
+0.13
+0.22
+0.05
+0
+0.3OB
+QJT 11-WMAP K
+0.05
+0.12
+0.06
+0.25
+0.08
+0.36
+0.16
+0.13
+0.06
+0
+0.3OB
+SPASS-WMAP K
+0.08
+0.03
+0.05
+0.02
+0.04
+.04
+0.06
+18
+0.07
+0.03
+0
+0.318
+F. Guidi et al.
+The main aim of this work is the characterization of the Haze
+with the QUIJOTE data at lower frequencies (e.g., 11 and 13 GHz).
+Since QUIJOTE is a ground based experiment located in the north-
+ern hemisphere it does not cover the southern sky area enclosing
+the South Haze Bubble (region 9). However, with QUIJOTE data,
+we have access to a fraction of region 7, which we call region 8 in
+this work. In Sect. 4.1 we presented the intensity analysis in this
+restricted area, including the low frequency QUIJOTE data, at 11
+and 13 GHz. A Haze component is detected in region 8 as shown
+in Fig. 6. The observed excess of diffuse signal is detected with
+∼ 9𝜎 confidence level, at 11 GHz. We computed the spectrum of
+the emission in this region, as shown in Fig. 7, obtaining a spectral
+index of the Haze 𝛽𝐻 = −2.79 ± 0.08 and of the total synchrotron
+𝛽𝐻 = −2.98 ± 0.04. The spectrum of the Haze in region 8 is flatter
+than the total synchrotron by Δ𝛽 = 0.19 ± 0.09, with the difference
+significant at 2 𝜎. The central value of the Haze spectral index in re-
+gion 8 (𝛽 = −2.79±0.08) is slightly steeper than that obtained with
+WMAP and Planck-LFI data alone in region 7 (𝛽 = −2.70 ± 0.05),
+but the difference is not significant.
+A similar analysis is also performed, for the first time, in po-
+larization. A map of the polarization residuals is shown in Fig. 9,
+where we can observe residuals across the southern Haze area at
+QUIJOTE frequencies. The average residual signal in region 8 ex-
+ceeds the noise level with high significance. The residual struc-
+ture observed in polarization is slightly displaced with respect to
+that detected in intensity. The residual plus synchrotron component
+in region 8 has a spectrum at 11 ≲ 𝜈 ≲ 70 GHz that, if fitted
+with a simple power-law, has 𝛽 = −3.07+0.37
+−0.45, which is consistent
+with that of the isolated synchrotron within the large uncertainty,
+which has 𝛽 = −2.91 ± 0.11, as shown in Fig. 10. The difference
+is Δ𝛽 = 0.16 ± 0.43. However when fitting a modified power-law
+with curvature to the residual plus synchrotron there are hints for a
+positive curvature, although with low significance.
+More solid hints of a positive curvature are observed with
+the T-T plots analysis shown in Fig. 11, with which we observe a
+steepening of the polarized emission within the South Haze Bubble
+at low frequencies (2.3 and 11 GHz). It is evident from Fig. 11 that
+the spectral indices in region 7, 8 and 9, so in the whole South Haze
+complex, are flat ("red") at 23–30 GHz and steep ("blue") at 11–
+23 GHz and 2.3–23 GHz. This low frequency steepening behaviour,
+however, is not only valid for the South Haze, but for the full complex
+associated with the Galactic centre, represented by regions 2–13.
+The only region where the low frequency steepening is not observed
+is the NPS, which indeed is thought to be a distinct component from
+the Haze (see e.g., Planck Collaboration et al. 2016c; Panopoulou
+et al. 2021) or from activity of the Galactic centre in general.
+We mentioned also about two depolarized spots at 2.3 GHz,
+corresponding to region "A" and to the nearby supernova remnant
+G353.34. In order to check that the determination of the spectral
+index of the South Haze Bubble is not affected by the presence of
+these two extra structures in the area, we repeated the T-T plot by
+masking region "A" and G353.34 (region 10 in Fig. 3). As reported
+in Table 6 and in Fig. 11, we obtained 𝛽 = −2.81 ± 0.13 at 23–
+30 GHz and 𝛽 = −3.10 ± 0.07 at 2.3–30 GHz, which are in perfect
+agreement with the spectral indices computed with the same T-T
+plots methodology in the whole South Haze Bubble, which are
+𝛽 = −2.82 ± 0.13 at 23–30 GHz and 𝛽 = −3.11 ± 0.06 at 2.3–
+30 GHz. We conclude that the depolarized regions across the South
+Haze do not bias the spectral index determination of the bubble.
+5.2
+North Haze Bubble
+The North Haze Bubble (region 5) is the region, among those
+studied in this paper, with the flattest spectral index. From the
+analysis with the intensity data, in the range of frequencies 23-
+60 GHz18 (Fig. 8, right panel) we measured a spectral index of
+the Haze 𝛽𝐻 = −2.40 ± 0.05, and of the Haze plus synchrotron
+𝛽𝑆 = −2.51±0.05. Both 𝛽𝐻 and 𝛽𝑆 are far from the typical sky av-
+erage synchrotron spectral index 𝛽 ≈ −3, meaning that, in this area
+and frequency range, the emission of the Haze is dominant over the
+Galactic diffuse synchrotron. The flat spectral index in this region
+could also be due to residual free-free emission, which is bright
+in this area. However, we can compare this result with the spectral
+index in polarization between 23 and 30 GHz, where there is no con-
+tamination from free-free emission. We obtained, with the T-T plots
+in the North Haze Bubble, a spectral index 𝛽 = −2.54 ± 0.14 be-
+tween 23 and 30 GHz. We emphasize that the results derived from
+T-T plots in polarization are compatible with those derived from
+the intensity template fitting for the total synchrotron emission, at
+WMAP and Planck-LFI frequencies, within 1𝜎. We therefore infer
+that the observed flat intensity and polarization spectral index in
+the North Haze Bubble can be ascribed to the synchrotron emission
+produced by the Haze component, which dominates over the typical
+(steeper) synchrotron in this region.
+On the other hand, with the polarization template fitting analy-
+sis, we observe that, similarly to region 8, the spectrum of the resid-
+ual plus synchrotron component fitted with a simple power-law at
+11 ≲ 𝜈 ≲ 70 GHz in region 5 is compatible, within the large uncer-
+tainties, with that of the synchrotron alone, as shown in Fig. 10 (left
+panel). The difference of the spectral indices is Δ𝛽 = 0.06 ± 0.65.
+However, T-T plots have shown that the spectral index of the to-
+tal emission between 23 and 30 GHz is significantly flatter than that
+at lower frequencies, especially when including 2.3 GHz data in the
+analysis, providing hints of a detection of curvature of the spectrum
+across this region. This behaviour could be originated by a double
+electron population that generates the polarized synchrotron signal
+in region 5: one with a flat (𝛽 ∼ −2.5) spectra index that dominates
+in the frequency range 20 GHz – 44 GHz, and one with a steeper
+spectrum (𝛽 ∼ −3.2) that emerges at 𝜈 < 20 GHz. QUIJOTE data
+provide a characterization that is compatible with that presented
+by Carretti et al. (2013) based on S-PASS data, fitting well with
+the interpretation presented in Crocker et al. (2015). According to
+Crocker et al. (2015) the observed emission is produced by: i) shock
+re-accelerated young cosmic-rays electrons that are responsible for
+the flat (or hard) synchrotron emission of the microwave Haze; ii)
+an old population of cosmic-rays electrons that escape the contact
+discontinuity of the shock, and emit the steeper synchrotron radia-
+tion observed in the S-PASS plume; iii) colliding hadrons enclosed
+in the contact-discontinuity surface that radiate the 𝛾-rays, which is
+what we observe in the Fermi bubbles. A 𝛾-ray component of IC
+emision, from the same electrons that radiate the microwave Haze,
+is also present, but it is subdominant. This model agrees with the
+results obtained in this work for both the North and South polarized
+lobes.
+18 We do not include QUIJOTE low frequency intensity data here, due to
+the not well understood structures in the residual, which could be due to
+atmospheric 1/f noise.
+MNRAS 00, 1–31 (2023)
+
+The Haze as seen by QUIJOTE
+19
+5.3
+Comparison between South and North Haze bubbles
+An interesting consideration is connected with the recent results
+presented by Jew & Grumitt (2020), who computed with a novel
+technique the spectral indices of the North and South Haze bub-
+bles between 30 and 44 GHz, using Planck data. They reported a
+difference between the polarization spectral index of the two bub-
+bles, being 𝛽 = −2.36 ± 0.09 in the North and 𝛽 = −3.00 ± 0.05
+in the South Haze.19 In this work, we measure an asymmetry of
+the spectral indices of the northern and southern Haze bubbles in
+intensity, in the frequency range 23-60 GHz, consistent with what
+Jew & Grumitt (2020) found in polarization. We obtain a total syn-
+chrotron index 𝛽 = −2.51 ± 0.05 in the North Haze Bubble, and
+𝛽 = −2.99 ± 0.05 in the South Haze Bubble, as shown in Fig. 8 us-
+ing only WMAP and Planck data. There is consistency between our
+total synchrotron intensity spectrum and the polarization spectrum
+at 30-44 GHz measured by Jew & Grumitt (2020).
+In addition, our results with T-T plots confirm that the asym-
+metry between the North and South Haze bubbles is also seen
+in polarization, at 23-30 GHz: the spectral index across the North
+Haze Bubble is 𝛽 = −2.54 ± 0.14, and in the South Haze Bubble it
+is 𝛽 = −2.82±0.13. The South Haze Bubble has a steeper spectrum
+than the North Haze Bubble, both in intensity and polarization. In-
+terestingly, at lower frequencies, this trend is inverted. The T-T plots
+between 2.3 GHz and 23 GHz show that the polarization spectrum
+of the North Haze Bubble (𝛽 = −3.22±0.03) is slightly steeper than
+that in the South Haze Bubble (𝛽 = −3.11±0.06), with a difference
+Δ𝛽 = 0.11 ± 0.07 (1.6𝜎).
+5.4
+North Haze filament
+The North Haze filament (region 3) is an interesting case of study.
+It corresponds to the structure identified by Vidal et al. (2015) and
+Planck Collaboration et al. (2016c) as the filament surrounding
+the northern Fermi bubble in 𝛾-rays, and the microwave Haze in the
+north. In Sect. 5.5 of Planck Collaboration et al. (2016c), a measure-
+ment of the spectral index of the filament using Planck 30 GHz and
+WMAP K-band data is reported. They measured 𝛽 = −2.54 ± 0.16
+with T-T plots of the unbiased 𝑃MAS maps at 30 and 23 GHz,
+with a methodology that is essentially the same as that described in
+Sect. 3.2.1. In this work, we performed the measurement in the same
+region, but using a different technique as described in Sect. 3.2.2,
+obtaining 𝛽 = −2.66 ± 0.18 (see Table 6 and Fig. 11).
+In the attempt of reproducing the result of Planck Collaboration
+et al. (2016c) with T-T plots of 𝑃MAS, we identified a possible source
+of bias that can introduce significant differences in the estimate of
+the 𝛽. Although the polarization amplitude 𝑃MAS is not affected by
+noise bias if computed as in Eq. 14, it is a positive quantity, and, in
+regions with low signal to noise the determination of the spectral
+index with the classical T-T plot methodology (Sect. 3.2.1) can be
+biased. In addition, when allowing uncertainties in both axes, the
+correlation between zero-level and slope is strong. For example, in
+the northern Haze filament (region 3), we obtained 𝛽 = −2.84±0.08
+using a T-T plot of the 𝑃MAS maps, where we allowed to fit both the
+slope and an offset between the maps. However, if the zero level of
+𝑃MAS is correctly set, as it is in this case where we first adjust the
+19 Note that the regions studied in Jew & Grumitt (2020) do not perfectly
+match with ours. They integrated two approximately symmetric bubbles in
+the north and in the south corresponding to the 𝛾-ray Fermi bubbles, while
+we restrict our analysis to the brightest region of the plumes as observed at
+low frequency (2.3 GHz), in polarization.
+Figure 12. T-T plot with 𝑃MAS in the North Haze filament (region 3),
+comparing the case where we fix or do not fix the offset of the linear fit, to
+illustrate the effect of Eddington bias.
+relative offset of the 𝑄 and 𝑈 maps with the reference, we can force
+the intercept of the T-T plot slope to be zero. In this case, we obtain
+a value of the spectral index 𝛽 = −2.67±0.03, which is inconsistent
+with the previous result, where the intercept was free to vary, but
+which is in full agreement with the result reported in Sect. 4.3
+(Table 6), obtained with the method described in Sect. 3.2.2 based
+on Fuskeland et al. (2014).
+In Fig. 12 we show the T-T plot of the unbiased polarization
+amplitude in the filament (region 3). The blue line is a fit of the
+points for both the slope and offset. The red line is the fit over the
+same data points, but where the intercept is forced to be zero. We
+can clearly see that the red and blue lines have a different slope,
+and that therefore the recovered spectral indices are also different.
+The small difference between the red and blue data points is due
+to the different colour correction that is applied to the same initial
+data, given that the spectral index resulting from the two fitting
+methodologies is different. Our final conclusion is that T-T plot of
+the positive definite unbiased polarization amplitude (𝑃MAS) could
+be affected by noise bias, which can be mitigated by fitting the T-T
+plot with the intercept fixed to zero. The method applied in this
+work (described in Sect. 3.2.2 and based on Fuskeland et al. 2014,
+2019), instead, is not significantly biased, since it uses T-T plots
+of a combination of Q and U data, which can be both positive and
+negative avoiding zero level problems.
+6
+CONCLUSIONS
+We derived the spectral properties of the microwave Haze with
+different methodologies, in intensity and in polarization. For this we
+used, for the first time, new Haze observations from the QUIJOTE
+experiment, at 11 and 13 GHz. In combination we used the publicly
+available S-PASS (2.3 GHz), WMAP (23–61 GHz) and Planck-LFI
+(30–70 GHz) data.
+We computed the spectrum of the Haze after applying template
+fitting. We used the intensity data of QUIJOTE, WMAP and Planck-
+LFI. In particular we measured the Haze spectrum in the South, in
+the overlap with the QUIJOTE sky coverage, within region 8. We
+obtained a synchrotron spectrum with spectral index 𝛽 = −2.79 ±
+0.08 (see Fig. 7) at frequencies 11–60 GHz. As a general trend, we
+MNRAS 00, 1–31 (2023)
+
+P Haze Filament PLA30 GHz WMAP23 GHz
+0.10
+β = -2.84±0.08
+q=0.001
+KRJ
+0.08
+β= -2.67±0.03
+q=0.0
+Z
+0.06
+GH
+LA30
+0.04
+0.02
+0.00
+0.00
+0.05
+0.10
+0.15
+WMAP23 GHz [mKrj]20
+F. Guidi et al.
+find that the spectrum of the Haze component in intensity is flatter
+than the typical diffuse synchrotron emission. Our results in the
+whole south Haze area (region 7), however, are in slight tension
+with those obtained by Dobler & Finkbeiner (2008) and Planck
+Collaboration et al. (2013) in the same region, as we obtain a spectral
+index of the Haze that is steeper than that obtained from previous
+works (e.g., 𝛽 = −2.70 ± 0.05 from this work and 𝛽 ∼ −2.56 ± 0.05
+from Planck Collaboration et al. 2013, at frequencies 23–60 GHz).
+We also studied the intensity spectrum of the Haze in the North
+and South bubbles (regions 5 and 9), but excluding QUIJOTE data
+that are not available or possibly affected by noise artifacts. We
+measured a synchrotron emission from a Haze component with a
+spectral index at 23–60 GHz of 𝛽𝐻 = −2.40 ± 0.05 in the North
+Haze Bubble and 𝛽𝐻 = −2.67 ± 0.05 in the South Haze Bubble,
+as shown in Fig. 8. We measured for the first time in intensity a
+difference of the spectral index in the North and South bubbles, in
+the frequency range 23–60 GHz, with a significance of ≈ 4𝜎. This
+behaviour is also observed in polarization in this work between 23
+and 30 GHz, in agreement with previous results by Jew & Grumitt
+(2020) between 30 and 44 GHz.
+In polarization, we studied the spectra of the Haze-related
+structures with both a template fitting (see Fig. 9 and 10) and corre-
+lation T-T plot technique (see Table 6 and Fig. 11) providing spectral
+indices for different frequency pairs. After fitting a synchrotron and
+dust component to the QUIJOTE maps, we observed residual po-
+larized structures that are inconsistent with the expected noise level
+with high significance (see Fig. 9). This result can be interpreted
+as a hint of curvature of the synchrotron spectral index across the
+area where we observe the positive residuals. However a study of
+the spectral properties in regions 5 and 8 does not have sufficient
+signal-to-noise to show clear differences between the synchrotron
+and residual plus synchrotron spectral indices (see Fig. 10). We also
+tried to constrain a curvature parameter, which is obtained to be
+compatible with zero given the large error bars.
+However, our results based on T-T plots (Fig. 11) show flat
+spectrum regions across the Haze area at 23–30 GHz, and an evident
+steepening at low frequencies, in agreement with Carretti et al.
+(2013). We observed in Fig. 11 that the Haze-related structures
+(regions 2–13) are significantly flat (−2.8 ≲ 𝛽 ≲ −2.6) compared
+with the sky average synchrotron (𝛽 ∼ −3) at 23–30 GHz, while at
+lower frequencies (11–30 GHz and 2.3–30 GHz) the spectrum of the
+Haze steepens significantly (−3.2 ≲ 𝛽 ≲ −3.0). On the other hand
+the NPS (region 1), which is thought to be a nearby supernova shell
+not related with the Haze structures, shows the opposite behaviour:
+its spectral index does not show significant differences across the
+frequencies presented in this work.
+Our results in polarization are compatible with those presented
+in Carretti et al. (2013). They can be therefore interpreted with the
+model presented in Crocker et al. (2015), according to whom young
+cosmic ray electrons enclosed in the contact discontinuity of a shock
+generated by Galactic centre nuclear activity radiate the flat syn-
+chrotron of the Haze, while older cosmic ray electron escaping the
+contact discontinuity produce the steeper synchrotron observed in
+the S-PASS lobes. However, in intensity, we do not observe a change
+of the Haze spectral index as we do see in polarization. The inten-
+sity spectrum in region 8 is well characterized by a single power-law
+with 𝛽𝐻 ∼ −2.8. Further investigation is needed to understand this
+behaviour. Possibly the use of stellar absorption like in Panopoulou
+et al. (2021), or the modelling of the magnetic field and of the cos-
+mic rays as proposed by the IMAGINE Consortium (Boulanger et al.
+2018) could help to formulate a more comprehensive interpretation
+of this complex area.
+ACKNOWLEDGEMENTS
+The QUIJOTE experiment is being developed by the Instituto
+de Astrofisica de Canarias (IAC), the Instituto de Fisica de
+Cantabria (IFCA), and the Universities of Cantabria, Manch-
+ester and Cambridge. We thank the staff of the Teide Obser-
+vatory for invaluable assistance in the commissioning and op-
+eration of QUIJOTE. Partial financial support was provided
+by the Spanish Ministry of Science and Innovation under
+the projects AYA2007-68058-C03-01, AYA2007-68058-C03-02,
+AYA2010-21766-C03-01, AYA2010-21766-C03-02, AYA2014-
+60438-P, ESP2015-70646-C2-1-R, AYA2017-84185-P, ESP2017-
+83921-C2-1-R,
+AYA2017-90675-REDC
+(co-funded
+with
+EU
+FEDER funds), PGC2018-101814-B-I00, PID2019-110610RB-
+C21, PID2020-120514GB-I00, IACA13-3E-2336, IACA15-BE-
+3707, EQC2018-004918-P, the Severo Ochoa Programs SEV-
+2015-0548 and CEX2019-000920-S, the Maria de Maeztu Pro-
+gram MDM-2017-0765, and by the Consolider-Ingenio project
+CSD2010-00064 (EPI: Exploring the Physics of Inflation). We
+acknowledge support from the ACIISI, Consejeria de Economia,
+Conocimiento y Empleo del Gobierno de Canarias and the European
+Regional Development Fund (ERDF) under grant with reference
+ProID2020010108. This project has received funding from the Eu-
+ropean Union’s Horizon 2020 research and innovation program un-
+der grant agreement number 687312 (RADIOFOREGROUNDS).
+This research made use of computing time available on the high-
+performance computing systems at the IAC. We thankfully acknowl-
+edge the technical expertise and assistance provided by the Spanish
+Supercomputing Network (Red Española de Supercomputación), as
+well as the computer resources used: the Deimos/Diva Supercom-
+puter, located at the IAC. FG acknowledges funding from the Eu-
+ropean Research Council (ERC) under the European Union’s Hori-
+zon 2020 research and innovation programme (grant agreement No
+101001897). EdlH acknowledge partial financial support from the
+Concepción Arenal Programme of the Universidad de Cantabria.
+FP acknowledges support from the Spanish State Research Agency
+(AEI) under grant number PID2019-105552RB-C43. BR-G ac-
+knowledges ASI-INFN Agreement 2014-037-R.0. DT acknowl-
+edges the support from the Chinese Academy of Sciences Presi-
+dent’s International Fellowship Initiative, Grant N. 2020PM0042.
+This work has made use of S-band Polarisation All Sky Survey
+(S-PASS) data. Some of the results in this paper have been de-
+rived using the HEALPix (Górski et al. 2005) and healpy (Zonca
+et al. 2019) packages. We also use Numpy (Harris et al. 2020), and
+Matplotlib (Hunter 2007).
+DATA AVAILABILITY
+The QUIJOTE raster scan data used in this paper are property of
+the QUIJOTE Collaboration and can only be shared on request to
+the corresponding authors. The QUIJOTE wide-survey maps will
+be made publicly available in the first QUIJOTE data release, as
+detailed in Rubiño-Martín et al. (2023). Ancillary data employed in
+the analysis for this paper are publicly available and can be accessed
+as referred along the paper text.
+REFERENCES
+Ackermann M., et al., 2014, ApJ, 793, 64
+Almy R. C., McCammon D., Digel S. W., Bronfman L., May J., 2000, ApJ,
+545, 290
+MNRAS 00, 1–31 (2023)
+
+The Haze as seen by QUIJOTE
+21
+Ashley T., Fox A. J., Cashman F. H., Lockman F. J., Bordoloi R., Jenkins
+E. B., Wakker B. P., Karim T., 2022, arXiv e-prints, p. arXiv:2207.08838
+Bennett C. L., et al., 2003, ApJS, 148, 1
+Bennett C. L., et al., 2013, ApJS, 208, 20
+Biermann P. L., Becker J. K., Caceres G., Meli A., Seo E.-S., Stanev T.,
+2010, ApJ, 710, L53
+Boulanger F., et al., 2018, J. Cosmology Astropart. Phys., 2018, 049
+Cardoso J.-F., Martin M., Delabrouille J., Betoule M., Patanchon G., 2008,
+arXiv e-prints, p. arXiv:0803.1814
+Carretti E., et al., 2013, Nature, 493, 66
+Carretti E., et al., 2019, MNRAS, 489, 2330
+Choi S. K., Page L. A., 2015, J. Cosmology Astropart. Phys., 2015, 020
+Cholis I., Goodenough L., Weiner N., 2009, Phys. Rev. D, 79, 123505
+Crocker R. M., 2012, MNRAS, 423, 3512
+Crocker R. M., Aharonian F., 2011, Phys. Rev. Lett., 106, 101102
+Crocker R. M., Bicknell G. V., Taylor A. M., Carretti E., 2015, ApJ, 808,
+107
+de la Hoz E., Vielva P., Barreiro R. B., Martínez-González E., 2020, J. Cos-
+mology Astropart. Phys., 2020, 006
+de la Hoz E., Barreiro R. B., Vielva P., et al., 2023, MNRAS, accepted
+Delahaye T., Böhm C., Silk J., 2012, MNRAS, 422, L16
+Dickinson C., Davies R. D., Davis R. J., 2003, MNRAS, 341, 369
+Dickinson C., Peel M., Vidal M., 2011, MNRAS, 418, L35
+Dickinson C., et al., 2018, New Astron. Rev., 80, 1
+Dobler G., 2012, ApJ, 750, 17
+Dobler G., Finkbeiner D. P., 2008, ApJ, 680, 1222
+Dobler G., Finkbeiner D. P., Cholis I., Slatyer T., Weiner N., 2010, ApJ, 717,
+825
+Egorov A. E., Gaskins J. M., Pierpaoli E., Pietrobon D., 2016, J. Cosmology
+Astropart. Phys., 2016, 060
+Eriksen H. K., et al., 2004, ApJS, 155, 227
+Eriksen H. K., Jewell J. B., Dickinson C., Banday A. J., Górski K. M.,
+Lawrence C. R., 2008, ApJ, 676, 10
+Finkbeiner D. P., 2003, ApJS, 146, 407
+Finkbeiner D. P., 2004, ApJ, 614, 186
+Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, PASP, 125,
+306
+Fox A. J., et al., 2015, ApJ, 799, L7
+Fuskeland U., Wehus I. K., Eriksen H. K., Næss S. K., 2014, ApJ, 790, 104
+Fuskeland U., et al., 2019, arXiv e-prints, p. arXiv:1909.05923
+Gaskins J. M., 2016, Contemporary Physics, 57, 496
+Génova-Santos R., et al., 2017, MNRAS, 464, 4107
+Górski K. M., Hivon E., Banday A. J., Wand elt B. D., Hansen F. K.,
+Reinecke M., Bartelmann M., 2005, ApJ, 622, 759
+Guidi F., et al., 2021, MNRAS, 507, 3707
+Guo F., Mathews W. G., 2012, ApJ, 756, 181
+Guo F., Mathews W. G., Dobler G., Oh S. P., 2012, ApJ, 756, 182
+Harris C. R., et al., 2020, Nature, 585, 357
+Haslam C. G. T., Salter C. J., Stoffel H., Wilson W. E., 1982, A&AS, 47, 1
+Hooper D., Finkbeiner D. P., Dobler G., 2007, Phys. Rev. D, 76, 083012
+Hoyland R. J., et al., 2012, in Millimeter, Submillimeter, and Far-
+Infrared Detectors and Instrumentation for Astronomy VI. p. 845233,
+doi:10.1117/12.925349
+Hunter J. D., 2007, Computing in Science & Engineering, 9, 90
+Hutschenreuter S., et al., 2022, A&A, 657, A43
+Iacobelli M., et al., 2014, A&A, 566, A5
+Jew L., Grumitt R. D. P., 2020, MNRAS,
+Jones D. I., Crocker R. M., Reich W., Ott J., Aharonian F. A., 2012, ApJ,
+747, L12
+Kataoka J., Yamamoto M., Nakamura Y., Ito S., Sofue Y., Inoue Y.,
+Nakamori T., Totani T., 2021, ApJ, 908, 14
+Keihänen E., Keskitalo R., Kurki-Suonio H., Poutanen T., Sirviö A. S., 2010,
+A&A, 510, A57
+Kogut A., 2012, ApJ, 753, 110
+Krachmalnicoff N., et al., 2018, A&A, 618, A166
+Lacki B. C., 2014, MNRAS, 444, L39
+Large M. I., Quigley M. J. S., Haslam C. G. T., 1962, MNRAS, 124, 405
+Li J.-T., Hodges-Kluck E., Stein Y., Bregman J. N., Irwin J. A., Dettmar
+R.-J., 2019, ApJ, 873, 27
+Merloni A., et al., 2012, arXiv e-prints, p. arXiv:1209.3114
+Panopoulou G. V., Dickinson C., Readhead A. C. S., Pearson T. J., Peel
+M. W., 2021, arXiv e-prints, p. arXiv:2106.14267
+Peel M. W., Dickinson C., Davies R. D., Band ay A. J., Jaffe T. R., Jonas
+J. L., 2012, MNRAS, 424, 2676
+Peel M. W., Genova-Santos R., Dickinson C., Leahy J. P., López-Caraballo
+C., Fernández-Torreiro M., Rubiño-Martín J. A., Spencer L. D., 2022,
+Research Notes of the American Astronomical Society, 6, 252
+Pietrobon D., et al., 2012, ApJ, 755, 69
+Pillepich A., Nelson D., Truong N., Weinberger R., Martin-Navarro I.,
+Springel V., Faber S. M., Hernquist L., 2021, MNRAS, 508, 4667
+Planck Collaboration et al., 2011, A&A, 536, A20
+Planck Collaboration et al., 2013, A&A, 554, A139
+Planck Collaboration et al., 2014a, A&A, 565, A103
+Planck Collaboration et al., 2014b, A&A, 571, A11
+Planck Collaboration et al., 2016a, A&A, 586, A141
+Planck Collaboration et al., 2016b, A&A, 594, A10
+Planck Collaboration et al., 2016c, A&A, 594, A25
+Planck Collaboration et al., 2016d, A&A, 594, A26
+Planck Collaboration et al., 2018, arXiv e-prints, p. arXiv:1807.06208
+Planck Collaboration et al., 2020a, A&A, 641, A1
+Planck Collaboration et al., 2020b, A&A, 641, A6
+Planck Collaboration et al., 2020c, A&A, 643, A42
+Plaszczynski S., Montier L., Levrier F., Tristram M., 2014, MNRAS, 439,
+4048
+Predehl P., et al., 2020, Nature, 588, 227
+Remazeilles M., Dickinson C., Banday A. J., Bigot-Sazy M. A., Ghosh T.,
+2015, MNRAS, 451, 4311
+Rubiño-Martín J. A., López-Caraballo C. H., Génova-Santos R., Rebolo R.,
+2012a, Advances in Astronomy, 2012, 351836
+Rubiño-Martín J. A., et al., 2012b, in Ground-based and Airborne Telescopes
+IV. p. 84442Y, doi:10.1117/12.926581
+Rubiño-Martín J. A., Guidi F., Génova Santos R. T., et al., 2023, MNRAS,
+accepted
+Sofue Y., 1977, A&A, 60, 327
+Sofue Y., 1994, ApJ, 431, L91
+Sofue Y., 2015, MNRAS, 447, 3824
+Su M., Slatyer T. R., Finkbeiner D. P., 2010, ApJ, 724, 1044
+Tristram M., Macías-Pérez J. F., Renault C., Santos D., 2005, MNRAS, 358,
+833
+Vidal M., Dickinson C., Davies R. D., Leahy J. P., 2015, MNRAS, 452, 656
+Vidal M., Leahy J. P., Dickinson C., 2016, MNRAS, 461, 698
+Yang H. Y. K., Ruszkowski M., Zweibel E. G., 2022, Nature Astronomy,
+Zhang R., Guo F., 2020, ApJ, 894, 117
+Zhang R., Guo F., 2021, arXiv e-prints, p. arXiv:2102.01710
+Zhang M., Li Z., Morris M. R., 2021, ApJ, 913, 68
+Zonca A., Singer L., Lenz D., Reinecke M., Rosset C., Hivon E., Gorski K.,
+2019, The Journal of Open Source Software, 4, 1298
+Zubovas K., Nayakshin S., 2012, MNRAS, 424, 666
+MNRAS 00, 1–31 (2023)
+
+22
+F. Guidi et al.
+APPENDIX A: INTENSITY AND POLARIZATION MAPS
+USED IN THE ANALYSIS
+Figs. A1, A2 and A3 show the I, Q and U maps that have been used
+for the first part of the study presented in this paper, which applies a
+template fitting technique (see Sect. 3.1) to the QUIJOTE, WMAP
+and Planck-LFI maps (results in Sect. 4.1 and 4.2).
+Fig. A4 shows the debiased polarization amplitude 𝑃MAS maps
+computed as described in Sect. 3.2 (Eq. 14), the corresponding
+uncertainties (centre) computed with Eq. 16 and accounting (in
+quadrature) for the calibration uncertainty, and the polarization an-
+gle (right). We show maps at the four frequencies that we selected to
+perform a study of the polarization spectral index analysis with T-T
+plots, which are, from top to bottom: S-PASS at 2.3 GHz, QUIJOTE
+11 GHz, WMAP K-band and Planck 30 GHz.
+Fig. A5 shows the Faraday rotation angle map at 2.3 GHz (left),
+and the corresponding uncertainty (centre), obtained from the ro-
+tation measure map derived from S-PASS data as 𝜙𝐹𝑅 = 𝑅𝑀 · 𝜆2
+(see Sect. B). The blank pixels are those where no 𝑅𝑀 is provided,
+and they are therefore excluded from the analysis. The same figure
+also shows, on the right, the S-PASS Faraday rotation corrected po-
+larization angle map, which is very similar to the polarization angle
+maps at higher frequencies shown in the right panels of Fig. A4.
+APPENDIX B: FARADAY ROTATION CORRECTION TO
+S-PASS
+Low frequency photons suffer the effect of Faraday rotation and
+depolarization along their path across a magnetized interstellar
+medium, before they reach the observer. Carretti et al. (2019), Ia-
+cobelli et al. (2014) and Fuskeland et al. (2019) discussed in detail
+these effects in the S-PASS data, which clearly shows depolarization
+in the Galactic plane, and rotation also at high Galactic latitudes.
+As we anticipated in Sect. 2.2, in this work we account for these
+effects by correcting the Faraday rotation and masking regions with
+evident depolarization.
+In order to correct for the Faraday rotation at 2.3 GHz, we
+applied a backwards rotation of the Q and U maps of S-PASS, by
+the Faraday rotation angle 𝜙𝐹𝑅 = 𝑅𝑀·𝜆2, where 𝑅𝑀 is the rotation
+measure map delivered by the S-PASS collaboration1 (Carretti et al.
+2019) and 𝜆 is the S-PASS observed wavelength. We produced an
+independent RM measurement using S-PASS, QUIJOTE, WMAP
+and Planck data. We obtained results that are consistent with the
+S-PASS RM map across the North and South Haze bubbles.
+The rotation is applied as follows:
+� 𝑄′
+𝑈′
+�
+=
+�
+cos(2𝜙𝑅𝑀)
+sin(2𝜙𝑅𝑀)
+− sin(2𝜙𝑅𝑀)
+cos(2𝜙𝑅𝑀)
+� � 𝑄
+𝑈
+�
+,
+(B1)
+where Q and U are the original S-PASS maps, and Q’ and U’ are the
+corrected ones.2 The final uncertainty of the Q’ and U’ maps is the
+propagation of the uncertainty of Q, U and 𝜙𝑅𝑀, through Eq. B1:
+𝜎2
+𝑄′ =𝜎2
+𝑄 cos2(2𝜙𝑅𝑀) + 𝜎2
+𝑈 sin2(2𝜙𝑅𝑀)
+(B2)
++ 4𝜎2
+𝜙𝑅𝑀 (𝑈 cos(2𝜙𝑅𝑀) − 𝑄 sin(2𝜙𝑅𝑀))2
+1 https://sites.google.com/inaf.it/spass/healpix-maps
+2 Note that, following what is now common practice in the CMB field, we
+apply the CMB convention for the polarization angle, while the S-PASS
+maps are delivered with the IAU convention. This inverts the sign of the
+U map, and therefore also rotates the polarization angle in the opposite
+direction relative to North.
+𝜎2
+𝑈′ =𝜎2
+𝑄 sin2(2𝜙𝑅𝑀) + 𝜎2
+𝑈 cos2(2𝜙𝑅𝑀)
+(B3)
++ 4𝜎2
+𝜙𝑅𝑀 (𝑈 sin(2𝜙𝑅𝑀) + 𝑄 cos(2𝜙𝑅𝑀))2.
+The pixels where no 𝑅𝑀 is provided are excluded from the analysis.
+This correction however is not sufficiently accurate at low Galactic
+latitudes where Faraday rotation angle could be larger than 90 deg,
+but our analysis is focused on the diffuse emission far from the
+Galactic plane, therefore this is not a critical issue for the stability
+of the results.
+We show in appendix A (Fig. A5) the Faraday rotation angle
+map at 2.3 GHz (left). The corresponding uncertainty is also shown
+in the same figure (centre), as well as the S-PASS polarization
+angle map after correcting for Faraday rotation (right). This last
+map can be compared with the polarization angle maps at higher
+frequencies (right panels in Fig. A4), showing that, after applying
+the correction, the spatial distribution of the S-PASS polarization
+angles is very similar to that of WMAP and Planck.
+APPENDIX C: NULL TESTS
+In order to characterize noise structures in the maps we used null-
+tests. In particular, the half-difference nulltest is the difference be-
+tween maps obtained from two independent splits selected by date
+of observation (see Rubiño-Martín et al. 2023). The half-difference
+maps are expected to show residual noise artifacts or systematics in
+the data. They are shown in Fig. C1, for intensity (first row), Stokes
+Q (second), Stokes U (third), polarization amplitude (fourth), at
+11 (left) and 13 GHz (right). It can be observed that residual noise
+structures are affecting the intensity maps at very large angular
+scales. However they are very smooth in the Haze region, and are
+not expected to affect the analysis. In polarization, especially in the
+P maps that are depicted with the same color scale as the polariza-
+tion residual maps in Fig. 9, no significant noise or systematics are
+observed, therefore the polarization results are expected to be very
+robust.
+APPENDIX D: POSTERIOR ANALYSIS OF THE T-T
+PLOTS
+Following the methodology presented in Sect. 3.2.2, in order to
+check the goodness of the linear regression of the T-T plots for
+each angle 𝛼𝑖, we compute the posterior distribution of the spectral
+index parameter 𝑃(𝛽). We noticed that in low signal-to-noise areas,
+the wings of the posterior distribution of the spectral index are not
+reaching zero, and therefore the determination of the spectral index
+is not appropriate, showing bias towards steep values. In order to
+be sure that the estimated 𝛽 is unbiased, we have to verify that the
+posterior of the T-T plots is well defined.
+We define the posterior of the slope between the data at fre-
+quency 𝜈 (y-axis data, with error 𝜎𝑦) and 𝜈0 (x-axis data, with error
+𝜎𝑥). It is:
+𝑃(𝑚(𝛽)) = 𝑁 · 𝑒−𝜒2/2,
+(D1)
+with 𝑁 being a normalization factor and 𝜒2 the chi-square of the
+linear regression:
+𝜒2 =
+∑︁
+𝑗
+(𝑦 𝑗 − 𝑚(𝛽) · 𝑥 𝑗 − 𝑞)2
+(𝜎2𝑦𝑗 + 𝑚2(𝛽) · 𝜎2𝑥𝑗 )
+,
+(D2)
+where 𝑗 runs over the pixels enclosed in the area selected for the T-T
+plots, and 𝑞 is the best-fit intercept for the given 𝑚 (𝑞 =< 𝑦−𝑚𝑥 >).
+MNRAS 00, 1–31 (2023)
+
+The Haze as seen by QUIJOTE
+23
+Figure A1. Intensity maps ordered in frequency: QUIJOTE 11 GHz, QUIJOTE 13 GHz, WMAP K-band, Planck 30 GHz, WMAP Ka-band, WMAP Q-band,
+Planck 44 GHz, WMAP V-band, Planck 70 GHz. The maps are in units of mK Rayleigh-Jeans, and the colorbar range values are scaled with a synchrotron-like
+power-law: 1.5 · (𝜈/11 GHz)𝛽, with 𝛽 = −3. The grey area represents the mask that is used for the analysis, which is a combination of the QUIJOTE sky
+coverage with the free-free and CMB mask, as described in Sect. 3.1.1.
+The slope 𝑚 is related with the spectral index 𝛽, so we can find the
+posterior of the spectral index by converting 𝑚 into 𝛽 with Eq. 12.
+Given that we solve a linear regression for a set of 18 angles 𝛼,
+we can compute a posterior distribution 𝑃(𝛽) = 𝑃(𝛽𝑖) for each
+of them. The final posterior is then the product 𝑃tot = �
+𝑖 𝑃(𝛽𝑖),
+whose maximum should coincide with the 𝛽 in Eq. 18.
+We show here the plots of the estimated spectral indices as
+a function of the projection angle 𝛼, and the relative posterior
+distributions. In Fig. D1 we show the results for Planck 30 GHz-
+WMAP K-band, in Fig. D2 for QUIJOTE 11 GHz-WMAP K-band,
+and in Fig. D3 for the Faraday rotation corrected (Sect. B) S-PASS
+2.3 GHz-WMAP K-band.
+The weighted average of the spectral indices, which is repre-
+sented as an horizontal black line in the 𝛽 vs 𝛼 figures, correspond
+to the final results of this work, which are shown in Fig. 11 and
+quoted in Table 6. Colour corrections are applied independently for
+the determination of the spectral index at each angle 𝛼.
+In the plots of the posteriors, each coloured line represents the
+posterior for a determined projection angle 𝛼, normalized with its
+maximum and computed with Eq. D1. Here no colour corrections
+are applied. The red thick line in the plots shows the final posterior
+normalized with its maximum, obtained as the product of each
+single posterior distribution. The vertical blue line shows the final
+spectral index computed with Eq. 18, with no colour corrections
+applied. We can notice that there is a very good match between
+the final posterior distribution and the estimated weighted average
+spectral index. When we apply colour correction to the spectral
+index, we obtain the value represented by the vertical black line in
+the posterior figures, which corresponds to the horizontal black line
+of the 𝛽 vs 𝛼 figures.
+We can see from Fig. D1-D3 that the posterior distributions
+of the spectral indices in all the regions and frequencies are closed
+and approximately Gaussian, and that therefore the spectral indices
+are well constrained. In addition, we can observe that, when we
+use the low frequency data such as QUIJOTE 11 GHz and S-PASS
+2.3 GHz, the posteriors are narrower than that of Planck 30 GHz,
+thanks to the wider frequency lever with respect to WMAP K-band,
+which leads to a more precise determination of the spectral index at
+low frequency.
+This paper has been typeset from a TEX/LATEX file prepared by the author.
+MNRAS 00, 1–31 (2023)
+
+ImapQJT11
+-1.50
+T,[mKRj]
+1.50I map QJT13
+-0.91
+Tb [mKR]]
+0.91mapWMAPK
+-0.17
+Tb [mKR]]
+0.17mapPLA30
+-0.09
+Tb [mKR]]
+0.09mapWMAPKa
+-0.06
+Tb [mKR]]
+0.06mapWMAPQ
+-0.03
+Tb [mKR]]
+0.03mapPLA44
+-0.02
+Tb [mKR]]
+0.02mapWMAPy
+-0.01
+T,[mKR]]
+0.01mapPLA70
+-0.01
+Tb [mKR]]
+0.0124
+F. Guidi et al.
+Figure A2. Same as in Fig. A1 for Stokes 𝑄 maps.
+Figure A3. Same as in Fig. A1 for Stokes 𝑈 maps.
+MNRAS 00, 1–31 (2023)
+
+Q map QJT11
+-1.50
+T,[mKRj]
+1.50Q map QJT13
+-0.91
+T,[mKR]]
+0.91Q map WMAPK
+-0.17
+T,[mKRj]
+0.17Q map PLA30
+-0.09
+T,[mKRj]
+0.09Q map WMAPKa
+-0.06
+T,[mKRj]
+0.06Q map WMAPQ
+-0.03
+Tp [mKR]]
+0.03Q map PLA44
+-0.02
+Tb [mKR]]
+0.02Q map WMAPV
+-0.01
+T,[mKRj]
+0.01Q map PLA70
+-0.01
+T,[mKRj]
+0.01U map QJT11
+-1.50
+T,[mKR]]
+1.50U map QJT13
+-0.91
+T,[mKR]]
+0.91UmapWMAPK
+-0.17
+T,[mKR]]
+0.17UmapPLA30
+-0.09
+T,[mKR]]
+0.09JmapWMAPKa
+-0.06
+Tb [mKR]]
+0.06JmapWMAPQ
+-0.03
+T,[mKRj]
+0.03UmapPLA44
+-0.02
+T,[mKR]]
+0.02UmapWMAPy
+-0.01
+T,[mKR]]
+0.01UmapPLA70
+-0.01
+T,[mKRj]
+0.01The Haze as seen by QUIJOTE
+25
+Figure A4. Debiased 𝑃 maps (left), corresponding error maps including calibration uncertainty (centre), and polarization angle (right) of S-PASS at 2.3 GHz,
+QUIJOTE at 11 GHz, WMAP at 23 GHz, and Planck at 30 GHz.
+Figure A5. S-PASS Faraday rotation angle (left) and uncertainty (centre), in units of degrees, and following the CMB convention on polarization angles. The
+right panel shows the S-PASS polarization angle map after correcting the Faraday rotation.
+MNRAS 00, 1–31 (2023)
+
+SPASS 2.3GHZ
+0.00
+T,[mKR]]
+98.02Op SPASS 2.3GHz
+0.000
+T,[mKRj]
+9.413Polarization angle SPASS 2.3GHz
+-90.00
+α [deg]
+90.00QJT 11GHz
+0.00
+T, [mKRj]
+0.75Op QJT 11GHz
+0.000
+Tb [mKR]
+0.084Polarization angle QJT 11GHz
+-90.00
+α[deg]
+90.00WMAP 23GHz
+0.00
+T,[mKR]]
+0.080p WMAP 23GHz
+0.000
+T, [mKr]]
+0.010Polarization angle WMAP 23GHz
+-90.00
+α[deg]
+90.00Planck 30GHz
+0.00
+T,[mKR]]
+0.04op PIanck 30GHz
+0.000
+T,[mKr]
+0.005Polarization angle Planck 3oGHz
+-90.00
+α[deg]
+90.00Faraday Rotation Angle SPASs
+-96.0
+ΦRM [deg]
+96.5ErrorFaradayRotationAngle SPASs
+0.0
+Oprm [deg]
+26.4Polarization angle SPASS 2.3GHz
+-90.00
+α [deg]
+90.0026
+F. Guidi et al.
+Figure C1. Nulltest of the intensity (first row), Stokes-Q (second), Stokes-U (third), and polarization amplitude (forth) maps obtained from the half-difference
+nulltest (see Rubiño-Martín et al. 2023), of the 11 GHz (left) and 13 GHz (right) QUIJOTE-MFI nominal plus Haze and 𝜌-Ophiuchi raster maps. For comparison
+purposes, the colour scale is the same as in Fig. 6 for intensity, and of Fig. 9 for polarization.
+MNRAS 00, 1–31 (2023)
+
+Half null-test D) QlT11.0
+-2.00
+T,[mKRJ]
+2.00Half null-test () QJT13.0
+-1.21
+T,[mKR]]
+1.21Half null-test (Q) QlT11.0
+-0.20
+T,[mKRJ]
+0.20Half null-test (Q) QJT13.0
+-0.12
+Tb[mKR]
+0.12Half null-test (U) Q111.0
+-0.20
+T, [mKR]]
+0.20Half null-test (U) Ql113.0
+-0.12
+T,[mKR]
+0.12Half null-test (P) QlT11.0
+0.00
+T,[mKR]]
+0.50Half null-test (P) QJT13.0
+0.00
+T,[mKRj]
+0.30The Haze as seen by QUIJOTE
+27
+Figure D1. Validation of T-T plots of Planck 30 GHz-WMAP K-band for different regions, showing the spectral index 𝛽 as a function of the projection angle
+(odd rows) and the posterior distributions for each projection angle (even rows). The black lines and shaded area show the final estimated spectral index 𝛽
+±1𝜎 uncertainty with colour corrections applied, while the dark blue lines and shaded area represent the estimated spectral index 𝛽 ±1𝜎 uncertainty before
+applying colour corrections.
+MNRAS 00, 1–31 (2023)
+
+Planck30GHz.WMAP23:
+NPS
+-3.05
+-3.10
+B
+-3.15
+<β>=-3.11±0.04
+1g min(err)
+-3.20
+1g
+0
+20
+40
+60
+80
+α [deg]Planck 30GHz,WMAP23
+ExtHazeFilament
+-2.40
+-2.60
+-2.80
+B -3.00
+-3.20
+<β>=-2.99±0.19
+1g min(err)
+-3.40
+1g
+0
+20
+40
+60
+80
+α [deg]Planck 30GHz, WMAP23:
+HazeFilament
+-2.30
+<β>=-2.66±0.18
+lo min(err)
+-2.40
+1g
+-2.50
+B
+-2.60
+-2.70
+-2.80
+-2.90
+0
+20
+40
+09
+80
+α [deg]Posterior Planck 30GHz, WMAP 23GHz:
+NPS
+1.0
+α= 0.
+α= 55
+α= 5.
+α= 59
+ Posterior
+0.8
+α= 10
+α= 65
+α= 14
+α= 70
+α=20
+α= 75
+0.6
+α= 25
+α= 80
+Normalized 
+α= 29
+α= 85
+α=35
+β CC
+0.4
+α=40
+β no CC
+α= 45
+Ptot
+0.2
+α= 50
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosteriorPlanck30GHz.WMAP23GHz
+Ext Haze Filament
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior Planck 30GHz, WMAP 23GHz:
+HazeFilament
+1.0
+Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPlanck 30GHz,WMAP23:
+Int Haze Filament
+-2.00
+B -2.50
+<β>=-2.17±0.31
+-3.00
+1o min(err)
+1g
+-3.50
+0
+20
+40
+60
+80
+α [deg]Planck 30GHz,WMAP23
+NorthHazeBubble
+<β>=-2.54±0.14
+-2.20
+1o min(err)
+1g
+-2.40
+B
+-2.60
+-2.80
+0
+20
+40
+60
+80
+α [deg]Planck 30GHz, WMAP23
+GCS
+-2.20
+<β > =-2.77±0.25
+-2.40
+lo min(err)
+1g
+-2.60
+B -2.80
+-3.00
+-3.20
+-3.40
+0
+20
+40
+60
+80
+α [deg]Posterior Planck 30GHz, WMAP 23GHz:
+Int Haze Filament
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosteriorPlanck30GHz.WMAP23GHz
+NorthHazeBubble
+1.0
+Posterior
+0.8
+0.6
+Normalized F
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior Planck 30GHz, WMAP 23GHz
+GCS
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+β28
+F. Guidi et al.
+Figure D1 – continued
+MNRAS 00, 1–31 (2023)
+
+Planck30GHz,WMAP23:
+RectangleSouthHaze
+-2.65
+-2.70
+-2.75
+-2.85
+<β>=-2.79±0.06
+1g min(err)
+-2.90
+1g
+0
+20
+40
+60
+80
+α [deg]Planck 30GHz,WMAP23:
+QJTRectangleSouthHaze
+<β>=-2.77±0.15
+-2.40
+1g min(err)
+1g
+-2.60
+B
+-2.80
+-3.00
+0
+20
+40
+60
+80
+α [deg]Planck 30GHz,WMAP23
+SouthHazeBubble
+<β> =-2.82±0.13
+2.50
+lg min(err)
+-2.60
+1g
+m -2.70
+-2.80
+-2.90
+-3.00
+0
+20
+40
+60
+80
+α [deg]PosteriorPlanck30GHz,WMAP23GHz
+RectangleSouthHaze
+1.0
+Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+BPosteriorPlanck30GHz.WMAP23GHz
+QlTRectangleSouthHaze
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior Planck 30GHz, WMAP 23GHz:
+SouthHazeBubble
+1.0
+Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPlanck 30GHz,WMAP23:
+eRositaWest
+-1.60
+-1.80
+-2.00
+-2.40
+<β>=-2.16±0.22
+1g min(err)
+-2.60
+1g
+0
+20
+40
+60
+80
+α [deg]Planck 30GHz,WMAP23:
+eRositaEast
+-2.25
+-2.50
+-2.75
+Bβ -3.00
+-3.25
+<β> =-2.83±0.33
+1o min(err)
+-3.50
+1g
+0
+20
+40
+60
+80
+α [deg]Planck 30GHz, WMAP23:
+Region 12
+2.00
+<β>=-2.74±0.34
+-2.25
+1o min(err)
+1g
+-2.50
+B -2.75
+-3.00
+-3.25
+-3.50
+0
+20
+40
+60
+80
+α [deg]Posterior Planck 30GHz, WMAP 23GHz:
+eRositaWest
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior Planck 30GHz, WMAP 23GHz:
+eRosita East
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior Planck 30GHz, WMAP 23GHz
+Region 12
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βThe Haze as seen by QUIJOTE
+29
+Figure D2. Same as in Fig. D1 for QUIJOTE 11 GHz-WMAP K-band.
+MNRAS 00, 1–31 (2023)
+
+QJT 11GHZ, WMAP23
+NPS
+-3.00
+-3.05
+B -3.10
+<β>=-3.06±0.05
+-3.15
+lo min(err)
+1g
+0
+20
+40
+60
+80
+α [deg]QJT11GHz,WMAP23:
+Ext Haze Filament
+-3.20
+-3.30
+B
+-3.40
+<β> =-3.25±0.06
+1g min(err)
+1g
+-3.50
+0
+20
+40
+60
+80
+α [deg]QJT 11GHz, WMAP23
+Haze Filament
+-3.00
+-3.10
+B -3.20
+<β>=-3.10±0.12
+-3.30
+lg min(err)
+1g
+-3.40
+0
+20
+40
+60
+80
+α [deg]Posterior QJT 11GHz,WMAP 23GHz:
+NPS
+1.0
+α=0.
+α= 55
+α= 5.
+α= 59
+Posterior
+0.8
+α= 10
+α= 65
+α= 14
+α= 70
+α=20
+α= 75
+0.6
+α=25
+α= 80
+Normalized
+α= 29
+α= 85
+α= 35
+β CC
+0.4
+α= 40
+β no CC
+α=45
+Ptot
+α=50
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior QJT 11GHz,WMAP 23GHz
+ExtHazeFilament
+1.0
+Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior QJT 11GHz,WMAP 23GHz
+Haze Filament
+1.0
+Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βQJT11GHz,WMAP23:
+North Haze Bubble
+-3.00
+-3.20
+B -3.40
+-3.60
+<β>=-3.24±0.25
+1o min(err)
+-3.80
+1g
+0
+20
+40
+60
+80
+α [deg]QJT 11GHZ, WMAP23
+GCS
+-3.20
+<β>=-3.40±0.08
+lg min(err)
+-3.30
+1g
+B -3.40
+-3.50
+0
+20
+40
+60
+80
+α [deg]QJT11GHz,WMAP23:
+QJTRectangle SouthHaze
+-3.00
+-3.20
+-3.40
+B
+-3.60
+-3.80
+<β>=-3.50±0.36
+1g min(err)
+-4.00
+1g
+0
+20
+40
+60
+80
+α [deg]Posterior QJT11GHz,WMAP 23GHz:
+NorthHazeBubble
+1.0
+IPosterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior QJT 11GHz,WMAP 23GHz
+GCS
+1.0
+I Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior QJT 11GHz,WMAP 23GHz
+QjTRectangleSouthHaze
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βQJT11GHz,WMAP23:
+eRosita West
+<β>=-3.79±0.13
+-3.50
+lg min(err)
+-3.60
+1g
+m -3.70
+-3.80
+-3.90
+-4.00
+0
+20
+40
+60
+80
+α [deg]QJT11GHz,WMAP23
+Region 12
+-3.00
+-3.20
+B
+-3.40
+<β>=-3.29±0.16
+lg min(err)
+-3.60
+1g
+0
+20
+40
+60
+80
+α[deg]Posterior QJT 11GHz,WMAP 23GHz
+eRositaWest
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior QJT 11GHz,WMAP 23GHz
+Region 12
+1.0
+Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+β30
+F. Guidi et al.
+Figure D3. Same as in Fig. D1 for S-PASS 2.3 GHz-WMAP K-band.
+MNRAS 00, 1–31 (2023)
+
+SPASS2.3GHZ,WMAP23:
+HazeFilament
+-2.85
+-2.90
+-2.95
+B
+-3.00
+<β>=-3.01±0.08
+-3.05
+1g min(err)
+-3.10
+1g
+0
+20
+40
+60
+80
+α [deg]SPASS 2.3GHZ, WMAP23:
+Int Haze Filament
+0.00
+<β>=-3.01±0.21
+1g min(err)
+-1.00
+1g
+B
+-2.00
+-3.00
+0
+20
+40
+60
+80
+α [deg]SPASS2.3GHZ,WMAP23:
+NorthHazeBubble
+-3.16
+<β> =-3.22±0.03
+-3.18
+1o min(err)
+1g
+-3.20
+B -3.22
+-3.24
+-3.26
+-3.28
+0
+20
+40
+60
+80
+α[deg]Haze Filament
+1.0
+α=0.
+α= 55
+α= 5.
+α= 59
+Posterior
+0.8
+α=10
+α=65
+α= 14
+α= 70
+α=20
+α= 75
+0.6
+α=25
+α= 80
+Normalized I
+α= 29
+α= 85
+α= 35
+β CC
+0.4
+α=40
+β no CC
+α= 45
+Ptot
+α= 50
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosteriorSPASS 2.3GHz,WMAP 23GHz:
+ntHazeFilament
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior SPASS 2.3GHz, WMAP 23GHz:
+NorthHazeBubble
+1.0
+I Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βSPASS2.3GHZ,WMAP23:
+GCS
+-3.05
+-3.10
+B
+-3.15
+<β>=-3.09±0.05
+1g min(err)
+-3.20
+1g
+0
+20
+40
+60
+80
+α [deg]SPASS2.3GHZ,WMAP23
+RectangleSouthHaze
+-3.10
+m -3.12
+<β>=-3.12±0.02
+-3.14
+1g min(err)
+1g
+0
+20
+40
+60
+80
+α [deg]SPASS2.3GHZ,WMAP23:
+QjTRectangleSouthHaze
+-3.05
+-3.10
+B
+-3.15
+<β>=-3.10±0.04
+1g min(err)
+-3.20
+1g
+0
+20
+40
+60
+80
+α [deg]Posterior SPASS 2.3GHz, WMAP 23GHz:
+GCS
+1.0
+I Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0PosteriorSPASS2.3GHz,WMAP23GHz
+RectangleSouthHaze
+1.0
+I Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0Posterior SPASS 2.3GHz, WMAP 23GHz
+QJTRectangleSouthHaze
+1.0
+I Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βSPASS 2.3GHZ, WMAP23
+SouthHazeBubble
+-3.05
+-3.10
+-3.15
+<β> =-3.11±0.06
+-3.20
+1o min(err)
+1g
+0
+20
+40
+09
+80
+α [deg]SPASS2.3GHZ,WMAP23
+SouthHazeBubbleclean
+-3.05
+-3.10
+-3.15
+<β>=-3.10±0.07
+-3.20
+1g min(err)
+1g
+-3.25
+0
+20
+40
+60
+80
+α [deg]Posterior SPASS 2.3GHz, WMAP 23GHz
+SouthHazeBubble
+1.0
+I Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosteriorSPASS2.3GHz.WMAP23GHz:
+SouthHazeBubbleclean
+1.0
+I Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βThe Haze as seen by QUIJOTE
+31
+Figure D3 – continued
+MNRAS 00, 1–31 (2023)
+
+SPASS 2.3GHz, WMAP23:
+eRosita West
+-3.35
+m -3.40
+<β>=-3.36±0.03
+-3.45
+1o min(err)
+1g
+0
+20
+40
+60
+80
+α [deg]SPASS2.3GHZ,WMAP23:
+eRositaEast
+-3.20
+-3.25
+B
+-3.30
+<β>=-3.28±0.04
+-3.35
+1g min(err)
+1g
+0
+20
+40
+60
+80
+α [deg]SPASS 2.3GHz, WMAP23:
+Region 12
+-3.20
+-3.40
+B
+-3.60
+<β>=-3.28±0.18
+-3.80
+1g min(err)
+1g
+-4.00
+0
+20
+40
+60
+80
+α [deg]Posterior SPASS 2.3GHz, WMAP 23GHz:
+eRositaWest
+1.0
+I Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior SPASS 2.3GHz, WMAP 23GHz
+eRosita East
+1.0
+I Posterior
+0.8
+0.6
+Normalized
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+βPosterior SPASS 2.3GHz, WMAP 23GHz:
+Region 12
+1.0
+Normalized Posterior
+0.8
+0.6
+0.4
+0.2
+0.0
+-4.0
+-3.5
+-3.0
+-2.5
+-2.0
+β
\ No newline at end of file
diff --git a/GtE4T4oBgHgl3EQfgQ2M/content/tmp_files/load_file.txt b/GtE4T4oBgHgl3EQfgQ2M/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a66b057e8bc6423b1c890a7b6a195697a0272b66
--- /dev/null
+++ b/GtE4T4oBgHgl3EQfgQ2M/content/tmp_files/load_file.txt
@@ -0,0 +1,3292 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf,len=3291
+page_content='MNRAS 00, 1–31 (2023)  Preprint 13 January 2023  Compiled using MNRAS LATEX style file v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  QUIJOTE scientific results – VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The Haze as seen by QUIJOTE  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi,1,2,3★ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Génova-Santos,1,2† J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Rubiño-Martín,1,2 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Peel,1,2  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Fernández-Torreiro,1,2 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' López-Caraballo,1,2 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Vignaga,1,2 E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' de la Hoz,4,5  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Vielva,4 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Watson,6 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Ashdown,7,8 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Dickinson,6 E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Artal,9 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Barreiro,4  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Casas,4 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Herranz,4 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Hoyland,1,2 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Lasenby,7,8 E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Martinez-Gonzalez,4  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Piccirillo,6 F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Poidevin,1,2 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Rebolo,1,2,10 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Ruiz-Granados,1,2,11 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Tramonte,12,13,1,2  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Vansyngel1,2  1Instituto de Astrofísica de Canarias, E-38200 La Laguna, Tenerife, Spain  2Departamento de Astrofísica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain  3Institut d’Astrophysique de Paris, UMR 7095, CNRS & Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France  4Instituto de Fisica de Cantabria (IFCA), CSIC-Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' de Cantabria, Avda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' los Castros, s/n, E-39005 Santander, Spain  5Dpto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' de Física Moderna, Universidad de Cantabria, Avda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' los Castros s/n, E-39005 Santander, Spain  6Jodrell Bank Centre for Astrophysics, Alan Turing Building, Department of Physics and Astronomy, School of Nature Sciences, University of Manchester,  Oxford Road, Manchester M13 9PL, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='K  7Astrophysics Group, Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK  8Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA  9Departamento de Ingenieria de COMunicaciones (DICOM), Edificio Ingenieria de Telecomunicacion, Plaza de la Ciencia s/n, E-39005 Santander, Spain  10Consejo Superior de Investigaciones Cientificas, E-28006 Madrid, Spain  11Departamento de Física.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Facultad de Ciencias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Universidad de Córdoba.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Campus de Rabanales, Edif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Planta Baja.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' E-14071 Córdoba, Spain  12Purple Mountain Observatory, CAS, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10 Yuanhua Road, Qixia District, Nanjing 210034, China  13NAOC-UKZN Computational Astrophysics Center (NUCAC), University of Kwazulu-Natal, Durban 4000, South Africa  Accepted XXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Received YYY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' in original form ZZZ  ABSTRACT  The Haze is an excess of microwave intensity emission surrounding the Galactic centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It  is spatially correlated with the 𝛾-ray Fermi bubbles, and with the S-PASS radio polarization  plumes, suggesting a possible common provenance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The models proposed to explain the origin  of the Haze, including energetic events at the Galactic centre and dark matter decay in the  Galactic halo, do not yet provide a clear physical interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In this paper we present a re-  analysis of the Haze including new observations from the Multi-Frequency Instrument (MFI)  of the Q-U-I Joint TEnerife (QUIJOTE) experiment, at 11 and 13 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We analyze the Haze in  intensity and polarization, characterizing its spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We detect an excess of diffuse intensity  signal ascribed to the Haze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The spectrum at frequencies 11 ≤ 𝜈 ≤ 70 GHz is a power-law with  spectral index 𝛽H = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08, which is flatter than the Galactic synchrotron in the same  region (𝛽S = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04), but steeper than that obtained from previous works (𝛽H ∼ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5 at  23 ≤ 𝜈 ≤ 70 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We also observe an excess of polarized signal in the QUIJOTE-MFI maps  in the Haze area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This is a first hint detection of polarized Haze, or a consequence of curvature  of the synchrotron spectrum in that area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Finally, we show that the spectrum of polarized  structures associated with Galactic centre activity is steep at low frequencies (𝛽 ∼ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 at  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 ≤ 𝜈 ≤ 23 GHz), and becomes flatter above 11 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Key words: diffuse radiation – Galaxy: centre – ISM: bubbles – cosmology: observations  1  INTRODUCTION  During the last decades multiple high sensitivity surveys have been  carried out in order to provide an accurate characterization of the  ★ E-mail: federica.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='guidi@iap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='fr  † E-mail: rgs@iac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='es  Galactic foregrounds at radio and microwave wavelengths, with  the final goal of doing cosmology with the Cosmic Microwave  Background (CMB;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The main target of the two satellite missions Wilkinson Microwave  Anisotropy Probe (WMAP;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2003) and Planck  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020a) was the CMB, which im-  © 2023 The Authors  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05115v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='HE]  12 Jan 2023  2  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  plied the generation of full sky images of the Galactic emission at  multiple frequencies, between 23 and 857 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' These data provided  an accurate picture of the emission of our own Galaxy, and enabled  a number of discoveries, among them that of the microwave Haze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The Haze was discovered in the process of disentangling the  Galactic emission from the cosmological CMB signal using WMAP  data between 23 and 60 GHz by Finkbeiner (2004), and it was con-  firmed by further studies (Dobler & Finkbeiner 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Dobler 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Pietrobon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' During this  process, a diffuse and extended signal became evident in the residu-  als after removing all the already known emission mechanisms from  the WMAP frequency maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The microwave (or sometimes WMAP)  Haze is indeed an excess of diffuse emission with an elliptically  symmetric shape centred on the Galactic centre, extending towards  the north and the south of the Galactic plane and reaching high  Galactic latitudes |𝑏| ≈ 35◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The Haze has been measured to have a  relatively flat spectrum (𝛽 ≈ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5) at the lowest WMAP frequencies  compared to that of typical Galactic synchrotron emission at high  Galactic latitudes (𝛽 ≈ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The Planck Collaboration also detected the Haze excess  (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013) with an independent dataset be-  tween 30 and 70 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' They measured the spectrum of the South  Haze bubble using Planck and WMAP data, showing a synchrotron-  like power-law with a spectral index 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='56 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This spec-  trum is in agreement with what had been previously observed with  WMAP data alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The microwave Haze has a 𝛾-ray counterpart, the so-called  Fermi bubbles, which were discovered in the Fermi-LAT data at  energies 2–50 GeV (Dobler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Su et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The Fermi  bubbles are two extended 𝛾-ray lobes located at a position coin-  cident to that of the WMAP Haze, but with a larger extension in  Galactic latitude, reaching |𝑏| ≈ 50◦, and with a flat spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This  multi-wavelength correspondence confirmed the interpretation of  the microwave Haze as a real sky component and it was ascribed  to synchrotron emission of a young population of cosmic-ray elec-  trons (Dobler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Cosmic-ray electrons with energies 10–  100 GeV produce microwave synchrotron during their interaction  with a magnetic field, but also 𝛾-ray photons through Inverse Comp-  ton scattering (IC) with the Interstellar Radiation Field (ISRF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In addition, recent observations of the eRosita X-ray space tele-  scope (Merloni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012) detected a distinct but possibly related  structure: two circular and symmetric soft-X-ray (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 keV) bub-  bles, which extended up to high Galactic latitude |𝑏| ≈ 85◦ (Predehl  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The eRosita bubbles enclose the Fermi bubbles, and the  northern one partially overlaps with the North Polar Spur (NPS), a  large and polarized filament that emerges from the Galactic centre  and goes toward the north.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This spatial correlation points towards a  possible connection between the NPS and the Haze, which could be  generated by an explosive event in the Galactic centre (Sofue 1977,  1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Several works support this hypothesis by locating the NPS  at a distance of ∼10 kpc, which is comparable to the distance to the  Galactic centre (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Sofue 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Predehl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Kataoka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However this aspect is still controversial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' According with dif-  ferent works (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Panopoulou  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2021) the distance to the NPS is smaller than to the Galactic  centre, being of the order of ∼ 100–200 pc, identifying therefore the  NPS and the Haze as two different components, with respectively a  local and a Galactic centre origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The Haze, moreover, is not peculiar to our own Galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Li  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2019) reported the first detection of a Haze-like structure  in an external galaxy, using radio (C-band) and X-ray (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8–8 keV)  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The spectral index of this extra-galactic Haze is 𝛽 ≈ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1 at  radio wavelengths, which is typical for synchrotron emission, and  takes the slightly flatter value 𝛽 ≈ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8 in the joint fit of radio and  X-ray data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  It is well known that the synchrotron emission is polarized,  and to confirm that the Haze has a synchrotron origin it should  be possible to observe an associated polarized component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Such a  component was identified for the first time by the S-PASS southern  sky survey at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz, which detected two giant radio polarized  plumes extending from the centre of our Galaxy (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The plumes spatially correlate with the Fermi bubbles, with  the microwave Haze, and with X-ray structures observed by ROSAT  (Almy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013) that connect the plumes  with the centre of the Galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Interestingly, the radio polarized  plumes appear to be more extended than the Fermi bubbles, reaching  |𝑏| ≈ 60◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The radio polarized plumes can also be roughly identified in the  low frequency maps of Planck and WMAP, although the signal-to-  noise is not as good as in S-PASS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The combination of S-PASS and  WMAP data allowed the measurement of the spectral index of the  polarized emission between 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz and 23 GHz, which is 𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It should be noted that the spectral index is  significantly flatter in intensity than in polarization, making the in-  terpretation of the Haze/bubbles to be very puzzling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The difference  in the spectral index might suggest that the cosmic-ray electrons  that generate the intensity of the Haze and the polarization of the  plumes belong to two different electron populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Alternatively,  the superposition of different components along the line-of-sight  could explain the different spectral index in polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  A variety of scenarios have been proposed in order to explain  the possible origin of the Haze signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' One intriguing proposal is  that it is generated by secondary emission of dark matter particles  (Hooper et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Cholis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Dobler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Delahaye  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Gaskins 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Egorov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However the exis-  tence of 𝛾-ray bubbles with sharp edges (Su et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2010) and radio  polarized sharp filaments and plumes (Biermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Jones  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Crocker & Aharonian 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Planck  Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016c) contradict the dark matter hypothesis as  a complete explanation of this phenomenon, while energetic events  in the Galactic centre provide a much more likely scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Still, it  cannot be excluded that a small fraction of the Haze emission could  have a dark matter origin (Egorov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Other proposed progenitors for the Haze emission demand  energetic events in the Galactic centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' AGN activity of the super-  massive black hole in the centre of the Milky Way (SgrA*) (Zubovas  & Nayakshin 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guo & Mathews 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Ack-  ermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Fox et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Zhang & Guo 2020, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Pillepich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2022), nuclear activity in the  central Galactic region such as star-formation, star-bursts, or su-  pernovae explosions, which could power outflows of hot and mag-  netized plasma and accelerate cosmic rays (Crocker & Aharonian  2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Crocker 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Lacki 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2021), or more complex scenarios (Ashley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  A study from Crocker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2015) proposed a unified model for  the microwave Haze, radio plumes, and Fermi bubbles, as generated  by outflows powered by nuclear activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For the first time, this  model provided an explanation for the change of the spectral index  in the outer and inner part of the bubbles at microwave or radio  wavelengths, as suggested by observations (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  However, even if the scenarios proposed in the literature par-  tially explain some of the Haze characteristics, none of them provide  a complete description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' New observations are crucial for the under-  standing of the origin of the Haze, and independent determinations  MNRAS 00, 1–31 (2023)  The Haze as seen by QUIJOTE  3  Survey  Freq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  FWHM  𝜎c  Reference  [GHz]  [deg]  [%]  S-PASS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  5  Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2019)  QUIJOTE  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='93  5  Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2023)  QUIJOTE  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='9  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='92  5  Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2023)  WMAP K-band  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='88  3  Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013)  Planck-LFI  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54  3  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2020c)  WMAP Ka-band  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='66  3  Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013)  WMAP Q-band  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='51  3  Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013)  Planck-LFI  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='45  3  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2020c)  WMAP V-band  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='35  3  Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013)  Planck-LFI  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22  3  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2020c)  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Summary of the data that are used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We show central  frequencies, beam FWHMs and adopted calibration uncertainties (𝜎c) of  each survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  of the spectral index of the emission across the Haze area, as well  as polarization measurements, can yield a clearer picture of this  complex region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In this paper we provide new observational constraints on the  Haze microwave emission using data from the Multi-Frequency In-  strument of the Q-U-I Joint TEnerife experiment (Rubiño-Martín  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Hoyland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We performed a full reanalysis  of the Haze bubbles and filaments first reproducing, in an inde-  pendent manner, previous results obtained with WMAP (Dobler &  Finkbeiner 2008), Planck-LFI (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013),  and S-PASS (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013) data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Afterwards we included in  the analysis microwave data from QUIJOTE-MFI at 11 and 13 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In particular, we performed for the first time a component separa-  tion in polarization, searching for a polarized Haze component at  the QUIJOTE frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Note that there is a gap of available  data between 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz and 23 GHz, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz data are affected  by Faraday rotation and depolarization (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' QUI-  JOTE effectively extends the frequency coverage of WMAP and  Planck down to 11 GHz, where the signal is relatively strong and  not significantly affected by Faraday effects, providing robust spec-  tral measurements in intensity and polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The paper is organized as follows: we present the new QUI-  JOTE maps of the Haze and the ancillary data used for the analysis  in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2, we then describe the methodologies applied for this work  in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3, consisting of a template fitting component separation  described in Sec 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1, and a correlation T-T plots analysis in polar-  ization, as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Afterwards, in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4 we present  the results of the template fitting (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1 in intensity and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 in  polarization), and of the T-T plots in polarization (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Finally,  we summarize and we conclude in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 5 and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2  DATA  We describe here the dataset that is used in this work, which is com-  posed of the QUIJOTE-MFI data at 11 and 13 GHz (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1),  in combination with ancillary data (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2) from S-PASS  at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2019), WMAP at ∼23, 33, 41, 61 GHz  (Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013), and Planck-LFI at ∼30, 44, 70 GHz (Planck  Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A summary of the dataset can be found  in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  QUIJOTE-MFI data  QUIJOTE is a polarimetric ground-based CMB experiment located  at the Teide observatory (Tenerife, Spain), at 2400 m above sea level  (Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The MFI instrument of QUIJOTE  observes the sky of the Northern hemisphere at four frequency  bands in the range 10–20 GHz, and with an angular resolution of  ≈ 1◦ (Hoyland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The reference dataset for this paper is the survey of the full  northern sky performed with QUIJOTE-MFI (hereafter the wide-  survey).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This survey provides an average sensitivity in polarization  of ∼ 40–55 𝜇K deg−1 in the four bands centred around 11, 13, 17  and 19 GHz (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 in Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This paper  is part of the release that describes the survey and the associated  scientific results, concerning principally the characterization of dif-  fuse synchrotron radiation and Anomalous Microwave Emission  (AME).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A complete description of the wide survey can be found in  Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The QUIJOTE-MFI maps used in this work are a combination  of this wide-survey data with additional raster-scan observations  that were performed specifically around the Haze region in order  to improve the signal-to-noise ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' These raster scan observations  consisted of back-and-forth constant elevation scans of the telescope  performed with a scanning speed of 1 deg/s on the sky in the period  June 2013 – August 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In particular, four sky fields have been ob-  served, which we call the "HAZE", "HAZE2" and "HAZE3" fields,  as well as a sky patch enclosing the 𝜌-Ophiuchi cloud complex,1  covering, in total, a sky fraction 𝑓sky ∼ 5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The approximate cen-  tral coordinates of each raster scan field are indicated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2 and  in Table 2, where also their total observing time is reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Although we have produced the maps for all the QUIJOTE-  MFI channels, here we use only the 11 and 13 GHz frequency  maps from horn 3 (central frequencies 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1 and 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='9 GHz), which  have sufficiently good signal-to-noise for this analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Note that  there are some difficulties inherent to the observations, which are:  (1) the contamination of Radio Frequency Interference (RFI) from  geostationary satellites that requires the flagging of a declination  band with −10◦ ≲ 𝛿 ≲ −1◦;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2) the fact that elevation of the Haze  area from the Teide Observatory (geographical latitude +28◦) is very  low (𝑒𝑙 ≲ 35◦), so all the observations are taken looking through a  large air-mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Point (2) is the main reason why the two additional  QUIJOTE maps at 17 and 19 GHz are not used here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The maps are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 1, where we present the I, Q, and U  maps at the original angular resolution and pixel size (𝑁side = 512 in  the HEALPix2 pixelization scheme;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Górski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The maps  have been generated with the PICASSO map-making code, which  was implemented for the construction of maps from the QUIJOTE-  MFI data (Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The maps have been obtained with a  single run of PICASSO, combining simultaneously the wide-survey  data and the additional raster observations with an efficient sub-  traction of the correlated 1/ 𝑓 noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The parameters adopted for  this run (priors on noise properties, baseline length, etc) are iden-  tical to those used for the wide survey (see details in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 of  Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2 we show the statistical white noise level (𝜎) of the  11 GHz map in intensity, computed from the propagation of the  weights in the TOD through the map-making procedure, and with  pixel resolution 𝑁side = 512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The location of the raster observa-  tions can be seen as the bluish regions at the center of these maps,  corresponding to a decrease of 𝜎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The raster scan data result in  1 𝜌-Ophiuchi observations had a different scientific goal, specifically the  study of this specific cloud complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, since they lie nearby the  Haze fields, we included them in this analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2 https://sourceforge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='net/projects/healpix/  MNRAS 00, 1–31 (2023)  4  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' I, Q, and U maps from QUIJOTE-MFI at 11 GHz (top) and 13 GHz (bottom) at the original angular resolution and pixel size (𝑁side = 512).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The  maps are mollweide projections and in Galactic coordinates, with the centre of the projection at (𝑙, 𝑏) = (0◦, 0◦), and with longitude increasing to the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Colour scales are linear and grey represents missing data or regions contaminated by RFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The data used to generate these maps combine the wide-survey and  the dedicated raster scan observations described in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Uncertainty (𝜎) of the Intensity map from QUIJOTE at 11 GHz,  at the original angular resolution and pixel size (𝑁side = 512;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' the uncertainty  distribution is similar for Q and U, and at 13 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The location of the three  fields observed with raster-scans are indicated in the maps (see Table 2), as  well as the position of “a” and “b” where noise estimates are provided (see  Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  an improvement of the noise level with respect to the wide-survey  data alone in two specific areas: in the Galactic centre region (with  “HAZE” and “HAZE2”, around the location identified by “a” in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2), and in the proximity of the NPS (with “HAZE3”, around  “b” in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We report in Table 3 the typical noise levels of the  new QUIJOTE maps in a 1◦ FWHM beam, including wide-survey  and raster data, and we compare these values with the noise lev-  els achieved with wide-survey data alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The numbers have been  obtained by computing the median value of the uncertainty maps  within circles with a radius of 5◦, centred in two different positions:  close to the Galactic centre at (𝑙, 𝑏) = (5◦, 0◦) (a), and in the  proximity of the NPS at (𝑙, 𝑏) = (40◦, 20◦) (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We observe that  the raster scan data improve the noise level, both in intensity and  polarization, by a factor ∼ 3 in the Galactic centre, and by ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  in the NPS region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The 𝜎-maps are scaled-up by a multiplicative  factor obtained from the QUIJOTE weight maps (𝜎 = 1/√𝑤) that  accounts for the 1/ 𝑓 noise contribution, which is characterized by  the half-mission wide-survey null-test, as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1 of  Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The factors are: 𝑓 = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='214 (I), 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='333  (Q), 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='335 (U) at 11 GHz, and 𝑓 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='682 (I), 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='320 (Q), 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='321 (U)  at 13 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Finally, given the integration time in the same area,  we found that the estimated global noise level correspond to an  instantaneous sensitivity of ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='42–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='44 mK√s in intensity, and  ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='14 mK√s in polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In the analysis presented in this paper, we use the QUIJOTE-  MFI maps convolved to 1◦ angular resolution with the window  function of QUIJOTE-MFI (Génova-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', in preparation),  and degraded to 𝑁side = 64 (pixel resolution ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='9◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In order to  obtain uncertainty maps at this resolution, we performed 100 white  noise realizations, whose amplitude is given by the 𝜎 maps pre-  sented above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We applied the same smoothing and degradation of  the data to the noise simulations, and we computed the standard de-  viation of the noise realizations to obtain a smoothed and degraded  variance map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We also tested different methodologies to determine  the variance maps, accounting for 1/ 𝑓 noise correlation at large an-  gular scales, and we obtained no significant differences in the final  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Finally, the noise of the 11 GHz and 13 GHz maps of QUI-  JOTE is partially correlated between the frequency channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The  correlation of the noise in intensity is 𝜌 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='76 and in polarization  it is 𝜌 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='35 (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 in Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We ac-  count for this correlation in this work, and for an overall calibration  uncertainty of 5 % (for more details see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 5 of Rubiño-Martín  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2023 and Génova-Santos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', in preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  Ancillary data  We use as ancillary data the WMAP 9-year maps (Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2013) in the K, Ka, Q and V bands (central frequencies 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8, 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0,  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7 and 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7 GHz) and the NPIPE Planck-LFI maps (Planck Col-  laboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020c), at 30, 44 and 70 GHz (central frequencies  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4, 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1, and 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In addition, for the analysis in polariza-  MNRAS 00, 1–31 (2023)  11 GHz ()  mKcMB  2011GHz (Q)  mKcMB  211GHz (U)  mKcMB  213GHz (D  mKcMB  2013 GHz (Q)  mKcMB  213 GHz (U)  mKcMB  2o11GHz(  HAZE2  d  HAZE3  Oph  a  HAZE  mKcMB  0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5The Haze as seen by QUIJOTE  5  HAZE  HAZE 2  HAZE 3  𝜌-Ophiuchi  (𝑙, 𝑏)  (16◦, 2◦)  (352◦, 22◦)  (37◦, 13◦)  (352◦, 16◦)  Δ𝑎𝑧  47◦  33◦  86◦  18◦  𝑒𝑙  30◦– 40◦  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5◦, 36◦, 37◦  39◦, 62◦  32◦, 33◦, 37◦  Time [h]  742.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  494.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  258.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' General characteristics of the raster scan observations for the four  fields used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We report the central coordinates of the fields (in  Galactic coordinates), the typical length of the azimuth rasters, the approx-  imate elevation at which they were taken, and the total number of hours of  the observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Map  Area  11 GHz [𝜇𝐾CMB/1◦]  13 GHz [𝜇𝐾CMB/1◦]  𝐼  𝑄  𝑈  𝐼  𝑄  𝑈  Rasters +  wide-survey  a  47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7  b  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  wide-survey  a  145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='9  140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  b  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Noise level of the QUIJOTE maps of the rasters plus wide-survey  data (top two lines), and of the wide-survey data alone (bottom two lines), in  a 1◦-FWHM beam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This is obtained as the median of the uncertainty maps  (shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2), computed within a 5◦ radius circle centred in two different  positions: close to the Galactic centre (a) at (𝑙, 𝑏) = (5◦, 0◦), and in the  proximity of the NPS (b) at (𝑙, 𝑏) = (40◦, 20◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  tion, we include the S-PASS data (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2019) at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  As in previous works (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2011, 2014a), in  order to take into account the uncertainty due to, for example, beam  asymmetries and colour corrections, we adopt a calibration uncer-  tainty of 3% in WMAP and in Planck-LFI, and of 5% in S-PASS  (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We summarize the main data parameters in  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  All the maps are smoothed to the common angular resolution  of 1◦, and degraded to 𝑁side = 64, which corresponds to a pixel  size of ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='9◦ and prevents noise pixel-to-pixel correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For  the computation of spectral indices we apply colour corrections by  using the python code fastcc presented in Peel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2022), which  includes colour correction models for different datasets including  QUIJOTE-MFI, Planck, and WMAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' No colour correction for S-  PASS data is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3  A collection of figures representing the full dataset is shown  in appendix A (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A1, A2 and A3 for, respectively, 𝐼, 𝑄 and 𝑈).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A4 we also show the debiased polarization amplitude maps  (𝑃MAS, given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 14) at some selected frequencies: S-PASS at  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz, QUIJOTE 11 GHz, WMAP K-band and Planck 30 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  From a quick visual inspection of the polarization amplitude and  polarization angle maps in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A4, we can see that, while the QUI-  JOTE, WMAP and Planck maps show very high similarity in the  synchrotron polarized structures and angles, at the S-PASS fre-  quency there is evident depolarization in the Galactic plane, up to  |𝑏| ≈ 15 deg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We can also see a rotation of the polarization angle  up to high Galactic latitudes, which is produced by Faraday rotation  along the line-of-sight (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Iacobelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Faraday rotation is important at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz in some of the regions that  are studied in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We therefore correct the S-PASS maps for  Faraday rotation as described in appendix B, and shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  QUIJOTE, WMAP and Planck data are not corrected for Faraday  rotation, since the effect in the regions we are studying is expected  3 S-PASS uses a spectral back-end which allows to flatten the bandpass and  to reduce the necessary colour correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Selected regions for the analysis overlaid on the WMAP K-band  polarization amplitude map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The regions are listed and described in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  to be negligible at these frequencies, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', within the uncertainty of  the calibration angle (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Hutschenreuter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2022 and Vidal  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2015, where Faraday rotation is shown to be lower than 1◦ in  WMAP, everywhere except in the Galactic centre).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  For the subsequent analysis, in order to assign uncertainties to  the data, we use uncertainty maps at the same angular and pixel res-  olution as for the maps (𝑁side = 64 and 1◦ resolution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The variance  maps are generated with Monte Carlo realizations, as described in  more detail in Peel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (in preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3  Selection of the regions  We identified thirteen regions of particular interest for the study of  the Haze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Six of them are within the footprint of our QUIJOTE map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  They are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3 and are listed and described in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We  use the numbering in the table to identify specific regions throughout  this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Regions 7 and 8 have been selected in order to reproduce the  analysis of the diffuse Haze in intensity presented in Dobler &  Finkbeiner (2008);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We extend  the same analysis including QUIJOTE data, using for the first time  also polarization data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Region 3 has been used in order to reproduce the result by  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2016c), who measured the polarization  spectral index of the filament.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We repeated here the analysis also  using QUIJOTE data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We also define as regions 2 and 4 two features  of diffuse emission extending, respectively, outside and inside the  border of region 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Regions 5, 9 and 10 have been defined to identify the polarized  radio plumes observed by S-PASS (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013), in order to  carry out a spectral index analysis using QUIJOTE and ancillary  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Region 6 is the Galactic Centre Spur (GCS, Vidal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2015),  which is a very bright polarized feature connected to the Galactic  Center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Its relation with the Haze is still unclear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Regions 11 and 13 have been identified as the borders of the  eROSITA bubbles (Predehl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020), and have been used for a  spectral index analysis using QUIJOTE and ancillary data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Region 12 is defined as an area with some faint diffuse po-  larized emission with unknown origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It was identified during the  analysis of the polarization template fitting residuals (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Finally, region 0 is the sky observed by each survey, after  MNRAS 00, 1–31 (2023)  G353-34  Tb [mKr]]  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='086  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Region  Description  Coordinates  Reference  0  High-latitudes sky observed by each survey  1  North Polar Spur (NPS)  (𝑙, 𝑏) ∼ (30◦, 45◦)  Large et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (1962)  2  Bright polarized feature between the NPS and the Haze filament  (𝑙, 𝑏) ∼ (30◦, 35◦)  Defined in this work  3  Filament surrounding the northern Fermi bubble in 𝛾-rays  (𝑙, 𝑏) ∼ (7◦, 47◦)  Vidal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2015) (region IX)  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2016c)  4  Polarized structure below the Haze filament  (𝑙, 𝑏) ∼ (20◦, 27◦)  Defined in this work  5  North Haze Bubble  (𝑙, 𝑏) ∼ (−4◦, 31◦)  Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013)  6  The Galactic Centre Spur (GCS)  (𝑙, 𝑏) ∼ (5◦, 16◦)  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',) Vidal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2015)  7  Rectangle enclosing the South Haze Bubble  |𝑙| < 35◦  −35◦ < 𝑏 < −10◦  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013  8  Same as region 7, restricted to the QUIJOTE map area  |𝑙| < 35◦  −35◦ < 𝑏 < −10◦  −32◦ ≲ 𝛿 ≲ −10◦  Defined in this work  9  South Haze Bubble  (𝑙, 𝑏) ∼ (−1◦, −30◦)  Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013)  10  Region 9 excluding Faraday depolarized regions:  "A" and G353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='34  (𝑙, 𝑏) ∼ (−1◦, −30◦)  Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013)  Iacobelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2014)  "A": (𝑙, 𝑏) ∼ (20◦, −52◦)  G353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='34: (𝑙, 𝑏) ∼ (30◦, −62◦)  11  Western eRosita bubble or South Polar Spur (SPS)  (𝑙, 𝑏) ∼ (58◦, −45◦)  Predehl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2020)  Vidal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2015) (region VIIb)  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2016c)  12  Faint polarized spur with unknown origin  (𝑙, 𝑏) ∼ (53◦, −35◦)  Defined in this work  13  Eastern eRosita bubble  (𝑙, 𝑏) ∼ (−29◦, −26◦)  Predehl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2020)  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' List and description of the regions selected for this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3 for visualisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  excluding the Galactic plane with the mask described in 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1, and  region 1 corresponds to the North Polar Spur (NPS, Large et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  1962).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' These two regions are used for comparison purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  3  METHODOLOGY  In this section, we describe the two methodologies that are applied  in this work: the template fitting procedure, both in intensity and in  polarization, and the correlation T-T plots analysis in polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  Template fitting  In order to isolate the diffuse emission of the Haze from the other  Galactic foregrounds, we apply a template fitting technique, fol-  lowing the same formalism as in Finkbeiner (2004);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Dobler &  Finkbeiner (2008);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This method-  ology relies on the assumption that each frequency map is a linear  combination of several templates, which spatially trace the Galactic  emission of different mechanisms, such as the synchrotron, free-  free, thermal dust and AME.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This can be represented analytically  as:  𝑑𝜈 = 𝑎𝜈 · P𝜈,  (1)  where 𝑑𝜈 is the map at frequency 𝜈, P𝜈 is a the template matrix  that contains one template map per column, estimated at frequency  𝜈, and 𝑎𝜈 is a vector of coefficients indicating the amplitude of  the templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The template fitting problem consists in determining  the amplitudes 𝑎𝜈 that provide the best description of the data  with the templates in P𝜈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We solve the problem with a maximum  likelihood approach, by applying an extended formalism to include  the correlation between different templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4 The logarithm of the  posterior of this problem, including priors for the fitted amplitudes  𝑎𝜈 is given by:  ln P ∝ (𝑑 − 𝑎 · P)𝑇 𝐶−1  w (𝑑 − 𝑎 · P) + (𝑎 − 𝑎0)𝑇 𝐶−1  a (𝑎 − 𝑎0) + 𝑐, (2)  where we neglect the frequency subscript 𝜈 for brevity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Here, 𝐶w  is the noise covariance matrix of the data, 𝑎0 is the central value  of the amplitude priors, 𝐶a is the covariance matrix of the template  amplitudes, and 𝑐 is a global constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The solution of equation 2  is:  𝑎 = (P𝑇 𝐶−1  w P + 𝐶−1  a )−1 · (𝑃𝑇 𝐶−1  w 𝑑 + 𝐶−1  a 𝑎0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (3)  By means of the term 𝐶−1  a 𝑎0, we can apply priors on the fitting of  the foreground templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In particular, the off-diagonal elements  of 𝐶a allow us to introduce in the fitting the degree of correlation  between the templates, which is measured for synchrotron and dust  to be at the order of 20–40 %, with some evident spatial variation  (Peel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Choi & Page 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Krachmalnicoff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This improved template fitting technique has been tested with  simulations based on the foreground templates and frequency scal-  ing used in this work (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We observed that a more  precise separation of the foregrounds is achieved by applying priors  that account for their spatial correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In particular we noticed  that, at low frequencies, where the dust component is subdominant  but spatially correlated with the synchrotron, the separation of syn-  chrotron and dust is significantly improved by applying priors as in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Simulations have also been used to check for biases in the  results, when including or excluding priors in the fitting procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We observed that the results on the spectrum of the Haze are not  4 This formalism was developed and applied for the radio/microwaves map-  making problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' See for example Keihänen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2010), or Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (2021)  MNRAS 00, 1–31 (2023)  The Haze as seen by QUIJOTE  7  significantly different in the two cases, while the spectra of the fore-  grounds components, especially that of the synchrotron, is affected  by significant biases if priors are not adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We concluded that  the use of priors allows us to have better control on the fitting of the  foreground components, while not significantly affecting the results  on the spectrum of the Haze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  Templates  The fitting is performed in intensity and polarization, using inde-  pendently the 𝐼 map, and the 𝑄 and 𝑈 Stokes parameters maps  simultaneously for polarization, assuming a negligible Q and U  correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' All the templates are convolved to 1◦ angular resolu-  tion and degraded to 𝑁side = 64 in order to avoid pixel-to-pixel  correlation, as we did for the data (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The intensity and  polarization templates are shown, respectively, in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A  detailed description follows in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Synchrotron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The full-sky intensity map by Haslam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (1982),  at 408 MHz, is dominated by synchrotron emission, and it is only  marginally contaminated by free-free along the Galactic plane and in  bright free-free sources (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', M42).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This makes the 408 MHz map  a good tracer of diffuse synchrotron emission in intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We use  the reprocessed version of this map by Remazeilles et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2015) as a  template, and we scale5 it in frequency using a power-law spectrum  assuming a spatially-constant spectral index 𝛽s = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1 across the  full sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In addition, as indicated by Dobler (2012), the cosmic  ray propagation length is energy dependent, and this results in a  synchrotron radiation that is more extended around the Galactic disk  at 408 MHz compared with the higher frequencies (like QUIJOTE,  Planck and WMAP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In order to trace this excess at low frequency,  and following Dobler (2012) and Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013),  we adopt an elliptic Gaussian template centred in the Galactic centre,  with extension (𝜎𝑙, 𝜎𝑏) = (±20◦, ±5◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The diffuse synchrotron  and the disk-like synchrotron excess are fitted independently with  two separate templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In polarization, we use the 2018 Stokes Q and U Commander6  synchrotron solution (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2018), scaled to  each central frequency with a power-law with a spectral index  𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1, which is assumed to be constant across the sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Thermal dust and AME Thermal and AME are two distinct fore-  ground components produced by dust grains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The thermal dust fol-  lows a modified black body spectrum that shows up mainly at high  frequencies (𝜈>100 GHz), while the spinning dust is significant at  intermediate frequencies (10 GHz ≲ 𝜈 ≲ 60 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The carriers of  the AME have not been unequivocally identified yet, but the most  accredited hypothesis to date is that AME is produced by the rotation  of small dust grains (for a review see Dickinson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We could use two independent templates to fit thermal dust and  AME, using the Commander solution (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  5 The frequency scaling of a template map is usually irrelevant for tem-  plate fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Indeed, given the spatial morphology of the template, we fit  for a global amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, in order to assign priors as explained in  Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2, frequency scaling is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  6 Commander is a software developed for the component separation of  Planck data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It consists of a pixel based Bayesian parametric method (MCMC  Gibbs sampling algorithm), aimed to fit the parameters describing different  Galactic foreground components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' See Eriksen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2004, 2008) for more  details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2016b) for the two components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, AME and thermal dust  are highly correlated, and a simultaneous fit of the two components  could be affected by strong degeneracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In addition, we noticed that  the Commander AME map presents an excess of emission with a  shape similar to that of the Haze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' There is the possibility that a frac-  tion of the Haze emission leaked into this map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Moreover, Planck  Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2016c) reported that the degeneracy between  the AME and free-free components could affect the stability of the  Commander AME solution, due to the lack of low-frequency infor-  mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Therefore, in order to perform a blind and unbiased fit of the  foregrounds we decided not to use the Commander AME map, fitting  the combination of thermal dust and AME with a single template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We adopt the 2015 Commander solution for thermal dust, scaled at  each central frequency with the modified black body spectrum of  thermal dust reported in Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2016b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Due to  the dust and AME correlation, this template will capture, in addition  to the thermal dust component, the AME emission at intermediate  frequencies (∼20–60 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Note also that, thanks to the fact that  the AME (𝜈 ≲ 60 GHz) and the thermal dust (𝜈 ≳ 800 GHz;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Planck  Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016b) emissions do not overlap in frequency,  even if we use a single template to fit the two components, they are  easily distinguishable in the frequency spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In this work we assume no polarized AME, which is well  justified given the observational constraints that set the AME polar-  ization to be ≲1% (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2012a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Génova-Santos  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Dickinson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Therefore no AME is fitted in  polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Thermal dust instead is typically 5–10 % polarized  (Dickinson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016b,a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We  fit therefore the polarized dust emission using the 𝑄 and 𝑈 2018  Commander thermal dust maps (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2018)  as templates, after scaling to each central frequency as indicated in  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2016b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Free-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We construct the free-free intensity template using the  H𝛼 map by Finkbeiner (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We correct the H𝛼 map for dust  absorption by applying the methodology of Dickinson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2003),  and using the reddening 𝐸(𝐵 − 𝑉) map7 of Planck (Planck Col-  laboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2014b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We assume uniform mixing between gas  and dust by setting an effective dust fraction along the line of sight8  𝑓𝑑 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5, an average electron temperature 𝑇𝑒 = 7000 K across the  full sky, and we scale the corrected H𝛼 map from Rayleigh (R) to  𝜇K, at each central frequency, by computing the conversion factor  with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (11) in Dickinson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Despite these approxima-  tions, what is important here is to construct a good enough tracer  of the spatial distribution of free-free emission, independently from  the absolute scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' With this aim, applying a good correction of dust  absorption is important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This template provides a sufficiently good approximation of the  free-free in the sky, except for the regions with high dust absorption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Furthermore, we expect large fluctuations of the gas temperature in  the brightest H𝛼 regions, which can produce some inaccuracies in  the template (Dickinson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In order to avoid such problematic regions, we mask the  pixels with absorption larger than one magnitude (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='51·𝐸(𝐵−𝑉) >  7 https://irsa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='ipac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='caltech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='edu/data/Planck/release_1/  all-sky-maps/previews/HFI_CompMap_DustOpacity_2048_R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  10/  8 We also tried 𝑓d = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='33, but this change did not affect the resulting Haze  morphology and spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  8  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Intensity template maps at 11 GHz at 𝑁side = 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' They are: a simple model of the Haze as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1 (top left), a disk template  for the Galactic plane diffuse synchrotron emission (multiplied by 10 for display purposes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' top centre), free-free (multiplied by 10 for display purposes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' top  right), synchrotron (bottom left), dust (multiplied by 103 for display purposes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' bottom centre), which is used to fit both thermal dust and AME, and the CMB  anisotropies (bottom right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The maps are in units of mK Rayleigh-Jeans, and have had the mean subtracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The grey area represents the mask that is used for  the analysis, which is a combination of the QUIJOTE sky coverage with the free-free and CMB mask, as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Polarization template maps at 11 GHz, of Stokes 𝑄 (top) and 𝑈 (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' They are, from left to right: synchrotron, thermal dust (multiplied by 104  for display purposes) and the CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The maps are in units of mK Rayleigh-Jeans, and are mean corrected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The grey area represents the mask that is used for  the analysis, which is a combination of the QUIJOTE sky coverage with the free-free and CMB mask, as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  1 mag), or with H𝛼 intensity greater than 10 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The free-free has  negligible polarization, therefore it is fitted only in intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The 2018 SMICA9 CMB map (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2018) is subtracted from each frequency map, both in intensity and  in polarization, at 1◦ angular resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' As discussed in Dobler  9 Spectral Matching Independent Component Analysis (SMICA) is one of  the methods that was implemented for the component-separation of Planck  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It is based on a linear combination between the Planck frequency  channels, using weights that depend on the multipole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' See Cardoso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (2008) for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (2012), the foreground contamination of the CMB map could pro-  duce a bias in the determination of the Haze spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However,  the last version of maps produced with the Planck data provide now  a high quality CMB map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We assume therefore that the CMB bias  mentioned above is negligible as compared with other sources on  uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In order to confirm that, we repeated the analysis us-  ing the Commander CMB map, obtaining compatible results on the  Haze separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The Haze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Following Dobler & Finkbeiner (2008) and Planck Col-  laboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013), we include a template that approximately  traces the emission of the Haze in the fitting of the intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Even  MNRAS 00, 1–31 (2023)  Disk Template 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='oGHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  Tb [mKr/] · 10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50Free-Free 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  Tb [mKr/] · 10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50Synchrotron 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='oGHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  Tb [mKR]]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50LhermalDustIt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='oGHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  T, [mKr] · 103  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50CMB Smica  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='23  T,[mKcMB]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50LhermalDuststokes-ot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='oGHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  T, [mKr] · 104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50Q CMB Smica  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='003  T,[mKcMB]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='003Synchrotron Stokes-U 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='oGHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50LhermalDuststokes-ul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='oGHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  T, [mKrj] · 104  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50UCMBSmica  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='003  T,[mKcMB]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='003Haze Template 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  T,[mKRj]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50The Haze as seen by QUIJOTE  9  if we do not have a precise characterization of the spatial distri-  bution of the Haze, an approximated template is needed in order  to avoid a bias in the fit of other foreground templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We use a  Gaussian ellipse in Galactic coordinates, centred in the Galactic  centre, and with major axes perpendicular to the Galactic plane line  (𝑏 = 0◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The minor and major axes are, respectively, 𝜎𝑙 = 15◦ and  𝜎𝑏 = 25◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The template has the same unitary amplitude at different  frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Monopole and dipole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In order to overcome any possible issue  related with zero levels, we subtract the average value of the un-  masked pixels from the maps and from the templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In addition,  we fit a monopole component at each frequency in order to ad-  just any residual zero level mismatch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Finally, from the residual  maps at frequencies 𝜈 > 40 GHz, we noticed a residual dipole pat-  tern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For this reason, before applying the template fitting to these  maps, we remove the residual dipole with the HEALPix routine  remove_dipole, after masking pixels with |𝑏| < 20◦ to avoid  Galactic contamination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Following Dobler & Finkbeiner (2008) and Planck Collab-  oration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013), we mask all the regions where the templates  can deviate from the real foreground emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The mask includes,  as described above for the free-free, the regions where the H𝛼 emis-  sion exceeds 10 R, or where the dust extinction is larger than 1  magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In addition, we mask the point sources from the Planck  LFI catalog (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We used the mask  excluding the LFI compact sources that is available in the Planck  Legacy Archive10 (PLA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Finally, in order to avoid any possible bias  from foreground residuals in the CMB map, we mask the pixels that  are outside the confidence region11 of the CMB map that we are  using.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  Priors  Our implementation of the template fitting procedure, which is  described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1, allows us to apply priors on the amplitudes  of the foreground templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The priors are introduced by the vector  𝑎0, which contains the central values of the prior at frequency12 𝜈,  and by the covariance matrix 𝐶a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The elements of the covariance  matrix are defined as:  𝐶a,𝑖 𝑗 = 𝑐𝑜𝑣(𝑎𝑖, 𝑎 𝑗) = 𝐸  �  (𝑎𝑖 − 𝑎0𝑖)(𝑎 𝑗 − 𝑎0 𝑗)  �  ,  (4)  where 𝐸[·] denotes the expected value operator, 𝑎0 the expected  amplitude, and the indices 𝑖 and 𝑗 indicate the foreground maps at  the frequency 𝜈 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 𝑖=thermal dust, 𝑗=synchrotron, at 11 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The diagonal elements of 𝐶a are:  𝐶a,𝑖𝑖 = 𝑐𝑜𝑣(𝑎𝑖, 𝑎𝑖) = 𝜎2  𝑖 ,  (5)  10 The  mask  used  in  this  work  can  be  found  in  the  PLA:  http://pla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='esac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='esa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='int/pla/aio/product-action?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='MAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='MAP_  ID=LFI_Mask_PointSrc_2048_R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='fits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Relevant  information  about the mask can be found in the PLA Explanatory Supplement at  https://wiki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='cosmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='esa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='int/planck-legacy-archive/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  php/Frequency_maps#Masks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  11 The CMB mask used in this work is taken from the fits file containing  the CMB map (SMICA, PR3-2018), downloaded from the PLA (http:  //pla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='esac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='esa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='int/pla).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Relevant information about the mask can be  found in the PLA Explanatory Supplement at https://wiki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='cosmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  esa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='int/planck-legacy-archive/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='php/CMB_maps#SMICA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  12 For brevity in the notation, the subscript 𝜈 is not explicit, keeping in  mind that the fitting is always performed at a given frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  where 𝜎𝑖 is our choice for the width of the Gaussian prior for the  amplitude of the template 𝑖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We assign to the width of the priors the  analytic uncertainty on 𝑎𝑖 that is obtained by the second derivative  of the logarithm of the posterior in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2, neglecting the priors term  (𝐶−1  a  = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It is:  𝜎2  𝑖 = (P𝑇  𝑖 𝐶−1  w P𝑖)−1,  (6)  where P𝑖 is the 𝑖𝑡ℎ column of the templates matrix P, so it is simply  the map of the 𝑖𝑡ℎ template (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 𝑖=thermal dust).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The off diagonal  elements of 𝐶a are:  𝐶a,𝑖 𝑗 = 𝑐𝑜𝑣(𝑎𝑖, 𝑎 𝑗) = 𝜌𝑖 𝑗 · 𝜎𝑖𝜎𝑗,  (7)  where 𝜌𝑖 𝑗 is the correlation between the templates 𝑖 and 𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It is  known that different foreground mechanisms are spatially correlated  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Choi & Page 2015), therefore 𝜌𝑖 𝑗 ≠ 0 and 𝐶a is not diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In this work, we assign average values of correlation between the  intensity templates of the foregrounds, by computing 𝜌𝑖 𝑗 as:  𝜌𝑖 𝑗 =  �  𝐶P𝑖×P 𝑗  ℓ  √︃  𝐶P𝑖  ℓ · 𝐶P 𝑗  ℓ )  �  2<ℓ<100  ,  (8)  where 𝐶P𝑖×P𝑗  ℓ  is the cross power spectrum between the template  maps 𝑖 and 𝑗 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 𝑖=thermal dust, 𝑗=synchrotron, at 11 GHz), while  𝐶P𝑖  ℓ  and 𝐶P𝑗  ℓ  are their auto power spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The level of correlation  between templates is not the same at large and small angular scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  As 𝜌𝑖 𝑗 is a function of the multipole ℓ, in order to provide an average  level of correlation, we compute the mean value of 𝜌𝑖 𝑗 (ℓ) in the  multipole range 2 < ℓ < 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We computed the power spectra of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 8 with the publicly  available code Xpol13 (Tristram et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2005), and we used a mask  of the full sky, excluding a band in Galactic latitude |𝑏| < 5◦ to  mask the brightest Galactic plane emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The averages in the  multipole range 2 < ℓ < 200, are 𝜌𝑠,𝑑 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='30 for synchrotron  and thermal dust, 𝜌𝑠, 𝑓 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='14 for synchrotron and free-free, and  𝜌𝑑, 𝑓  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='26 for thermal dust and free-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In polarization we  have 𝜌𝑠,𝑑 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20 for synchrotron and thermal dust, in agreement  with Choi & Page (2015), who measured a correlation 𝜌 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  between Planck 353 GHz and WMAP 23 GHz in the multipole range  30 < ℓ < 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Finally we define the central values of the priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For syn-  chrotron and free-free we use 𝑎0,𝑠 = 𝑎0, 𝑓 = 1, since the template  maps are specifically computed at each central frequency, and the  expected emission by synchrotron and free-free are the template map  themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For the fitting of the thermal dust and the AME we use  a single template, which is the thermal dust of Commander, scaled  at the corresponding central frequency, as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Here we assume that AME and the thermal dust are totally corre-  lated, and that we can capture these two components with the same  template, with an expected amplitude 𝑎0,𝑑 = 1 + 𝑟, where 𝑟 is an  average AME to thermal dust ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We define 𝑟 as a representative  value of the ratio between the Commander AME and the thermal  dust maps, computed (following Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016b)  at the same central frequency 𝜈:  𝑟(𝜈) =  � AME(𝜈)  th-dust(𝜈)  �  ,  (9)  where <> indicates the median over the pixels enclosed in the  mask described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We impose a prior on the total dust  13 https://gitlab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='in2p3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='fr/tristram/Xpol  MNRAS 00, 1–31 (2023)  10  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  amplitude which is centred in 𝑎0,𝑑 = 1 + 𝑟.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For the rest of the  templates, which are the Galactic ellipse of diffuse synchrotron, the  monopole and the Haze, we do not want to impose any stringent  prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Therefore we assign to them 𝑎0 = 0 and 𝜎 ≈ ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In polarization, we fit a synchrotron and a thermal dust tem-  plate, separately in 𝑄 and 𝑈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Similarly to intensity, the templates  are computed to match the emission of the foreground at the corre-  sponding central frequency, therefore we assign the expected central  value with the prior 𝑎𝑄,𝑈  0,𝑠  = 𝑎𝑄,𝑈  0,𝑑  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The width of the priors are  computed with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The off-diagonal elements of the covariance  matrix are computed as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 7 and 8, giving 𝜌𝑄,𝑈  𝑠,𝑑  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  Polarization T-T plots  In order to analyze the polarization data with a different and inde-  pendent technique, we use correlation plots, commonly called T-T  plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This methodology is widely used in the literature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Planck  Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Fuskeland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2019), therefore we ap-  plied it in order to reproduce results presented in previous works  (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013), and extend  them using the new QUIJOTE data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The specifics of the applied  methodology are described as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  T-T plots of 𝑃MAS  The low frequency polarized foregrounds are dominated by syn-  chrotron radiation, which is described by a power-law spectrum:  𝑑𝜈 =  � 𝜈  𝜈0  �𝛽  𝑑𝜈0,  (10)  where 𝑑𝜈 are the polarization data at frequency 𝜈, 𝑑𝜈0 are the po-  larization data at a reference frequency 𝜈0, and 𝛽 is the synchrotron  spectral index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  It is possible, therefore, to derive the synchrotron spectral index  across a coherent region with a simple correlation analysis between  the polarized emission of two frequency maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We can fit a linear  dependence of 𝑑𝜈 as a function of 𝑑𝜈0:  𝑑𝜈 = 𝑚 · 𝑑𝜈0 + 𝑞,  (11)  where 𝑞 is a relative offset, and the slope 𝑚 is related to the spectral  index 𝛽 (with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10 and 11) as:  𝛽 =  ln(𝑚)  ln(𝜈/𝜈0) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (12)  The uncertainty on 𝛽 can be derived as the propagation of the  uncertainty on 𝑚, 𝜎𝑚, as:  𝜎𝛽 = 𝜎𝑚  𝑚  1  ln(𝜈/𝜈0) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (13)  This technique is commonly used to compute the spectral in-  dex of the polarization amplitude 𝑃 =  √︁  𝑄2 + 𝑈2, in Rayleigh-Jeans  temperature units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, with 𝑃 being a positive definite quan-  tity, it is affected by noise bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Several techniques have been pro-  posed to estimate an unbiased polarization amplitude (Plaszczynski  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Vidal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In this paper, we use the unbiased  polarization amplitude 𝑃MAS by applying the Modified Asymptotic  estimator (MAS) presented in Plaszczynski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2014), as:  𝑃MAS = 𝑃 − 𝑏2 1 − 𝑒−𝑃2/𝑏2  2𝑃  ,  (14)  with  𝑏 =  √︃  (𝑄𝜎𝑈)2 + (𝑈𝜎𝑄)2/𝑃,  (15)  where 𝑃 is the noise biased polarization amplitude (as defined  above), and 𝜎𝑄 and 𝜎𝑈 represent the uncertainties on the mea-  sured 𝑄 and 𝑈 parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The uncertainty on 𝑃MAS is given by:  𝜎𝑃MAS =  √︃  (𝑄𝜎𝑄)2 + (𝑈𝜎𝑈)2/𝑃.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (16)  This estimator is unbiased for pixels with signal-to-noise larger than  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  T-T plots of Q and U combined projection  In order to overcome problems related with polarization noise bias  in the data, due to zero-level mismatch, and also to variation of  the spectral index with the polarization angle of the emission, we  apply the technique that was proposed in Fuskeland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The T-T plot method described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 has been widely used in  previous works (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016c), so we have  also applied it for the sake of reproducing their results, however we  believe that the Fuskeland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2014) method is more reliable, and  hence we use that by default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This methodology does not compute the polarization ampli-  tude 𝑃, which is affected by noise bias, and allows to marginalize  the result over the polarization angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We make direct use of the Q  and U Stokes maps that, after a projection into a rotated reference,  are mixed to construct the data vector 𝑑(𝛼):  𝑑(𝛼) = 𝑄 cos(2𝛼) + 𝑈 sin(2𝛼),  (17)  where 𝛼 is the rotation angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We can use the data 𝑑(𝛼) and Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 12  and 13 to compute the spectral index as a function of 𝛼, for a set  of 18 angles distributed in the range 𝛼 ∈ [0◦, 85◦], in steps of 5◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The resulting (strongly correlated) spectral indices 𝛽𝑖 = 𝛽(𝛼𝑖) are  finally averaged with weights:  𝛽 =  �18  𝑖=1(𝛽𝑖/𝜎2  𝛽𝑖)  �18  𝑖=1(1/𝜎2  𝛽𝑖)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (18)  Due to correlation of the estimated 𝛽(𝛼𝑖) as a function of the angle,  the statistical uncertainty on the final spectral index 𝛽 is taken to be  the minimum uncertainty among the 18 measurements:  𝜎stat  𝛽  =  min  𝑖∈[1,18]  �𝜎𝛽𝑖  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (19)  However, variations of the spectral index as a function of the polar-  ization angle can induce an additional uncertainty on the determina-  tion of 𝛽 across a wide region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We can define an intrinsic uncertainty  due to this effect as the standard deviation of the 𝛽𝑖 estimated at  different rotation angles, as:  𝜎int  𝛽 = std𝑖 (𝛽𝑖) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (20)  In order to account for the effect that dominates the uncertainty of  the spectral index in each particular region (statistical or intrinsic  uncertainty), we adopt as a final uncertainty the maximum between  the two estimates of the error:  𝜎𝛽 = max  �  𝜎stat  𝛽 , 𝜎int  𝛽  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (21)  In the process of estimating the spectral index with correlation  plots of 𝑑(𝛼), we perform the linear fit considering the uncertain-  ties of 𝑑(𝛼) in both axes, and, for each angle 𝛼, we apply colour  MNRAS 00, 1–31 (2023)  The Haze as seen by QUIJOTE  11  corrections (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2) in an iterative way, until the spectral in-  dex variations are lower than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The main results of this work,  in polarization (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3), are obtained by applying the methodol-  ogy described in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, in a few special cases, we  compare the resulting spectral indices with those obtained with the  more common methodology described Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1, the T-T plots of  the polarization amplitude 𝑃MAS in order to give strength to the  reliability of the result, and show some possible sources of error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In  addition, in order to check the robustness of the linear regression  of the T-T plots for each angle 𝛼𝑖, we compute the posterior distri-  bution of the spectral index parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Appendix D provides the  details and the results of this last check.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  4  RESULTS  Here we report first the results obtained for the Haze with the  methodology of template fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The aim is to compare with the  results from Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013) in intensity (in  Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1), and to present our results in polarization (in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2),  which is the main novelty from this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In this part of the anal-  ysis, after fitting the foreground templates across the full sky, we  perform a detailed study of the residuals in regions of particular  interest among those listed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Subsequently, in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 we show the results obtained with  the correlation T-T plots in polarization, following the methodol-  ogy described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Also in this case, we concentrate the  analysis on the regions that are presented in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  As noted in Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2023) (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 and  Appendix B) and in de la Hoz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2023), the filter that is applied  to the QUIJOTE-MFI data to clean residual RFI contamination (so-  called FDEC) removes from the maps a monopole term at constant  declination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We have checked that the effect of the FDEC filter does  not induce any significant bias on the results presented in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  Intensity template fitting  We performed a template-fitting component separation using the  intensity frequency maps of QUIJOTE, WMAP and Planck (see  Table 1 and Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2 for a more detailed description of the data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We show in the appendix (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A1) the CMB subtracted sky maps  within the sky area used in this analysis, which is limited by the  QUIJOTE sky coverage and by the mask of reliable foregrounds  description (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1 for further details on the mask).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The templates that are used for the component separation in  intensity are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' They are: synchrotron, free-free, dust  (thermal dust and AME are adjusted with the same template of  thermal dust), a disk template14 for the Galactic plane diffuse syn-  chrotron emission, and the Haze, as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The  CMB is fixed and subtracted from the maps before the fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The  fitted amplitudes for these templates are reported in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  As a result of this simple component separation, we construct  the residual map 𝑅𝜈, by subtracting the foreground templates P𝜈  scaled by the fitted amplitudes 𝑎𝜈 from the corresponding frequency  map 𝑑𝜈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It is:  𝑅𝜈 = 𝑑𝜈 − 𝑎𝜈 · P𝜈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (22)  14 The reconstruction of the Haze signal does not change significantly if we  exclude the Galactic diffuse disk and Haze templates from the fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Ideally, the residual 𝑅𝜈 is a map of the noise at frequency 𝜈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' How-  ever, the foreground templates may not perfectly trace the real fore-  ground spatial structure, and some residual sky structure could leak  in the residual map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In particular, we are interested in the Haze com-  ponent, which we fit with an approximate Gaussian elliptic template  centred in the Galactic centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This template is not expected to trace  perfectly the spatial distribution of the Haze, therefore part of it  could remain as a residual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For this reason, following Dobler &  Finkbeiner (2008) and Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013), we con-  struct a residual plus Haze map as:  𝑅𝐻  𝜈 = 𝑅𝜈 + 𝑎𝐻  𝜈 · P𝐻  𝜈 ,  (23)  where P𝐻  𝜈 is the Haze template and 𝑎𝐻  𝜈 is the fitted Haze amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The residual maps can then be used to study the physical prop-  erties of the isolated emission of the Haze as compared with the  global synchrotron emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' With this aim we define the total syn-  chrotron map as the residual map, plus the fitted Haze and syn-  chrotron as:  𝑅𝑆  𝜈 = 𝑅𝐻  𝜈 + 𝑎𝑠  𝜈 · P𝑠  𝜈,  (24)  where P𝑠𝜈 is the synchrotron template, 𝑎𝑠𝜈 its amplitude at frequency  𝜈, and 𝑅𝐻  𝜈 the residual plus Haze map (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We show the resulting maps in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 6, and we study the Haze  spectrum, which is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 7 and 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  Intensity Haze maps  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 6 we show the residual plus Haze maps (𝑅𝐻  𝜈 ) across region 8  (defined in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3), for several selected frequencies (QUIJOTE  11 and 13 GHz, WMAP K-band and Planck 30 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We observe  that the bulk of the Haze component is detected in all the maps,  including QUIJOTE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Nulltest maps of QUIJOTE (see appendix C and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' C1) have  been used to validate the sky origin of the observed signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The  nulltest maps do not show evident residual systematics, therefore  the structures observed in the residual maps are associated with sky  signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Beyond the Haze, we notice that the bottom part of the NPS  (region 1), close to the Galactic centre at (𝑙, 𝑏) ∼ (31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5◦, 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5◦),  is visible in the residual maps of QUIJOTE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This indicates that  our templates do not perfectly match the base of the NPS region,  and this could be associated with a synchrotron component with a  spectrum that is different with respect to the sky average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Note that  the NPS residual that we observe in this work corresponds to the  region that Panopoulou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2021) identified as possibly associated  with Galactic centre activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In contrast, the NPS emission at high  galactic latitudes is usually ascribed to a nearby supernova shell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A  detailed study of the NPS with QUIJOTE data is beyond the scope  of this work and will be presented in Watson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (in preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  Intensity Haze spectrum  Under the hypothesis that the Haze is synchrotron emission, both  the Haze and the total synchrotron are characterized by a power-law  spectrum (as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10), which is defined by two parameters: the  amplitude and the spectral index 𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We performed the measurement of the spectral index of the  Haze and of the total synchrotron by fitting the SED of the signal  within a selected area: region 8 in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We computed the  average of the emission in the unmasked 𝑅𝐻 and 𝑅𝑆 pixels within  the selected region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The zero level must be properly set at each  MNRAS 00, 1–31 (2023)  12  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  I  Map  Sync  Free-free  Dust  Disk  Mono  Haze  [mKRJ]  [mKRJ]  [mKRJ]  QUIJOTE 11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='93  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='28  357.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='38  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='85  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0×10−3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70  QUIJOTE 13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='89  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='26  231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='44  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6×10−3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54  WMAP K-band  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='85  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='37  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='39  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5×10−15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19  Planck 30  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='87  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3×10−16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  WMAP Ka-band  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='85  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6×10−16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  WMAP Q-band  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='89  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='88  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='74  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6×10−17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  Planck 44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='90  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='90  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='69  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3×10−17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  WMAP V-band  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='86  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='83  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5×10−16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  Planck 70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='85  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='82  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4×10−17  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  Q,U  Sync  Dust  Mono  [mKRJ]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='87  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='51  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8×10−3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='92  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='59  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6×10−3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='98  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='33  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='9×10−5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='29  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1×10−6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='59  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8×10−5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='94  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='7×10−5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='82  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4×10−5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='69  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4×10−5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='72  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0×10−3  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Stokes I (left) and Q,U (right) template fitting coefficients, fitted as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Residual plus Haze intensity maps in the southern Haze region (region 8, see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3), for, from left to right: QUIJOTE 11 GHz, QUIJOTE 13 GHz,  WMAP K-band, Planck 30 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The grid is centred at coordinates (𝑙, 𝑏) = (20◦, −23◦) and is spaced by 10◦ in Galactic latitude and longitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The maps are  in mK Rayleigh-Jeans temperature units, and the colour bar is scaled with a synchrotron-like power-law: 2 mK·(𝜈/11 GHz)𝛽, with 𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  frequency 𝜈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We therefore fitted a linear slope to the pixel-to-pixel  correlation plot of 𝑅𝐻  𝜈 against 𝑅𝐻  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8 (or 𝑅𝑆𝜈 against 𝑅𝑆  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8), given  by:  𝑅𝐻,𝑆  𝜈  = 𝑚𝜈 · 𝑅𝐻,𝑆  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8 + 𝑞𝜈,  (25)  obtaining the relative offset to WMAP K-band, 𝑞𝜈, and the slope 𝑚𝜈.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This is done with a linear fit accounting for errors in both axes,15  where the uncertainty is calculated as the standard deviation of the  residual map in the selected area, propagated in quadrature with the  uncertainty on the fitted amplitude of the templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The uncertainty on the SED points is given as the standard  deviation of the residual map, scaled by the square-root of the  number of averaged pixels, and summed in quadrature with the  calibration uncertainty of each frequency map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We assume a power-  law behaviour for the spectrum of the Haze (  �  𝑅𝐻  𝜈  �  − 𝑞𝐻  𝜈 ) and of  the total synchrotron (  �  𝑅𝑆𝜈  �  − 𝑞𝑆𝜈) at our frequencies, therefore we  can write the linear relation of ln  ��  𝑅𝐻,𝑆  𝜈  �  − 𝑞𝐻,𝑆  𝜈  �  against ln(𝜈),  as:  ln  ��  𝑅𝐻,𝑆  𝜈  �  − 𝑞𝐻,𝑆  𝜈  �  = 𝛽𝐻,𝑆 · ln(𝜈) + 𝑐𝑜𝑛𝑠𝑡.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  (26)  whose slope provides the spectral index 𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Here we look at the southern Haze area (region 7) that has been  identified by previous works (Dobler & Finkbeiner 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Planck  Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, the sky observed by QUIJOTE  does not cover the full area of region 7, and we restrict our analysis  15 For this fit we used the Orthogonal Distance Regression (ODR)  SciPy package (https://docs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='scipy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='org/doc/scipy/reference/  odr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='html).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Intensity SED of the Haze enclosed in region 8 (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 and  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The data and the fit of the residual plus Haze spectrum (multiplied  by three for display purposes) are shown in red, while the data and the fit of  the total synchrotron are shown in green.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  in the overlap with the QUIJOTE sky coverage (region 8), which is  also shown on the right in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The SED with the integrated spectrum in region 8 is given in  MNRAS 00, 1–31 (2023)  QlT11:TResidual+Haze  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5/pix,200x200pix  (20,-23)  Tb [mKR]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00QlT13:TResidual+Haze  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5/pix,200x200pix  (20,-23)  Tb [mKR]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='21  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='21WMAPK:TResidual+Haze  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5°/pix,200x200 pix  (20,-23)  Tb [mKR]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22PLA3O:TResidual+Haze  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5/pix,200x200pix  (20,-23)  Tb [mKr/]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12I QiT Rectangle South Haze  (RH),β= 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  (RS),β= -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='98±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  [<R>-B)(v/23)2 [mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  10  20  30  40  50  60  70  freq [GHz]The Haze as seen by QUIJOTE  13  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Intensity SED of the rectangle enclosing the southern Haze region (region 7), in the South Haze Bubble (region 9) and in the North Haze Bubble  (region 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In red is the spectrum of the residual plus Haze, and in green is the total synchrotron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  the legend of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' With a linear fit to these data,16 we measure  𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08 and 𝛽𝑆 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We can observe that the spectrum of the Haze is flatter than that  of the total synchrotron, with a difference in the spectral index of  about Δ𝛽 = 𝛽𝐻 −𝛽𝑆 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='26±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The difference has a significance  of 2𝜎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Notice that if we remove the QUIJOTE data from the SED  fit, the spectral indices are 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='76 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12 and 𝛽𝑆 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02 ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06, showing that QUIJOTE data does not significantly change the  central value of the fit, but improves the precision with which the  spectral indices are determined, by a factor 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The correlation plots mentioned above, which we performed  to set the zero level for the SED, also provided an estimate of the  spectral index as obtained from the slope of the linear fit 𝑚𝜈 with  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We obtained 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='78 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19 and 𝛽𝑆 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This secondary measurement is consistent with the results that are  obtained from the SED fitting, but the methodology is less precise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We can also discuss the effect of using, instead of region 8,  the broader region 7, which is the subject of the studies presented  in Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Excluding QUIJOTE data  and applying our methodology that uses priors to fit the various  foregrounds, we measure the values 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 and 𝛽𝑆 =  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04 (see left panel in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We first notice that our  measurement of the Haze spectrum in region 7 is slightly flatter  than what we obtain in region 8 (by Δ𝛽𝐻 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06), although they  are consistent within the uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In region 7, Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013) reports values  of 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='56 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 and 𝛽𝑆 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' If we compare this with  our results we can see that, in agreement with the Planck paper, the  Haze in region 7 emits with a flatter index than that of the total syn-  chrotron, but there is a discrepancy in the recovered Haze spectral  index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In order to test the origin of this discrepancy, we reproduced  the results of Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013) by applying their  same methodology, with no priors, excluding QUIJOTE data, and  integrating the same southern Haze area (region 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In this case,  we obtain 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='47 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06 and 𝛽𝑆 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04, which is  consistent with the Planck’s results, showing that the main source of  the observed difference is the use of priors, which results in a shift  of the Haze spectral index towards steeper values, by Δ𝛽𝐻 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='23  in region 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The use of priors in the pipeline of this work has been  tested with simulations (as discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1), with which we  noticed a clear improvement in the fitting of the foregrounds when  16 The fit is performed with a MCMC sampling of the full posterior of the  data, implemented with the Python emcee package (Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2013, https://emcee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='io/en/stable/).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  compared with the case with no-priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For this reason we finally  applied priors in our analysis, despite the slightly different results  in the Haze region as compared with previous works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3  Spectra of regions 5, 7 and 9  There are more regions that are interesting for the study of the  Haze, but which are unfortunately not accessible by QUIJOTE,  in the northern hemisphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' These are: the South Haze Bubble  (region 9), which is located in the southern sky and can only be  partially observed with QUIJOTE, and the North Haze Bubble  (region 5), which is observed by QUIJOTE but coincides with a  region with large residuals that are not fully understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We studied  these two regions by applying our template fitting methodology  (with priors), using only WMAP and Planck data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We show their  integrated spectra in the central and right panels in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In the  South Haze Bubble (region 9) we obtain the spectral indices 𝛽𝐻 =  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 and 𝛽𝑆 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05, which are compatible with the  already discussed results for the rectangle enclosing the southern  Haze (region 7;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' left panel in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In the North Haze Bubble,  instead, we obtain a flatter Haze spectrum, with 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05,  and also a flatter total synchrotron spectrum, it being 𝛽𝑆 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='51 ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We detect a significant difference between the spectral index  of the North and South Haze bubbles in intensity, with the spectrum  of the northern bubble flatter than that in the South.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' As in other  regions, the Haze component is flatter than the total synchrotron,  but in the northern bubble the total synchrotron spectrum is also  significantly flatter than that in other regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Interestingly, as we  report later (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3), the polarization between 23 GHz and 30 GHz  shows the same behaviour, with the northern bubble having a flatter  spectrum than the southern one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In addition, the polarization spectral  index of the North Haze Bubble is compatible with that of the total  synchrotron in intensity, while the polarization spectral index of the  South Haze Bubble is between the intensity 𝛽𝐻 and 𝛽𝑆 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  Polarization template fitting  We applied the template fitting procedure in polarization, by fitting a  synchrotron and thermal dust component to the Q and U frequency  maps simultaneously across the full unmasked sky (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  for a detailed description of the methodology).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The CMB is fixed  and subtracted from the maps before the fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The resulting fitted  amplitudes are reported in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We computed the residual polarization amplitude maps as:  𝑅P,𝜈 =  √︃  𝑅2  𝑄,𝜈 + 𝑅2  𝑈,𝜈,  (27)  MNRAS 00, 1–31 (2023)  I Rectangle South Haze  2 × 10-1  (RH),β=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  (RS),β= -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  6 ×10-2  4 × 10-2  3× 10-2  10  20  30  40  50  60  70  freq [GHz]I South Haze Bubble  2 ×10-1  (RH), β = -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='67 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  (RS),β= -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  6×10-2  4×10-2  3 × 10-2  10  20  30  40  50  60  70  freg[GHz]LNorthHazeBubble  2 ×10-  (<R>-B)·(v/23)2 [mKrj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  (RH),β=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  6 ×10-2  (RS),β= -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  10  20  30  40  50  60  70  freg[GHz]14  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  with17 𝑅𝑄,𝑈 = 𝑅0  𝑄,𝑈 − (𝑄0,𝑈0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Here, 𝑅0  𝑄,𝑈 are the residual  Q,U maps obtained after subtracting the fitted foregrounds from  the original Q,U frequency maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 𝑄0,𝑈0 are constant offsets to be  subtracted to 𝑅0  𝑄,𝑈 in order to adjust the zero level across frequen-  cies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 𝑄0 and 𝑈0 are obtained with T-T plots of 𝑅0  𝑄,𝑈 at frequency 𝜈  with respect to the residual map at 𝜈 = 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8 GHz (WMAP K-band),  across the unmasked sky pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' At this stage we do not attempt to  debias the polarization amplitude maps, so 𝑅P could be marginally  affected by noise bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We also define the fitted polarization amplitude synchrotron  map as:  𝑆P,𝜈 =  √︃  𝑆2  𝑄,𝜈 + 𝑆2  𝑈,𝜈,  (28)  where 𝑆𝑄,𝑈 = 𝑎𝑠  𝑄,𝑈 (𝑄𝑠,𝑈𝑠) are the fitted synchrotron maps,  with 𝑄𝑠,𝑈𝑠 being the polarization synchrotron template maps, and  𝑎𝑠  𝑄,𝑎𝑠  𝑈 the correspondent fitted amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Finally, we define the residual plus synchrotron map as:  𝑅𝑆  P,𝜈 =  √︂�  𝑅𝑆  Q,𝜈  �2  +  �  𝑅𝑆  U,𝜈  �2  ,  (29)  where 𝑅𝑆  Q,U = 𝑅𝑄,𝑈 + 𝑆𝑄,𝑈 − (𝑄′  0,𝑈′  0) are the 𝑄,𝑈 residual plus  synchrotron maps, with 𝑄′  0,𝑈′  0 adjusting the relative zero levels  across frequencies, computed with T-T plots across the unmasked  sky pixels with respect to WMAP K-band (22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  Polarization residual maps  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 9 shows maps of the residual polarization amplitude 𝑅P (left,  see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 27) and of the residual plus synchrotron 𝑅S  P (centre, see  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 29) of QUIJOTE 11 and 13 GHz, of WMAP K-band and of  Planck 30 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Similar to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 6, we also show a zoom-in of the 𝑅P  maps across region 8 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We can observe that the WMAP K-band  and Planck 30 GHz residual maps are mostly noise with potentially  some low level systematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In particular, the residual polarization  map of Planck 30 GHz has very low values as compared with the  other residual maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This is due to the fact that for the template  fitting procedure we use the Commander synchrotron solution (see  Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1), which strongly relies, by construction, on the 30 GHz  Planck polarization data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The QUIJOTE polarization residual maps, instead, show struc-  tures that can be associated with residual sky signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The detection  of similar structures was not possible in previous works based only  on WMAP or Planck data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' QUIJOTE data is now providing hints  of a detection of a previously unknown polarized diffuse signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Indeed we can observe, at 11 GHz and 13 GHz, evident structures  across the full Haze area, towards the South in region 8, but also  towards the North reaching high Galactic latitudes (𝑏 ∼ 85◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We  also detect residual signal in the lower part of the NPS, close to  the Galactic plane (at (𝑙, 𝑏) ∼ (31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5◦, 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5◦), bottom of region 1),  which is seen also in the intensity residual maps (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We refer to Watson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (in preparation) for a detailed study of the  NPS using QUIJOTE data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In order to validate the sky origin of the observed polarization  excesses, we analyzed noise maps of QUIJOTE obtained with null-  tests (as shown in appendix C, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' C1), showing that the noise level  can not explain the observed residuals, which are therefore ascribed  to sky signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  17 We drop the specification of 𝜈 subscript for brevity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This kind of residuals could possibly be originated by spatial  variations of the synchrotron spectral index, which has not been  taken into account in the fitting procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We tested this hypothesis  by repeating the analysis allowing the synchrotron spectral index  to vary across the sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We used for this purpose the synchrotron  spectral index map extracted by de la Hoz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2023), which is  derived from a pixel-based component separation (B-SeCRET, de  la Hoz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020) using data from QUIJOTE, WMAP and Planck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In this case we recover similar residual polarization maps as those  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 9, concluding that the observed residuals are not  attributable to spatial variations of the synchrotron index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' On the  other hand, they could be due to a curvature of the spectrum at  low frequencies (𝜈 < 23 GHz), across the area where we observe a  positive residual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  Polarization residual spectrum  Following the same procedure that is applied in intensity, we com-  puted the spectrum of maps integrated in several selected regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In this case, as stated in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1, we do not perform the fit of an  independent Haze template, because the projection of the Haze in  the Stokes Q and U maps is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Therefore, if the data contain  a Haze component that is not identified as synchrotron with the  sky average spectral index, or as thermal dust (even if it is a very  minor component at these frequencies), it will be revealed in the  residual maps 𝑅Q, 𝑅U, or 𝑅P defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 27 and shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We therefore look for a polarized Haze component in the residual  plus synchrotron spectrum (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 29), by comparing it with the  spectrum of the synchrotron alone (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We computed the spectrum of the combination of Stokes Q  and U parameters with a sinusoidal function, as defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 17,  projecting them in the direction of the polarization angle 𝛼 of the  region, and averaging the resulting signal within the selected region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This allows us to overcome problems related with noise bias of the  polarization amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The representative projection angle 𝛼 in the region is deter-  mined by inverting the median value of sin(2𝛼), which is a con-  tinuum function when the angle has a discontinuity (at 𝛼 ± 90◦).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The angle is computed using the WMAP K-band data, and it is used  for all the other frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We use 𝛼 = 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5◦ in region 8 and  𝛼 = 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3◦ in region 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10 we show the spectrum of the average Q and U com-  bination for the polarized synchrotron (𝑆, in black) and for the  residual plus synchrotron (𝑅𝑆, in green) as a function of the fre-  quency, within two different regions: the North Haze Bubble (region  5) and the southern Haze area (region 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The Q and U uncertainties (𝜎𝑄 , 𝜎𝑈) for the WMAP and Planck  data points are estimates of the scatter of the residual 𝑅𝑄 and 𝑅𝑈  maps, between pixels enclosed in the region being examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For  QUIJOTE, instead, the residual maps show an evident signal con-  tribution, therefore we derive 𝜎𝑄 and 𝜎𝑈 as the standard deviation  of the null-test 𝑄 and 𝑈 maps shown in appendix A, within the  selected region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Finally, the Q and U uncertainties are normalized  by the square-root of the number of unmasked pixels, are summed  in quadrature with the corresponding calibration uncertainty, and  are propagated through Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We fit to the synchrotron and residual plus synchrotron spectra  the amplitude 𝐴, the spectral index 𝛽, and the curvature 𝑐 of a  modified power-law (as in e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Kogut 2012):  𝑑(𝜈) = 𝐴  � 𝜈  𝜈0  �𝛽+𝑐 ln 𝜈  𝜈0 ,  (30)  MNRAS 00, 1–31 (2023)  The Haze as seen by QUIJOTE  15  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Residual (left, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 27) and residual plus synchrotron (centre, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 29) polarization amplitude maps of, from top to bottom, QUIJOTE 11 GHz,  QUIJOTE 13 GHz, WMAP K-band, Planck 30 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The right column figures show the residual 𝑃 maps zoomed in the southern Haze region (region 8, see  Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3, same grid as the right panels in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The maps are in mK Rayleigh-Jeans temperature units, and the colour bar is scaled with a synchrotron-like  power-law: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5 mK · (𝜈/11 GHz)𝛽, with 𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  where 𝜈0 = 23 GHz a reference frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The range of frequency  used is 11 ≲ 𝜈 ≲ 70 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The fit is performed with a MCMC  sampling of the full posterior of the data with emcee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For the fit of  the residual plus synchrotron we applied a flat prior on the spectral  index −4 < 𝛽 < −2, and a Gaussian prior to the curvature parameter,  with a width 𝜎𝑐 = 1 and central values 𝜇𝑐 = 0 (dashed green line  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The synchrotron alone instead is fitted with no priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  For comparison we also fit the 𝐴 and 𝛽 parameters for a simple  power-law, given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 30 with 𝑐 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The fitted spectra in this  case are shown as thick lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10, and the respective 𝛽 are  reported in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' No priors are applied in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  It can be observed in region 8 (left panel in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10) that  the spectral index of a simple power-law for the residual plus  synchrotron is 𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='37  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='45, and for the synchrotron it is  𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='91 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The two spectral indices are compatible within  the uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' When including the curvature parameter in the fit,  the estimated 𝛽 are in even better agreement, with 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='97+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='48  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='41  for the residual plus synchrotron and 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='97+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16 for the syn-  chrotron alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Although the residual plus synchrotron shows slight  preference for a positive value of 𝑐, and the synchrotron alone  MNRAS 00, 1–31 (2023)  Residual P QlT11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='49Residual+Synchrotron P QlT1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='49QlT11:P Residua  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5/pix,200x200pix  (20,-23)  Tb [mKR]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='49Residual P QlT13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  T,[mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='31Residual+Synchrotron P QjT13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='31QIT13: P Residual  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5/pix,200x200pix  (20,-23)  Tb[mKR]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='31ResidualPWMAPK  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06Residual+Synchrotron P WMAPK  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06WMAPK:PResidual  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5/pix,200x200pix  (20,-23)  Tb[mKR]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06ResidualPPLA30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03Residual+SynchrotronPPLA3o  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03PLA3O: P Residua  200x200 pix  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5/pix,  (20,-23)  Tb [mKr]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0316  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Polarization SED after template fitting in the rectangle enclosing the southern Haze area in the overlap with the QUIJOTE sky (region 8, left), and  in the North Haze Bubble (region 5, right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The green points and lines represent the averaged and colour-corrected residual plus synchrotron spectrum (𝑅S,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 29), fitted with a simple (thick green line) and modified (dashed green line) power-law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The same, in black color, is for synchrotron (𝑆, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The fitted spectra indices are reported in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  shows a preference for negative 𝑐, curvature is not detected with  this methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In region 5 (see right panel in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10) the spectral index  of a simple power-law for the residual plus synchrotron is 𝛽 =  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='87+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='62  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='71, and for the synchrotron alone it is 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The  two spectral indices are compatible within the uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Also in  this case, when including the curvature parameter in the fit, the esti-  mated spectral indices are in better agreement, with 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='96+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='57  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54  for the residual plus synchrotron, and 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='96+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03 for the syn-  chrotron alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Although both the residual plus synchrotron and  the synchrotron alone show slight preference for values of 𝑐 < 0,  curvature is not detected with this analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  To summarize, no clear differences between the synchrotron  and residual plus synchrotron spectral indices are detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The  curvature is obtained to be compatible with zero given the large  error bars, especially on the spectral index of the residuals plus syn-  chrotron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, estimates of the curvature on these two regions  are also presented in de la Hoz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2023), where a negative curva-  ture is detected at high significance using the parametric component  separation method B-SeCRET (de la Hoz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020), although there  is not enough statistical evidence to favour the curvature against the  single power-law model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  An independent but complementary analysis of the polariza-  tion spectrum is shown in the next section, where we performed a  detailed analysis with T-T plots in polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3  T-T plots of Haze polarized plumes and spurs  With the aim of studying the Haze region in polarization with a  different approach to that presented in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2, we performed a  correlation T-T plot analysis as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2, in the re-  gions presented in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In this analysis, we also include the  S-PASS data at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz, corrected for Faraday rotation as described  in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We computed the spectral indices between the fre-  quency pairs:  23–30 GHz (WMAP K-band – Planck 30 GHz)  11–30 GHz (QUIJOTE 11 GHz – Planck 30 GHz)  11–23 GHz (QUIJOTE 11 GHz – WMAP K-band)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–30 GHz (S-PASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz – Planck 30 GHz)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–23 GHz (S-PASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz – WMAP K-band)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–11 GHz (S-PASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz – QUIJOTE 11 GHz)  A summary of the results is reported in Table 6, and a graphical  representation of the estimated spectral indices and uncertainties  is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11 for three selected frequency cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In order to  validate our results, we present a detailed analysis of the posterior  distribution of the T-T plots in appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  By looking at Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11 (or Table 6), we can notice that the Haze  in polarization appears as two extended and slightly asymmetric  bubbles (region 5,7–10), surrounded and connected to the Galactic  plane with filaments and spurs (region 2, 3, 4, 6, 11, 12, 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Our  interpretation is that the regions 2–13 are related to the Haze, or in  general to emission related to activity of the Galactic centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Indeed,  our measurements show that the spectral index of these regions is  flat at high frequencies (23–30 GHz) and uniformly moves towards  steeper values at lower frequencies (11–23 GHz and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–23 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The typical spectral indices of the Haze regions at 23–30 GHz are  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8 ≲ 𝛽 ≲ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6, while at lower frequencies they became steeper,  being −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 ≲ 𝛽 ≲ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0 at 11–23 GHz and at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–23 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We quote for comparison the average spectral indices of the  full-sky available from each survey combined with the mask de-  scribed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1, and of the NPS (region 1), which is a widely  studied region, currently modeled as synchrotron emission originat-  ing from the expanding shell of a nearby supernova explosion (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Panopoulou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2021 and Wat-  son et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (in preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We can notice that the spectral indices of  the full-sky and of the NPS at 23–30 GHz are steeper than those of  the Haze associated regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Instead, at 11–23 GHz we observe the  opposite behaviour: the full sky and NPS spectral indices are flatter  than those of the Haze associated regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We will extend the discussion of these results in Sec 5, where  we provide an overview and an interpretation of the measurements  obtained with different methodologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  QTRectangleSouthHaze  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='001  Qcos(2α)+Usin(2α)>  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='002  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='003  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='004  RS β= -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07±037  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='45  RS β = - 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='97+0-48 c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='26+078  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='005  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='63  Sβ= -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='91+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='006  V  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='29  10  20  30  40  50  60  70  freq [GHz]North Haze Bubble  RS β = - 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='87+02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='050  07  RS βB= -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='96+057  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54  6L0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='040  S β= - 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='93±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='93  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='030  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='020  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='010  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='000  V  10  20  30  40  50  60  70  freq [GHz]The Haze as seen by QUIJOTE  17  Region  Description  𝛽 23–30  𝛽 11–23  𝛽 11–30  𝛽 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–23  𝛽 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–30  𝛽 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–11  0  Full high-latitudes sky  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='42 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12  1  NPS  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06 2  Ext Haze Filament  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='99 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 3  Haze Filament  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='66 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='18  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='96 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19  4  Int Haze Filament  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='31  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='21  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='92 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='32 5  North Haze Bubble  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='14  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='18  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='18 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11  6  GCS  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='77 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='30 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='94 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  7  Rectangle South Haze  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='24  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='31 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  8  QJT Rectangle South Haze  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='77 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='36  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='32 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='23  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  9  South Haze Bubble  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='26 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='97 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  10  South Haze Bubble clean  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='81 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='33 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='96 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  11  eRosita West  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='24 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='41 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='26  12  unknown residual  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='34  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='29 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='18  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='31 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  13  eRosita East  −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='83 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='33 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Polarization spectral indices in the selected regions obtained with a T-T plots analysis based on data from Planck 30 GHz, WMAP K-band, QUIJOTE  11 GHz, and S-PASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For the determination of the spectral indices we use the methodology described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Polarization spectral indices in the selected regions (top) and uncertainties (bottom), obtained with a T-T plots analysis based on data from Planck  30 GHz (left), QUIJOTE 11 GHz (center), and S-PASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz (right), with WMAP K-band as a pivot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  5  SUMMARY AND DISCUSSION  We discuss here the results presented in the previous section, and  summarize what we obtained in some specific regions, particularly  in the southern Haze area (regions 7–10), in the North Haze Bubble  (region 5), and in North Haze filament (region 3), in intensity and  polarization, and with different methodologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1  South Haze area  Previous studies of the Haze emission in intensity have been concen-  trating in the area below the Galactic centre (region 7 in this work)  because of the apparently little complexity and low foregrounds  contamination of the intensity signal at WMAP and Planck-LFI  frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, the S-PASS polarization data (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A4)  provided a more detailed picture of the area, showing an extended  polarized plume in the south (region 9), but also localized contam-  inated areas that appear to be depolarized, and whose location is  indicated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' These depolarized areas are, in particular, re-  gion "A" identified by Iacobelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2014) and G353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='34, a nearby  supernova remnant (see Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Moreover, S-PASS data in polar-  ization show that almost the full southern bubble is affected by  Faraday rotation at low frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Indeed, from the polarization  angle maps shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A4, we can observe that the polarization  angle across the South Haze Bubble (region 9) has a transition from  positive to negative values when comparing the high (23 GHz and  30 GHz) and low (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz) frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In this work, according to  these considerations, we identified several regions in the area be-  low the Galactic centre (region 7, 8, 9, 10 - see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3) and we  studied them with different methodologies, including also the new  QUIJOTE data, both in intensity and polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  First of all, we reproduced the analysis of the Haze in intensity  by using Planck and WMAP data in region 7, and applying a similar  technique to that in Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We obtained  a spectrum of the Haze in region 7, using only Planck and WMAP  data (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 8), with 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05, and of the total synchrotron  with 𝛽𝑆 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We repeated the same analysis in region  9, which encloses the brightest part of the South Haze Bubble,  obtaining 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 and 𝛽𝑆 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='99 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' From these  results we can notice that the intensity Haze spectrum in region 9  (the South Haze Bubble) is consistent with the spectrum in region  7, although the latter is more extended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  β PLA 30-WMAP K  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='66  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79  2  83  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='74  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='81  16  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4β QJT 11-WMAP K  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06 -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='24  :3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  39  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4β SPASS-WMAP K  01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  36  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4Oβ PLA 30-WMAP K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='14  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='31  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='34  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3OB  QJT 11-WMAP K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3OB  SPASS-WMAP K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  18  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='318  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The main aim of this work is the characterization of the Haze  with the QUIJOTE data at lower frequencies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 11 and 13 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Since QUIJOTE is a ground based experiment located in the north-  ern hemisphere it does not cover the southern sky area enclosing  the South Haze Bubble (region 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, with QUIJOTE data,  we have access to a fraction of region 7, which we call region 8 in  this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1 we presented the intensity analysis in this  restricted area, including the low frequency QUIJOTE data, at 11  and 13 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A Haze component is detected in region 8 as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The observed excess of diffuse signal is detected with  ∼ 9𝜎 confidence level, at 11 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We computed the spectrum of  the emission in this region, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 7, obtaining a spectral  index of the Haze 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08 and of the total synchrotron  𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The spectrum of the Haze in region 8 is flatter  than the total synchrotron by Δ𝛽 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09, with the difference  significant at 2 𝜎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The central value of the Haze spectral index in re-  gion 8 (𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08) is slightly steeper than that obtained with  WMAP and Planck-LFI data alone in region 7 (𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05),  but the difference is not significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  A similar analysis is also performed, for the first time, in po-  larization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A map of the polarization residuals is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 9,  where we can observe residuals across the southern Haze area at  QUIJOTE frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The average residual signal in region 8 ex-  ceeds the noise level with high significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The residual struc-  ture observed in polarization is slightly displaced with respect to  that detected in intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The residual plus synchrotron component  in region 8 has a spectrum at 11 ≲ 𝜈 ≲ 70 GHz that, if fitted  with a simple power-law, has 𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='37  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='45, which is consistent  with that of the isolated synchrotron within the large uncertainty,  which has 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='91 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The difference  is Δ𝛽 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However when fitting a modified power-law  with curvature to the residual plus synchrotron there are hints for a  positive curvature, although with low significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  More solid hints of a positive curvature are observed with  the T-T plots analysis shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11, with which we observe a  steepening of the polarized emission within the South Haze Bubble  at low frequencies (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 and 11 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It is evident from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11 that  the spectral indices in region 7, 8 and 9, so in the whole South Haze  complex, are flat ("red") at 23–30 GHz and steep ("blue") at 11–  23 GHz and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–23 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This low frequency steepening behaviour,  however, is not only valid for the South Haze, but for the full complex  associated with the Galactic centre, represented by regions 2–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The only region where the low frequency steepening is not observed  is the NPS, which indeed is thought to be a distinct component from  the Haze (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2016c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Panopoulou  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2021) or from activity of the Galactic centre in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We mentioned also about two depolarized spots at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz,  corresponding to region "A" and to the nearby supernova remnant  G353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In order to check that the determination of the spectral  index of the South Haze Bubble is not affected by the presence of  these two extra structures in the area, we repeated the T-T plot by  masking region "A" and G353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='34 (region 10 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' As reported  in Table 6 and in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11, we obtained 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='81 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13 at 23–  30 GHz and 𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07 at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–30 GHz, which are in perfect  agreement with the spectral indices computed with the same T-T  plots methodology in the whole South Haze Bubble, which are  𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13 at 23–30 GHz and 𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06 at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–  30 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We conclude that the depolarized regions across the South  Haze do not bias the spectral index determination of the bubble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  North Haze Bubble  The North Haze Bubble (region 5) is the region, among those  studied in this paper, with the flattest spectral index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' From the  analysis with the intensity data, in the range of frequencies 23-  60 GHz18 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 8, right panel) we measured a spectral index of  the Haze 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05, and of the Haze plus synchrotron  𝛽𝑆 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='51±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Both 𝛽𝐻 and 𝛽𝑆 are far from the typical sky av-  erage synchrotron spectral index 𝛽 ≈ −3, meaning that, in this area  and frequency range, the emission of the Haze is dominant over the  Galactic diffuse synchrotron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The flat spectral index in this region  could also be due to residual free-free emission, which is bright  in this area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, we can compare this result with the spectral  index in polarization between 23 and 30 GHz, where there is no con-  tamination from free-free emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We obtained, with the T-T plots  in the North Haze Bubble, a spectral index 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='14 be-  tween 23 and 30 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We emphasize that the results derived from  T-T plots in polarization are compatible with those derived from  the intensity template fitting for the total synchrotron emission, at  WMAP and Planck-LFI frequencies, within 1𝜎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We therefore infer  that the observed flat intensity and polarization spectral index in  the North Haze Bubble can be ascribed to the synchrotron emission  produced by the Haze component, which dominates over the typical  (steeper) synchrotron in this region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  On the other hand, with the polarization template fitting analy-  sis, we observe that, similarly to region 8, the spectrum of the resid-  ual plus synchrotron component fitted with a simple power-law at  11 ≲ 𝜈 ≲ 70 GHz in region 5 is compatible, within the large uncer-  tainties, with that of the synchrotron alone, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10 (left  panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The difference of the spectral indices is Δ𝛽 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  However, T-T plots have shown that the spectral index of the to-  tal emission between 23 and 30 GHz is significantly flatter than that  at lower frequencies, especially when including 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz data in the  analysis, providing hints of a detection of curvature of the spectrum  across this region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This behaviour could be originated by a double  electron population that generates the polarized synchrotron signal  in region 5: one with a flat (𝛽 ∼ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5) spectra index that dominates  in the frequency range 20 GHz – 44 GHz, and one with a steeper  spectrum (𝛽 ∼ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2) that emerges at 𝜈 < 20 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' QUIJOTE data  provide a characterization that is compatible with that presented  by Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013) based on S-PASS data, fitting well with  the interpretation presented in Crocker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' According to  Crocker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2015) the observed emission is produced by: i) shock  re-accelerated young cosmic-rays electrons that are responsible for  the flat (or hard) synchrotron emission of the microwave Haze;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' ii)  an old population of cosmic-rays electrons that escape the contact  discontinuity of the shock, and emit the steeper synchrotron radia-  tion observed in the S-PASS plume;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' iii) colliding hadrons enclosed  in the contact-discontinuity surface that radiate the 𝛾-rays, which is  what we observe in the Fermi bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A 𝛾-ray component of IC  emision, from the same electrons that radiate the microwave Haze,  is also present, but it is subdominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This model agrees with the  results obtained in this work for both the North and South polarized  lobes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  18 We do not include QUIJOTE low frequency intensity data here, due to  the not well understood structures in the residual, which could be due to  atmospheric 1/f noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  The Haze as seen by QUIJOTE  19  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3  Comparison between South and North Haze bubbles  An interesting consideration is connected with the recent results  presented by Jew & Grumitt (2020), who computed with a novel  technique the spectral indices of the North and South Haze bub-  bles between 30 and 44 GHz, using Planck data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' They reported a  difference between the polarization spectral index of the two bub-  bles, being 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09 in the North and 𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  in the South Haze.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19 In this work, we measure an asymmetry of  the spectral indices of the northern and southern Haze bubbles in  intensity, in the frequency range 23-60 GHz, consistent with what  Jew & Grumitt (2020) found in polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We obtain a total syn-  chrotron index 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 in the North Haze Bubble, and  𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='99 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 in the South Haze Bubble, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 8 us-  ing only WMAP and Planck data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' There is consistency between our  total synchrotron intensity spectrum and the polarization spectrum  at 30-44 GHz measured by Jew & Grumitt (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In addition, our results with T-T plots confirm that the asym-  metry between the North and South Haze bubbles is also seen  in polarization, at 23-30 GHz: the spectral index across the North  Haze Bubble is 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='14, and in the South Haze Bubble it  is 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The South Haze Bubble has a steeper spectrum  than the North Haze Bubble, both in intensity and polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In-  terestingly, at lower frequencies, this trend is inverted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The T-T plots  between 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz and 23 GHz show that the polarization spectrum  of the North Haze Bubble (𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03) is slightly steeper than  that in the South Haze Bubble (𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06), with a difference  Δ𝛽 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6𝜎).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  North Haze filament  The North Haze filament (region 3) is an interesting case of study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  It corresponds to the structure identified by Vidal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2015) and  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2016c) as the filament surrounding  the northern Fermi bubble in 𝛾-rays, and the microwave Haze in the  north.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5 of Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2016c), a measure-  ment of the spectral index of the filament using Planck 30 GHz and  WMAP K-band data is reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' They measured 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16  with T-T plots of the unbiased 𝑃MAS maps at 30 and 23 GHz,  with a methodology that is essentially the same as that described in  Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In this work, we performed the measurement in the same  region, but using a different technique as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2,  obtaining 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='66 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='18 (see Table 6 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In the attempt of reproducing the result of Planck Collaboration  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2016c) with T-T plots of 𝑃MAS, we identified a possible source  of bias that can introduce significant differences in the estimate of  the 𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Although the polarization amplitude 𝑃MAS is not affected by  noise bias if computed as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 14, it is a positive quantity, and, in  regions with low signal to noise the determination of the spectral  index with the classical T-T plot methodology (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1) can be  biased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In addition, when allowing uncertainties in both axes, the  correlation between zero-level and slope is strong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For example, in  the northern Haze filament (region 3), we obtained 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  using a T-T plot of the 𝑃MAS maps, where we allowed to fit both the  slope and an offset between the maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, if the zero level of  𝑃MAS is correctly set, as it is in this case where we first adjust the  19 Note that the regions studied in Jew & Grumitt (2020) do not perfectly  match with ours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' They integrated two approximately symmetric bubbles in  the north and in the south corresponding to the 𝛾-ray Fermi bubbles, while  we restrict our analysis to the brightest region of the plumes as observed at  low frequency (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz), in polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' T-T plot with 𝑃MAS in the North Haze filament (region 3),  comparing the case where we fix or do not fix the offset of the linear fit, to  illustrate the effect of Eddington bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  relative offset of the 𝑄 and 𝑈 maps with the reference, we can force  the intercept of the T-T plot slope to be zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In this case, we obtain  a value of the spectral index 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03, which is inconsistent  with the previous result, where the intercept was free to vary, but  which is in full agreement with the result reported in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3  (Table 6), obtained with the method described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 based  on Fuskeland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 12 we show the T-T plot of the unbiased polarization  amplitude in the filament (region 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The blue line is a fit of the  points for both the slope and offset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The red line is the fit over the  same data points, but where the intercept is forced to be zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We  can clearly see that the red and blue lines have a different slope,  and that therefore the recovered spectral indices are also different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The small difference between the red and blue data points is due  to the different colour correction that is applied to the same initial  data, given that the spectral index resulting from the two fitting  methodologies is different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Our final conclusion is that T-T plot of  the positive definite unbiased polarization amplitude (𝑃MAS) could  be affected by noise bias, which can be mitigated by fitting the T-T  plot with the intercept fixed to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The method applied in this  work (described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 and based on Fuskeland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2014,  2019), instead, is not significantly biased, since it uses T-T plots  of a combination of Q and U data, which can be both positive and  negative avoiding zero level problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  6  CONCLUSIONS  We derived the spectral properties of the microwave Haze with  different methodologies, in intensity and in polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For this we  used, for the first time, new Haze observations from the QUIJOTE  experiment, at 11 and 13 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In combination we used the publicly  available S-PASS (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz), WMAP (23–61 GHz) and Planck-LFI  (30–70 GHz) data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We computed the spectrum of the Haze after applying template  fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We used the intensity data of QUIJOTE, WMAP and Planck-  LFI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In particular we measured the Haze spectrum in the South, in  the overlap with the QUIJOTE sky coverage, within region 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We  obtained a synchrotron spectrum with spectral index 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79 ±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 7) at frequencies 11–60 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' As a general trend, we  MNRAS 00, 1–31 (2023)  P Haze Filament PLA30 GHz WMAP23 GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  β = -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='001  KRJ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  β= -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  q=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Z  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  GH  LA30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  WMAP23 GHz [mKrj]20  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  find that the spectrum of the Haze component in intensity is flatter  than the typical diffuse synchrotron emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Our results in the  whole south Haze area (region 7), however, are in slight tension  with those obtained by Dobler & Finkbeiner (2008) and Planck  Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013) in the same region, as we obtain a spectral  index of the Haze that is steeper than that obtained from previous  works (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 𝛽 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 from this work and 𝛽 ∼ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='56 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  from Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2013, at frequencies 23–60 GHz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We also studied the intensity spectrum of the Haze in the North  and South bubbles (regions 5 and 9), but excluding QUIJOTE data  that are not available or possibly affected by noise artifacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We  measured a synchrotron emission from a Haze component with a  spectral index at 23–60 GHz of 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 in the North  Haze Bubble and 𝛽𝐻 = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05 in the South Haze Bubble,  as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We measured for the first time in intensity a  difference of the spectral index in the North and South bubbles, in  the frequency range 23–60 GHz, with a significance of ≈ 4𝜎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This  behaviour is also observed in polarization in this work between 23  and 30 GHz, in agreement with previous results by Jew & Grumitt  (2020) between 30 and 44 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In polarization, we studied the spectra of the Haze-related  structures with both a template fitting (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 9 and 10) and corre-  lation T-T plot technique (see Table 6 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11) providing spectral  indices for different frequency pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' After fitting a synchrotron and  dust component to the QUIJOTE maps, we observed residual po-  larized structures that are inconsistent with the expected noise level  with high significance (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This result can be interpreted  as a hint of curvature of the synchrotron spectral index across the  area where we observe the positive residuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However a study of  the spectral properties in regions 5 and 8 does not have sufficient  signal-to-noise to show clear differences between the synchrotron  and residual plus synchrotron spectral indices (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We also  tried to constrain a curvature parameter, which is obtained to be  compatible with zero given the large error bars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  However, our results based on T-T plots (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11) show flat  spectrum regions across the Haze area at 23–30 GHz, and an evident  steepening at low frequencies, in agreement with Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11 that the Haze-related structures  (regions 2–13) are significantly flat (−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8 ≲ 𝛽 ≲ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6) compared  with the sky average synchrotron (𝛽 ∼ −3) at 23–30 GHz, while at  lower frequencies (11–30 GHz and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3–30 GHz) the spectrum of the  Haze steepens significantly (−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 ≲ 𝛽 ≲ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' On the other hand  the NPS (region 1), which is thought to be a nearby supernova shell  not related with the Haze structures, shows the opposite behaviour:  its spectral index does not show significant differences across the  frequencies presented in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Our results in polarization are compatible with those presented  in Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' They can be therefore interpreted with the  model presented in Crocker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2015), according to whom young  cosmic ray electrons enclosed in the contact discontinuity of a shock  generated by Galactic centre nuclear activity radiate the flat syn-  chrotron of the Haze, while older cosmic ray electron escaping the  contact discontinuity produce the steeper synchrotron observed in  the S-PASS lobes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However, in intensity, we do not observe a change  of the Haze spectral index as we do see in polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The inten-  sity spectrum in region 8 is well characterized by a single power-law  with 𝛽𝐻 ∼ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Further investigation is needed to understand this  behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Possibly the use of stellar absorption like in Panopoulou  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2021), or the modelling of the magnetic field and of the cos-  mic rays as proposed by the IMAGINE Consortium (Boulanger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2018) could help to formulate a more comprehensive interpretation  of this complex area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  ACKNOWLEDGEMENTS  The QUIJOTE experiment is being developed by the Instituto  de Astrofisica de Canarias (IAC), the Instituto de Fisica de  Cantabria (IFCA), and the Universities of Cantabria, Manch-  ester and Cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We thank the staff of the Teide Obser-  vatory for invaluable assistance in the commissioning and op-  eration of QUIJOTE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Partial financial support was provided  by the Spanish Ministry of Science and Innovation under  the projects AYA2007-68058-C03-01,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' AYA2007-68058-C03-02,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  AYA2010-21766-C03-01,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' AYA2010-21766-C03-02,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' AYA2014-  60438-P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' ESP2015-70646-C2-1-R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' AYA2017-84185-P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' ESP2017-  83921-C2-1-R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  AYA2017-90675-REDC  (co-funded  with  EU  FEDER funds),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' PGC2018-101814-B-I00,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' PID2019-110610RB-  C21,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' PID2020-120514GB-I00,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' IACA13-3E-2336,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' IACA15-BE-  3707,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' EQC2018-004918-P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' the Severo Ochoa Programs SEV-  2015-0548 and CEX2019-000920-S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' the Maria de Maeztu Pro-  gram MDM-2017-0765,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' and by the Consolider-Ingenio project  CSD2010-00064 (EPI: Exploring the Physics of Inflation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We  acknowledge support from the ACIISI, Consejeria de Economia,  Conocimiento y Empleo del Gobierno de Canarias and the European  Regional Development Fund (ERDF) under grant with reference  ProID2020010108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This project has received funding from the Eu-  ropean Union’s Horizon 2020 research and innovation program un-  der grant agreement number 687312 (RADIOFOREGROUNDS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This research made use of computing time available on the high-  performance computing systems at the IAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We thankfully acknowl-  edge the technical expertise and assistance provided by the Spanish  Supercomputing Network (Red Española de Supercomputación), as  well as the computer resources used: the Deimos/Diva Supercom-  puter, located at the IAC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' FG acknowledges funding from the Eu-  ropean Research Council (ERC) under the European Union’s Hori-  zon 2020 research and innovation programme (grant agreement No  101001897).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' EdlH acknowledge partial financial support from the  Concepción Arenal Programme of the Universidad de Cantabria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  FP acknowledges support from the Spanish State Research Agency  (AEI) under grant number PID2019-105552RB-C43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' BR-G ac-  knowledges ASI-INFN Agreement 2014-037-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' DT acknowl-  edges the support from the Chinese Academy of Sciences Presi-  dent’s International Fellowship Initiative, Grant N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020PM0042.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This work has made use of S-band Polarisation All Sky Survey  (S-PASS) data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Some of the results in this paper have been de-  rived using the HEALPix (Górski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2005) and healpy (Zonca  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2019) packages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We also use Numpy (Harris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2020), and  Matplotlib (Hunter 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  DATA AVAILABILITY  The QUIJOTE raster scan data used in this paper are property of  the QUIJOTE Collaboration and can only be shared on request to  the corresponding authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The QUIJOTE wide-survey maps will  be made publicly available in the first QUIJOTE data release, as  detailed in Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Ancillary data employed in  the analysis for this paper are publicly available and can be accessed  as referred along the paper text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  REFERENCES  Ackermann M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2014, ApJ, 793, 64  Almy R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', McCammon D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Digel S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Bronfman L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', May J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2000, ApJ,  545, 290  MNRAS 00, 1–31 (2023)  The Haze as seen by QUIJOTE  21  Ashley T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Fox A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Cashman F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Lockman F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Bordoloi R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Jenkins  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Wakker B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Karim T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2022, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08838  Bennett C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2003, ApJS, 148, 1  Bennett C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2013, ApJS, 208, 20  Biermann P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Becker J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Caceres G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Meli A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Seo E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Stanev T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  2010, ApJ, 710, L53  Boulanger F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2018, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2018, 049  Cardoso J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Martin M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Delabrouille J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Betoule M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Patanchon G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2008,  arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' arXiv:0803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1814  Carretti E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2013, Nature, 493, 66  Carretti E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2019, MNRAS, 489, 2330  Choi S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Page L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2015, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2015, 020  Cholis I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Goodenough L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Weiner N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2009, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D, 79, 123505  Crocker R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, MNRAS, 423, 3512  Crocker R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Aharonian F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2011, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 106, 101102  Crocker R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Bicknell G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Taylor A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Carretti E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2015, ApJ, 808,  107  de la Hoz E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Vielva P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Barreiro R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Martínez-González E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2020, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Cos-  mology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2020, 006  de la Hoz E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Barreiro R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Vielva P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2023, MNRAS, accepted  Delahaye T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Böhm C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Silk J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, MNRAS, 422, L16  Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Davies R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Davis R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2003, MNRAS, 341, 369  Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Peel M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Vidal M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2011, MNRAS, 418, L35  Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2018, New Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 80, 1  Dobler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, ApJ, 750, 17  Dobler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Finkbeiner D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2008, ApJ, 680, 1222  Dobler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Finkbeiner D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Cholis I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Slatyer T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Weiner N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2010, ApJ, 717,  825  Egorov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Gaskins J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Pierpaoli E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Pietrobon D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2016, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Cosmology  Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2016, 060  Eriksen H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2004, ApJS, 155, 227  Eriksen H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Jewell J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Banday A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Górski K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  Lawrence C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2008, ApJ, 676, 10  Finkbeiner D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2003, ApJS, 146, 407  Finkbeiner D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2004, ApJ, 614, 186  Foreman-Mackey D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Hogg D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Lang D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Goodman J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2013, PASP, 125,  306  Fox A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2015, ApJ, 799, L7  Fuskeland U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Wehus I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Eriksen H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Næss S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2014, ApJ, 790, 104  Fuskeland U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2019, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05923  Gaskins J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2016, Contemporary Physics, 57, 496  Génova-Santos R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2017, MNRAS, 464, 4107  Górski K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Hivon E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Banday A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Wand elt B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Hansen F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  Reinecke M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Bartelmann M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2005, ApJ, 622, 759  Guidi F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2021, MNRAS, 507, 3707  Guo F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Mathews W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, ApJ, 756, 181  Guo F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Mathews W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dobler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Oh S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, ApJ, 756, 182  Harris C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2020, Nature, 585, 357  Haslam C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Salter C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Stoffel H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Wilson W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 1982, A&AS, 47, 1  Hooper D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Finkbeiner D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dobler G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2007, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D, 76, 083012  Hoyland R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, in Millimeter, Submillimeter, and Far-  Infrared Detectors and Instrumentation for Astronomy VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 845233,  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='925349  Hunter J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2007, Computing in Science & Engineering, 9, 90  Hutschenreuter S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2022, A&A, 657, A43  Iacobelli M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2014, A&A, 566, A5  Jew L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Grumitt R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2020, MNRAS,  Jones D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Crocker R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Reich W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Ott J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Aharonian F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, ApJ,  747, L12  Kataoka J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Yamamoto M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Nakamura Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Ito S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Sofue Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Inoue Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  Nakamori T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Totani T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2021, ApJ, 908, 14  Keihänen E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Keskitalo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Kurki-Suonio H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Poutanen T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Sirviö A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2010,  A&A, 510, A57  Kogut A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, ApJ, 753, 110  Krachmalnicoff N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2018, A&A, 618, A166  Lacki B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2014, MNRAS, 444, L39  Large M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Quigley M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Haslam C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 1962, MNRAS, 124, 405  Li J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Hodges-Kluck E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Stein Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Bregman J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Irwin J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dettmar  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2019, ApJ, 873, 27  Merloni A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' arXiv:1209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3114  Panopoulou G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Readhead A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Pearson T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Peel  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2021, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='14267  Peel M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Davies R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Band ay A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Jaffe T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Jonas  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, MNRAS, 424, 2676  Peel M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Genova-Santos R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Leahy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', López-Caraballo  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Fernández-Torreiro M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Rubiño-Martín J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Spencer L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2022,  Research Notes of the American Astronomical Society, 6, 252  Pietrobon D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, ApJ, 755, 69  Pillepich A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Nelson D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Truong N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Weinberger R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Martin-Navarro I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  Springel V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Faber S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Hernquist L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2021, MNRAS, 508, 4667  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2011, A&A, 536, A20  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2013, A&A, 554, A139  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2014a, A&A, 565, A103  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2014b, A&A, 571, A11  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2016a, A&A, 586, A141  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2016b, A&A, 594, A10  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2016c, A&A, 594, A25  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2016d, A&A, 594, A26  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2018, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06208  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2020a, A&A, 641, A1  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2020b, A&A, 641, A6  Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2020c, A&A, 643, A42  Plaszczynski S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Montier L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Levrier F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Tristram M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2014, MNRAS, 439,  4048  Predehl P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2020, Nature, 588, 227  Remazeilles M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Banday A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Bigot-Sazy M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Ghosh T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  2015, MNRAS, 451, 4311  Rubiño-Martín J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', López-Caraballo C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Génova-Santos R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Rebolo R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  2012a, Advances in Astronomy, 2012, 351836  Rubiño-Martín J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012b, in Ground-based and Airborne Telescopes  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 84442Y, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='926581  Rubiño-Martín J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Guidi F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Génova Santos R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2023, MNRAS,  accepted  Sofue Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 1977, A&A, 60, 327  Sofue Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 1994, ApJ, 431, L91  Sofue Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2015, MNRAS, 447, 3824  Su M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Slatyer T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Finkbeiner D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2010, ApJ, 724, 1044  Tristram M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Macías-Pérez J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Renault C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Santos D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2005, MNRAS, 358,  833  Vidal M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Davies R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Leahy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2015, MNRAS, 452, 656  Vidal M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Leahy J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Dickinson C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2016, MNRAS, 461, 698  Yang H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Ruszkowski M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Zweibel E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2022, Nature Astronomy,  Zhang R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Guo F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2020, ApJ, 894, 117  Zhang R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Guo F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2021, arXiv e-prints, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01710  Zhang M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Li Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Morris M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2021, ApJ, 913, 68  Zonca A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Singer L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Lenz D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Reinecke M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Rosset C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Hivon E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Gorski K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=',  2019, The Journal of Open Source Software, 4, 1298  Zubovas K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', Nayakshin S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=', 2012, MNRAS, 424, 666  MNRAS 00, 1–31 (2023)  22  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  APPENDIX A: INTENSITY AND POLARIZATION MAPS  USED IN THE ANALYSIS  Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A1, A2 and A3 show the I, Q and U maps that have been used  for the first part of the study presented in this paper, which applies a  template fitting technique (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1) to the QUIJOTE, WMAP  and Planck-LFI maps (results in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A4 shows the debiased polarization amplitude 𝑃MAS maps  computed as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 14), the corresponding  uncertainties (centre) computed with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 16 and accounting (in  quadrature) for the calibration uncertainty, and the polarization an-  gle (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We show maps at the four frequencies that we selected to  perform a study of the polarization spectral index analysis with T-T  plots, which are, from top to bottom: S-PASS at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz, QUIJOTE  11 GHz, WMAP K-band and Planck 30 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A5 shows the Faraday rotation angle map at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz (left),  and the corresponding uncertainty (centre), obtained from the ro-  tation measure map derived from S-PASS data as 𝜙𝐹𝑅 = 𝑅𝑀 · 𝜆2  (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The blank pixels are those where no 𝑅𝑀 is provided,  and they are therefore excluded from the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The same figure  also shows, on the right, the S-PASS Faraday rotation corrected po-  larization angle map, which is very similar to the polarization angle  maps at higher frequencies shown in the right panels of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  APPENDIX B: FARADAY ROTATION CORRECTION TO  S-PASS  Low frequency photons suffer the effect of Faraday rotation and  depolarization along their path across a magnetized interstellar  medium, before they reach the observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2019), Ia-  cobelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2014) and Fuskeland et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' (2019) discussed in detail  these effects in the S-PASS data, which clearly shows depolarization  in the Galactic plane, and rotation also at high Galactic latitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  As we anticipated in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2, in this work we account for these  effects by correcting the Faraday rotation and masking regions with  evident depolarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In order to correct for the Faraday rotation at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz, we  applied a backwards rotation of the Q and U maps of S-PASS, by  the Faraday rotation angle 𝜙𝐹𝑅 = 𝑅𝑀·𝜆2, where 𝑅𝑀 is the rotation  measure map delivered by the S-PASS collaboration1 (Carretti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  2019) and 𝜆 is the S-PASS observed wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We produced an  independent RM measurement using S-PASS, QUIJOTE, WMAP  and Planck data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We obtained results that are consistent with the  S-PASS RM map across the North and South Haze bubbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The rotation is applied as follows:  � 𝑄′  𝑈′  �  =  �  cos(2𝜙𝑅𝑀)  sin(2𝜙𝑅𝑀)  − sin(2𝜙𝑅𝑀)  cos(2𝜙𝑅𝑀)  � � 𝑄  𝑈  �  ,  (B1)  where Q and U are the original S-PASS maps, and Q’ and U’ are the  corrected ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2 The final uncertainty of the Q’ and U’ maps is the  propagation of the uncertainty of Q, U and 𝜙𝑅𝑀, through Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' B1:  𝜎2  𝑄′ =𝜎2  𝑄 cos2(2𝜙𝑅𝑀) + 𝜎2  𝑈 sin2(2𝜙𝑅𝑀)  (B2)  + 4𝜎2  𝜙𝑅𝑀 (𝑈 cos(2𝜙𝑅𝑀) − 𝑄 sin(2𝜙𝑅𝑀))2  1 https://sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='com/inaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='it/spass/healpix-maps  2 Note that, following what is now common practice in the CMB field, we  apply the CMB convention for the polarization angle, while the S-PASS  maps are delivered with the IAU convention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This inverts the sign of the  U map, and therefore also rotates the polarization angle in the opposite  direction relative to North.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  𝜎2  𝑈′ =𝜎2  𝑄 sin2(2𝜙𝑅𝑀) + 𝜎2  𝑈 cos2(2𝜙𝑅𝑀)  (B3)  + 4𝜎2  𝜙𝑅𝑀 (𝑈 sin(2𝜙𝑅𝑀) + 𝑄 cos(2𝜙𝑅𝑀))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The pixels where no 𝑅𝑀 is provided are excluded from the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This correction however is not sufficiently accurate at low Galactic  latitudes where Faraday rotation angle could be larger than 90 deg,  but our analysis is focused on the diffuse emission far from the  Galactic plane, therefore this is not a critical issue for the stability  of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We show in appendix A (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A5) the Faraday rotation angle  map at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The corresponding uncertainty is also shown  in the same figure (centre), as well as the S-PASS polarization  angle map after correcting for Faraday rotation (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' This last  map can be compared with the polarization angle maps at higher  frequencies (right panels in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A4), showing that, after applying  the correction, the spatial distribution of the S-PASS polarization  angles is very similar to that of WMAP and Planck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  APPENDIX C: NULL TESTS  In order to characterize noise structures in the maps we used null-  tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In particular, the half-difference nulltest is the difference be-  tween maps obtained from two independent splits selected by date  of observation (see Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The half-difference  maps are expected to show residual noise artifacts or systematics in  the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' They are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' C1, for intensity (first row), Stokes  Q (second), Stokes U (third), polarization amplitude (fourth), at  11 (left) and 13 GHz (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It can be observed that residual noise  structures are affecting the intensity maps at very large angular  scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' However they are very smooth in the Haze region, and are  not expected to affect the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In polarization, especially in the  P maps that are depicted with the same color scale as the polariza-  tion residual maps in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 9, no significant noise or systematics are  observed, therefore the polarization results are expected to be very  robust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  APPENDIX D: POSTERIOR ANALYSIS OF THE T-T  PLOTS  Following the methodology presented in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2, in order to  check the goodness of the linear regression of the T-T plots for  each angle 𝛼𝑖, we compute the posterior distribution of the spectral  index parameter 𝑃(𝛽).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We noticed that in low signal-to-noise areas,  the wings of the posterior distribution of the spectral index are not  reaching zero, and therefore the determination of the spectral index  is not appropriate, showing bias towards steep values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In order to  be sure that the estimated 𝛽 is unbiased, we have to verify that the  posterior of the T-T plots is well defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We define the posterior of the slope between the data at fre-  quency 𝜈 (y-axis data, with error 𝜎𝑦) and 𝜈0 (x-axis data, with error  𝜎𝑥).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' It is:  𝑃(𝑚(𝛽)) = 𝑁 · 𝑒−𝜒2/2,  (D1)  with 𝑁 being a normalization factor and 𝜒2 the chi-square of the  linear regression:  𝜒2 =  ∑︁  𝑗  (𝑦 𝑗 − 𝑚(𝛽) · 𝑥 𝑗 − 𝑞)2  (𝜎2𝑦𝑗 + 𝑚2(𝛽) · 𝜎2𝑥𝑗 )  ,  (D2)  where 𝑗 runs over the pixels enclosed in the area selected for the T-T  plots, and 𝑞 is the best-fit intercept for the given 𝑚 (𝑞 =< 𝑦−𝑚𝑥 >).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  The Haze as seen by QUIJOTE  23  Figure A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Intensity maps ordered in frequency: QUIJOTE 11 GHz, QUIJOTE 13 GHz, WMAP K-band, Planck 30 GHz, WMAP Ka-band, WMAP Q-band,  Planck 44 GHz, WMAP V-band, Planck 70 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The maps are in units of mK Rayleigh-Jeans, and the colorbar range values are scaled with a synchrotron-like  power-law: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5 · (𝜈/11 GHz)𝛽, with 𝛽 = −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The grey area represents the mask that is used for the analysis, which is a combination of the QUIJOTE sky  coverage with the free-free and CMB mask, as described in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The slope 𝑚 is related with the spectral index 𝛽, so we can find the  posterior of the spectral index by converting 𝑚 into 𝛽 with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Given that we solve a linear regression for a set of 18 angles 𝛼,  we can compute a posterior distribution 𝑃(𝛽) = 𝑃(𝛽𝑖) for each  of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The final posterior is then the product 𝑃tot = �  𝑖 𝑃(𝛽𝑖),  whose maximum should coincide with the 𝛽 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We show here the plots of the estimated spectral indices as  a function of the projection angle 𝛼, and the relative posterior  distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D1 we show the results for Planck 30 GHz-  WMAP K-band, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D2 for QUIJOTE 11 GHz-WMAP K-band,  and in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D3 for the Faraday rotation corrected (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' B) S-PASS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz-WMAP K-band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  The weighted average of the spectral indices, which is repre-  sented as an horizontal black line in the 𝛽 vs 𝛼 figures, correspond  to the final results of this work, which are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 11 and  quoted in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Colour corrections are applied independently for  the determination of the spectral index at each angle 𝛼.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  In the plots of the posteriors, each coloured line represents the  posterior for a determined projection angle 𝛼, normalized with its  maximum and computed with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Here no colour corrections  are applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The red thick line in the plots shows the final posterior  normalized with its maximum, obtained as the product of each  single posterior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The vertical blue line shows the final  spectral index computed with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 18, with no colour corrections  applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' We can notice that there is a very good match between  the final posterior distribution and the estimated weighted average  spectral index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' When we apply colour correction to the spectral  index, we obtain the value represented by the vertical black line in  the posterior figures, which corresponds to the horizontal black line  of the 𝛽 vs 𝛼 figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  We can see from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D1-D3 that the posterior distributions  of the spectral indices in all the regions and frequencies are closed  and approximately Gaussian, and that therefore the spectral indices  are well constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' In addition, we can observe that, when we  use the low frequency data such as QUIJOTE 11 GHz and S-PASS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz, the posteriors are narrower than that of Planck 30 GHz,  thanks to the wider frequency lever with respect to WMAP K-band,  which leads to a more precise determination of the spectral index at  low frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  This paper has been typeset from a TEX/LATEX file prepared by the author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  ImapQJT11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  T,[mKRj]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50I map QJT13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='91  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='91mapWMAPK  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17mapPLA30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09mapWMAPKa  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06mapWMAPQ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03mapPLA44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02mapWMAPy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01mapPLA70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0124  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A1 for Stokes 𝑄 maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure A3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' A1 for Stokes 𝑈 maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  Q map QJT11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  T,[mKRj]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50Q map QJT13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='91  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='91Q map WMAPK  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17  T,[mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17Q map PLA30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09  T,[mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09Q map WMAPKa  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  T,[mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06Q map WMAPQ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  Tp [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03Q map PLA44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02Q map WMAPV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  T,[mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01Q map PLA70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  T,[mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01U map QJT11  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  T,[mKR]]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50U map QJT13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='91  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='91UmapWMAPK  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17UmapPLA30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09JmapWMAPKa  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  Tb [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06JmapWMAPQ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  T,[mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03UmapPLA44  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02UmapWMAPy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01UmapPLA70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01  T,[mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01The Haze as seen by QUIJOTE  25  Figure A4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Debiased 𝑃 maps (left), corresponding error maps including calibration uncertainty (centre), and polarization angle (right) of S-PASS at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz,  QUIJOTE at 11 GHz, WMAP at 23 GHz, and Planck at 30 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure A5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' S-PASS Faraday rotation angle (left) and uncertainty (centre), in units of degrees, and following the CMB convention on polarization angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The  right panel shows the S-PASS polarization angle map after correcting the Faraday rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  T,[mKR]]  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02Op SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='000  T,[mKRj]  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='413Polarization angle SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  α [deg]  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00QJT 11GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  T, [mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='75Op QJT 11GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='000  Tb [mKR]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='084Polarization angle QJT 11GHz  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  α[deg]  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00WMAP 23GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='080p WMAP 23GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='000  T, [mKr]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='010Polarization angle WMAP 23GHz  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  α[deg]  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00Planck 30GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04op PIanck 30GHz  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='000  T,[mKr]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='005Polarization angle Planck 3oGHz  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  α[deg]  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00Faraday Rotation Angle SPASs  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  ΦRM [deg]  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5ErrorFaradayRotationAngle SPASs  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Oprm [deg]  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4Polarization angle SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  α [deg]  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0026  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Nulltest of the intensity (first row), Stokes-Q (second), Stokes-U (third), and polarization amplitude (forth) maps obtained from the half-difference  nulltest (see Rubiño-Martín et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 2023), of the 11 GHz (left) and 13 GHz (right) QUIJOTE-MFI nominal plus Haze and 𝜌-Ophiuchi raster maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' For comparison  purposes, the colour scale is the same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 6 for intensity, and of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' 9 for polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  Half null-test D) QlT11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  T,[mKRJ]  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00Half null-test () QJT13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='21  T,[mKR]]  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='21Half null-test (Q) QlT11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  T,[mKRJ]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20Half null-test (Q) QJT13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12  Tb[mKR]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12Half null-test (U) Q111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  T, [mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20Half null-test (U) Ql113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12  T,[mKR]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12Half null-test (P) QlT11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  T,[mKR]]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50Half null-test (P) QJT13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  T,[mKRj]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='30The Haze as seen by QUIJOTE  27  Figure D1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Validation of T-T plots of Planck 30 GHz-WMAP K-band for different regions, showing the spectral index 𝛽 as a function of the projection angle  (odd rows) and the posterior distributions for each projection angle (even rows).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' The black lines and shaded area show the final estimated spectral index 𝛽  ±1𝜎 uncertainty with colour corrections applied, while the dark blue lines and shaded area represent the estimated spectral index 𝛽 ±1𝜎 uncertainty before  applying colour corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  Planck30GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='WMAP23:  NPS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  B  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  1g min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  1g  0  20  40  60  80  α [deg]Planck 30GHz,WMAP23  ExtHazeFilament  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  B -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  <β>=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='99±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='19  1g min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  1g  0  20  40  60  80  α [deg]Planck 30GHz, WMAP23:  HazeFilament  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='30  <β>=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='66±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='18  lo min(err)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  1g  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  B  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='90  0  20  40  09  80  α [deg]Posterior Planck 30GHz, WMAP 23GHz:  NPS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  α= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  α= 55  α= 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  α= 59  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  α= 10  α= 65  α= 14  α= 70  α=20  α= 75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  α= 25  α= 80  Normalized  α= 29  α= 85  α=35  β CC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  α=40  β no CC  α= 45  Ptot  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  α= 50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosteriorPlanck30GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='WMAP23GHz  Ext Haze Filament  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior Planck 30GHz, WMAP 23GHz:  HazeFilament  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPlanck 30GHz,WMAP23:  Int Haze Filament  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  B -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  <β>=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='17±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='31  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  1o min(err)  1g  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  0  20  40  60  80  α [deg]Planck 30GHz,WMAP23  NorthHazeBubble  <β>=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='54±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='14  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  1o min(err)  1g  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  B  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  0  20  40  60  80  α [deg]Planck 30GHz, WMAP23  GCS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  <β > =-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  lo min(err)  1g  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  B -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  0  20  40  60  80  α [deg]Posterior Planck 30GHz, WMAP 23GHz:  Int Haze Filament  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosteriorPlanck30GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='WMAP23GHz  NorthHazeBubble  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized F  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior Planck 30GHz, WMAP 23GHz  GCS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  β28  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure D1 – continued  MNRAS 00, 1–31 (2023)  Planck30GHz,WMAP23:  RectangleSouthHaze  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='65  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='75  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='85  <β>=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  1g min(err)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='90  1g  0  20  40  60  80  α [deg]Planck 30GHz,WMAP23:  QJTRectangleSouthHaze  <β>=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='77±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  1g min(err)  1g  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  B  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0  20  40  60  80  α [deg]Planck 30GHz,WMAP23  SouthHazeBubble  <β> =-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='82±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  lg min(err)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  1g  m -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='90  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0  20  40  60  80  α [deg]PosteriorPlanck30GHz,WMAP23GHz  RectangleSouthHaze  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  BPosteriorPlanck30GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='WMAP23GHz  QlTRectangleSouthHaze  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior Planck 30GHz, WMAP 23GHz:  SouthHazeBubble  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPlanck 30GHz,WMAP23:  eRositaWest  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  <β>=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22  1g min(err)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  1g  0  20  40  60  80  α [deg]Planck 30GHz,WMAP23:  eRositaEast  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='75  Bβ -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  <β> =-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='83±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='33  1o min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  1g  0  20  40  60  80  α [deg]Planck 30GHz, WMAP23:  Region 12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  <β>=-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='74±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='34  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  1o min(err)  1g  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  B -2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='75  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  0  20  40  60  80  α [deg]Posterior Planck 30GHz, WMAP 23GHz:  eRositaWest  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior Planck 30GHz, WMAP 23GHz:  eRosita East  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior Planck 30GHz, WMAP 23GHz  Region 12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βThe Haze as seen by QUIJOTE  29  Figure D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D1 for QUIJOTE 11 GHz-WMAP K-band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  QJT 11GHZ, WMAP23  NPS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  B -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  lo min(err)  1g  0  20  40  60  80  α [deg]QJT11GHz,WMAP23:  Ext Haze Filament  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='30  B  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  <β> =-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  1g min(err)  1g  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  0  20  40  60  80  α [deg]QJT 11GHz, WMAP23  Haze Filament  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  B -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='30  lg min(err)  1g  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  0  20  40  60  80  α [deg]Posterior QJT 11GHz,WMAP 23GHz:  NPS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  α= 55  α= 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  α= 59  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  α= 10  α= 65  α= 14  α= 70  α=20  α= 75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  α=25  α= 80  Normalized  α= 29  α= 85  α= 35  β CC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  α= 40  β no CC  α=45  Ptot  α=50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior QJT 11GHz,WMAP 23GHz  ExtHazeFilament  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior QJT 11GHz,WMAP 23GHz  Haze Filament  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βQJT11GHz,WMAP23:  North Haze Bubble  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  B -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  1o min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  1g  0  20  40  60  80  α [deg]QJT 11GHZ, WMAP23  GCS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  lg min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='30  1g  B -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  0  20  40  60  80  α [deg]QJT11GHz,WMAP23:  QJTRectangle SouthHaze  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  B  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='36  1g min(err)  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  1g  0  20  40  60  80  α [deg]Posterior QJT11GHz,WMAP 23GHz:  NorthHazeBubble  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  IPosterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior QJT 11GHz,WMAP 23GHz  GCS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  I Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior QJT 11GHz,WMAP 23GHz  QjTRectangleSouthHaze  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βQJT11GHz,WMAP23:  eRosita West  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='79±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='13  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='50  lg min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  1g  m -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='70  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='90  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0  20  40  60  80  α [deg]QJT11GHz,WMAP23  Region 12  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  B  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='29±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16  lg min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  1g  0  20  40  60  80  α[deg]Posterior QJT 11GHz,WMAP 23GHz  eRositaWest  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior QJT 11GHz,WMAP 23GHz  Region 12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  β30  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Guidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  Figure D3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' Same as in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content=' D1 for S-PASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3 GHz-WMAP K-band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  MNRAS 00, 1–31 (2023)  SPASS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ,WMAP23:  HazeFilament  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='85  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='90  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='95  B  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='08  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  1g min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  1g  0  20  40  60  80  α [deg]SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ, WMAP23:  Int Haze Filament  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='01±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='21  1g min(err)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  1g  B  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0  20  40  60  80  α [deg]SPASS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ,WMAP23:  NorthHazeBubble  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='16  <β> =-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='18  1o min(err)  1g  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  B -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='22  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='24  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='26  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='28  0  20  40  60  80  α[deg]Haze Filament  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  α= 55  α= 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='  α= 59  Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  α=10  α=65  α= 14  α= 70  α=20  α= 75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  α=25  α= 80  Normalized I  α= 29  α= 85  α= 35  β CC  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  α=40  β no CC  α= 45  Ptot  α= 50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosteriorSPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz,WMAP 23GHz:  ntHazeFilament  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz, WMAP 23GHz:  NorthHazeBubble  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  I Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βSPASS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ,WMAP23:  GCS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  B  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='09±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  1g min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  1g  0  20  40  60  80  α [deg]SPASS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ,WMAP23  RectangleSouthHaze  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  m -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='12±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='02  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='14  1g min(err)  1g  0  20  40  60  80  α [deg]SPASS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ,WMAP23:  QjTRectangleSouthHaze  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  B  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  1g min(err)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  1g  0  20  40  60  80  α [deg]Posterior SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz, WMAP 23GHz:  GCS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  I Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0PosteriorSPASS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz,WMAP23GHz  RectangleSouthHaze  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  I Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0Posterior SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz, WMAP 23GHz  QJTRectangleSouthHaze  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  I Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βSPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ, WMAP23  SouthHazeBubble  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  <β> =-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='11±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='06  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  1o min(err)  1g  0  20  40  09  80  α [deg]SPASS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ,WMAP23  SouthHazeBubbleclean  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='05  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='15  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='10±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='07  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  1g min(err)  1g  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  0  20  40  60  80  α [deg]Posterior SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz, WMAP 23GHz  SouthHazeBubble  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  I Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosteriorSPASS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='WMAP23GHz:  SouthHazeBubbleclean  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  I Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βThe Haze as seen by QUIJOTE  31  Figure D3 – continued  MNRAS 00, 1–31 (2023)  SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz, WMAP23:  eRosita West  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='35  m -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='03  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='45  1o min(err)  1g  0  20  40  60  80  α [deg]SPASS2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHZ,WMAP23:  eRositaEast  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='25  B  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='30  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='04  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='35  1g min(err)  1g  0  20  40  60  80  α [deg]SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz, WMAP23:  Region 12  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='20  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='40  B  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='60  <β>=-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='28±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='18  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='80  1g min(err)  1g  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='00  0  20  40  60  80  α [deg]Posterior SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz, WMAP 23GHz:  eRositaWest  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  I Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz, WMAP 23GHz  eRosita East  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  I Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  Normalized  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  βPosterior SPASS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='3GHz, WMAP 23GHz:  Region 12  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  Normalized Posterior  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
+page_content='0  β' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/GtE4T4oBgHgl3EQfgQ2M/content/2301.05115v1.pdf'}
diff --git a/H9AyT4oBgHgl3EQfTPcY/content/tmp_files/2301.00100v1.pdf.txt b/H9AyT4oBgHgl3EQfTPcY/content/tmp_files/2301.00100v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..860aa43145c04926562da67056c5af8e97799d06
--- /dev/null
+++ b/H9AyT4oBgHgl3EQfTPcY/content/tmp_files/2301.00100v1.pdf.txt
@@ -0,0 +1,1251 @@
+arXiv:2301.00100v1  [math.AP]  31 Dec 2022
+COBORDISM INVARIANCE OF THE INDEX FOR
+REALIZATIONS OF ELLIPTIC OPERATORS REVISITED
+THOMAS KRAINER
+Abstract. We revisit an argument due to Lesch [11, 12] for proving the cobor-
+dism invariance of the index of Dirac operators on even-dimensional closed
+manifolds and combine this with recent work by the author [10] to show van-
+ishing results for the spectral flow for families of selfadjoint Fredholm realiza-
+tions of elliptic operators in case the family is induced on the boundary by an
+elliptic operator on a compact space. This work is motivated by studying the
+behavior of the index of realizations of elliptic operators under cobordisms of
+statified manifolds.
+1. Introduction
+One of the original proofs of the Atiyah-Singer Index Theorem is based on showing
+that the index of Dirac type operators is invariant under cobordisms, see Palais
+[17]. This proof is analytic in nature and rooted in the classical theory of elliptic
+boundary value problems. Other proof strategies for the index theorem such as the
+heat equation proof have generally been favored because these proofs require less
+sophisticated analytic techniques than the original cobordism proof.
+Higson [9] gave a proof of the cobordism invariance of the index by attaching an
+infinite half-cylinder to the boundary and extending the operator from the manifold
+with boundary to the manifold with cylindrical end. The Dirac type operator on
+the resulting odd-dimensional complete manifold is essentially selfadjoint, and the
+analytic arguments involved in Higson’s proof are considerably simpler compared
+to the original proof. Lesch [11], on the other hand, gave a proof by attaching a
+(generalized) cone to the boundary and extended the operator from the manifold
+with boundary to a cone operator; while conic manifolds are incomplete and thus
+dealing with domains of realizations of the resulting conic Dirac type operator is
+needed, Lesch’s approach is still much simpler from a functional analytic point of
+view than the original proof because the maximal and minimal domains of L2-
+based realizations in the conic case differ only by a finite-dimensional space – the
+price to pay is the more intricate analysis to deal with the singularity which at
+this juncture has been introduced artificially. Several other analytic proofs of the
+cobordism invariance of the index [3, 16], a K-theory proof [5], and generalizations
+[4, 8, 14, 19] have since been found.
+This note is motivated by recent advances in elliptic theory on stratified man-
+ifolds with incomplete iterated wedge metrics [1, 2, 6, 7, 15, 18] and gives an ap-
+plication of the spectral flow formula for indicial operators obtained in our recent
+paper [10]. Stratified cobordisms and the cobordism invariance of the index for the
+2020 Mathematics Subject Classification. Primary: 58J20; Secondary: 58J05, 58J32, 58J30.
+Key words and phrases. Manifolds with singularities, index theory, cobordism.
+1
+
+2
+THOMAS KRAINER
+signature operator have been considered in [1, 2], where especially in [2] the opera-
+tor is no longer essentially selfadjoint and suitable boundary conditions associated
+with the singular strata are considered; stratified cobordism and the invariance of
+the index are used in an essential way to establish the properties of the signature
+of a Cheeger space considered in that paper.
+From our point of view Lesch’s proof [11, 12] of the cobordism invariance of
+the index is very natural in the context of elliptic theory on stratified manifolds
+because, unlike in the classical smooth case, singular analysis and dealing with
+boundary conditions associated with singular strata already are essential features
+of the investigations here.
+In this note we will revisit and extend Lesch’s proof from the Dirac case to more
+general operators of any order, and what amounts to the vanishing of the index in
+the Dirac case (for null-cobordisms) will accordingly generalize to the vanishing of
+the spectral flow for indicial families. Our recent paper [10] on indicial operators,
+which are abstract functional analytic model operators associated to generalized
+conical singularities, is the basis for this. We will only be concerned with null-
+cobordisms and proving vanishing results here; more general notions of cobordisms
+and cobordism invariance follow upon reduction to this case. Without detailing the
+precise assumptions, the argument proceeds as follows:
+Let (M, g) be a Riemannian manifold, and let U = U(Y ) ⊂ M be an open subset
+that is isometric to (0, ε) × Y with product metric dx2 + gY for some ε > 0, where
+(Y, gY ) is another Riemannian manifold. The reader ought to think of both M and
+Y as the open interior of compact stratified manifolds M and Y equipped with
+incomplete iterated wedge metrics, where Y is a boundary hypersurface of M, and
+U(Y ) is a collar neighborhood. Let E → M be a Hermitian vector bundle such
+that E
+��
+U(Y ) ∼= π∗
+Y E isometrically, where E → Y is a Hermitian vector bundle, and
+πY : (0, ε) × Y → Y is the canonical projection. Let
+A : C∞
+c (M; E ) → C∞
+c (M; E )
+be an elliptic differential operator of order µ ≥ 1 that is symmetric with respect to
+the inner product induced by the Riemannian and Hermitian metrics, and suppose
+that A is in U(Y ) of the form
+A ∼= A∧ = x−1
+µ
+�
+j=0
+aj(y, Dy)(xDx)j : C∞
+c ((0, ε) × Y ; π∗
+Y E) → C∞
+c ((0, ε) × Y ; π∗
+Y E),
+where aj(y, Dy) ∈ Diffµ−j(Y ; E). Let
+p(σ) =
+µ
+�
+j=0
+aj(y, Dy)σj : C∞
+c (Y ; E) → C∞
+c (Y ; E), σ ∈ C,
+be the indicial family. Now suppose that
+Amin : Dmin(A) ⊂ L2(M; E ) → L2(M; E )
+(1.1)
+is some closed symmetric extension of A : C∞
+c (M; E ) ⊂ L2(M; E ) → L2(M; E ),
+and let Amax : Dmax(A) ⊂ L2(M; E ) → L2(M; E ) be the adjoint – we point out
+here that Amin is not necessarily the minimal extension of A from C∞
+c (M; E ), and
+
+COBORDISM INVARIANCE OF THE INDEX REVISITED
+3
+therefore Amax is not the largest L2-based closed extension either, i.e. we only have
+Dmin(A) ⊃ {u ∈ L2(M; E ); ∃uk ∈ C∞
+c (M; E ), uk → u in L2(M; E ),
+and Auk ⊂ L2(M; E ) Cauchy},
+Dmax(A) ⊂ {u ∈ L2(M; E ); ∃v ∈ L2(M; E ) :
+⟨Aφ, u⟩L2(M;E ) = ⟨φ, v⟩L2(M;E ) ∀φ ∈ C∞
+c (M; E )},
+and these inclusions are generally proper. The reader ought to think of the operator
+A as an elliptic iterated incomplete wedge operator on M, and the domain Dmin(A)
+as determined by previously chosen boundary conditions for A associated with
+singular strata of M away from the boundary hypersurface Y ⊂ M.
+One of the main points now is that under suitable localization and compatibility
+assumptions these extensions of A should localize to U(Y ) and be fully captured
+by the extensions of the indicial operator
+A∧ : C∞
+c (R+; E1) ⊂ L2(R+ × Y ; π∗
+Y E) → L2(R+ × Y ; π∗
+Y E).
+(1.2)
+Here
+Hµ
+comp(Y ; E) ⊂ E1 ⊂ Hµ
+loc(Y ; E)
+is the common domain for the indicial family p(σ) : E1 ⊂ E0 → E0, σ ∈ C,
+where E0 = L2(Y ; E), giving rise to a holomorphic family of unbounded Fredholm
+operators that are selfadjoint for σ ∈ R.
+The reader ought to think of E1 as
+determined by certain lateral boundary conditions associated with the singular
+strata of Y , obtained via restriction to U(Y ) by the previously determined boundary
+conditions on M for A that gave rise to Dmin(A); the localization and compatibility
+assumptions are such that the boundary conditions previously chosen for A on M
+should be selfadjoint away from the boundary hypersurface Y . The upshot of all
+of this is that we obtain a unitary equivalence
+�
+Dmax(A)/Dmin(A), [·, ·]A
+� ∼=
+�
+Dmax(A∧)/Dmin(A∧), [·, ·]A∧
+�
+of finite-dimensional indefinite inner product spaces by passing to representatives
+supported in U(Y ) ∼= (0, ε)×Y , thus allowing transitioning between M and R+×Y ;
+here
+[·, ·]A : Dmax(A) × Dmax(A) → C,
+[u, v]A = 1
+i
+�
+⟨Amaxu, v⟩L2 − ⟨u, Amaxv⟩L2
+�
+is the adjoint pairing, and likewise for [·, ·]A∧, while Dmin(A∧) is the domain of the
+closure A∧,min of (1.2), and Dmax(A∧) is the domain of the adjoint A∧,max = A∗
+∧,min.
+In particular, we have
+sgn
+�
+Dmax(A)/Dmin(A), [·, ·]A
+�
+= sgn
+�
+Dmax(A∧)/Dmin(A∧), [·, ·]A∧
+�
+for the signatures of these spaces. On the one hand, using the spectral flow formula
+from [10], we have
+sgn
+�
+Dmax(A∧)/Dmin(A∧), [·, ·]A∧
+�
+= SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ],
+while on the other hand sgn
+�
+Dmax(A)/Dmin(A), [·, ·]A
+�
+= 0 if (1.1) is Fredholm or
+the embedding Dmax(A) ֒→ L2(M; E ) is compact, which combined leads to the
+desired conclusion that
+SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ] = 0.
+
+4
+THOMAS KRAINER
+In the Dirac case the spectral flow of the indicial family is easily seen to equal
+the Fredholm index of the operator D : D(D) ⊂ L2(Y ; E−) → L2(Y ; E+) on the
+even-dimensional boundary Y , thus recovering cobordism invariance of the index
+in this context.
+The structure of this paper is as follows: In Section 2 we briefly review what is
+needed from extension theory of symmetric operators, in particular the criteria that
+ensure that
+�
+Dmax(A)/Dmin(A), [·, ·]A
+�
+is finite-dimensional with signature zero. In
+Section 3 we review results from our paper [10] on indicial operators in the form in
+which they are needed here; we also address in this section how indicial operators of
+first order that model the Dirac case fit into this framework in order to obtain the
+desired conclusions about the cobordism invariance of the index when specializing to
+such operators. In Section 4 we fill in the details of the outline above and prove the
+null-cobordism theorem (Theorem 4.2). Finally, in Appendix A, we discuss the null-
+cobordism theorem for smooth manifolds; assumptions appear much weaker here
+on the geometry and the participating objects because the analytic tools available
+in this case are rich enough to create the preconditions needed to apply the null-
+cobordism theorem rather than having to assume them from the outset.
+With
+the ongoing further development of singular analysis on stratified manifolds we
+anticipate similar reductions and simplifications for such cases in the future as well.
+2. Preliminaries from extension theory
+Let H be a separable complex Hilbert space, and suppose Amin : Dmin ⊂ H → H
+is closed, densely defined, and symmetric. Let Amax := A∗
+min : Dmax ⊂ H → H be
+the adjoint. We equip Dmax with the graph inner product
+⟨u, v⟩Amax = ⟨u, v⟩ + ⟨Amaxu, Amaxv⟩
+and associated graph norm. Then Dmin ⊂
+�
+Dmax, ∥ · ∥Amax
+�
+is a closed subspace,
+and
+Dmax = Dmin ⊕ ker(Amax + i) ⊕ ker(Amax − i)
+by von Neumann’s formulas. The dimensions
+n± = dim ker(Amax ∓ λi) ∈ N0 ∪ {∞},
+λ > 0,
+are the deficiency indices of the operator Amin and independent of λ > 0. The
+operators
+Amin ± iλ : Dmin ⊂ H → H,
+λ > 0,
+are injective and have closed range, and we have n± < ∞ if and only if Amin ± iλ
+is Fredholm, in which case n± = − ind(Amin ± iλ). The adjoint pairing
+[·, ·]A : Dmax × Dmax → C,
+[u, v]A = 1
+i
+�
+⟨Amaxu, v⟩ − ⟨u, Amaxv⟩
+�
+descends to a nondegenerate Hermitian sesquilinear form (indefinite inner product)
+[·, ·] : Dmax/Dmin × Dmax/Dmin → C.
+If dim Dmax/Dmin < ∞, i.e. if Amin has finite deficiency indices, the signature of
+the adjoint pairing is given by
+sgn
+�
+Dmax/Dmin, [·, ·]
+�
+= n+ − n−.
+The following criteria are standard and useful for verification that n+ = n− < ∞.
+
+COBORDISM INVARIANCE OF THE INDEX REVISITED
+5
+Proposition 2.1. Suppose Amin : Dmin ⊂ H → H is Fredholm. Then Amin has
+finite and equal deficiency indices, and therefore
+sgn
+�
+Dmax/Dmin, [·, ·]
+�
+= 0.
+Proof. Because Amin : Dmin ⊂ H → H is Fredholm there exists ε > 0 such that
+Amin + iλ : Dmin ⊂ H → H is Fredholm for −ε < λ < ε, and consequently both
+n± < ∞ and Amin + iλ is Fredholm for all λ ∈ R. Now
+R ∋ λ �→ Amin + iλ : Dmin ⊂ H → H
+is a continuous Fredholm function and therefore has constant index. Thus
+n+ = − ind(Amin + i) = − ind(Amin − i) = n−.
+□
+Proposition 2.2. If the embedding
+�
+Dmax, ∥ · ∥Amax
+�
+֒→ H is compact then Amin
+has finite and equal deficiency indices.
+Proof. The norms ∥·∥Amax and ∥·∥H are equivalent on ker(Amax±i), and the identity
+map
+�
+ker(Amax ± i), ∥ · ∥Amax
+�
+→
+�
+ker(Amax ± i), ∥ · ∥H
+�
+is compact by assumption.
+Thus dim ker(Amax ± i) < ∞. Now Amin ± i : Dmin ⊂ H → H are both Fredholm,
+and because Dmin ֒→ H is compact we have ind(Amin − i) = ind(Amin + i). The
+proposition is proved.
+□
+3. Indicial operators
+We consider indicial operators of the form
+A∧ = x−1
+µ
+�
+j=0
+aj(xDx)j : C∞
+c (R+; E1) ⊂ L2(R+; E0) → L2(R+; E0),
+(3.1)
+where µ ∈ N and E0 and E1 are separable complex Hilbert spaces such that E1 ֒→
+E0 is continuous and dense, and the operators aj : E1 → E0 are continuous for
+j = 0, . . . , µ. Let
+p(σ) =
+µ
+�
+j=0
+ajσj : E1 → E0,
+σ ∈ C
+(3.2)
+be the indicial family associated with A∧. We make the following assumptions:
+(i) p(σ) : E1 ⊂ E0 → E0 is closed, densely defined, and Fredholm for σ ∈ C, and
+the map C ∋ σ �→ p(σ) ∈ L (E1, E0) is holomorphic.
+(ii) We have p(σ)∗ = p(σ) : E1 ⊂ E0 → E0 as unbounded operators in E0.
+(iii) For (λ, σ) ∈ R2 and |λ, σ| ≥ R ≫ 0 sufficiently large p(σ) + iλ : E1 → E0 is
+invertible with
+sup
+|λ,σ|≥R
+�
+(1 + λ2 + σ2µ)
+1
+2 ���
+p(σ) + iλ
+�−1��
+L (E0) +
+���
+p(σ) + iλ
+�−1��
+L (E0,E1)
+�
+< ∞,
+and for every k ∈ {1, . . ., µ} we have
+sup
+|λ,σ|≥R
+(1 + λ2 + σ2µ)
+k
+2µ ���
+∂k
+σp(σ)
+��
+p(σ) + iλ
+�−1��
+L (E0) < ∞.
+In [10] we systematically studied operators of the kind (3.1) under such assumptions.
+We summarize some of the findings below:
+
+6
+THOMAS KRAINER
+(1) The operator (3.1) is symmetric and densely defined in L2(R+; E0). Let
+A∧,min be its closure, and A∧,max = A∗
+∧,min be the adjoint. Then
+dim Dmax(A∧)/Dmin(A∧) < ∞,
+i.e., A∧ has finite deficiency indices.
+(2) The boundary spectrum
+specb(p) = {σ ∈ C; p(σ) : E1 → E0 is not invertible} ⊂ C
+is discrete, and every strip |ℑ(σ)| ≤ K, K > 0, contains only finitely many
+elements of specb(p). The elements of the boundary spectrum are generally
+referred to as indicial roots.
+(3) Fix an arbitrary cut-off function ω ∈ C∞
+c (R+) with ω ≡ 1 near x = 0. For
+each indicial root σ0 ∈ specb(p) let
+Eσ0(p) =
+�
+u = ω
+k
+�
+j=0
+ej logj(x)xiσ0; k ∈ N0 and ej ∈ E1,
+and p(σ)(Mu)(σ) is holomorphic at σ = σ0
+�
+,
+(3.3)
+where
+�
+Mu
+�
+(σ) =
+� ∞
+0
+x−iσu(x) dx
+x
+is the Mellin transform of u. This space is finite-dimensional for every σ0,
+and we have
+Dmax(A∧) = Dmin(A∧) ⊕
+�
+σ0∈specb(p)
+− 1
+2 <ℑ(σ0)< 1
+2
+Eσ0(p).
+(3.4)
+(4) We have
+x
+1
+2 H (R+; E1) ∩ L2(R+; E0) ֒→ Dmin(A∧),
+and Dmin(A∧) = x
+1
+2 H (R+; E1) ∩ L2(R+; E0) if and only if p(σ) : E1 → E0
+is invertible for all ℑ(σ) = − 1
+2.
+The space H (R+; E1) is the completion of C∞
+c (R+; E1) with respect to
+the norm
+∥u∥2
+H =
+�
+R
+∥p(σ + iγ0)(Mu)(σ)∥2
+E0 dσ,
+where γ0 ∈ R is arbitrary such that p(σ + iγ0) : E1 → E0 is invertible for
+all σ ∈ R. We have
+H (R+; E1) ֒→ Hµ
+b (R+; E0) ∩ L2
+b(R+; E1),
+and in typical situations these spaces are equal; this is the case, for instance,
+if
+sup
+σ∈R
+∥p(σ + iγ0)(⟨σ⟩µ + iΛ)−1∥L (E0) < ∞,
+(3.5)
+where Λ : E1 ⊂ E0 → E0 is selfadjoint (e.g. for Λ = p(0)).
+(5) While not discussed in [10] it is not hard to see that, under the added
+assumption that the embedding E1 ֒→ E0 is compact, multiplication by a
+
+COBORDISM INVARIANCE OF THE INDEX REVISITED
+7
+cut-off function ω ∈ C∞
+c (R+) with ω ≡ 1 near x = 0 induces a compact
+operator ω : xαH (R+; E1) → L2
+b(R+; E0) for every α > 01.
+Consequently, if additionally p(σ) : E1 → E0 is invertible for all ℑ(σ) =
+− 1
+2, we obtain a compact map ω : Dmax(A∧) → L2(R+; E0), and a bounded
+map 1 − ω : Dmax(A∧) → Dmin(A∧). The latter is based on the identity
+Dmin(A∧) = x
+1
+2 H (R+; E1) ∩ L2(R+; E0) and localization properties of the
+space H (R+; E1) (see [10, Proposition 7.6]).
+(6) The adjoint pairing
+[·, ·]A∧ : Dmax(A∧) × Dmax(A∧) → C,
+[u, v]A∧ = 1
+i
+�
+⟨A∧,maxu, v⟩L2(R+;E0) − ⟨u, A∧,maxv⟩L2(R+;E0)
+�
+induces a nondegenerate Hermitian sesquilinear form
+[·, ·] : Dmax(A∧)/Dmin(A∧) × Dmax(A∧)/Dmin(A∧) → C,
+and its signature is given by the spectral flow of the indicial family (3.2)
+along the real line:
+sgn
+�
+Dmax(A∧)/Dmin(A∧), [·, ·]
+�
+= SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ].
+(3.6)
+Note that p(σ) : E1 → E0 is invertible for |σ| ≥ T ≫ 0 large enough,
+σ ∈ R, and the spectral flow in (3.6) then refers to p(σ) on the interval
+−T ≤ σ ≤ T . Only crossings of real indicial roots contribute terms to the
+spectral flow.
+The focus in this paper is on the signature of the adjoint pairing, and by (3.6)
+only real indicial roots are relevant. In order to obtain simple expressions for the
+minimal domain and the maximal domain (3.4) of A∧ it is sometimes convenient
+to introduce a scaling parameter t > 0 to remove any small non-real indicial roots
+from the strip |ℑ(σ)| ≤ 1
+2. This leads to
+A∧,t = x−1
+µ
+�
+j=0
+ajtj(xDx)j : C∞
+c (R+; E1) ⊂ L2(R+; E0) → L2(R+; E0)
+with indicial family
+pt(σ) = p(tσ) : E1 ⊂ E0 → E0,
+σ ∈ C,
+and the standing assumptions on p(σ) imply that the analogous properties are also
+satisfied for pt(σ), and all estimates are locally uniform with respect to t > 0. In
+particular, the spectral flow
+SF[ pt(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ]
+is independent of t > 0 by homotopy invariance, and thus
+sgn
+�
+Dmax(A∧,t)/Dmin(A∧,t), [·, ·]
+�
+1The function a0(x, σ) = xαω(x)p(σ + iγ0)−1 is a Mellin symbol taking values in the com-
+pact operators E0 → E0, and we have sup{⟨log(x)⟩j⟨σ⟩µ+k∥(xDx)l∂k
+σa0(x, σ)∥L (E0); (x, σ) ∈
+R+ × R} < ∞ for all j, k, l ∈ N0.
+Thus the Mellin pseudodifferential operator opM(a0) :
+L2
+b(R+; E0) → L2
+b(R+; E0) is compact, which implies compactness of the multiplication opera-
+tor ω : xαH (R+; E1) → L2
+b(R+; E0) as asserted.
+
+8
+THOMAS KRAINER
+is independent of t > 0. For 0 < t ≤ t0 small enough, pt(σ) : E1 ⊂ E0 → E0 is
+invertible for all 0 < |ℑ(σ)| ≤ 1
+2. We then have
+Dmin(A∧,t) = x
+1
+2 H (R+; E1) ∩ L2(R+; E0),
+where the definition of H (R+; E1) is accordingly based on pt(σ), and
+Dmax(A∧,t) = Dmin(A∧,t) ⊕
+�
+σ0∈specb(pt)∩R
+Eσ0(pt).
+If (3.5) holds for p(σ) it is true for all pt(σ), and in this case the space
+H (R+; E1) = Hµ
+b (R+; E0) ∩ L2
+b(R+; E1)
+is independent of t > 0; thus the minimal domain
+Dmin(A∧) = x
+1
+2 Hµ
+b (R+; E0) ∩ x
+1
+2 L2
+b(R+; E1) ∩ L2(R+; E0)
+is independent of 0 < t ≤ t0.
+Operators of first order. Let D : D(D) ⊂ H1 → H2 be closed and densely
+defined, and let D∗ : D(D∗) ⊂ H2 → H1 be the adjoint. Write
+E0 =
+H1
+⊕
+H2
+and E1 =
+D(D)
+⊕
+D(D∗)
+֒→ E0.
+We assume that D (and therefore also D∗) is Fredholm, and that the embeddings
+for both domains D(D) ֒→ H1 and D(D∗) ֒→ H2 are compact. Consider then
+D∧ = x−1
+��1
+0
+0
+−1
+�
+(xDx)+
+� 0
+D∗
+D
+0
+��
+: C∞
+c (R+; E1) ⊂ L2(R+; E0) → L2(R+; E0)
+with indicial family
+D(σ) =
+�
+σ
+D∗
+D
+−σ
+�
+: E1 ⊂ E0 → E0,
+σ ∈ C.
+Now D(σ) satisfies the assumptions previously stated for indicial families with
+µ = 1, including (3.5) with Λ = D(0); see Lemma 3.8 for the required estimates.
+Therefore the conclusions summarized above hold for D∧, and by Lemma 3.9 we
+have
+sgn
+�
+Dmax(D∧)/Dmin(D∧), [·, ·]
+�
+= ind[D : D(D) ⊂ H1 → H2].
+(3.7)
+The only real indicial root is σ0 = 0, and after possibly introducing a sufficiently
+small scaling parameter t > 0 and replacing D∧ by
+D∧,t = x−1
+�
+t
+�
+1
+0
+0
+−1
+�
+(xDx) +
+�
+0
+D∗
+D
+0
+��
+we have
+Dmin(D∧,t) = x
+1
+2 H1
+b (R+; E0) ∩ x
+1
+2 L2
+b(R+; E1) ∩ L2(R+; E0),
+Dmax(D∧,t) = Dmin(D∧,t) ⊕ E0(Dt).
+In this case E0(Dt) = E0(D) is also independent of t > 0, and we have
+E0(D) =
+�
+u = ω
+� k
+k∗
+�
+; k ∈ ker(D), k∗ ∈ ker(D∗)
+�
+.
+
+COBORDISM INVARIANCE OF THE INDEX REVISITED
+9
+This follows from (3.3) in view of
+D(σ)−1 = σ
+�
+1
+0
+0
+−1
+�
+[D(0)2 + σ2]−1 + D(0)[D(0)2 + σ2]−1
+=
+�ΠD
+0
+0
+−ΠD∗
+� 1
+σ + holomorphic
+near σ = 0, where ΠD : H1 → ker(D) and ΠD∗ : H2 → ker(D∗) are the orthogonal
+projections onto the kernels of D and D∗, respectively. For sufficiently small t > 0
+a brief calculation shows that the adjoint pairing is given by
+�
+ω
+�
+k1
+k∗
+1
+�
+, ω
+�
+k2
+k∗
+2
+��
+D∧,t = t
+�
+⟨k1, k2⟩H1 − ⟨k∗
+1, k∗
+2⟩H2
+�
+for kj ∈ ker(D) and k∗
+j ∈ ker(D∗), j = 1, 2, which provides a direct justification for
+(3.7) for D∧,t (for small t > 0) that does not rely on the spectral flow.
+Lemma 3.8. For (λ, σ) ∈ R2 write z = σ + iλ ∈ C and consider
+D(z) = D(σ) + iλ =
+� z
+D∗
+D
+−z
+�
+: E1 ⊂ E0 → E0.
+Then D(z) is invertible for all z ∈ C \ {0}, and
+sup
+|z|≥1
+{|z| · ∥D(z)−1∥L (E0) + ∥D(z)−1∥L (E0,E1)} < ∞.
+Proof. We have D(z)∗ = D(z), and
+D(z)∗D(z) = D(z)D(z)∗ =
+�|z|2 + D∗D
+0
+0
+|z|2 + DD∗
+�
+= D(0)2 + |z|2.
+This operator is invertible for z ∈ C \ {0}, and consequently D(z) is invertible with
+D(z)−1 = D(z)∗[D(z)D(z)∗]−1 = [zΠ1−zΠ2][D(0)2+|z|2]−1+D(0)[D(0)2+|z|2]−1,
+where Πj : E0 → Hj ⊂ E0 is the orthogonal projection, j = 1, 2.
+In view of
+D(0)[zΠ1 − zΠ2] = [zΠ2 − zΠ1]D(0) we have
+D(0)D(z)−1 = [zΠ2 − zΠ1]D(0)[D(0)2 + |z|2]−1 + D(0)2[D(0)2 + |z|2]−1.
+The Spectral Theorem implies
+sup
+|z|≥1
+{∥D(0)2[D(0)2+|z|2]−1∥+∥zD(0)[D(0)2+|z|2]−1∥+∥z2[D(0)2+|z|2]−1∥} < ∞,
+where ∥ · ∥ = ∥ · ∥L (E0). The lemma now follows.
+□
+Lemma 3.9. We have
+ind[D : D(D) ⊂ H1 → H2] = SF
+�
+D(σ) : E1 ⊂ E0 → E0, σ ∈ R
+�
+.
+Proof. Let K = ker(D(0)) = ker(D) ⊕ ker(D∗). Then
+D(σ) =
+�DK(σ)
+0
+0
+DK⊥(σ)
+�
+:
+K
+⊕
+K⊥ ∩ E1
+→
+K
+⊕
+K⊥
+,
+σ ∈ R.
+
+10
+THOMAS KRAINER
+Now DK(σ) : K → K, σ ̸= 0, has eigenvalues σ, −σ of multiplicities dim ker(D) and
+dim ker(D∗), respectively, and DK⊥(σ) is invertible for all σ ∈ R. Thus
+ind D = dim ker(D) − dim ker(D∗)
+= SF
+�
+DK(σ) : K → K, σ ∈ R
+�
+= SF
+�
+D(σ) : E1 ⊂ E0 → E0, σ ∈ R
+�
+.
+□
+4. The null-cobordism theorem
+We now revisit the setting discussed in the introduction to prove the null-cobordism
+theorem. We make the following product type assumptions on the geometry and
+the operator:
+Let (M, g) be a Riemannian manifold, and let U = U(Y ) ⊂ M be an open subset
+that is isometric to (0, ε) × Y with product metric dx2 + gY for some ε > 0, where
+(Y, gY ) is another Riemannian manifold. Let E → M be a Hermitian vector bundle
+such that E
+��
+U(Y ) ∼= π∗
+Y E isometrically, where E → Y is a Hermitian vector bundle,
+and πY : (0, ε) × Y → Y is the canonical projection. Let
+A : C∞
+c (M; E ) → C∞
+c (M; E )
+be an elliptic differential operator of order µ ≥ 1 that is symmetric with respect to
+the inner product induced by the Riemannian and Hermitian metrics, and suppose
+that A is in U(Y ) of the form
+A ∼= A∧ = x−1
+µ
+�
+j=0
+aj(y, Dy)(xDx)j : C∞
+c ((0, ε) × Y ; π∗
+Y E) → C∞
+c ((0, ε) × Y ; π∗
+Y E),
+where aj(y, Dy) ∈ Diffµ−j(Y ; E). Let
+p(σ) =
+µ
+�
+j=0
+aj(y, Dy)σj : C∞
+c (Y ; E) → C∞
+c (Y ; E), σ ∈ C,
+be the indicial family. We assume that p(σ) : E1 ⊂ E0 → E0 satisfies the assump-
+tions stated in Section 3 with E0 = L2(Y ; E) and some domain
+Hµ
+comp(Y ; E) ⊂ E1 ⊂ Hµ
+loc(Y ; E).
+We also assume that the embedding E1 ֒→ E0 is compact, and that p(σ) : E1 → E0
+is invertible for 0 < |ℑ(σ)| ≤ 1
+2; as explained in Section 3, the latter can generally
+be achieved by introducing a scaling parameter (which for geometric operators
+typically corresponds to scaling the metric). The closed extensions of the indicial
+operator
+A∧ : C∞
+c (R+; E1) ⊂ L2(R+ × Y ; π∗
+Y E) → L2(R+ × Y ; π∗
+Y E)
+are then described as explained in Section 3. Let
+Amin : Dmin(A) ⊂ L2(M; E ) → L2(M; E )
+be a closed symmetric extension of A : C∞
+c (M; E ) ⊂ L2(M; E ) → L2(M; E ), and
+let Amax : Dmax(A) ⊂ L2(M; E ) → L2(M; E ) be the adjoint; as discussed in the
+introduction, Amin is generally not the minimal extension of A from C∞
+c (M; E ),
+
+COBORDISM INVARIANCE OF THE INDEX REVISITED
+11
+and thus Amax is not the largest L2-based closed extension. By elliptic regularity
+we have
+Hµ
+comp(M; E ) ⊂ Dmin(A) ⊂ Dmax(A) ⊂ Hµ
+loc(M; E ).
+By a cut-off function we mean any function ω ∈ C∞
+c ([0, ε)) such that ω ≡ 1 near
+x = 0, and we consider ω a function on M supported in U(Y ).
+We make the
+following localization and compatibility assumptions between A and A∧:
+• For every cut-off function ω, multiplication by 1 − ω gives a continuous
+operator Dmax(A) → Dmin(A). We also assume that 1 − ω : Dmin(A) →
+L2(M; E ) is compact.
+• For every cut-off function ω, multiplication by ω gives continuous operators
+Dmin(A) → Dmin(A∧) and Dmin(A∧) → Dmin(A).
+To make sense of the mappings above note that
+M ⊃ U(Y ) ∼= (0, ε) × Y ⊂ R+ × Y,
+which allows transitioning both ways between functions on M supported in U(Y )
+and functions on R+ × Y supported in (0, ε) × Y . We will use these transitions
+freely in what follows.
+Proposition 4.1. Let ω ∈ C∞
+c ([0, ε)) be any cut-off function. The map
+Dmax(A)/Dmin(A) ∋ u + Dmin(A) �−→ ωu + Dmin(A∧) ∈ Dmax(A∧)/Dmin(A∧)
+is well-defined, and induces a unitary equivalence between the indefinite inner prod-
+uct spaces
+�
+Dmax(A)/Dmin(A), [·, ·]A
+� ∼=
+�
+Dmax(A∧)/Dmin(A∧), [·, ·]A∧
+�
+.
+Proof. We first prove that multiplication by ω gives a well-defined map
+Dmax(A) ∋ u �→ ωu ∈ Dmax(A∧).
+Note that with u also ωu ∈ Dmax(A) by our localization assumption. Now pick
+another cut-off function ˜ω ∈ C∞
+c ([0, ε)) such that ˜ω ≡ 1 in a neighborhood of
+supp(ω). Let φ ∈ Dmin(A∧) be arbitrary, and write φ = ˜ωφ + (1 − ˜ω)φ. Since
+Dmin(A∧) = x
+1
+2 H (R+; E1) ∩ L2(R+; E0)
+as a consequence of our assumptions we have that both ˜ωφ, (1 − ˜ω)φ ∈ Dmin(A∧),
+see Section 3. We also have ˜ωφ ∈ Dmin(A) by our localization and compatibility as-
+sumption with respect to the minimal domains. Using the locality of the differential
+operators A∧ and A we get
+⟨A∧φ, ωu⟩ = ⟨A∧(˜ωφ), ωu⟩ = ⟨A(˜ωφ), ωu⟩ = ⟨˜ωφ, Amax(ωu)⟩
+= ⟨φ, ˜ωAmax(ωu)⟩ = ⟨φ, Amax(ωu)⟩.
+As this is valid for all φ ∈ Dmin(A∧) we see that ωu ∈ Dmax(A∧) with A∧,max(ωu)
+given as the restriction of Amax(ωu) to U(Y ) and extended trivially to R+ × Y . As
+for u ∈ Dmin(A) we also have ωu ∈ Dmin(A∧) by assumption, we thus obtain that
+the map
+Dmax(A)/Dmin(A) ∋ u + Dmin(A) �−→ ωu + Dmin(A∧) ∈ Dmax(A∧)/Dmin(A∧)
+is well-defined.
+Conversely, multiplication by ω likewise gives a well-defined map
+Dmax(A∧) ∋ u �→ ωu ∈ Dmax(A).
+
+12
+THOMAS KRAINER
+Note that if u ∈ Dmax(A∧) then ωu ∈ Dmax(A∧) and (1 − ω)u ∈ Dmin(A∧) by
+Section 3.
+Now let ˜ω ∈ C∞
+c ([0, ε)) be such that ˜ω ≡ 1 in a neighborhood of
+supp(ω). Let φ ∈ Dmin(A) be arbitrary, and write φ = ˜ωφ + (1 − ˜ω)φ; by the
+localization and compatibility assumptions both terms are in Dmin(A), and we also
+have ˜ωφ ∈ Dmin(A∧). We get
+⟨Aφ, ωu⟩ = ⟨A(˜ωφ), ωu⟩ = ⟨A∧(˜ωφ), ωu⟩ = ⟨˜ωφ, A∧,max(ωu)⟩
+= ⟨φ, ˜ωA∧,max(ωu)⟩ = ⟨φ, A∧,max(ωu)⟩.
+This shows that ωu ∈ Dmax(A) with Amax(ωu) given by A∧,max(ωu) in U(Y ) and
+extended trivially to M. We thus obtain a map
+Dmax(A∧)/Dmin(A∧) ∋ u + Dmin(A∧) �−→ ωu + Dmin(A) ∈ Dmax(A)/Dmin(A),
+and both maps are inverses of each other.
+Finally, as for both A and A∧ each class in Dmax/Dmin has a representative
+supported in U(Y ), and by the standing product type assumptions both adjoint
+pairings agree on those representatives, the proposition follows.
+□
+Theorem 4.2 (Null-Cobordism Theorem). Under the stated product type, local-
+ization, and compatibility assumptions we have
+SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ] = 0.
+If moreover
+p(σ) =
+�
+σ
+D∗
+D
+−σ
+�
+:
+D(D)
+⊕
+D(D∗)
+⊂ L2
+�
+Y ;
+E−
+⊕
+E+
+�
+→ L2
+�
+Y ;
+E−
+⊕
+E+
+�
+with an elliptic Fredholm operator of first order
+D : D(D) ⊂ L2(Y ; E−) → L2(Y ; E+),
+then ind[D : D(D) ⊂ L2(Y ; E−) → L2(Y ; E+)] = 0.
+Proof. By Proposition 4.1 we have a unitary equivalence between the indefinite
+inner product spaces
+�
+Dmax(A)/Dmin(A), [·, ·]A
+� ∼=
+�
+Dmax(A∧)/Dmin(A∧), [·, ·]A∧
+�
+.
+Because
+sgn
+�
+Dmax(A∧)/Dmin(A∧), [·, ·]A∧
+�
+= SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ]
+by (3.6) it suffices to show that
+sgn
+�
+Dmax(A)/Dmin(A), [·, ·]A
+�
+= 0,
+and by Proposition 2.2 this will be the case if the embedding Dmax(A) ֒→ L2(M; E )
+is compact. Because A has finite deficiency indices we only need to prove that
+Dmin(A) ֒→ L2(M; E ) is compact. Now let ω, ˜ω ∈ C∞
+c ([0, ε)) be cut-off functions
+such that ˜ω ≡ 1 in a neighborhood of supp(ω). By assumption the multiplication
+operator
+1 − ω : Dmin(A) → L2(M; E )
+is compact, and
+˜ω : Dmin(A) → Dmin(A∧)
+is continuous. Now
+Dmin(A∧) = x
+1
+2 H (R+; E1) ∩ L2(R+; E0),
+
+COBORDISM INVARIANCE OF THE INDEX REVISITED
+13
+and because E1 ֒→ E0 is compact, multiplication by ω is a compact operator
+ω : Dmin(A∧) → L2(R+; E0),
+see Section 3. Consequently, using the product type assumptions, the composition
+ω = ω˜ω : Dmin(A) → L2(M; E )
+is compact, which shows that the embedding ι = ω+(1−ω) : Dmin(A) → L2(M; E )
+is compact. Finally, the vanishing of the index in the special case of operators of
+first order follows from (3.7).
+□
+Appendix A. The null-cobordism theorem for closed manifolds
+In this appendix we discuss a version of the null-cobordism Theorem 4.2 for closed
+manifolds. Most of the previous assumptions no longer explicitly appear in this
+version, e.g., we do not assume product type geometry, and there isn’t an operator
+A on M at the outset, but symbolic assumptions instead. As mentioned in the
+introduction this is due to the richness of analytic tools available for this situation
+that allows to create the preconditions needed to apply Theorem 4.2 instead of
+having to assume them from the outset.
+Let Y be a closed, compact Riemannian manifold and E → Y be a Hermitian
+vector bundle, and consider a family
+p(σ) =
+µ
+�
+j=0
+aj(y, Dy)σj : C∞(Y ; E) → C∞(Y ; E), σ ∈ R,
+(A.1)
+where aj(y, Dy) ∈ Diffµ−j(Y ; E), and µ ≥ 1.
+We assume that the parameter-
+dependent principal symbol
+σσ(p)(y, η; σ) =
+µ
+�
+j=0
+σσ(aj)(y, η)σj : Ey → Ey
+(A.2)
+is invertible on
+�
+T ∗Y × R
+�
+\ 0, and that p(σ) = p(σ)∗ is (formally) selfadjoint. By
+elliptic and analytic Fredholm theory,
+R ∋ σ �→ p(σ) : Hµ(Y ; E) ⊂ L2(Y ; E) → L2(Y ; E)
+is a family of selfadjoint unbounded Fredholm operators acting in L2(Y ; E) that
+is invertible for all σ ∈ R except at finitely many points, and it makes sense to
+consider the spectral flow
+SF[p(σ)] := SF[p(σ) : Hµ(Y ; E) ⊂ L2(Y ; E) → L2(Y ; E), −∞ < σ < ∞] ∈ Z
+associated with p(σ).
+Lemma A.3. The spectral flow is an invariant of the principal symbol (A.2) in
+the sense that if pj(σ), j = 1, 2, are two elliptic selfadjoint families of order µ ≥ 1
+of the form (A.1) with σσ(p1)(y, η; σ) = σσ(p2)(y, η; σ) then SF[p1(σ)] = SF[p2(σ)].
+Proof. Let R > 0 be such that
+p1(σ) + s[p2(σ) − p1(σ)] : Hµ(Y ; E) ⊂ L2(Y ; E) → L2(Y ; E)
+is invertible for |σ| ≥ R > 0 and all 0 ≤ s ≤ 1. Consequently, this family is a ho-
+motopy of selfadjoint Fredholm functions on [−R, R], invertible at both endpoints,
+and by the homotopy invariance of the spectral flow for such families we see that
+SF[p1(σ)] = SF[p2(σ)].
+□
+
+14
+THOMAS KRAINER
+Suppose there exists a compact Riemannian manifold M with ∂M = Y . Utilizing
+the geodesic flow from the boundary in the direction of the inner normal vector field
+shows that there exists ε > 0 and a collar neighborhood map U(Y ) ∼= [0, ε) × Y
+near the boundary such that the metric in U(Y ) takes the form dx2 + gY (x) with
+a smooth family of metrics gY (x) on Y , 0 ≤ x < ε, and such that gY (0) = gY is
+the given metric on Y . Moreover, by choosing ε > 0 small enough, there exists a
+defining function for ∂M on M that in U(Y ) is represented by projection onto the
+coordinate in [0, ε). We’ll also denote this global defining function by x : M → R+.
+In particular,
+T ∗M
+��
+Y = T ∗Y ⊕ span{dx
+��
+Y }
+subject to these choices, and we can split variables (y, η; σ) ∈ T ∗M
+��
+Y accordingly.
+Theorem A.4 (Null-Cobordism Theorem). Let M be a compact Riemannian man-
+ifold M with ∂M = Y , and let E → M be a Hermitian vector bundle with E
+��
+Y = E.
+Let T ∗M
+��
+Y ∼= T ∗Y × R subject to the choices described above, and suppose there ex-
+ists a symmetric, elliptic, differential principal symbol a ∈ C∞(T ∗M \0; End(π∗E ))
+of order µ such that
+a(y, η; σ) = σσ(p)(y, η; σ) for (y, η; σ) ∈
+�
+T ∗M \ 0
+���
+Y ,
+where π : T ∗M → M is the canonical projection. Then SF[p(σ)] = 0.
+With the family p(σ) from (A.1) we associate the indicial operator
+A∧ = x−1
+µ
+�
+j=0
+aj(y, Dy)(xDx)j : C∞
+c (R+×Y ; E) ⊂ L2(R+×Y ; E) → L2(R+×Y ; E).
+(A.5)
+Here we also write E for its pull-back to R+ ×Y with respect to the projection onto
+Y , and equip R+ × Y with the product metric dx2 + gY . Then A∧ is symmetric
+and densely defined. Let Dmin(A∧) be the domain of the closure, and Dmax(A∧)
+be the domain of the adjoint.
+Proof of Theorem A.4. In the previously fixed collar neighborhood U(Y ) ∼= [0, ε)×
+Y we utilize standard deformations of the Riemannian metric on M, the Hermitian
+metric on E , and the principal symbol a to reduce to a product type structure near
+the boundary, as follows:
+Pick an isomorphism E
+��
+U(Y ) ∼= π∗
+Y E that is the identity over Y , where πY :
+[0, ε) × Y → Y is the projection map. With respect to the pull-back of the given
+Hermitian metric on E to π∗
+Y E, the metric on E
+��
+U(Y ) under this isomorphism is
+then represented by h(x, y) ∈ C∞([0, ε) × Y ; End(π∗
+Y E)) such that h = h∗ > 0 and
+h(0, y) = Id. Choose C∞-functions φ, ψ : [0, ε) → R with
+φ ≡ 0 on 0 ≤ x ≤ ε
+3, 0 < φ < 2ε
+3 on ε
+3 < x < 2ε
+3 , and φ ≡ x on 2ε
+3 ≤ x < ε;
+ψ ≡ x on 0 ≤ x ≤ ε
+3, ψ > 0 on ε
+3 < x < 2ε
+3 , and ψ ≡ 1 on 2ε
+3 ≤ x < ε.
+We then deform the Riemannian metric on U(Y ) and Hermitian metric on E
+��
+U(Y )
+to
+˜g = dx2 + gY (φ(x)) and ˜h(x, y) = h(φ(x), y) ∈ C∞([0, ε) × Y ; End(π∗
+Y E)),
+respectively, which both connect seamlessly with the Riemannian metric on M
+outside U(Y ), and the Hermitian metric on E . We also change the principal symbol
+
+COBORDISM INVARIANCE OF THE INDEX REVISITED
+15
+in
+◦U(Y ) to
+˜a(x, y, η; σ) = ψ(x)−1a(φ(x), y, η; ψ(x)σ) : Ey → Ey
+(A.6)
+for (x, y, η; σ) ∈ T ∗�
+(0, ε)×Y
+�
+\0 with the obvious identifications of variables, which
+again connects seamlessly outside the collar neighborhood. The new homogeneous
+principal symbol ˜a ∈ C∞(T ∗
+◦M \ 0, End(π∗E )) is symmetric with respect to the
+new metric on E , and elliptic over
+◦
+M. In
+◦
+U(Y ) we have
+˜a(x, y, η; σ) = x−1 σσ(p)(y, η; xσ) : Ey → Ey for 0 < x < ε
+3
+by construction, which aligns with the principal symbol of A∧ from (A.5). Let
+now A ∈ Diffµ(
+◦M; E ) be symmetric C∞
+c (
+◦M; E ) → C∞
+c (
+◦M; E ) with respect to the
+L2-inner product associated with the modified metrics on M and E , respectively,
+such that the principal symbol σσ(A) = ˜a on T ∗
+◦M \ 0, and such that in
+◦U(Y ) we
+have A = A∧ on C∞
+c ((0, ε
+4) × Y ; E). Then
+A = x−1P : C∞
+c (
+◦
+M; E ) ⊂ L2(M; E ) = x− 1
+2 L2
+b(M; E ) → x− 1
+2 L2
+b(M; E )
+is symmetric, and P ∈ Diffµ
+b (M; E ) is b-elliptic (see [13]). Moreover, by construction
+p(σ) is the indicial family of the operator P.
+By analytic Fredholm theory p(σ) : Hµ(Y ; E) → L2(Y ; E) is invertible for σ ∈ C
+except for the discrete set specb(p). In the sequel it will be convenient to assume
+that specb(p) ∩ {σ ∈ C; 0 < |ℑ(σ)| ≤
+1
+2} = ∅. As explained in Section 3, this
+can be achieved by replacing p(σ) by p(tσ) for sufficiently small t > 0 if necessary,
+which does not impact the spectral flow. Moreover, the assumptions of the theorem
+pertaining to the principal symbol of p(σ) also hold for p(tσ); to see this pick a
+C∞-function χ : [0, ε) → R with
+χ ≡ t on 0 ≤ x ≤ ε
+3, χ > 0 on ε
+3 < x < 2ε
+3 , and χ ≡ 1 on 2ε
+3 ≤ x < ε,
+and alter the principal symbol (A.6) in
+◦U(Y ) to
+˜a(x, y, η; σ) = ψ(x)−1a(φ(x), y, η; ψ(x)χ(x)σ) : Ey → Ey
+for (x, y, η; σ) ∈ T ∗�
+(0, ε) × Y
+�
+\ 0. We may thus proceed without loss of generality
+under the assumption that specb(p) ∩ {σ ∈ C; 0 < |ℑ(σ)| ≤ 1
+2} = ∅. In view of
+Section 3 for A∧ and by invoking elliptic regularity for A we then get
+Dmin(A∧) = x
+1
+2 Hµ
+b (R+; L2(Y ; E)) ∩ x
+1
+2 L2
+b(R+; Hµ(Y ; E)) ∩ L2(R+ × Y ; E),
+Dmin(A) = x
+1
+2 Hµ
+b (M; E ),
+and
+Dmax(A∧) = Dmin(A∧) ⊕
+�
+σ0∈specb(p)∩R
+Eσ0(p),
+Dmax(A) = Dmin(A) ⊕
+�
+σ0∈specb(p)∩R
+Eσ0(p),
+where Eσ0(p) is defined as in (3.3) based on a cut-off function ω ∈ C∞
+c ([0, ε
+4)) with
+ω ≡ 1 near x = 0 so that elements in Eσ0(p) can interchangeably be regarded both
+as sections of E on R+ × Y , as well as sections of E on M supported near the
+boundary. In particular, this implies that
+�
+Dmax(A)/Dmin(A), [·, ·]A
+� ∼=
+�
+Dmax(A∧)/Dmin(A∧), [·, ·]A∧
+�
+
+16
+THOMAS KRAINER
+because [u, v]A∧ = [u, v]A for u, v ∈
+�
+σ0∈specb(p)∩R
+Eσ0(p) by construction. Finally, it
+remains to note that Dmax ֒→ x− 1
+4 Hµ
+b (M; E ), and the embedding x− 1
+4 Hµ
+b (M; E ) ֒→
+x− 1
+2 L2
+b(M; E ) = L2(M; E ) is compact.
+□
+Theorem A.4 and Lemma 3.9 imply:
+Corollary A.7 (Cobordism Invariance of the Index). Suppose that E = E− ⊕ E+
+is an orthogonal direct sum, and that the family (A.1) is of the form
+D(σ) =
+�σ
+D∗
+D
+−σ
+�
+: C∞
+�
+Y ;
+E−
+⊕
+E+
+�
+→ C∞
+�
+Y ;
+E−
+⊕
+E+
+�
+, σ ∈ R,
+where D : C∞(Y ; E−) → C∞(Y ; E+) is an elliptic differential operator of first
+order, and D∗ : C∞(Y ; E+) → C∞(Y ; E−) is its (formal) adjoint. Then
+SF[D(σ)] = ind D = dim ker(D) − dim ker(D∗).
+In particular, if the assumptions of Theorem A.4 hold, then ind(D) = 0.
+References
+[1] P. Albin, E. Leichtnam, R. Mazzeo, and P. Piazza, The signature package on Witt spaces,
+Ann. Sci. ´Ec. Norm. Sup´er. (4) 45 (2012), no. 2, 241–310.
+[2]
+, Hodge theory on Cheeger spaces, J. Reine Angew. Math. 744 (2018), 29–102.
+[3] M. Braverman, New proof of the cobordism invariance of the index, Proc. Amer. Math. Soc.
+130 (2002), no. 4, 1095–1101.
+[4] M. Braverman and P. Shi, Cobordism invariance of the index of Callias-type operators,
+Comm. Partial Differential Equations 41 (2016), no. 8, 1183–1203.
+[5] C. Carvalho, A K-theory proof of the cobordism invariance of the index, K-Theory 36 (2005),
+no. 1-2, 1–31.
+[6] L. Hartmann, M. Lesch, and B. Vertman, On the domain of Dirac and Laplace type operators
+on stratified spaces, J. Spectr. Theory 8 (2018), no. 4, 1295–1348.
+[7]
+, Resolvent trace asymptotics on stratified spaces, Pure Appl. Anal. 3 (2021), no. 1,
+75–108.
+[8] M. Hilsum, Bordism invariance in KK-theory, Math. Scand. 107 (2010), no. 1, 73–89.
+[9] N. Higson, A note on the cobordism invariance of the index, Topology 30 (1991), no. 3,
+439–443.
+[10] T. Krainer, Extensions of symmetric operators that are invariant under scaling and applica-
+tions to indicial operators, New York J. Math. 28 (2022), 705–772.
+[11] M. Lesch, Deficiency indices for symmetric Dirac operators on manifolds with conic singu-
+larities, Topology 32 (1993), no. 3, 611–623.
+[12]
+, Operators of Fuchs Type, Conical Singularities, and Asymptotic Methods, Teubner-
+Texte zur Math. vol 136, B.G. Teubner, Stuttgart, Leipzig, 1997.
+[13] R. Melrose, The Atiyah-Patodi-Singer index theorem, Research Notes in Mathematics,
+A K Peters, Ltd., Wellesley, MA, 1993.
+[14] S. Moroianu, Cusp geometry and the cobordism invariance of the index, Adv. Math. 194
+(2005), no. 2, 504–519.
+[15] V.E. Nazaikinskii, A.Yu. Savin, B.-W. Schulze, and B.Yu. Sternin, Elliptic theory on singular
+manifolds, Differential and Integral Equations and Their Applications, vol. 7, Chapman &
+Hall/CRC, Boca Raton, FL, 2006.
+[16] L. Nicolaescu, On the cobordism invariance of the index of Dirac operators, Proc. Amer.
+Math. Soc. 125 (1997), no. 9, 2797–2801.
+[17] R. Palais, Seminar on the Atiyah-Singer index theorem, Annals of Mathematics Studies,
+No. 57, Princeton University Press, Princeton, NJ, 1965.
+[18] B.-W. Schulze,
+Pseudo-differential calculus on manifolds with geometric singularities,
+Pseudo-differential operators:
+Partial differential equations and time-frequency analysis,
+pp. 37–83, Fields Inst. Commun., vol. 52, Amer. Math. Soc., Providence, RI, 2007.
+
+COBORDISM INVARIANCE OF THE INDEX REVISITED
+17
+[19] C. Wulff, Bordism invariance of the coarse index, Proc. Amer. Math. Soc. 140 (2012), no. 8,
+2693–2697.
+Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601-3760
+Email address: krainer@psu.edu
+
diff --git a/H9AyT4oBgHgl3EQfTPcY/content/tmp_files/load_file.txt b/H9AyT4oBgHgl3EQfTPcY/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..821d0d713f06891bcc9b693266a714344be221e3
--- /dev/null
+++ b/H9AyT4oBgHgl3EQfTPcY/content/tmp_files/load_file.txt
@@ -0,0 +1,605 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf,len=604
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='00100v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='AP]  31 Dec 2022  COBORDISM INVARIANCE OF THE INDEX FOR  REALIZATIONS OF ELLIPTIC OPERATORS REVISITED  THOMAS KRAINER  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We revisit an argument due to Lesch [11, 12] for proving the cobor-  dism invariance of the index of Dirac operators on even-dimensional closed  manifolds and combine this with recent work by the author [10] to show van-  ishing results for the spectral flow for families of selfadjoint Fredholm realiza-  tions of elliptic operators in case the family is induced on the boundary by an  elliptic operator on a compact space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' This work is motivated by studying the  behavior of the index of realizations of elliptic operators under cobordisms of  statified manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Introduction  One of the original proofs of the Atiyah-Singer Index Theorem is based on showing  that the index of Dirac type operators is invariant under cobordisms, see Palais  [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' This proof is analytic in nature and rooted in the classical theory of elliptic  boundary value problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Other proof strategies for the index theorem such as the  heat equation proof have generally been favored because these proofs require less  sophisticated analytic techniques than the original cobordism proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Higson [9] gave a proof of the cobordism invariance of the index by attaching an  infinite half-cylinder to the boundary and extending the operator from the manifold  with boundary to the manifold with cylindrical end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The Dirac type operator on  the resulting odd-dimensional complete manifold is essentially selfadjoint, and the  analytic arguments involved in Higson’s proof are considerably simpler compared  to the original proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Lesch [11], on the other hand, gave a proof by attaching a  (generalized) cone to the boundary and extended the operator from the manifold  with boundary to a cone operator;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' while conic manifolds are incomplete and thus  dealing with domains of realizations of the resulting conic Dirac type operator is  needed,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Lesch’s approach is still much simpler from a functional analytic point of  view than the original proof because the maximal and minimal domains of L2-  based realizations in the conic case differ only by a finite-dimensional space – the  price to pay is the more intricate analysis to deal with the singularity which at  this juncture has been introduced artificially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Several other analytic proofs of the  cobordism invariance of the index [3, 16], a K-theory proof [5], and generalizations  [4, 8, 14, 19] have since been found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  This note is motivated by recent advances in elliptic theory on stratified man-  ifolds with incomplete iterated wedge metrics [1, 2, 6, 7, 15, 18] and gives an ap-  plication of the spectral flow formula for indicial operators obtained in our recent  paper [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Stratified cobordisms and the cobordism invariance of the index for the  2020 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Primary: 58J20;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Secondary: 58J05, 58J32, 58J30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Manifolds with singularities, index theory, cobordism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  1  2  THOMAS KRAINER  signature operator have been considered in [1, 2], where especially in [2] the opera-  tor is no longer essentially selfadjoint and suitable boundary conditions associated  with the singular strata are considered;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' stratified cobordism and the invariance of  the index are used in an essential way to establish the properties of the signature  of a Cheeger space considered in that paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  From our point of view Lesch’s proof [11, 12] of the cobordism invariance of  the index is very natural in the context of elliptic theory on stratified manifolds  because, unlike in the classical smooth case, singular analysis and dealing with  boundary conditions associated with singular strata already are essential features  of the investigations here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  In this note we will revisit and extend Lesch’s proof from the Dirac case to more  general operators of any order, and what amounts to the vanishing of the index in  the Dirac case (for null-cobordisms) will accordingly generalize to the vanishing of  the spectral flow for indicial families.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Our recent paper [10] on indicial operators,  which are abstract functional analytic model operators associated to generalized  conical singularities, is the basis for this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We will only be concerned with null-  cobordisms and proving vanishing results here;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' more general notions of cobordisms  and cobordism invariance follow upon reduction to this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Without detailing the  precise assumptions, the argument proceeds as follows:  Let (M, g) be a Riemannian manifold, and let U = U(Y ) ⊂ M be an open subset  that is isometric to (0, ε) × Y with product metric dx2 + gY for some ε > 0, where  (Y, gY ) is another Riemannian manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The reader ought to think of both M and  Y as the open interior of compact stratified manifolds M and Y equipped with  incomplete iterated wedge metrics, where Y is a boundary hypersurface of M, and  U(Y ) is a collar neighborhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let E → M be a Hermitian vector bundle such  that E  ��  U(Y ) ∼= π∗  Y E isometrically, where E → Y is a Hermitian vector bundle, and  πY : (0, ε) × Y → Y is the canonical projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let  A : C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )  be an elliptic differential operator of order µ ≥ 1 that is symmetric with respect to  the inner product induced by the Riemannian and Hermitian metrics, and suppose  that A is in U(Y ) of the form  A ∼= A∧ = x−1  µ  �  j=0  aj(y, Dy)(xDx)j : C∞  c ((0, ε) × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' π∗  Y E) → C∞  c ((0, ε) × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' π∗  Y E),  where aj(y, Dy) ∈ Diffµ−j(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let  p(σ) =  µ  �  j=0  aj(y, Dy)σj : C∞  c (Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) → C∞  c (Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E), σ ∈ C,  be the indicial family.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Now suppose that  Amin : Dmin(A) ⊂ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1)  is some closed symmetric extension of A : C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) ⊂ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ),  and let Amax : Dmax(A) ⊂ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) be the adjoint – we point out  here that Amin is not necessarily the minimal extension of A from C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ), and  COBORDISM INVARIANCE OF THE INDEX REVISITED  3  therefore Amax is not the largest L2-based closed extension either, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' we only have  Dmin(A) ⊃ {u ∈ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' ∃uk ∈ C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ), uk → u in L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ),  and Auk ⊂ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) Cauchy},  Dmax(A) ⊂ {u ∈ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E );' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' ∃v ∈ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) :  ⟨Aφ, u⟩L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='E ) = ⟨φ, v⟩L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='E ) ∀φ ∈ C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )},  and these inclusions are generally proper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The reader ought to think of the operator  A as an elliptic iterated incomplete wedge operator on M, and the domain Dmin(A)  as determined by previously chosen boundary conditions for A associated with  singular strata of M away from the boundary hypersurface Y ⊂ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  One of the main points now is that under suitable localization and compatibility  assumptions these extensions of A should localize to U(Y ) and be fully captured  by the extensions of the indicial operator  A∧ : C∞  c (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ⊂ L2(R+ × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' π∗  Y E) → L2(R+ × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' π∗  Y E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2)  Here  Hµ  comp(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) ⊂ E1 ⊂ Hµ  loc(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E)  is the common domain for the indicial family p(σ) : E1 ⊂ E0 → E0, σ ∈ C,  where E0 = L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E), giving rise to a holomorphic family of unbounded Fredholm  operators that are selfadjoint for σ ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  The reader ought to think of E1 as  determined by certain lateral boundary conditions associated with the singular  strata of Y , obtained via restriction to U(Y ) by the previously determined boundary  conditions on M for A that gave rise to Dmin(A);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' the localization and compatibility  assumptions are such that the boundary conditions previously chosen for A on M  should be selfadjoint away from the boundary hypersurface Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The upshot of all  of this is that we obtain a unitary equivalence  �  Dmax(A)/Dmin(A), [·, ·]A  � ∼=  �  Dmax(A∧)/Dmin(A∧), [·, ·]A∧  �  of finite-dimensional indefinite inner product spaces by passing to representatives  supported in U(Y ) ∼= (0, ε)×Y , thus allowing transitioning between M and R+×Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  here  [·, ·]A : Dmax(A) × Dmax(A) → C,  [u, v]A = 1  i  �  ⟨Amaxu, v⟩L2 − ⟨u, Amaxv⟩L2  �  is the adjoint pairing, and likewise for [·, ·]A∧, while Dmin(A∧) is the domain of the  closure A∧,min of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2), and Dmax(A∧) is the domain of the adjoint A∧,max = A∗  ∧,min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  In particular, we have  sgn  �  Dmax(A)/Dmin(A), [·, ·]A  �  = sgn  �  Dmax(A∧)/Dmin(A∧), [·, ·]A∧  �  for the signatures of these spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' On the one hand, using the spectral flow formula  from [10], we have  sgn  �  Dmax(A∧)/Dmin(A∧), [·, ·]A∧  �  = SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ],  while on the other hand sgn  �  Dmax(A)/Dmin(A), [·, ·]A  �  = 0 if (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1) is Fredholm or  the embedding Dmax(A) ֒→ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) is compact, which combined leads to the  desired conclusion that  SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  4  THOMAS KRAINER  In the Dirac case the spectral flow of the indicial family is easily seen to equal  the Fredholm index of the operator D : D(D) ⊂ L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E−) → L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E+) on the  even-dimensional boundary Y , thus recovering cobordism invariance of the index  in this context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  The structure of this paper is as follows: In Section 2 we briefly review what is  needed from extension theory of symmetric operators, in particular the criteria that  ensure that  �  Dmax(A)/Dmin(A), [·, ·]A  �  is finite-dimensional with signature zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' In  Section 3 we review results from our paper [10] on indicial operators in the form in  which they are needed here;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' we also address in this section how indicial operators of  first order that model the Dirac case fit into this framework in order to obtain the  desired conclusions about the cobordism invariance of the index when specializing to  such operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' In Section 4 we fill in the details of the outline above and prove the  null-cobordism theorem (Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Finally, in Appendix A, we discuss the null-  cobordism theorem for smooth manifolds;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' assumptions appear much weaker here  on the geometry and the participating objects because the analytic tools available  in this case are rich enough to create the preconditions needed to apply the null-  cobordism theorem rather than having to assume them from the outset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  With  the ongoing further development of singular analysis on stratified manifolds we  anticipate similar reductions and simplifications for such cases in the future as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Preliminaries from extension theory  Let H be a separable complex Hilbert space, and suppose Amin : Dmin ⊂ H → H  is closed, densely defined, and symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let Amax := A∗  min : Dmax ⊂ H → H be  the adjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We equip Dmax with the graph inner product  ⟨u, v⟩Amax = ⟨u, v⟩ + ⟨Amaxu, Amaxv⟩  and associated graph norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Then Dmin ⊂  �  Dmax, ∥ · ∥Amax  �  is a closed subspace,  and  Dmax = Dmin ⊕ ker(Amax + i) ⊕ ker(Amax − i)  by von Neumann’s formulas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The dimensions  n± = dim ker(Amax ∓ λi) ∈ N0 ∪ {∞},  λ > 0,  are the deficiency indices of the operator Amin and independent of λ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The  operators  Amin ± iλ : Dmin ⊂ H → H,  λ > 0,  are injective and have closed range, and we have n± < ∞ if and only if Amin ± iλ  is Fredholm, in which case n± = − ind(Amin ± iλ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The adjoint pairing  [·, ·]A : Dmax × Dmax → C,  [u, v]A = 1  i  �  ⟨Amaxu, v⟩ − ⟨u, Amaxv⟩  �  descends to a nondegenerate Hermitian sesquilinear form (indefinite inner product)  [·, ·] : Dmax/Dmin × Dmax/Dmin → C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  If dim Dmax/Dmin < ∞, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' if Amin has finite deficiency indices, the signature of  the adjoint pairing is given by  sgn  �  Dmax/Dmin, [·, ·]  �  = n+ − n−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  The following criteria are standard and useful for verification that n+ = n− < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  COBORDISM INVARIANCE OF THE INDEX REVISITED  5  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Suppose Amin : Dmin ⊂ H → H is Fredholm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Then Amin has  finite and equal deficiency indices, and therefore  sgn  �  Dmax/Dmin, [·, ·]  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Because Amin : Dmin ⊂ H → H is Fredholm there exists ε > 0 such that  Amin + iλ : Dmin ⊂ H → H is Fredholm for −ε < λ < ε, and consequently both  n± < ∞ and Amin + iλ is Fredholm for all λ ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Now  R ∋ λ �→ Amin + iλ : Dmin ⊂ H → H  is a continuous Fredholm function and therefore has constant index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Thus  n+ = − ind(Amin + i) = − ind(Amin − i) = n−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  □  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' If the embedding  �  Dmax, ∥ · ∥Amax  �  ֒→ H is compact then Amin  has finite and equal deficiency indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The norms ∥·∥Amax and ∥·∥H are equivalent on ker(Amax±i), and the identity  map  �  ker(Amax ± i), ∥ · ∥Amax  �  →  �  ker(Amax ± i), ∥ · ∥H  �  is compact by assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Thus dim ker(Amax ± i) < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Now Amin ± i : Dmin ⊂ H → H are both Fredholm,  and because Dmin ֒→ H is compact we have ind(Amin − i) = ind(Amin + i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The  proposition is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  □  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Indicial operators  We consider indicial operators of the form  A∧ = x−1  µ  �  j=0  aj(xDx)j : C∞  c (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ⊂ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) → L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0),  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1)  where µ ∈ N and E0 and E1 are separable complex Hilbert spaces such that E1 ֒→  E0 is continuous and dense, and the operators aj : E1 → E0 are continuous for  j = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' , µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let  p(σ) =  µ  �  j=0  ajσj : E1 → E0,  σ ∈ C  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2)  be the indicial family associated with A∧.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We make the following assumptions:  (i) p(σ) : E1 ⊂ E0 → E0 is closed, densely defined, and Fredholm for σ ∈ C, and  the map C ∋ σ �→ p(σ) ∈ L (E1, E0) is holomorphic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (ii) We have p(σ)∗ = p(σ) : E1 ⊂ E0 → E0 as unbounded operators in E0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (iii) For (λ, σ) ∈ R2 and |λ, σ| ≥ R ≫ 0 sufficiently large p(σ) + iλ : E1 → E0 is  invertible with  sup  |λ,σ|≥R  �  (1 + λ2 + σ2µ)  1  2 ���  p(σ) + iλ  �−1��  L (E0) +  ���  p(σ) + iλ  �−1��  L (E0,E1)  �  < ∞,  and for every k ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=', µ} we have  sup  |λ,σ|≥R  (1 + λ2 + σ2µ)  k  2µ ���  ∂k  σp(σ)  ��  p(σ) + iλ  �−1��  L (E0) < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  In [10] we systematically studied operators of the kind (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1) under such assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  We summarize some of the findings below:  6  THOMAS KRAINER  (1) The operator (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1) is symmetric and densely defined in L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let  A∧,min be its closure, and A∧,max = A∗  ∧,min be the adjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Then  dim Dmax(A∧)/Dmin(A∧) < ∞,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=', A∧ has finite deficiency indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (2) The boundary spectrum  specb(p) = {σ ∈ C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' p(σ) : E1 → E0 is not invertible} ⊂ C  is discrete, and every strip |ℑ(σ)| ≤ K, K > 0, contains only finitely many  elements of specb(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The elements of the boundary spectrum are generally  referred to as indicial roots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (3) Fix an arbitrary cut-off function ω ∈ C∞  c (R+) with ω ≡ 1 near x = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' For  each indicial root σ0 ∈ specb(p) let  Eσ0(p) =  �  u = ω  k  �  j=0  ej logj(x)xiσ0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' k ∈ N0 and ej ∈ E1,  and p(σ)(Mu)(σ) is holomorphic at σ = σ0  �  ,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='3)  where  �  Mu  �  (σ) =  � ∞  0  x−iσu(x) dx  x  is the Mellin transform of u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' This space is finite-dimensional for every σ0,  and we have  Dmax(A∧) = Dmin(A∧) ⊕  �  σ0∈specb(p)  − 1  2 <ℑ(σ0)< 1  2  Eσ0(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='4)  (4) We have  x  1  2 H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ∩ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) ֒→ Dmin(A∧),  and Dmin(A∧) = x  1  2 H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ∩ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) if and only if p(σ) : E1 → E0  is invertible for all ℑ(σ) = − 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  The space H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) is the completion of C∞  c (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) with respect to  the norm  ∥u∥2  H =  �  R  ∥p(σ + iγ0)(Mu)(σ)∥2  E0 dσ,  where γ0 ∈ R is arbitrary such that p(σ + iγ0) : E1 → E0 is invertible for  all σ ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We have  H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ֒→ Hµ  b (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) ∩ L2  b(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1),  and in typical situations these spaces are equal;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' this is the case, for instance,  if  sup  σ∈R  ∥p(σ + iγ0)(⟨σ⟩µ + iΛ)−1∥L (E0) < ∞,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='5)  where Λ : E1 ⊂ E0 → E0 is selfadjoint (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' for Λ = p(0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (5) While not discussed in [10] it is not hard to see that, under the added  assumption that the embedding E1 ֒→ E0 is compact, multiplication by a  COBORDISM INVARIANCE OF THE INDEX REVISITED  7  cut-off function ω ∈ C∞  c (R+) with ω ≡ 1 near x = 0 induces a compact  operator ω : xαH (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) → L2  b(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) for every α > 01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Consequently, if additionally p(σ) : E1 → E0 is invertible for all ℑ(σ) =  − 1  2, we obtain a compact map ω : Dmax(A∧) → L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0), and a bounded  map 1 − ω : Dmax(A∧) → Dmin(A∧).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The latter is based on the identity  Dmin(A∧) = x  1  2 H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ∩ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) and localization properties of the  space H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) (see [10, Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='6]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (6) The adjoint pairing  [·, ·]A∧ : Dmax(A∧) × Dmax(A∧) → C,  [u, v]A∧ = 1  i  �  ⟨A∧,maxu, v⟩L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='E0) − ⟨u, A∧,maxv⟩L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='E0)  �  induces a nondegenerate Hermitian sesquilinear form  [·, ·] : Dmax(A∧)/Dmin(A∧) × Dmax(A∧)/Dmin(A∧) → C,  and its signature is given by the spectral flow of the indicial family (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2)  along the real line:  sgn  �  Dmax(A∧)/Dmin(A∧), [·, ·]  �  = SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='6)  Note that p(σ) : E1 → E0 is invertible for |σ| ≥ T ≫ 0 large enough,  σ ∈ R, and the spectral flow in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='6) then refers to p(σ) on the interval  −T ≤ σ ≤ T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Only crossings of real indicial roots contribute terms to the  spectral flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  The focus in this paper is on the signature of the adjoint pairing, and by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='6)  only real indicial roots are relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' In order to obtain simple expressions for the  minimal domain and the maximal domain (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='4) of A∧ it is sometimes convenient  to introduce a scaling parameter t > 0 to remove any small non-real indicial roots  from the strip |ℑ(σ)| ≤ 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' This leads to  A∧,t = x−1  µ  �  j=0  ajtj(xDx)j : C∞  c (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ⊂ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) → L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0)  with indicial family  pt(σ) = p(tσ) : E1 ⊂ E0 → E0,  σ ∈ C,  and the standing assumptions on p(σ) imply that the analogous properties are also  satisfied for pt(σ), and all estimates are locally uniform with respect to t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' In  particular, the spectral flow  SF[ pt(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ]  is independent of t > 0 by homotopy invariance, and thus  sgn  �  Dmax(A∧,t)/Dmin(A∧,t), [·, ·]  �  1The function a0(x, σ) = xαω(x)p(σ + iγ0)−1 is a Mellin symbol taking values in the com-  pact operators E0 → E0, and we have sup{⟨log(x)⟩j⟨σ⟩µ+k∥(xDx)l∂k  σa0(x, σ)∥L (E0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' (x, σ) ∈  R+ × R} < ∞ for all j, k, l ∈ N0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Thus the Mellin pseudodifferential operator opM(a0) :  L2  b(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) → L2  b(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) is compact, which implies compactness of the multiplication opera-  tor ω : xαH (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) → L2  b(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) as asserted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  8  THOMAS KRAINER  is independent of t > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' For 0 < t ≤ t0 small enough, pt(σ) : E1 ⊂ E0 → E0 is  invertible for all 0 < |ℑ(σ)| ≤ 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We then have  Dmin(A∧,t) = x  1  2 H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ∩ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0),  where the definition of H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) is accordingly based on pt(σ), and  Dmax(A∧,t) = Dmin(A∧,t) ⊕  �  σ0∈specb(pt)∩R  Eσ0(pt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  If (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='5) holds for p(σ) it is true for all pt(σ), and in this case the space  H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) = Hµ  b (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) ∩ L2  b(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1)  is independent of t > 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' thus the minimal domain  Dmin(A∧) = x  1  2 Hµ  b (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) ∩ x  1  2 L2  b(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ∩ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0)  is independent of 0 < t ≤ t0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Operators of first order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let D : D(D) ⊂ H1 → H2 be closed and densely  defined, and let D∗ : D(D∗) ⊂ H2 → H1 be the adjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Write  E0 =  H1  ⊕  H2  and E1 =  D(D)  ⊕  D(D∗)  ֒→ E0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  We assume that D (and therefore also D∗) is Fredholm, and that the embeddings  for both domains D(D) ֒→ H1 and D(D∗) ֒→ H2 are compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Consider then  D∧ = x−1  ��1  0  0  −1  �  (xDx)+  � 0  D∗  D  0  ��  : C∞  c (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ⊂ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) → L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0)  with indicial family  D(σ) =  �  σ  D∗  D  −σ  �  : E1 ⊂ E0 → E0,  σ ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Now D(σ) satisfies the assumptions previously stated for indicial families with  µ = 1, including (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='5) with Λ = D(0);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' see Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='8 for the required estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Therefore the conclusions summarized above hold for D∧, and by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='9 we  have  sgn  �  Dmax(D∧)/Dmin(D∧), [·, ·]  �  = ind[D : D(D) ⊂ H1 → H2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='7)  The only real indicial root is σ0 = 0, and after possibly introducing a sufficiently  small scaling parameter t > 0 and replacing D∧ by  D∧,t = x−1  �  t  �  1  0  0  −1  �  (xDx) +  �  0  D∗  D  0  ��  we have  Dmin(D∧,t) = x  1  2 H1  b (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0) ∩ x  1  2 L2  b(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ∩ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0),  Dmax(D∧,t) = Dmin(D∧,t) ⊕ E0(Dt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  In this case E0(Dt) = E0(D) is also independent of t > 0, and we have  E0(D) =  �  u = ω  � k  k∗  �  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' k ∈ ker(D), k∗ ∈ ker(D∗)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  COBORDISM INVARIANCE OF THE INDEX REVISITED  9  This follows from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='3) in view of  D(σ)−1 = σ  �  1  0  0  −1  �  [D(0)2 + σ2]−1 + D(0)[D(0)2 + σ2]−1  =  �ΠD  0  0  −ΠD∗  � 1  σ + holomorphic  near σ = 0, where ΠD : H1 → ker(D) and ΠD∗ : H2 → ker(D∗) are the orthogonal  projections onto the kernels of D and D∗, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' For sufficiently small t > 0  a brief calculation shows that the adjoint pairing is given by  �  ω  �  k1  k∗  1  �  , ω  �  k2  k∗  2  ��  D∧,t = t  �  ⟨k1, k2⟩H1 − ⟨k∗  1, k∗  2⟩H2  �  for kj ∈ ker(D) and k∗  j ∈ ker(D∗), j = 1, 2, which provides a direct justification for  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='7) for D∧,t (for small t > 0) that does not rely on the spectral flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' For (λ, σ) ∈ R2 write z = σ + iλ ∈ C and consider  D(z) = D(σ) + iλ =  � z  D∗  D  −z  �  : E1 ⊂ E0 → E0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Then D(z) is invertible for all z ∈ C \\ {0}, and  sup  |z|≥1  {|z| · ∥D(z)−1∥L (E0) + ∥D(z)−1∥L (E0,E1)} < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We have D(z)∗ = D(z), and  D(z)∗D(z) = D(z)D(z)∗ =  �|z|2 + D∗D  0  0  |z|2 + DD∗  �  = D(0)2 + |z|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  This operator is invertible for z ∈ C \\ {0}, and consequently D(z) is invertible with  D(z)−1 = D(z)∗[D(z)D(z)∗]−1 = [zΠ1−zΠ2][D(0)2+|z|2]−1+D(0)[D(0)2+|z|2]−1,  where Πj : E0 → Hj ⊂ E0 is the orthogonal projection, j = 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  In view of  D(0)[zΠ1 − zΠ2] = [zΠ2 − zΠ1]D(0) we have  D(0)D(z)−1 = [zΠ2 − zΠ1]D(0)[D(0)2 + |z|2]−1 + D(0)2[D(0)2 + |z|2]−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  The Spectral Theorem implies  sup  |z|≥1  {∥D(0)2[D(0)2+|z|2]−1∥+∥zD(0)[D(0)2+|z|2]−1∥+∥z2[D(0)2+|z|2]−1∥} < ∞,  where ∥ · ∥ = ∥ · ∥L (E0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The lemma now follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  □  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We have  ind[D : D(D) ⊂ H1 → H2] = SF  �  D(σ) : E1 ⊂ E0 → E0, σ ∈ R  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let K = ker(D(0)) = ker(D) ⊕ ker(D∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Then  D(σ) =  �DK(σ)  0  0  DK⊥(σ)  �  :  K  ⊕  K⊥ ∩ E1  →  K  ⊕  K⊥  ,  σ ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  10  THOMAS KRAINER  Now DK(σ) : K → K, σ ̸= 0, has eigenvalues σ, −σ of multiplicities dim ker(D) and  dim ker(D∗), respectively, and DK⊥(σ) is invertible for all σ ∈ R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Thus  ind D = dim ker(D) − dim ker(D∗)  = SF  �  DK(σ) : K → K, σ ∈ R  �  = SF  �  D(σ) : E1 ⊂ E0 → E0, σ ∈ R  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The null-cobordism theorem  We now revisit the setting discussed in the introduction to prove the null-cobordism  theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We make the following product type assumptions on the geometry and  the operator:  Let (M, g) be a Riemannian manifold, and let U = U(Y ) ⊂ M be an open subset  that is isometric to (0, ε) × Y with product metric dx2 + gY for some ε > 0, where  (Y, gY ) is another Riemannian manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let E → M be a Hermitian vector bundle  such that E  ��  U(Y ) ∼= π∗  Y E isometrically, where E → Y is a Hermitian vector bundle,  and πY : (0, ε) × Y → Y is the canonical projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let  A : C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )  be an elliptic differential operator of order µ ≥ 1 that is symmetric with respect to  the inner product induced by the Riemannian and Hermitian metrics, and suppose  that A is in U(Y ) of the form  A ∼= A∧ = x−1  µ  �  j=0  aj(y, Dy)(xDx)j : C∞  c ((0, ε) × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' π∗  Y E) → C∞  c ((0, ε) × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' π∗  Y E),  where aj(y, Dy) ∈ Diffµ−j(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let  p(σ) =  µ  �  j=0  aj(y, Dy)σj : C∞  c (Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) → C∞  c (Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E), σ ∈ C,  be the indicial family.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We assume that p(σ) : E1 ⊂ E0 → E0 satisfies the assump-  tions stated in Section 3 with E0 = L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) and some domain  Hµ  comp(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) ⊂ E1 ⊂ Hµ  loc(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  We also assume that the embedding E1 ֒→ E0 is compact, and that p(σ) : E1 → E0  is invertible for 0 < |ℑ(σ)| ≤ 1  2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' as explained in Section 3, the latter can generally  be achieved by introducing a scaling parameter (which for geometric operators  typically corresponds to scaling the metric).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The closed extensions of the indicial  operator  A∧ : C∞  c (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ⊂ L2(R+ × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' π∗  Y E) → L2(R+ × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' π∗  Y E)  are then described as explained in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let  Amin : Dmin(A) ⊂ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )  be a closed symmetric extension of A : C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) ⊂ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ), and  let Amax : Dmax(A) ⊂ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) be the adjoint;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' as discussed in the  introduction, Amin is generally not the minimal extension of A from C∞  c (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ),  COBORDISM INVARIANCE OF THE INDEX REVISITED  11  and thus Amax is not the largest L2-based closed extension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' By elliptic regularity  we have  Hµ  comp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) ⊂ Dmin(A) ⊂ Dmax(A) ⊂ Hµ  loc(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  By a cut-off function we mean any function ω ∈ C∞  c ([0, ε)) such that ω ≡ 1 near  x = 0, and we consider ω a function on M supported in U(Y ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  We make the  following localization and compatibility assumptions between A and A∧:  For every cut-off function ω, multiplication by 1 − ω gives a continuous  operator Dmax(A) → Dmin(A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We also assume that 1 − ω : Dmin(A) →  L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  For every cut-off function ω, multiplication by ω gives continuous operators  Dmin(A) → Dmin(A∧) and Dmin(A∧) → Dmin(A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  To make sense of the mappings above note that  M ⊃ U(Y ) ∼= (0, ε) × Y ⊂ R+ × Y,  which allows transitioning both ways between functions on M supported in U(Y )  and functions on R+ × Y supported in (0, ε) × Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We will use these transitions  freely in what follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let ω ∈ C∞  c ([0, ε)) be any cut-off function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The map  Dmax(A)/Dmin(A) ∋ u + Dmin(A) �−→ ωu + Dmin(A∧) ∈ Dmax(A∧)/Dmin(A∧)  is well-defined, and induces a unitary equivalence between the indefinite inner prod-  uct spaces  �  Dmax(A)/Dmin(A), [·, ·]A  � ∼=  �  Dmax(A∧)/Dmin(A∧), [·, ·]A∧  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We first prove that multiplication by ω gives a well-defined map  Dmax(A) ∋ u �→ ωu ∈ Dmax(A∧).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Note that with u also ωu ∈ Dmax(A) by our localization assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Now pick  another cut-off function ˜ω ∈ C∞  c ([0, ε)) such that ˜ω ≡ 1 in a neighborhood of  supp(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let φ ∈ Dmin(A∧) be arbitrary, and write φ = ˜ωφ + (1 − ˜ω)φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Since  Dmin(A∧) = x  1  2 H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ∩ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0)  as a consequence of our assumptions we have that both ˜ωφ, (1 − ˜ω)φ ∈ Dmin(A∧),  see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We also have ˜ωφ ∈ Dmin(A) by our localization and compatibility as-  sumption with respect to the minimal domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Using the locality of the differential  operators A∧ and A we get  ⟨A∧φ, ωu⟩ = ⟨A∧(˜ωφ), ωu⟩ = ⟨A(˜ωφ), ωu⟩ = ⟨˜ωφ, Amax(ωu)⟩  = ⟨φ, ˜ωAmax(ωu)⟩ = ⟨φ, Amax(ωu)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  As this is valid for all φ ∈ Dmin(A∧) we see that ωu ∈ Dmax(A∧) with A∧,max(ωu)  given as the restriction of Amax(ωu) to U(Y ) and extended trivially to R+ × Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' As  for u ∈ Dmin(A) we also have ωu ∈ Dmin(A∧) by assumption, we thus obtain that  the map  Dmax(A)/Dmin(A) ∋ u + Dmin(A) �−→ ωu + Dmin(A∧) ∈ Dmax(A∧)/Dmin(A∧)  is well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Conversely, multiplication by ω likewise gives a well-defined map  Dmax(A∧) ∋ u �→ ωu ∈ Dmax(A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  12  THOMAS KRAINER  Note that if u ∈ Dmax(A∧) then ωu ∈ Dmax(A∧) and (1 − ω)u ∈ Dmin(A∧) by  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Now let ˜ω ∈ C∞  c ([0, ε)) be such that ˜ω ≡ 1 in a neighborhood of  supp(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let φ ∈ Dmin(A) be arbitrary, and write φ = ˜ωφ + (1 − ˜ω)φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' by the  localization and compatibility assumptions both terms are in Dmin(A), and we also  have ˜ωφ ∈ Dmin(A∧).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We get  ⟨Aφ, ωu⟩ = ⟨A(˜ωφ), ωu⟩ = ⟨A∧(˜ωφ), ωu⟩ = ⟨˜ωφ, A∧,max(ωu)⟩  = ⟨φ, ˜ωA∧,max(ωu)⟩ = ⟨φ, A∧,max(ωu)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  This shows that ωu ∈ Dmax(A) with Amax(ωu) given by A∧,max(ωu) in U(Y ) and  extended trivially to M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We thus obtain a map  Dmax(A∧)/Dmin(A∧) ∋ u + Dmin(A∧) �−→ ωu + Dmin(A) ∈ Dmax(A)/Dmin(A),  and both maps are inverses of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Finally, as for both A and A∧ each class in Dmax/Dmin has a representative  supported in U(Y ), and by the standing product type assumptions both adjoint  pairings agree on those representatives, the proposition follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  □  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2 (Null-Cobordism Theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Under the stated product type, local-  ization, and compatibility assumptions we have  SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  If moreover  p(σ) =  �  σ  D∗  D  −σ  �  :  D(D)  ⊕  D(D∗)  ⊂ L2  �  Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  E−  ⊕  E+  �  → L2  �  Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  E−  ⊕  E+  �  with an elliptic Fredholm operator of first order  D : D(D) ⊂ L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E−) → L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E+),  then ind[D : D(D) ⊂ L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E−) → L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E+)] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' By Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1 we have a unitary equivalence between the indefinite  inner product spaces  �  Dmax(A)/Dmin(A), [·, ·]A  � ∼=  �  Dmax(A∧)/Dmin(A∧), [·, ·]A∧  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Because  sgn  �  Dmax(A∧)/Dmin(A∧), [·, ·]A∧  �  = SF[ p(σ) : E1 ⊂ E0 → E0, −∞ < σ < ∞ ]  by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='6) it suffices to show that  sgn  �  Dmax(A)/Dmin(A), [·, ·]A  �  = 0,  and by Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2 this will be the case if the embedding Dmax(A) ֒→ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )  is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Because A has finite deficiency indices we only need to prove that  Dmin(A) ֒→ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Now let ω, ˜ω ∈ C∞  c ([0, ε)) be cut-off functions  such that ˜ω ≡ 1 in a neighborhood of supp(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' By assumption the multiplication  operator  1 − ω : Dmin(A) → L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )  is compact, and  ˜ω : Dmin(A) → Dmin(A∧)  is continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Now  Dmin(A∧) = x  1  2 H (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E1) ∩ L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0),  COBORDISM INVARIANCE OF THE INDEX REVISITED  13  and because E1 ֒→ E0 is compact, multiplication by ω is a compact operator  ω : Dmin(A∧) → L2(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E0),  see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Consequently, using the product type assumptions, the composition  ω = ω˜ω : Dmin(A) → L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )  is compact, which shows that the embedding ι = ω+(1−ω) : Dmin(A) → L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )  is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Finally, the vanishing of the index in the special case of operators of  first order follows from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  □  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The null-cobordism theorem for closed manifolds  In this appendix we discuss a version of the null-cobordism Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2 for closed  manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Most of the previous assumptions no longer explicitly appear in this  version, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=', we do not assume product type geometry, and there isn’t an operator  A on M at the outset, but symbolic assumptions instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' As mentioned in the  introduction this is due to the richness of analytic tools available for this situation  that allows to create the preconditions needed to apply Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2 instead of  having to assume them from the outset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Let Y be a closed, compact Riemannian manifold and E → Y be a Hermitian  vector bundle, and consider a family  p(σ) =  µ  �  j=0  aj(y, Dy)σj : C∞(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) → C∞(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E), σ ∈ R,  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1)  where aj(y, Dy) ∈ Diffµ−j(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E), and µ ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  We assume that the parameter-  dependent principal symbol  σσ(p)(y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) =  µ  �  j=0  σσ(aj)(y, η)σj : Ey → Ey  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2)  is invertible on  �  T ∗Y × R  �  \\ 0, and that p(σ) = p(σ)∗ is (formally) selfadjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' By  elliptic and analytic Fredholm theory,  R ∋ σ �→ p(σ) : Hµ(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) ⊂ L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) → L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E)  is a family of selfadjoint unbounded Fredholm operators acting in L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) that  is invertible for all σ ∈ R except at finitely many points, and it makes sense to  consider the spectral flow  SF[p(σ)] := SF[p(σ) : Hµ(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) ⊂ L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) → L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E), −∞ < σ < ∞] ∈ Z  associated with p(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The spectral flow is an invariant of the principal symbol (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='2) in  the sense that if pj(σ), j = 1, 2, are two elliptic selfadjoint families of order µ ≥ 1  of the form (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1) with σσ(p1)(y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) = σσ(p2)(y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) then SF[p1(σ)] = SF[p2(σ)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let R > 0 be such that  p1(σ) + s[p2(σ) − p1(σ)] : Hµ(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) ⊂ L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) → L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E)  is invertible for |σ| ≥ R > 0 and all 0 ≤ s ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Consequently, this family is a ho-  motopy of selfadjoint Fredholm functions on [−R, R], invertible at both endpoints,  and by the homotopy invariance of the spectral flow for such families we see that  SF[p1(σ)] = SF[p2(σ)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  □  14  THOMAS KRAINER  Suppose there exists a compact Riemannian manifold M with ∂M = Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Utilizing  the geodesic flow from the boundary in the direction of the inner normal vector field  shows that there exists ε > 0 and a collar neighborhood map U(Y ) ∼= [0, ε) × Y  near the boundary such that the metric in U(Y ) takes the form dx2 + gY (x) with  a smooth family of metrics gY (x) on Y , 0 ≤ x < ε, and such that gY (0) = gY is  the given metric on Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Moreover, by choosing ε > 0 small enough, there exists a  defining function for ∂M on M that in U(Y ) is represented by projection onto the  coordinate in [0, ε).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We’ll also denote this global defining function by x : M → R+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  In particular,  T ∗M  ��  Y = T ∗Y ⊕ span{dx  ��  Y }  subject to these choices, and we can split variables (y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) ∈ T ∗M  ��  Y accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='4 (Null-Cobordism Theorem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let M be a compact Riemannian man-  ifold M with ∂M = Y , and let E → M be a Hermitian vector bundle with E  ��  Y = E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Let T ∗M  ��  Y ∼= T ∗Y × R subject to the choices described above, and suppose there ex-  ists a symmetric, elliptic, differential principal symbol a ∈ C∞(T ∗M \\0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' End(π∗E ))  of order µ such that  a(y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) = σσ(p)(y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) for (y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) ∈  �  T ∗M \\ 0  ���  Y ,  where π : T ∗M → M is the canonical projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Then SF[p(σ)] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  With the family p(σ) from (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1) we associate the indicial operator  A∧ = x−1  µ  �  j=0  aj(y, Dy)(xDx)j : C∞  c (R+×Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) ⊂ L2(R+×Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) → L2(R+×Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='5)  Here we also write E for its pull-back to R+ ×Y with respect to the projection onto  Y , and equip R+ × Y with the product metric dx2 + gY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Then A∧ is symmetric  and densely defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let Dmin(A∧) be the domain of the closure, and Dmax(A∧)  be the domain of the adjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Proof of Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' In the previously fixed collar neighborhood U(Y ) ∼= [0, ε)×  Y we utilize standard deformations of the Riemannian metric on M, the Hermitian  metric on E , and the principal symbol a to reduce to a product type structure near  the boundary, as follows:  Pick an isomorphism E  ��  U(Y ) ∼= π∗  Y E that is the identity over Y , where πY :  [0, ε) × Y → Y is the projection map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' With respect to the pull-back of the given  Hermitian metric on E to π∗  Y E, the metric on E  ��  U(Y ) under this isomorphism is  then represented by h(x, y) ∈ C∞([0, ε) × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' End(π∗  Y E)) such that h = h∗ > 0 and  h(0, y) = Id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Choose C∞-functions φ, ψ : [0, ε) → R with  φ ≡ 0 on 0 ≤ x ≤ ε  3, 0 < φ < 2ε  3 on ε  3 < x < 2ε  3 , and φ ≡ x on 2ε  3 ≤ x < ε;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  ψ ≡ x on 0 ≤ x ≤ ε  3, ψ > 0 on ε  3 < x < 2ε  3 , and ψ ≡ 1 on 2ε  3 ≤ x < ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  We then deform the Riemannian metric on U(Y ) and Hermitian metric on E  ��  U(Y )  to  ˜g = dx2 + gY (φ(x)) and ˜h(x, y) = h(φ(x), y) ∈ C∞([0, ε) × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' End(π∗  Y E)),  respectively, which both connect seamlessly with the Riemannian metric on M  outside U(Y ), and the Hermitian metric on E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We also change the principal symbol  COBORDISM INVARIANCE OF THE INDEX REVISITED  15  in  U(Y ) to  ˜a(x, y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) = ψ(x)−1a(φ(x), y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' ψ(x)σ) : Ey → Ey  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='6)  for (x, y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) ∈ T ∗�  (0, ε)×Y  �  \\0 with the obvious identifications of variables, which  again connects seamlessly outside the collar neighborhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' The new homogeneous  principal symbol ˜a ∈ C∞(T ∗  M \\ 0, End(π∗E )) is symmetric with respect to the  new metric on E , and elliptic over M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' In U(Y ) we have  ˜a(x, y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) = x−1 σσ(p)(y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' xσ) : Ey → Ey for 0 < x < ε  3  by construction, which aligns with the principal symbol of A∧ from (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Let  now A ∈ Diffµ(  M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) be symmetric C∞  c (  M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → C∞  c (  M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) with respect to the  L2-inner product associated with the modified metrics on M and E , respectively,  such that the principal symbol σσ(A) = ˜a on T ∗  M \\ 0, and such that in  U(Y ) we  have A = A∧ on C∞  c ((0, ε  4) × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Then  A = x−1P : C∞  c ( M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) ⊂ L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) = x− 1  2 L2  b(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) → x− 1  2 L2  b(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E )  is symmetric, and P ∈ Diffµ  b (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) is b-elliptic (see [13]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Moreover, by construction  p(σ) is the indicial family of the operator P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  By analytic Fredholm theory p(σ) : Hµ(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) → L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E) is invertible for σ ∈ C  except for the discrete set specb(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' In the sequel it will be convenient to assume  that specb(p) ∩ {σ ∈ C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 0 < |ℑ(σ)| ≤  1  2} = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' As explained in Section 3, this  can be achieved by replacing p(σ) by p(tσ) for sufficiently small t > 0 if necessary,  which does not impact the spectral flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Moreover, the assumptions of the theorem  pertaining to the principal symbol of p(σ) also hold for p(tσ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' to see this pick a  C∞-function χ : [0, ε) → R with  χ ≡ t on 0 ≤ x ≤ ε  3, χ > 0 on ε  3 < x < 2ε  3 , and χ ≡ 1 on 2ε  3 ≤ x < ε,  and alter the principal symbol (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='6) in  U(Y ) to  ˜a(x, y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) = ψ(x)−1a(φ(x), y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' ψ(x)χ(x)σ) : Ey → Ey  for (x, y, η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' σ) ∈ T ∗�  (0, ε) × Y  �  \\ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' We may thus proceed without loss of generality  under the assumption that specb(p) ∩ {σ ∈ C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 0 < |ℑ(σ)| ≤ 1  2} = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' In view of  Section 3 for A∧ and by invoking elliptic regularity for A we then get  Dmin(A∧) = x  1  2 Hµ  b (R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' L2(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E)) ∩ x  1  2 L2  b(R+;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Hµ(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E)) ∩ L2(R+ × Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E),  Dmin(A) = x  1  2 Hµ  b (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ),  and  Dmax(A∧) = Dmin(A∧) ⊕  �  σ0∈specb(p)∩R  Eσ0(p),  Dmax(A) = Dmin(A) ⊕  �  σ0∈specb(p)∩R  Eσ0(p),  where Eσ0(p) is defined as in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='3) based on a cut-off function ω ∈ C∞  c ([0, ε  4)) with  ω ≡ 1 near x = 0 so that elements in Eσ0(p) can interchangeably be regarded both  as sections of E on R+ × Y , as well as sections of E on M supported near the  boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' In particular, this implies that  �  Dmax(A)/Dmin(A), [·, ·]A  � ∼=  �  Dmax(A∧)/Dmin(A∧), [·, ·]A∧  �  16  THOMAS KRAINER  because [u, v]A∧ = [u, v]A for u, v ∈  �  σ0∈specb(p)∩R  Eσ0(p) by construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Finally, it  remains to note that Dmax ֒→ x− 1  4 Hµ  b (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ), and the embedding x− 1  4 Hµ  b (M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) ֒→  x− 1  2 L2  b(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) = L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E ) is compact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  □  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='4 and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='9 imply:  Corollary A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='7 (Cobordism Invariance of the Index).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Suppose that E = E− ⊕ E+  is an orthogonal direct sum, and that the family (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='1) is of the form  D(σ) =  �σ  D∗  D  −σ  �  : C∞  �  Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  E−  ⊕  E+  �  → C∞  �  Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  E−  ⊕  E+  �  , σ ∈ R,  where D : C∞(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E−) → C∞(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E+) is an elliptic differential operator of first  order, and D∗ : C∞(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E+) → C∞(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' E−) is its (formal) adjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Then  SF[D(σ)] = ind D = dim ker(D) − dim ker(D∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  In particular, if the assumptions of Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='4 hold, then ind(D) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  References  [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Albin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Leichtnam, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Mazzeo, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Piazza, The signature package on Witt spaces,  Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' ´Ec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Sup´er.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' (4) 45 (2012), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 2, 241–310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [2]  , Hodge theory on Cheeger spaces, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Reine Angew.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 744 (2018), 29–102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [3] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Braverman, New proof of the cobordism invariance of the index, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  130 (2002), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 4, 1095–1101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Braverman and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Shi, Cobordism invariance of the index of Callias-type operators,  Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Partial Differential Equations 41 (2016), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 8, 1183–1203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Carvalho, A K-theory proof of the cobordism invariance of the index, K-Theory 36 (2005),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 1-2, 1–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [6] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Hartmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Lesch, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Vertman, On the domain of Dirac and Laplace type operators  on stratified spaces, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Spectr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Theory 8 (2018), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 4, 1295–1348.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [7]  , Resolvent trace asymptotics on stratified spaces, Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 3 (2021), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 1,  75–108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Hilsum, Bordism invariance in KK-theory, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Scand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 107 (2010), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 1, 73–89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [9] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Higson, A note on the cobordism invariance of the index, Topology 30 (1991), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 3,  439–443.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [10] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Krainer, Extensions of symmetric operators that are invariant under scaling and applica-  tions to indicial operators, New York J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 28 (2022), 705–772.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Lesch, Deficiency indices for symmetric Dirac operators on manifolds with conic singu-  larities, Topology 32 (1993), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 3, 611–623.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [12]  , Operators of Fuchs Type, Conical Singularities, and Asymptotic Methods, Teubner-  Texte zur Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' vol 136, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Teubner, Stuttgart, Leipzig, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [13] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Melrose, The Atiyah-Patodi-Singer index theorem, Research Notes in Mathematics,  A K Peters, Ltd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=', Wellesley, MA, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Moroianu, Cusp geometry and the cobordism invariance of the index, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 194  (2005), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 2, 504–519.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [15] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Nazaikinskii, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Savin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Schulze, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='Yu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Sternin, Elliptic theory on singular  manifolds, Differential and Integral Equations and Their Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 7, Chapman &  Hall/CRC, Boca Raton, FL, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [16] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Nicolaescu, On the cobordism invariance of the index of Dirac operators, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 125 (1997), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 9, 2797–2801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Palais, Seminar on the Atiyah-Singer index theorem, Annals of Mathematics Studies,  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 57, Princeton University Press, Princeton, NJ, 1965.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  [18] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Schulze,  Pseudo-differential calculus on manifolds with geometric singularities,  Pseudo-differential operators:  Partial differential equations and time-frequency analysis,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 37–83, Fields Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 52, Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=', Providence, RI, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  COBORDISM INVARIANCE OF THE INDEX REVISITED  17  [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Wulff, Bordism invariance of the coarse index, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 140 (2012), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content=' 8,  2693–2697.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='  Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601-3760  Email address: krainer@psu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
+page_content='edu' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/H9AyT4oBgHgl3EQfTPcY/content/2301.00100v1.pdf'}
diff --git a/H9AyT4oBgHgl3EQfrvmy/content/2301.00567v1.pdf b/H9AyT4oBgHgl3EQfrvmy/content/2301.00567v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..06de937ac565a8472f15c348a74b2e240e0e4a61
--- /dev/null
+++ b/H9AyT4oBgHgl3EQfrvmy/content/2301.00567v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:52bc1e2fdaf2ad98b392a60cfa0937d85958f7c16ac9fb41c1b8909c7c97339b
+size 481103
diff --git a/I9FJT4oBgHgl3EQfGCzl/content/tmp_files/2301.11446v1.pdf.txt b/I9FJT4oBgHgl3EQfGCzl/content/tmp_files/2301.11446v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d9ff6502ce425c6130e7c42c9b7ea48e7f8f4f85
--- /dev/null
+++ b/I9FJT4oBgHgl3EQfGCzl/content/tmp_files/2301.11446v1.pdf.txt
@@ -0,0 +1,877 @@
+ON GRANULARITY OF PROSODIC REPRESENTATIONS IN EXPRESSIVE
+TEXT-TO-SPEECH
+Mikolaj Babianski, Kamil Pokora, Raahil Shah, Rafal Sienkiewicz, Daniel Korzekwa, Viacheslav Klimkov
+Amazon Text-to-Speech Research
+{babiansk, kamipoko, vklimkov}@amazon.com
+ABSTRACT
+In expressive speech synthesis it is widely adopted to use
+latent prosody representations to deal with variability of the
+data during training.
+Same text may correspond to vari-
+ous acoustic realizations, which is known as a one-to-many
+mapping problem in text-to-speech.
+Utterance, word, or
+phoneme-level representations are extracted from target sig-
+nal in an auto-encoding setup, to complement phonetic input
+and simplify that mapping. This paper compares prosodic
+embeddings at different levels of granularity and examines
+their prediction from text. We show that utterance-level em-
+beddings have insufficient capacity and phoneme-level tend
+to introduce instabilities when predicted from text. Word-
+level representations impose balance between capacity and
+predictability. As a result, we close the gap in naturalness by
+90% between synthetic speech and recordings on LibriTTS
+dataset, without sacrificing intelligibility.
+Index Terms— speech synthesis, TTS, prosody, Text-to-
+Speech, representation learning
+1. INTRODUCTION
+Neural Text-to-Speech (NTTS) [1] is characterized by syn-
+thesizing speech waveform solely with deep neural networks.
+This paradigm greatly enhanced naturalness and flexibility of
+speech synthesis. It enables new applications such as expres-
+sive [2, 3] and low-resource [4] speech generation, speaker
+identity [5] and prosody transplantation [6, 7]. This paper
+focuses on expressive speech synthesis, i.e.
+generation of
+speech that originally contains great degree of variation in
+terms of intonation and inflections.
+This variation is not described by phoneme sequence, typ-
+ically used as input to NTTS. Thus, the statistical model has
+to perform a one-to-many mapping, where the same input
+text can correspond to different acoustic realizations. Vanilla
+modelling approaches suffer from averaging and fail to repro-
+duce the original variability of the training data.
+To avoid averaging, it is common to use additional input
+that describes variability in the data. Initially, it was proposed
+to extract a single latent representation of the target speech in
+an auto-encoder manner for the whole utterance [8]. Target
+speech is not available during inference, so either the cen-
+troid representation is used [9] or it is separately predicted
+from text [10, 11].
+A single representation for the whole
+utterance can’t store temporal information effectively, thus,
+it was proposed to use more fine-grained representations at
+the phoneme-level for the task of prosody transplantation [6,
+12]. This idea was further expanded to text-to-speech, where
+word-level [13, 14] and phoneme-level [15, 16, 17] represen-
+tations were utilized. At the fine-grained level, prosody can
+be represented with pre-extracted features such as pitch, en-
+ergy, spectral tilt, but learnt representations can convey more
+information and represent more abstract aspects of prosody
+such as emotions. Therefore, in the rest of the paper we focus
+on learnt representations.
+This paper provides a systematic comparison of prosodic
+representations at different levels of granularity. We compare
+performance of utterance, word, and phoneme-level prosody
+embeddings in terms of a) capacity: what if we have a perfect
+prosody predictor; b) predictability: how sensitive is the ap-
+proach to inaccurate prosody predictions. Main contributions
+of this study are:
+• We systematically compare prosody embeddings at dif-
+ferent levels of granularity.
+• A solution to intelligibility issues in the case of phoneme-
+level prosody reference is proposed.
+• We show the trade-off between capacity and pre-
+dictability of prosody embeddings, advocating the use
+of word-level representations.
+• We examine data quantity and input features needed for
+robust prosody prediction from text.
+The rest of the paper is organized as follows: Section 2
+describes the text-to-speech framework used; Section 3 elab-
+orates on prosody embedding prediction from text; Section 4
+compares prosody embeddings at different levels of granular-
+ity in objective and subjective evaluations; Section 5 presents
+ablation studies on prosody embedding prediction; Section 6
+concludes the paper.
+978-1-6654-7189-3/22/$31.00 ©2023 IEEE
+arXiv:2301.11446v1  [eess.AS]  26 Jan 2023
+
+(a)
+(b)
+Fig. 1. Schematic diagram of the TTS model during a) training and b) inference. The dashed arrow denotes sampling from
+parametric distribution. Components in red are of prosody embeddings granularity (utterance/word/phoneme). Green, dashed
+lines denote loss functions.
+2. ACOUSTIC MODEL
+The backbone of our acoustic model architecture (Figure 1) is
+similar to the explicit duration TTS model presented in Shah
+et al. [4]. It follows the encoder-decoder paradigm, where the
+input phoneme sequence x is encoded by a phoneme encoder
+presented in the Tacotron2 [1] paper. We concatenate the en-
+coded phoneme sequence with both speaker s and prosody z
+embeddings upsampled by repetition [15, 16] to the phoneme-
+level. Speaker embeddings are represented as corresponding
+entries in the embedding look-up table. Prosody embeddings
+are obtained via compression of the mel-spectrogram y with
+the use of variational prosody reference encoder described in
+Section 2.1. During inference, the encoded sequence is up-
+sampled accordingly to alignments produced by the duration
+model, described in Section 2.2. The upsampled sequence is
+then passed to the decoder to map the disentangled linguistic
+features, speaker and prosodic contents into acoustic param-
+eters represented as mel-spectrograms. In this work, we use
+the non-autoregressive decoder presented in Shah et al. [4].
+2.1. Variational Prosody Reference Encoder
+To alleviate the one-to-many problem of TTS we use the vari-
+ational prosody reference encoder [16]. We aim to learn the
+latent representation of the information, which cannot be de-
+rived from the other input streams - phoneme sequence and
+speaker embedding. For clarity of the architecture presenta-
+tion, here we describe only one level of granularity - word-
+level. Modification of the model architecture to adjust for dif-
+ferent prosody embedding granularities is described in Sec-
+tion 2.3. The variational reference encoder (Figure 1a) takes
+target mel-spectrogram frames as input and converts them
+into a sequence of n latent vectors z, which corresponds to
+the number of words in the utterance. We refer to this repre-
+sentation as word-level prosody embeddings.
+The encoder comprises a stack of six residual gated con-
+volution blocks [18]. Each residual gated convolution block
+is composed of a 1D-convolution with a kernel size of 15 and
+a hidden dimension of 512, followed by a tanh filter and a
+sigmoid activation gate which are element-wise multiplied
+and then added to a residual connection. The convolution
+stack is followed by a BiLSTM layer with a hidden dimension
+of 128. We use a dropout of 0.1 in convolutional and BiLSTM
+layers. The BiLSTM layer output is firstly aggregated to the
+word-level by taking a middle frame of each word. Then,
+after a dense projection we obtain a sequence of Gaussian
+distribution parameters µ and σ, which we use to sample a
+sequence of prosody embeddings corresponding to words z
+of dimension 8. Finally, we upsample the word-level prosody
+embeddings by repetition to the phoneme-level and concate-
+nate them with the phoneme encoder output (Figure 1a).
+As we do not have access to target mel-spectrograms at
+inference time (Figure 1b), a separate model is introduced to
+predict prosody embeddings z from text. The architecture for
+this model is described in Section 3.
+2.2. Duration Model
+Neural TTS requires learning the alignment between two dif-
+ferent length sequences, which are the text, represented by
+phonemes, and speech, represented by acoustic parameters
+i.e. mel-spectrogram frames. There are two major approaches
+to obtain the alignment: attention-based [1] and explicit-
+duration-based [4, 19, 16, 20]. Attention-based components
+typically used for this task have known instabilities, which
+exhibit in synthesised speech as mumbling, early cut-offs,
+word repetition and word skipping [21, 22, 23]. Following
+recent research in the field inspired by traditional parametric
+speech synthesis techniques [24, 25], these issues are mit-
+igated by explicitly modelling the durations of phonemes
+[4, 19, 16, 20] which we decide to use in this work.
+
+mel-spectrogram
+y
+6 x Gated Conv
+Duration Model
+BiLSTM
+Aggregation
+predicted duration
+Dense Proj.
+d
+N(0,1)
+: L2
+μ,a
+DKL
+predicted
+oracle duration
+mel-spectrogram
+d
+y
+prosody
+embeddings (z)
+Concat
+Upsampling
+Encoder
+Decoder
+speaker embedding
+phoneme sequence
+x
+sBERT embeddings
+phoneme sequence
+b
+x
+Prosody
+Embeddings
+Duration Model
+Predictor
+predicted
+predicted duration
+mel-spectrogram
+p
+y
+prosody embeddings
+Encoder
+Concat
+Upsampling
+Decoder
+phoneme sequence
+speaker embedding
+x
+sWe use forced alignment from a Gaussian Mixture Model
+(GMM) based external aligner in the Kaldi Speech Recog-
+nition Toolkit [26] to produce ground truth duration for
+each phoneme, represented as the integer number of mel-
+spectrogram frames it corresponds to. To predict these du-
+rations, we train a duration model component following the
+architecture detailed in Shah et al. [4], with the addition of
+speaker and prosody embeddings conditioning. The duration
+model is trained jointly with the acoustic model by minimiz-
+ing L2 loss function in the logarithmic domain between pre-
+dicted and ground truth phoneme durations. During training,
+teacher forcing is used, i.e. the acoustic model uses ground
+truth duration values to upsample a phoneme’s encoding to
+the respective number of mel-spectrogram frames.
+2.3. Prosody Embeddings Granularity
+The model described above uses word-level prosody embed-
+dings. Which means that there is one embedding correspond-
+ing to each word in the input text. In this work we also explore
+two other levels of prosody modelling granularity: phoneme-
+level (one embedding per each phoneme) and utterance-level
+(single embedding for the whole utterance). For the phoneme-
+level prosody modelling we change the reference encoder to
+output one embedding per each phoneme and reduce prosody
+embedding dimension from 8 to 3, which we found optimal
+in terms of stability, for this level of granularity. In the case
+of utterance-level prosody modelling we use a stride of 2 in
+the residual gated convolution blocks of the reference encoder
+in order to gradually downsample the time resolution [27].
+Then, we project the first and last state of the BiLSTM layer
+into two vectors of dimension 64, which represent mean µ
+and standard deviation σ of the posterior distribution. Finally
+we sample a single 64-dimensional prosody embedding z cor-
+responding to the whole utterance.
+2.4. Training Procedure
+To train the acoustic and duration models we use Adam opti-
+miser with β1 = 0.9 and β2 = 0.98. We use a linear warm-up
+of the learning rate from 0.1 to 1 for the first 10k steps, fol-
+lowed by an exponential decay from 10k steps to 100k steps
+with a minimum value of 10−5. Acoustic and duration models
+are trained jointly for 500K steps with a batch-size equal 32
+and are optimized with respect to the following loss function:
+Ltotal = L1melspectrogram + L2logduration + γ ∗ DKL (1)
+where L1melspectrogram is the L1-distance between pre-
+dicted and oracle mel-spectrograms and L2logduration is the
+L2-distance between predicted and ground truth durations
+calculated in the logarithmic domain.
+DKL is the Kull-
+back–Leibler divergence between outputs of the variational
+prosody reference encoder and N(0, 1). We find the optimal
+value of γ to be 10−3 for the phoneme-level and 10−5 for
+the utterance and word-level prosody modelling. We present
+ablation of the γ parameter in Section 4.4.
+3. PROSODY EMBEDDINGS PREDICTOR
+At inference time we do not have access to target mel-
+spectrograms, therefore, we use a separate model to pre-
+dict prosodic representations z from text (Figure 1b). The
+prosody embeddings predictor model (Figure 2) has three in-
+put streams: phoneme sequence, contextual word embeddings
+extracted with a pre-trained BERT model [28] and speaker
+embedding. Phoneme sequence and contextual word embed-
+dings are encoded by separate Tacotron2-based encoders. We
+upsample the encoded BERT embeddings from the word-
+level to the phoneme-level and the speaker embedding to the
+phoneme-level, before concatenating them with the encoded
+phoneme representations.
+Next, we pass the concatenated
+sequence to another Tactotron2-based encoder block. After
+that, in the case of word-level embeddings prediction, the
+encoded phoneme-level representation is aggregated to the
+word-level by taking the middle frame of each word.
+Fi-
+nally, we use an autoregressive decoder to predict prosody
+embeddings. The autoregressive decoder is inspired by the
+architecture of the Tacotron2 mel-spectrogram decoder. In
+order to adapt the decoder to the prosody prediction task, we
+reduce the hidden dimension of the LSTM-layers to 128 and
+pre-net hidden dimension to 6. To predict the utterance-level
+prosody representation, instead of the autoregressive decoder,
+we use a simple linear projection layer.
+We train this model using prosody embeddings extracted
+with previously trained acoustic model as target labels.
+Specifically, the model is trained to predict posterior mean µ
+for each target prosody embedding using L2 loss and teacher-
+forcing framework.
+Fig. 2. Schematic diagram of the prosody embeddings predic-
+tor model. Components with dashed border are used only for
+fine-grained (word or phoneme-level) prosody embeddings
+prediction.
+
+BERT embeddings
+phoneme sequence
+b
+x
+Encoder
+Encoder
+speaker embedding
+s
+predicted
+prosody embeddings
+Concat
+Autoregressive
+Encoder
+Decoder
+phoneme-level
+word-level
+Aggregation
+representation
+representation4. EXPERIMENTS - PROSODY EMBEDDINGS
+GRANULARITY
+In this section we conduct a systematic study of prosodic rep-
+resentations at different levels of granularity applied to the ex-
+pressive TTS task. The performance of utterance, word, and
+phoneme-level prosody embeddings is compared in terms of
+capacity and predictability. We evaluate naturalness as well
+as stability and intelligibility of synthesized speech.
+4.1. Data
+Evaluations are conducted on a publicly available corpus of
+audiobook recordings - LibriTTS [29]. From which we use
+only recordings marked as clean. The training set consists
+of approximately 250 hours of speech (split into 140,000 ut-
+terances) narrated in an expressive manner by 1229 speakers.
+For validation we use a held-out set of 1000 randomly se-
+lected utterances from the 100 most frequent speakers. We
+extract 80-band mel-spectrograms with a 12.5 ms frame-shift
+as acoustic features.
+4.2. Systems
+We use our acoustic model (Section 2) along with the prosody
+embeddings predictor (Section 3) to test 3 levels of prosody
+embeddings granularity:
+1) G-VAE - utterance-level.
+2)
+W-VAE - word-level. 3) P-VAE - phoneme-level. All mel-
+spectrogram prediction systems are used in combination with
+the Universal Neural Parallel WaveNet Vocoder [30] in order
+to obtain a 24kHz audio signal.
+4.3. Subjective Evaluation Protocol
+For the subjective evaluation we conduct MUSHRA tests [31]
+with the Amazon Mechanical Turk platform. 60 native En-
+glish speakers are presented with the samples in a random
+order side-by-side, and are asked to “Evaluate naturalness of
+the samples on the scale from 0 to 100.” A total of 1000 ut-
+terances are used for testing and the test is balanced in such a
+way that each test case is scored by 3 listeners independently.
+Ground truth mel-spectrograms vocoded with the Universal
+Parallel WaveNet Vocoder (Ref system) are used as an upper
+anchor. The significance of the MUSHRA results is analyzed
+using a Wilcoxon signed-rank test with Bonferroni-Holm cor-
+rection applied [32].
+4.4. Stability
+To quantify the stability of tested systems and the intelligibil-
+ity of synthesized speech we conduct Word Error Rate (WER)
+analysis. The whole test set of 1000 utterances described in
+Section 4.1 is used for the evaluation. We transcribe speech
+generated in the TTS mode (prosody embeddings predicted
+from text) with the ASpIRE Chain ASR model from Kaldi.
+Then the WER is computed between the sentence text and the
+corresponding transcription.
+The G-VAE and W-VAE models have WER scores (Ta-
+ble 1) comparable to recordings when trained with DKL loss
+weight (γ) equal to 10−5. Whereas, training the P-VAE model
+in an analogical setup results in significant stability issues.
+We believe that this is caused by the phoneme-level prosody
+embeddings distribution being very hard to predict from text.
+Only after applying more regularization during training by in-
+creasing DKL loss weight we are able to obtain a phoneme-
+level model matching other systems in terms of WER score.
+Intelligibility is a crucial property of TTS system. Therefore,
+for all the other experiments we use the G-VAE and W-VAE
+models trained with γ = 10−5 and the P-VAE model trained
+with γ = 10−3, as they are matching our stability require-
+ments. We found that further increasing γ parameter does not
+bring any significant improvements and may lead to degrada-
+tion in segmental quality of synthesized audio.
+System
+DKLγ
+WER ↓
+G-VAE
+1e − 5
+2.18% ± 0.30
+W-VAE
+1e − 5
+2.13% ± 0.30
+P-VAE
+1e − 5
+3.59% ± 0.36
+1e − 4
+2.47% ± 0.31
+1e − 3
+2.17% ± 0.29
+1e − 2
+2.17% ± 0.29
+Ref
+−
+2.29% ± 0.31
+Table 1. Word Error Rate with 95% confidence intervals [33]
+computed across the 1000 test utterances, along with DKL
+loss weight (γ).
+4.5. Capacity
+We analyse the best-case performance of acoustic models by
+simulating perfectly predicted prosody embeddings in the Or-
+acle Resynthesis setup. That is, at inference time we pro-
+vide ground truth latent representations from the variational
+reference encoder for all tested systems. We evaluate natu-
+ralness in a subjective test as described in Section 4.3 and
+summarize results in Figure 3a. In this setup, the G-VAE
+model scores significantly lower than the other systems (p-
+value < 0.01), suggesting that fine-grained embeddings are
+required for natural prosody modelling. There is no statisti-
+cally significant difference between W-VAE and P-VAE sys-
+tems (p-value > 0.01). It is worth mentioning, that we have
+also conducted an analogical experiment with a P-VAE model
+trained with lower DKL loss weight (γ = 10−5). With such
+model, when ground truth prosody embeddings provided dur-
+ing inference, we are able to reconstruct speech almost per-
+fectly. However, it comes at a cost of stability issues, when
+prosody embeddings predicted from text are used as described
+in Section 4.4.
+
+(a) Ground truth prosody embeddings
+(b) Prosody embeddings predicted from text
+Fig. 3. Subjective listeners ratings from the naturalness MUSHRA tests with a) ground truth prosody embeddings and b) prosody
+embeddings predicted from text (TTS). Mean scores are reported below the system names.
+To gain a deeper understanding of prosody representa-
+tions, we evaluate our acoustic models in the Oracle Resyn-
+thesis setup with changed speaker embedding. That is, we
+extract prosody from a source recording and resynthesize the
+same text with changed voice - a so-called Voice Conversion
+(VC). We convert all 1000 test utterances into 4 selected (two
+male and two female) target voices.
+To effectively measure how close the prosody patterns
+of converted speech are to the source recordings, we first
+extract fundamental frequency (F0) at the frame-level from
+source and converted audio pairs with the RAPT algorithm
+[34]. Then we calculate two metrics commonly used to mea-
+sure the linear dependence of prosody contours: Pearson
+Correlation Coefficient (PCC) and Root Mean Squared Error
+(RMSE) [35]. We can see that the results (Table 2) are very
+similar for the W-VAE and P-VAE models, while the G-VAE
+performs much worse in both metrics. This reinforces the
+subjective evaluation findings that utterance-level embed-
+dings do not provide sufficient capacity to capture expressive
+prosody and fine-grained modelling is required for expressive
+speech generation.
+System
+F0 RMSE ↓
+F0 PCC ↑
+G-VAE
+1.693 ± 0.012
+0.760 ± 0.003
+W-VAE
+1.535 ± 0.011
+0.801 ± 0.002
+P-VAE
+1.539 ± 0.012
+0.802 ± 0.003
+Table 2. Objective Voice Conversion evaluation metrics with
+95% confidence intervals computed between source and con-
+verted speech: F0 Root Mean Square Error (RMSE), F0 Pear-
+son Correlation Coefficient (PCC) [35].
+4.6. Predictability
+Finally, we evaluate our systems in the TTS scenario. That
+is, we generate speech from textual input only and provide
+prosody embeddings predicted from text during inference.
+The naturalness of synthesized speech is evaluated subjec-
+tively as described in Section 4.3. The results are summarised
+in Figure 3b (all comparisons are statistically significant with
+p-value < 0.01). The G-VAE model scores much worse
+than other systems. It fails to reproduce expressive speech
+variability and tends to output flat prosody contours due to
+averaging. We also observe issues with accurate phoneme
+duration prediction for the G-VAE model, e.g.
+unnatural,
+fast-paced speech. We hypothesise, that a single representa-
+tion for the whole utterance can’t store temporal information
+effectively. Such issues are not visible in the models using
+fine-grained prosody representations.
+While both of them
+score much higher than the G-VAE, the word-level model
+performs better in terms of fidelity and prosody naturalness
+and closes the gap between the P-VAE model and the ref-
+erence system by over 90%. We conclude that word-level
+representations impose a good compromise for expressive
+prosody modelling granularity. They have enough capacity to
+produce varied and natural speech and still can be accurately
+predicted from text.
+5. EXPERIMENTS - PROSODY PREDICTION
+In this section we focus on semantically concerted prosody
+prediction. First, we investigate the impact of data quantity
+used in the training procedure. Second, we conduct an abla-
+tion study of the prosody embeddings predictor input streams.
+5.1. Data Quantity
+We investigate the impact of training data quantity on our
+system, by looking into a single-speaker scenario with lim-
+ited amount of data.
+We build a dataset by taking 15000
+utterances from the HiFi corpus [36] coming from one male
+speaker (id 6097). Again, we keep a held-out set of 1000
+randomly selected utterances for validation.
+We train the
+
+100
+80
+ Score
+60
+MUSHRA
+40
+20
+0
+G-VAE
+W-VAE
+P-VAE
+Ref
+67.77
+72.72
+72.03
+74.00100
+80
+Score
+60
+MUSHRA
+40
+20
+0
+G-VAE
+W-VAE
+P-VAE
+Ref
+62.99
+71.65
+68.62
+71.80word-level acoustic model and the prosody embeddings pre-
+dictor in two setups: 1) HiFi - using only 15000 utterances
+from a single HiFi speaker. 2) HiFi+LibriTTS - addition-
+ally adding LibriTTS corpus, which results in approximately
+155000 utterances in the training set.
+We evaluate both
+scenarios using a MUSHRA subjective naturalness test anal-
+ogously to Section 4.6 and summarize results in Table 3.
+Using an additional, large-scale dataset during training sig-
+nificantly improves naturalness of synthesized speech (p-
+value < 0.01). Per-case analysis of listeners judgements
+reveal that both systems produce audio of similar segmental
+quality, but the HiFi+LibriTTS system provides more stable
+prosody, especially for longer utterances. We conclude that
+semantically concerted prosody prediction is a data hungry
+problem and limited amount of training data can result in less
+stable prosody of generated speech. However, using auxiliary
+data in the training procedure allows to obtain a more robust
+prosody predictor and mitigate this issue.
+HiFi
+HiFi+LibriTTS
+Ref
+64.26
+67.01
+67.17
+Table 3. Mean MUSHRA scores for the word-level models
+trained on a single speaker form the HiFi corpus with and
+without auxiliary LibriTTS data. All comparisons from this
+Table are statistically significant (p-value < 0.01).
+5.2. Prosody Predictor Input Streams Ablation Study
+In previous works, word-level prosody embeddings are typ-
+ically predicted at inference time from one of the following
+representations derived from text: word-level contextual em-
+beddings [13, 37] or phoneme sequence [14, 38]. We use both
+of them in our prosody embeddings predictor model. To de-
+termine the contribution of each input stream to the model
+performance we conduct an ablation study. We train the word-
+level prosody embeddings predictor model in three configura-
+tions: BERT & Phoneme - trained exactly as described in sec-
+tion 3; BERT - with only BERT embeddings input; Phoneme -
+with only phoneme sequence input. All three predictor mod-
+els are used in combination with the same W-VAE acoustic
+model to synthesize 1000 validation utterances from section
+4.1. As a subjective naturalness evaluation, a preference test
+is carried out using Amazon Mechanical Turk platform. Na-
+tive English speakers are asked to ”Select which audio sounds
+more natural” for pairs of audio samples generated with dif-
+ferent systems. We find that removing fine-grained phoneme
+sequence input stream (Figure 4a) causes less stable prosody
+prediction and results in significant degradation in naturalness
+(p-value < 0.01). Whereas, the difference between BERT &
+Phoneme and Phoneme systems (Figure 4b) is not statistically
+significant. Listening to samples revealed that the improve-
+ment of using contextual word embeddings comes mainly in
+better phrasing and pause prediction. However, differences
+are quite subtle and therefore are not reflected in the crowd-
+sourced naturalness evaluation results.
+This result contra-
+dicts the findings from [13], where significant quality degra-
+dation when removing BERT embeddings input was reported.
+However, in [13] authors proposed to use word-level syntax
+features e.g. part-of-speech labels, compound-noun flag and
+punctuation flag as a second input stream to the model pre-
+dicting prosody embeddings.
+We believe that fine-grained
+phoneme sequence input is more correlated with prosody than
+those syntax features, therefore, removing BERT input stream
+is less harmful in our work.
+(a)
+(b)
+Fig. 4.
+Results of naturalness preference tests.
+On the
+right the word-level prosody embeddings predictor model de-
+scribed in Section 3. On the left the same model but with
+only one input stream: a) BERT embeddings, b) phoneme se-
+quence.
+6. CONCLUSIONS
+In this paper we explored the design of prosodic representa-
+tions learned in an auto-encoder manner. First, we introduced
+a TTS framework allowing for a fair comparison of prosody
+embeddings of different granularity. Then a systematic study
+of utterance, word and phoneme-level representations was
+conducted on a large-scale, publicly available dataset - Lib-
+riTTS. Through our experiments, we demonstrated the trade-
+off between capacity and predictability of prosody represen-
+tations.
+We showed that utterance-level embeddings have
+insufficient capacity to model expressive speech variability.
+Whereas phoneme-level representations require strong reg-
+ularization for stable prediction from text at inference time.
+We found that word-level embeddings impose a good balance
+between capacity and predictability. As a result, we closed
+the gap in naturalness by 90% between synthetic speech
+and recordings without sacrificing intelligibility.
+Finally,
+we looked into applying the proposed approach in a single-
+speaker scenario.
+We showed that semantically concerted
+prosody prediction is a data hungry problem and limited
+amount of training data can result in less stable prosody of
+generated speech. However, this issue can be mitigated by
+using auxiliary data in the training procedure.
+
+BERT
+No-Pref
+BERT & Phoneme
+(32.87%)
+(31.78%)
+(35.35%)
+0
+25
+50
+75
+100Phoneme
+No-Pref
+BERT & Phoneme
+(34.26%)
+(31.27%)
+(34.47%)
+0
+25
+50
+75
+1007. REFERENCES
+[1] Jonathan Shen, Ruoming Pang, Ron J Weiss, Mike
+Schuster, Navdeep Jaitly, Zongheng Yang, Zhifeng
+Chen, Yu Zhang, Yuxuan Wang, Rj Skerrv-Ryan, et al.,
+“Natural tts synthesis by conditioning wavenet on mel
+spectrogram predictions,” in ICASSP. IEEE, 2018, pp.
+4779–4783.
+[2] Nishant Prateek, Mateusz Łajszczak, Roberto Barra-
+Chicote, Thomas Drugman, Jaime Lorenzo-Trueba,
+Thomas Merritt, Srikanth Ronanki, and Trevor Wood,
+“In other news: A bi-style text-to-speech model for syn-
+thesizing newscaster voice with limited data,”
+arXiv
+preprint arXiv:1904.02790, 2019.
+[3] Abdelhamid
+Ezzerg,
+Adam
+Gabrys,
+Bartosz
+Pu-
+trycz, Daniel Korzekwa, Daniel Saez-Trigueros, David
+McHardy, Kamil Pokora, Jakub Lachowicz, Jaime
+Lorenzo-Trueba, and Viacheslav Klimkov,
+“Enhanc-
+ing audio quality for expressive neural text-to-speech,”
+arXiv preprint arXiv:2108.06270, 2021.
+[4] Raahil Shah, Kamil Pokora, Abdelhamid Ezzerg, Vi-
+acheslav Klimkov, Goeric Huybrechts, Bartosz Pu-
+trycz, Daniel Korzekwa, and Thomas Merritt,
+“Non-
+Autoregressive TTS with Explicit Duration Modelling
+for Low-Resource Highly Expressive Speech,” in Proc.
+11th ISCA Speech Synthesis Workshop (SSW 11), 2021,
+pp. 96–101.
+[5] Sri Karlapati, Alexis Moinet, Arnaud Joly, Viacheslav
+Klimkov, Daniel S´aez-Trigueros, and Thomas Drug-
+man,
+“Copycat: Many-to-many fine-grained prosody
+transfer for neural text-to-speech,”
+arXiv preprint
+arXiv:2004.14617, 2020.
+[6] Viacheslav Klimkov, Srikanth Ronanki, Jonas Rohnke,
+and Thomas Drugman,
+“Fine-grained robust prosody
+transfer for single-speaker neural text-to-speech,” arXiv
+preprint arXiv:1907.02479, 2019.
+[7] Piotr Bilinski, Thomas Merritt, Abdelhamid Ezzerg,
+Kamil Pokora, Sebastian Cygert, Kayoko Yanagisawa,
+Roberto Barra-Chicote, and Daniel Korzekwa, “Creat-
+ing new voices using normalizing flows,” in accepted to
+Interspeech 2022, 2022.
+[8] RJ Skerry-Ryan, Eric Battenberg, Ying Xiao, Yuxuan
+Wang, Daisy Stanton, Joel Shor, Ron Weiss, Rob Clark,
+and Rif A Saurous, “Towards end-to-end prosody trans-
+fer for expressive speech synthesis with tacotron,” in
+international conference on machine learning. PMLR,
+2018, pp. 4693–4702.
+[9] Ya-Jie Zhang, Shifeng Pan, Lei He, and Zhen-Hua Ling,
+“Learning latent representations for style control and
+transfer in end-to-end speech synthesis,”
+in ICASSP
+2019-2019 IEEE International Conference on Acous-
+tics, Speech and Signal Processing (ICASSP). IEEE,
+2019, pp. 6945–6949.
+[10] Daisy Stanton, Yuxuan Wang, and RJ Skerry-Ryan,
+“Predicting expressive speaking style from text in end-
+to-end speech synthesis,” in 2018 IEEE Spoken Lan-
+guage Technology Workshop (SLT). IEEE, 2018, pp.
+595–602.
+[11] Sri Karlapati, Ammar Abbas, Zack Hodari, Alexis
+Moinet, Arnaud Joly, Penny Karanasou, and Thomas
+Drugman, “Prosodic representation learning and con-
+textual sampling for neural text-to-speech,” in ICASSP
+2021-2021 IEEE International Conference on Acous-
+tics, Speech and Signal Processing (ICASSP). IEEE,
+2021, pp. 6573–6577.
+[12] Younggun Lee and Taesu Kim,
+“Robust and fine-
+grained prosody control of end-to-end speech synthe-
+sis,”
+in ICASSP 2019-2019 IEEE International Con-
+ference on Acoustics, Speech and Signal Processing
+(ICASSP). IEEE, 2019, pp. 5911–5915.
+[13] Zack Hodari, Alexis Moinet, Sri Karlapati, Jaime
+Lorenzo-Trueba, Thomas Merritt, Arnaud Joly, Am-
+mar Abbas, Penny Karanasou, and Thomas Drugman,
+“Camp: A two-stage approach to modelling prosody
+in context,” in ICASSP 2021-2021 IEEE International
+Conference on Acoustics, Speech and Signal Processing
+(ICASSP). IEEE, 2021, pp. 6578–6582.
+[14] Konstantinos Klapsas, Nikolaos Ellinas, June Sig Sung,
+Hyoungmin Park, and Spyros Raptis, “Word-level style
+control for expressive, non-attentive speech synthesis,”
+in International Conference on Speech and Computer.
+Springer, 2021, pp. 336–347.
+[15] Yi Ren, Chenxu Hu, Xu Tan, Tao Qin, Sheng Zhao,
+Zhou Zhao, and Tie-Yan Liu, “Fastspeech 2: Fast and
+high-quality end-to-end text to speech,” arXiv preprint
+arXiv:2006.04558, 2020.
+[16] Isaac Elias, Heiga Zen, Jonathan Shen, Yu Zhang,
+Ye Jia, Ron J Weiss, and Yonghui Wu,
+“Parallel
+tacotron: Non-autoregressive and controllable tts,” in
+ICASSP. IEEE, 2021, pp. 5709–5713.
+[17] Yanqing Liu, Zhihang Xu, Gang Wang, Kuan Chen,
+Bohan Li, Xu Tan, Jinzhu Li, Lei He, and Sheng
+Zhao, “Delightfultts: The microsoft speech synthesis
+system for blizzard challenge 2021,”
+arXiv preprint
+arXiv:2110.12612, 2021.
+[18] Aaron van den Oord, Sander Dieleman, Heiga Zen,
+Karen Simonyan, Oriol Vinyals, Alex Graves, Nal
+
+Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu,
+“Wavenet: A generative model for raw audio,” arXiv
+preprint arXiv:1609.03499, 2016.
+[19] Yi Ren, Chenxu Hu, Xu Tan, Tao Qin, Sheng Zhao,
+Zhou Zhao, and Tie-Yan Liu, “Fastspeech 2: Fast and
+high-quality end-to-end text to speech,” in ICLR, 2021.
+[20] Jonathan Shen, Ye Jia, Mike Chrzanowski, Yu Zhang,
+Isaac Elias, Heiga Zen, and Yonghui Wu, “Non-attentive
+tacotron:
+Robust and controllable neural tts synthe-
+sis including unsupervised duration modeling,” arXiv
+preprint arXiv:2010.04301, 2020.
+[21] M. He, Y. Deng, and L. He,
+“Robust Sequence-to-
+Sequence Acoustic Modeling with Stepwise Monotonic
+Attention for Neural TTS,” in Interspeech, 2019, pp.
+1293–1297.
+[22] H. Guo, F. K. Soong, L. He, and L. Xie, “A New GAN-
+Based End-to-End TTS Training Algorithm,” in Inter-
+speech, 2019, pp. 1288–1292.
+[23] E. Battenberg, RJ Skerry-Ryan, S. Mariooryad, D. Stan-
+ton, D. Kao, M. Shannon, and T. Bagby,
+“Location-
+relative attention mechanisms for robust long-form
+speech synthesis,” in ICASSP, 2020, pp. 6194–6198.
+[24] Heiga Ze, Andrew Senior, and Mike Schuster,
+“Sta-
+tistical parametric speech synthesis using deep neural
+networks,”
+in 2013 IEEE International Conference
+on Acoustics, Speech and Signal Processing, 2013, pp.
+7962–7966.
+[25] Heiga Zen, Keiichi Tokuda, and Alan W. Black, “Statis-
+tical parametric speech synthesis,” Speech Communica-
+tion, vol. 51, no. 11, pp. 1039–1064, 2009.
+[26] Daniel Povey, Arnab Ghoshal, Gilles Boulianne, Lukas
+Burget, Ondrej Glembek, Nagendra Goel, Mirko Han-
+nemann, Petr Motlicek, Yanmin Qian, Petr Schwarz, Jan
+Silovsky, Georg Stemmer, and Karel Vesely, “The kaldi
+speech recognition toolkit,” in IEEE 2011 Workshop on
+Automatic Speech Recognition and Understanding. Dec.
+2011, IEEE Signal Processing Society, IEEE Catalog
+No.: CFP11SRW-USB.
+[27] Yuxuan Wang, Daisy Stanton, Yu Zhang, RJ-Skerry
+Ryan, Eric Battenberg, Joel Shor, Ying Xiao, Ye Jia,
+Fei Ren, and Rif A Saurous, “Style tokens: Unsuper-
+vised style modeling, control and transfer in end-to-end
+speech synthesis,” in International Conference on Ma-
+chine Learning. PMLR, 2018, pp. 5180–5189.
+[28] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and
+Kristina Toutanova, “Bert: Pre-training of deep bidirec-
+tional transformers for language understanding,” arXiv
+preprint arXiv:1810.04805, 2018.
+[29] Heiga Zen, Viet Dang, Rob Clark, Yu Zhang, Ron J
+Weiss, Ye Jia, Zhifeng Chen, and Yonghui Wu, “Lib-
+ritts: A corpus derived from librispeech for text-to-
+speech,” arXiv preprint arXiv:1904.02882, 2019.
+[30] Yunlong Jiao, Adam Gabry´s, Georgi Tinchev, Bartosz
+Putrycz, Daniel Korzekwa, and Viacheslav Klimkov,
+“Universal neural vocoding with parallel wavenet,” in
+ICASSP 2021-2021 IEEE International Conference on
+Acoustics, Speech and Signal Processing (ICASSP).
+IEEE, 2021, pp. 6044–6048.
+[31] Recommendation BS ITU-R, “1534-1,“method for the
+subjective assessment of intermediate quality levels of
+coding systems (mushra)”,” International Telecommu-
+nication Union, 2003.
+[32] Robert AJ Clark, Monika Podsiadlo, Mark Fraser,
+Catherine Mayo, and Simon King, “Statistical analy-
+sis of the blizzard challenge 2007 listening test results,”
+in Proc. Blizzard Challenge Workshop, 2007, vol. 2007.
+[33] Maximilian Bisani and Hermann Ney, “Bootstrap esti-
+mates for confidence intervals in asr performance eval-
+uation,”
+in 2004 IEEE International Conference on
+Acoustics, Speech, and Signal Processing. IEEE, 2004,
+vol. 1, pp. I–409.
+[34] David Talkin and W Bastiaan Kleijn, “A robust algo-
+rithm for pitch tracking (rapt),” Speech coding and syn-
+thesis, vol. 495, pp. 518, 1995.
+[35] Berrak Sisman, Junichi Yamagishi, Simon King, and
+Haizhou Li, “An overview of voice conversion and its
+challenges: From statistical modeling to deep learning,”
+IEEE/ACM Transactions on Audio, Speech, and Lan-
+guage Processing, vol. 29, pp. 132–157, 2020.
+[36] Evelina Bakhturina, Vitaly Lavrukhin, Boris Ginsburg,
+and Yang Zhang,
+“Hi-fi multi-speaker english tts
+dataset,” arXiv preprint arXiv:2104.01497, 2021.
+[37] Yi Ren, Ming Lei, Zhiying Huang, Shiliang Zhang, Qian
+Chen, Zhijie Yan, and Zhou Zhao, “Prosospeech: En-
+hancing prosody with quantized vector pre-training in
+text-to-speech,” in ICASSP 2022-2022 IEEE Interna-
+tional Conference on Acoustics, Speech and Signal Pro-
+cessing (ICASSP). IEEE, 2022, pp. 7577–7581.
+[38] Yiwei Guo, Chenpeng Du, and Kai Yu, “Unsupervised
+word-level prosody tagging for controllable speech syn-
+thesis,” in ICASSP 2022-2022 IEEE International Con-
+ference on Acoustics, Speech and Signal Processing
+(ICASSP). IEEE, 2022, pp. 7597–7601.
+
diff --git a/I9FJT4oBgHgl3EQfGCzl/content/tmp_files/load_file.txt b/I9FJT4oBgHgl3EQfGCzl/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1f7213cbac080638e73fba3905eebff93295d380
--- /dev/null
+++ b/I9FJT4oBgHgl3EQfGCzl/content/tmp_files/load_file.txt
@@ -0,0 +1,478 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf,len=477
+page_content='ON GRANULARITY OF PROSODIC REPRESENTATIONS IN EXPRESSIVE  TEXT-TO-SPEECH  Mikolaj Babianski, Kamil Pokora, Raahil Shah, Rafal Sienkiewicz, Daniel Korzekwa, Viacheslav Klimkov  Amazon Text-to-Speech Research  {babiansk, kamipoko, vklimkov}@amazon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='com  ABSTRACT  In expressive speech synthesis it is widely adopted to use  latent prosody representations to deal with variability of the  data during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Same text may correspond to vari-  ous acoustic realizations, which is known as a one-to-many  mapping problem in text-to-speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Utterance, word, or  phoneme-level representations are extracted from target sig-  nal in an auto-encoding setup, to complement phonetic input  and simplify that mapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' This paper compares prosodic  embeddings at different levels of granularity and examines  their prediction from text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We show that utterance-level em-  beddings have insufficient capacity and phoneme-level tend  to introduce instabilities when predicted from text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Word-  level representations impose balance between capacity and  predictability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' As a result, we close the gap in naturalness by  90% between synthetic speech and recordings on LibriTTS  dataset, without sacrificing intelligibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Index Terms— speech synthesis, TTS, prosody, Text-to-  Speech, representation learning  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' INTRODUCTION  Neural Text-to-Speech (NTTS) [1] is characterized by syn-  thesizing speech waveform solely with deep neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  This paradigm greatly enhanced naturalness and flexibility of  speech synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' It enables new applications such as expres-  sive [2, 3] and low-resource [4] speech generation, speaker  identity [5] and prosody transplantation [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' This paper  focuses on expressive speech synthesis, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  generation of  speech that originally contains great degree of variation in  terms of intonation and inflections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  This variation is not described by phoneme sequence, typ-  ically used as input to NTTS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Thus, the statistical model has  to perform a one-to-many mapping, where the same input  text can correspond to different acoustic realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Vanilla  modelling approaches suffer from averaging and fail to repro-  duce the original variability of the training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  To avoid averaging, it is common to use additional input  that describes variability in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Initially, it was proposed  to extract a single latent representation of the target speech in  an auto-encoder manner for the whole utterance [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Target  speech is not available during inference, so either the cen-  troid representation is used [9] or it is separately predicted  from text [10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  A single representation for the whole  utterance can’t store temporal information effectively, thus,  it was proposed to use more fine-grained representations at  the phoneme-level for the task of prosody transplantation [6,  12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' This idea was further expanded to text-to-speech, where  word-level [13, 14] and phoneme-level [15, 16, 17] represen-  tations were utilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' At the fine-grained level, prosody can  be represented with pre-extracted features such as pitch, en-  ergy, spectral tilt, but learnt representations can convey more  information and represent more abstract aspects of prosody  such as emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Therefore, in the rest of the paper we focus  on learnt representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  This paper provides a systematic comparison of prosodic  representations at different levels of granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We compare  performance of utterance, word, and phoneme-level prosody  embeddings in terms of a) capacity: what if we have a perfect  prosody predictor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' b) predictability: how sensitive is the ap-  proach to inaccurate prosody predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Main contributions  of this study are:  We systematically compare prosody embeddings at dif-  ferent levels of granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  A solution to intelligibility issues in the case of phoneme-  level prosody reference is proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We show the trade-off between capacity and pre-  dictability of prosody embeddings, advocating the use  of word-level representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We examine data quantity and input features needed for  robust prosody prediction from text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  The rest of the paper is organized as follows: Section 2  describes the text-to-speech framework used;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Section 3 elab-  orates on prosody embedding prediction from text;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Section 4  compares prosody embeddings at different levels of granular-  ity in objective and subjective evaluations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Section 5 presents  ablation studies on prosody embedding prediction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Section 6  concludes the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  978-1-6654-7189-3/22/$31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='00 ©2023 IEEE  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='11446v1  [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='AS]  26 Jan 2023  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Schematic diagram of the TTS model during a) training and b) inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The dashed arrow denotes sampling from  parametric distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Components in red are of prosody embeddings granularity (utterance/word/phoneme).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Green, dashed  lines denote loss functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' ACOUSTIC MODEL  The backbone of our acoustic model architecture (Figure 1) is  similar to the explicit duration TTS model presented in Shah  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' It follows the encoder-decoder paradigm, where the  input phoneme sequence x is encoded by a phoneme encoder  presented in the Tacotron2 [1] paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We concatenate the en-  coded phoneme sequence with both speaker s and prosody z  embeddings upsampled by repetition [15, 16] to the phoneme-  level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Speaker embeddings are represented as corresponding  entries in the embedding look-up table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Prosody embeddings  are obtained via compression of the mel-spectrogram y with  the use of variational prosody reference encoder described in  Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' During inference, the encoded sequence is up-  sampled accordingly to alignments produced by the duration  model, described in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The upsampled sequence is  then passed to the decoder to map the disentangled linguistic  features, speaker and prosodic contents into acoustic param-  eters represented as mel-spectrograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' In this work, we use  the non-autoregressive decoder presented in Shah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Variational Prosody Reference Encoder  To alleviate the one-to-many problem of TTS we use the vari-  ational prosody reference encoder [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We aim to learn the  latent representation of the information, which cannot be de-  rived from the other input streams - phoneme sequence and  speaker embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' For clarity of the architecture presenta-  tion, here we describe only one level of granularity - word-  level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Modification of the model architecture to adjust for dif-  ferent prosody embedding granularities is described in Sec-  tion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The variational reference encoder (Figure 1a) takes  target mel-spectrogram frames as input and converts them  into a sequence of n latent vectors z, which corresponds to  the number of words in the utterance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We refer to this repre-  sentation as word-level prosody embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  The encoder comprises a stack of six residual gated con-  volution blocks [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Each residual gated convolution block  is composed of a 1D-convolution with a kernel size of 15 and  a hidden dimension of 512, followed by a tanh filter and a  sigmoid activation gate which are element-wise multiplied  and then added to a residual connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The convolution  stack is followed by a BiLSTM layer with a hidden dimension  of 128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We use a dropout of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='1 in convolutional and BiLSTM  layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The BiLSTM layer output is firstly aggregated to the  word-level by taking a middle frame of each word.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Then,  after a dense projection we obtain a sequence of Gaussian  distribution parameters µ and σ, which we use to sample a  sequence of prosody embeddings corresponding to words z  of dimension 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Finally, we upsample the word-level prosody  embeddings by repetition to the phoneme-level and concate-  nate them with the phoneme encoder output (Figure 1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  As we do not have access to target mel-spectrograms at  inference time (Figure 1b), a separate model is introduced to  predict prosody embeddings z from text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The architecture for  this model is described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Duration Model  Neural TTS requires learning the alignment between two dif-  ferent length sequences, which are the text, represented by  phonemes, and speech, represented by acoustic parameters  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' mel-spectrogram frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' There are two major approaches  to obtain the alignment: attention-based [1] and explicit-  duration-based [4, 19, 16, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Attention-based components  typically used for this task have known instabilities, which  exhibit in synthesised speech as mumbling, early cut-offs,  word repetition and word skipping [21, 22, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Following  recent research in the field inspired by traditional parametric  speech synthesis techniques [24, 25], these issues are mit-  igated by explicitly modelling the durations of phonemes  [4, 19, 16, 20] which we decide to use in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  mel-spectrogram  y  6 x Gated Conv  Duration Model  BiLSTM  Aggregation  predicted duration  Dense Proj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  d  N(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='1)  : L2  μ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='a  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='DKL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='predicted  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='oracle duration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='mel-spectrogram  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='d  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='y  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='prosody  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='embeddings (z)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Concat  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Upsampling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Encoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='speaker embedding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='phoneme sequence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='sBERT embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='phoneme sequence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='b  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Prosody  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Duration Model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Predictor  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='predicted  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='predicted duration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='mel-spectrogram  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='p  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='y  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='prosody embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Encoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Concat  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Upsampling  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='phoneme sequence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='speaker embedding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='x  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='sWe use forced alignment from a Gaussian Mixture Model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='(GMM) based external aligner in the Kaldi Speech Recog-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='nition Toolkit [26] to produce ground truth duration for  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='each phoneme,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' represented as the integer number of mel-  spectrogram frames it corresponds to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' To predict these du-  rations, we train a duration model component following the  architecture detailed in Shah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' [4], with the addition of  speaker and prosody embeddings conditioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The duration  model is trained jointly with the acoustic model by minimiz-  ing L2 loss function in the logarithmic domain between pre-  dicted and ground truth phoneme durations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' During training,  teacher forcing is used, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' the acoustic model uses ground  truth duration values to upsample a phoneme’s encoding to  the respective number of mel-spectrogram frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Prosody Embeddings Granularity  The model described above uses word-level prosody embed-  dings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Which means that there is one embedding correspond-  ing to each word in the input text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' In this work we also explore  two other levels of prosody modelling granularity: phoneme-  level (one embedding per each phoneme) and utterance-level  (single embedding for the whole utterance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' For the phoneme-  level prosody modelling we change the reference encoder to  output one embedding per each phoneme and reduce prosody  embedding dimension from 8 to 3, which we found optimal  in terms of stability, for this level of granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' In the case  of utterance-level prosody modelling we use a stride of 2 in  the residual gated convolution blocks of the reference encoder  in order to gradually downsample the time resolution [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Then, we project the first and last state of the BiLSTM layer  into two vectors of dimension 64, which represent mean µ  and standard deviation σ of the posterior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Finally  we sample a single 64-dimensional prosody embedding z cor-  responding to the whole utterance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Training Procedure  To train the acoustic and duration models we use Adam opti-  miser with β1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='9 and β2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We use a linear warm-up  of the learning rate from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='1 to 1 for the first 10k steps, fol-  lowed by an exponential decay from 10k steps to 100k steps  with a minimum value of 10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Acoustic and duration models  are trained jointly for 500K steps with a batch-size equal 32  and are optimized with respect to the following loss function:  Ltotal = L1melspectrogram + L2logduration + γ ∗ DKL (1)  where L1melspectrogram is the L1-distance between pre-  dicted and oracle mel-spectrograms and L2logduration is the  L2-distance between predicted and ground truth durations  calculated in the logarithmic domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  DKL is the Kull-  back–Leibler divergence between outputs of the variational  prosody reference encoder and N(0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We find the optimal  value of γ to be 10−3 for the phoneme-level and 10−5 for  the utterance and word-level prosody modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We present  ablation of the γ parameter in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' PROSODY EMBEDDINGS PREDICTOR  At inference time we do not have access to target mel-  spectrograms, therefore, we use a separate model to pre-  dict prosodic representations z from text (Figure 1b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The  prosody embeddings predictor model (Figure 2) has three in-  put streams: phoneme sequence, contextual word embeddings  extracted with a pre-trained BERT model [28] and speaker  embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Phoneme sequence and contextual word embed-  dings are encoded by separate Tacotron2-based encoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We  upsample the encoded BERT embeddings from the word-  level to the phoneme-level and the speaker embedding to the  phoneme-level, before concatenating them with the encoded  phoneme representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Next, we pass the concatenated  sequence to another Tactotron2-based encoder block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' After  that, in the case of word-level embeddings prediction, the  encoded phoneme-level representation is aggregated to the  word-level by taking the middle frame of each word.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Fi-  nally, we use an autoregressive decoder to predict prosody  embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The autoregressive decoder is inspired by the  architecture of the Tacotron2 mel-spectrogram decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' In  order to adapt the decoder to the prosody prediction task, we  reduce the hidden dimension of the LSTM-layers to 128 and  pre-net hidden dimension to 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' To predict the utterance-level  prosody representation, instead of the autoregressive decoder,  we use a simple linear projection layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We train this model using prosody embeddings extracted  with previously trained acoustic model as target labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Specifically, the model is trained to predict posterior mean µ  for each target prosody embedding using L2 loss and teacher-  forcing framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Schematic diagram of the prosody embeddings predic-  tor model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Components with dashed border are used only for  fine-grained (word or phoneme-level) prosody embeddings  prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  BERT embeddings  phoneme sequence  b  x  Encoder  Encoder  speaker embedding  s  predicted  prosody embeddings  Concat  Autoregressive  Encoder  Decoder  phoneme-level  word-level  Aggregation  representation  representation4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' EXPERIMENTS - PROSODY EMBEDDINGS  GRANULARITY  In this section we conduct a systematic study of prosodic rep-  resentations at different levels of granularity applied to the ex-  pressive TTS task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The performance of utterance, word, and  phoneme-level prosody embeddings is compared in terms of  capacity and predictability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We evaluate naturalness as well  as stability and intelligibility of synthesized speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Data  Evaluations are conducted on a publicly available corpus of  audiobook recordings - LibriTTS [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' From which we use  only recordings marked as clean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The training set consists  of approximately 250 hours of speech (split into 140,000 ut-  terances) narrated in an expressive manner by 1229 speakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  For validation we use a held-out set of 1000 randomly se-  lected utterances from the 100 most frequent speakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We  extract 80-band mel-spectrograms with a 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='5 ms frame-shift  as acoustic features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Systems  We use our acoustic model (Section 2) along with the prosody  embeddings predictor (Section 3) to test 3 levels of prosody  embeddings granularity:  1) G-VAE - utterance-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  2)  W-VAE - word-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 3) P-VAE - phoneme-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' All mel-  spectrogram prediction systems are used in combination with  the Universal Neural Parallel WaveNet Vocoder [30] in order  to obtain a 24kHz audio signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Subjective Evaluation Protocol  For the subjective evaluation we conduct MUSHRA tests [31]  with the Amazon Mechanical Turk platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 60 native En-  glish speakers are presented with the samples in a random  order side-by-side, and are asked to “Evaluate naturalness of  the samples on the scale from 0 to 100.” A total of 1000 ut-  terances are used for testing and the test is balanced in such a  way that each test case is scored by 3 listeners independently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Ground truth mel-spectrograms vocoded with the Universal  Parallel WaveNet Vocoder (Ref system) are used as an upper  anchor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The significance of the MUSHRA results is analyzed  using a Wilcoxon signed-rank test with Bonferroni-Holm cor-  rection applied [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Stability  To quantify the stability of tested systems and the intelligibil-  ity of synthesized speech we conduct Word Error Rate (WER)  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The whole test set of 1000 utterances described in  Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='1 is used for the evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We transcribe speech  generated in the TTS mode (prosody embeddings predicted  from text) with the ASpIRE Chain ASR model from Kaldi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Then the WER is computed between the sentence text and the  corresponding transcription.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  The G-VAE and W-VAE models have WER scores (Ta-  ble 1) comparable to recordings when trained with DKL loss  weight (γ) equal to 10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Whereas, training the P-VAE model  in an analogical setup results in significant stability issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We believe that this is caused by the phoneme-level prosody  embeddings distribution being very hard to predict from text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Only after applying more regularization during training by in-  creasing DKL loss weight we are able to obtain a phoneme-  level model matching other systems in terms of WER score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Intelligibility is a crucial property of TTS system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Therefore,  for all the other experiments we use the G-VAE and W-VAE  models trained with γ = 10−5 and the P-VAE model trained  with γ = 10−3, as they are matching our stability require-  ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We found that further increasing γ parameter does not  bring any significant improvements and may lead to degrada-  tion in segmental quality of synthesized audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  System  DKLγ  WER ↓  G-VAE  1e − 5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='18% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='30  W-VAE  1e − 5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='13% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='30  P-VAE  1e − 5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='59% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='36  1e − 4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='47% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='31  1e − 3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='17% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='29  1e − 2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='17% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='29  Ref  −  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='29% ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='31  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Word Error Rate with 95% confidence intervals [33]  computed across the 1000 test utterances, along with DKL  loss weight (γ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Capacity  We analyse the best-case performance of acoustic models by  simulating perfectly predicted prosody embeddings in the Or-  acle Resynthesis setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' That is, at inference time we pro-  vide ground truth latent representations from the variational  reference encoder for all tested systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We evaluate natu-  ralness in a subjective test as described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='3 and  summarize results in Figure 3a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' In this setup, the G-VAE  model scores significantly lower than the other systems (p-  value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='01), suggesting that fine-grained embeddings are  required for natural prosody modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' There is no statisti-  cally significant difference between W-VAE and P-VAE sys-  tems (p-value > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' It is worth mentioning, that we have  also conducted an analogical experiment with a P-VAE model  trained with lower DKL loss weight (γ = 10−5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' With such  model, when ground truth prosody embeddings provided dur-  ing inference, we are able to reconstruct speech almost per-  fectly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' However, it comes at a cost of stability issues, when  prosody embeddings predicted from text are used as described  in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  (a) Ground truth prosody embeddings  (b) Prosody embeddings predicted from text  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Subjective listeners ratings from the naturalness MUSHRA tests with a) ground truth prosody embeddings and b) prosody  embeddings predicted from text (TTS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Mean scores are reported below the system names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  To gain a deeper understanding of prosody representa-  tions, we evaluate our acoustic models in the Oracle Resyn-  thesis setup with changed speaker embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' That is, we  extract prosody from a source recording and resynthesize the  same text with changed voice - a so-called Voice Conversion  (VC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We convert all 1000 test utterances into 4 selected (two  male and two female) target voices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  To effectively measure how close the prosody patterns  of converted speech are to the source recordings, we first  extract fundamental frequency (F0) at the frame-level from  source and converted audio pairs with the RAPT algorithm  [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Then we calculate two metrics commonly used to mea-  sure the linear dependence of prosody contours: Pearson  Correlation Coefficient (PCC) and Root Mean Squared Error  (RMSE) [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We can see that the results (Table 2) are very  similar for the W-VAE and P-VAE models, while the G-VAE  performs much worse in both metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' This reinforces the  subjective evaluation findings that utterance-level embed-  dings do not provide sufficient capacity to capture expressive  prosody and fine-grained modelling is required for expressive  speech generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  System  F0 RMSE ↓  F0 PCC ↑  G-VAE  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='693 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='760 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='003  W-VAE  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='535 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='011  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='801 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='002  P-VAE  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='539 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='012  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='802 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='003  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Objective Voice Conversion evaluation metrics with  95% confidence intervals computed between source and con-  verted speech: F0 Root Mean Square Error (RMSE), F0 Pear-  son Correlation Coefficient (PCC) [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Predictability  Finally, we evaluate our systems in the TTS scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' That  is, we generate speech from textual input only and provide  prosody embeddings predicted from text during inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  The naturalness of synthesized speech is evaluated subjec-  tively as described in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The results are summarised  in Figure 3b (all comparisons are statistically significant with  p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' The G-VAE model scores much worse  than other systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' It fails to reproduce expressive speech  variability and tends to output flat prosody contours due to  averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We also observe issues with accurate phoneme  duration prediction for the G-VAE model, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  unnatural,  fast-paced speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We hypothesise, that a single representa-  tion for the whole utterance can’t store temporal information  effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Such issues are not visible in the models using  fine-grained prosody representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  While both of them  score much higher than the G-VAE, the word-level model  performs better in terms of fidelity and prosody naturalness  and closes the gap between the P-VAE model and the ref-  erence system by over 90%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We conclude that word-level  representations impose a good compromise for expressive  prosody modelling granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' They have enough capacity to  produce varied and natural speech and still can be accurately  predicted from text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' EXPERIMENTS - PROSODY PREDICTION  In this section we focus on semantically concerted prosody  prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' First, we investigate the impact of data quantity  used in the training procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Second, we conduct an abla-  tion study of the prosody embeddings predictor input streams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Data Quantity  We investigate the impact of training data quantity on our  system, by looking into a single-speaker scenario with lim-  ited amount of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We build a dataset by taking 15000  utterances from the HiFi corpus [36] coming from one male  speaker (id 6097).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Again, we keep a held-out set of 1000  randomly selected utterances for validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We train the  100  80  Score  60  MUSHRA  40  20  0  G-VAE  W-VAE  P-VAE  Ref  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='77  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='72  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='03  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='00100  80  Score  60  MUSHRA  40  20  0  G-VAE  W-VAE  P-VAE  Ref  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='99  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='65  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='62  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='80word-level acoustic model and the prosody embeddings pre-  dictor in two setups: 1) HiFi - using only 15000 utterances  from a single HiFi speaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 2) HiFi+LibriTTS - addition-  ally adding LibriTTS corpus, which results in approximately  155000 utterances in the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We evaluate both  scenarios using a MUSHRA subjective naturalness test anal-  ogously to Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='6 and summarize results in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Using an additional, large-scale dataset during training sig-  nificantly improves naturalness of synthesized speech (p-  value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Per-case analysis of listeners judgements  reveal that both systems produce audio of similar segmental  quality, but the HiFi+LibriTTS system provides more stable  prosody, especially for longer utterances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We conclude that  semantically concerted prosody prediction is a data hungry  problem and limited amount of training data can result in less  stable prosody of generated speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' However, using auxiliary  data in the training procedure allows to obtain a more robust  prosody predictor and mitigate this issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  HiFi  HiFi+LibriTTS  Ref  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='26  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='01  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='17  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Mean MUSHRA scores for the word-level models  trained on a single speaker form the HiFi corpus with and  without auxiliary LibriTTS data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' All comparisons from this  Table are statistically significant (p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Prosody Predictor Input Streams Ablation Study  In previous works, word-level prosody embeddings are typ-  ically predicted at inference time from one of the following  representations derived from text: word-level contextual em-  beddings [13, 37] or phoneme sequence [14, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We use both  of them in our prosody embeddings predictor model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' To de-  termine the contribution of each input stream to the model  performance we conduct an ablation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We train the word-  level prosody embeddings predictor model in three configura-  tions: BERT & Phoneme - trained exactly as described in sec-  tion 3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' BERT - with only BERT embeddings input;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Phoneme -  with only phoneme sequence input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' All three predictor mod-  els are used in combination with the same W-VAE acoustic  model to synthesize 1000 validation utterances from section  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' As a subjective naturalness evaluation, a preference test  is carried out using Amazon Mechanical Turk platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Na-  tive English speakers are asked to ”Select which audio sounds  more natural” for pairs of audio samples generated with dif-  ferent systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' We find that removing fine-grained phoneme  sequence input stream (Figure 4a) causes less stable prosody  prediction and results in significant degradation in naturalness  (p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Whereas, the difference between BERT &  Phoneme and Phoneme systems (Figure 4b) is not statistically  significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Listening to samples revealed that the improve-  ment of using contextual word embeddings comes mainly in  better phrasing and pause prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' However, differences  are quite subtle and therefore are not reflected in the crowd-  sourced naturalness evaluation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  This result contra-  dicts the findings from [13], where significant quality degra-  dation when removing BERT embeddings input was reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  However, in [13] authors proposed to use word-level syntax  features e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' part-of-speech labels, compound-noun flag and  punctuation flag as a second input stream to the model pre-  dicting prosody embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We believe that fine-grained  phoneme sequence input is more correlated with prosody than  those syntax features, therefore, removing BERT input stream  is less harmful in our work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  (a)  (b)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Results of naturalness preference tests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  On the  right the word-level prosody embeddings predictor model de-  scribed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' On the left the same model but with  only one input stream: a) BERT embeddings, b) phoneme se-  quence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' CONCLUSIONS  In this paper we explored the design of prosodic representa-  tions learned in an auto-encoder manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' First, we introduced  a TTS framework allowing for a fair comparison of prosody  embeddings of different granularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Then a systematic study  of utterance, word and phoneme-level representations was  conducted on a large-scale, publicly available dataset - Lib-  riTTS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Through our experiments, we demonstrated the trade-  off between capacity and predictability of prosody represen-  tations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We showed that utterance-level embeddings have  insufficient capacity to model expressive speech variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Whereas phoneme-level representations require strong reg-  ularization for stable prediction from text at inference time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We found that word-level embeddings impose a good balance  between capacity and predictability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' As a result, we closed  the gap in naturalness by 90% between synthetic speech  and recordings without sacrificing intelligibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Finally,  we looked into applying the proposed approach in a single-  speaker scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  We showed that semantically concerted  prosody prediction is a data hungry problem and limited  amount of training data can result in less stable prosody of  generated speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' However, this issue can be mitigated by  using auxiliary data in the training procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  BERT  No-Pref  BERT & Phoneme  (32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='87%)  (31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='78%)  (35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='35%)  0  25  50  75  100Phoneme  No-Pref  BERT & Phoneme  (34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='26%)  (31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='27%)  (34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='47%)  0  25  50  75  1007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' REFERENCES  [1] Jonathan Shen, Ruoming Pang, Ron J Weiss, Mike  Schuster, Navdeep Jaitly, Zongheng Yang, Zhifeng  Chen, Yu Zhang, Yuxuan Wang, Rj Skerrv-Ryan, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=',  “Natural tts synthesis by conditioning wavenet on mel  spectrogram predictions,” in ICASSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  4779–4783.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [2] Nishant Prateek, Mateusz Łajszczak, Roberto Barra-  Chicote, Thomas Drugman, Jaime Lorenzo-Trueba,  Thomas Merritt, Srikanth Ronanki, and Trevor Wood,  “In other news: A bi-style text-to-speech model for syn-  thesizing newscaster voice with limited data,”  arXiv  preprint arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='02790, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [3] Abdelhamid  Ezzerg,  Adam  Gabrys,  Bartosz  Pu-  trycz, Daniel Korzekwa, Daniel Saez-Trigueros, David  McHardy, Kamil Pokora, Jakub Lachowicz, Jaime  Lorenzo-Trueba, and Viacheslav Klimkov,  “Enhanc-  ing audio quality for expressive neural text-to-speech,”  arXiv preprint arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='06270, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [4] Raahil Shah, Kamil Pokora, Abdelhamid Ezzerg, Vi-  acheslav Klimkov, Goeric Huybrechts, Bartosz Pu-  trycz, Daniel Korzekwa, and Thomas Merritt,  “Non-  Autoregressive TTS with Explicit Duration Modelling  for Low-Resource Highly Expressive Speech,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  11th ISCA Speech Synthesis Workshop (SSW 11), 2021,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 96–101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [5] Sri Karlapati, Alexis Moinet, Arnaud Joly, Viacheslav  Klimkov, Daniel S´aez-Trigueros, and Thomas Drug-  man,  “Copycat: Many-to-many fine-grained prosody  transfer for neural text-to-speech,”  arXiv preprint  arXiv:2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='14617, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [6] Viacheslav Klimkov, Srikanth Ronanki, Jonas Rohnke,  and Thomas Drugman,  “Fine-grained robust prosody  transfer for single-speaker neural text-to-speech,” arXiv  preprint arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='02479, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [7] Piotr Bilinski, Thomas Merritt, Abdelhamid Ezzerg,  Kamil Pokora, Sebastian Cygert, Kayoko Yanagisawa,  Roberto Barra-Chicote, and Daniel Korzekwa, “Creat-  ing new voices using normalizing flows,” in accepted to  Interspeech 2022, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [8] RJ Skerry-Ryan, Eric Battenberg, Ying Xiao, Yuxuan  Wang, Daisy Stanton, Joel Shor, Ron Weiss, Rob Clark,  and Rif A Saurous, “Towards end-to-end prosody trans-  fer for expressive speech synthesis with tacotron,” in  international conference on machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' PMLR,  2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 4693–4702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [9] Ya-Jie Zhang, Shifeng Pan, Lei He, and Zhen-Hua Ling,  “Learning latent representations for style control and  transfer in end-to-end speech synthesis,”  in ICASSP  2019-2019 IEEE International Conference on Acous-  tics, Speech and Signal Processing (ICASSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE,  2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 6945–6949.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [10] Daisy Stanton, Yuxuan Wang, and RJ Skerry-Ryan,  “Predicting expressive speaking style from text in end-  to-end speech synthesis,” in 2018 IEEE Spoken Lan-  guage Technology Workshop (SLT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  595–602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [11] Sri Karlapati, Ammar Abbas, Zack Hodari, Alexis  Moinet, Arnaud Joly, Penny Karanasou, and Thomas  Drugman, “Prosodic representation learning and con-  textual sampling for neural text-to-speech,” in ICASSP  2021-2021 IEEE International Conference on Acous-  tics, Speech and Signal Processing (ICASSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE,  2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 6573–6577.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [12] Younggun Lee and Taesu Kim,  “Robust and fine-  grained prosody control of end-to-end speech synthe-  sis,”  in ICASSP 2019-2019 IEEE International Con-  ference on Acoustics, Speech and Signal Processing  (ICASSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 5911–5915.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [13] Zack Hodari, Alexis Moinet, Sri Karlapati, Jaime  Lorenzo-Trueba, Thomas Merritt, Arnaud Joly, Am-  mar Abbas, Penny Karanasou, and Thomas Drugman,  “Camp: A two-stage approach to modelling prosody  in context,” in ICASSP 2021-2021 IEEE International  Conference on Acoustics, Speech and Signal Processing  (ICASSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 6578–6582.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [14] Konstantinos Klapsas, Nikolaos Ellinas, June Sig Sung,  Hyoungmin Park, and Spyros Raptis, “Word-level style  control for expressive, non-attentive speech synthesis,”  in International Conference on Speech and Computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  Springer, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 336–347.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [15] Yi Ren, Chenxu Hu, Xu Tan, Tao Qin, Sheng Zhao,  Zhou Zhao, and Tie-Yan Liu, “Fastspeech 2: Fast and  high-quality end-to-end text to speech,” arXiv preprint  arXiv:2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='04558, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [16] Isaac Elias, Heiga Zen, Jonathan Shen, Yu Zhang,  Ye Jia, Ron J Weiss, and Yonghui Wu,  “Parallel  tacotron: Non-autoregressive and controllable tts,” in  ICASSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 5709–5713.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [17] Yanqing Liu, Zhihang Xu, Gang Wang, Kuan Chen,  Bohan Li, Xu Tan, Jinzhu Li, Lei He, and Sheng  Zhao, “Delightfultts: The microsoft speech synthesis  system for blizzard challenge 2021,”  arXiv preprint  arXiv:2110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='12612, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [18] Aaron van den Oord, Sander Dieleman, Heiga Zen,  Karen Simonyan, Oriol Vinyals, Alex Graves, Nal  Kalchbrenner, Andrew Senior, and Koray Kavukcuoglu,  “Wavenet: A generative model for raw audio,” arXiv  preprint arXiv:1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='03499, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [19] Yi Ren, Chenxu Hu, Xu Tan, Tao Qin, Sheng Zhao,  Zhou Zhao, and Tie-Yan Liu, “Fastspeech 2: Fast and  high-quality end-to-end text to speech,” in ICLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [20] Jonathan Shen, Ye Jia, Mike Chrzanowski, Yu Zhang,  Isaac Elias, Heiga Zen, and Yonghui Wu, “Non-attentive  tacotron:  Robust and controllable neural tts synthe-  sis including unsupervised duration modeling,” arXiv  preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='04301, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' He, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Deng, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' He,  “Robust Sequence-to-  Sequence Acoustic Modeling with Stepwise Monotonic  Attention for Neural TTS,” in Interspeech, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  1293–1297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [22] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Guo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Soong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' He, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Xie, “A New GAN-  Based End-to-End TTS Training Algorithm,” in Inter-  speech, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 1288–1292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [23] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Battenberg, RJ Skerry-Ryan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Mariooryad, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Stan-  ton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Kao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Shannon, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Bagby,  “Location-  relative attention mechanisms for robust long-form  speech synthesis,” in ICASSP, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 6194–6198.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [24] Heiga Ze, Andrew Senior, and Mike Schuster,  “Sta-  tistical parametric speech synthesis using deep neural  networks,”  in 2013 IEEE International Conference  on Acoustics, Speech and Signal Processing, 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  7962–7966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [25] Heiga Zen, Keiichi Tokuda, and Alan W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Black, “Statis-  tical parametric speech synthesis,” Speech Communica-  tion, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 51, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 1039–1064, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [26] Daniel Povey, Arnab Ghoshal, Gilles Boulianne, Lukas  Burget, Ondrej Glembek, Nagendra Goel, Mirko Han-  nemann, Petr Motlicek, Yanmin Qian, Petr Schwarz, Jan  Silovsky, Georg Stemmer, and Karel Vesely, “The kaldi  speech recognition toolkit,” in IEEE 2011 Workshop on  Automatic Speech Recognition and Understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  2011, IEEE Signal Processing Society, IEEE Catalog  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' : CFP11SRW-USB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [27] Yuxuan Wang, Daisy Stanton, Yu Zhang, RJ-Skerry  Ryan, Eric Battenberg, Joel Shor, Ying Xiao, Ye Jia,  Fei Ren, and Rif A Saurous, “Style tokens: Unsuper-  vised style modeling, control and transfer in end-to-end  speech synthesis,” in International Conference on Ma-  chine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' PMLR, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 5180–5189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [28] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and  Kristina Toutanova, “Bert: Pre-training of deep bidirec-  tional transformers for language understanding,” arXiv  preprint arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='04805, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [29] Heiga Zen, Viet Dang, Rob Clark, Yu Zhang, Ron J  Weiss, Ye Jia, Zhifeng Chen, and Yonghui Wu, “Lib-  ritts: A corpus derived from librispeech for text-to-  speech,” arXiv preprint arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='02882, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [30] Yunlong Jiao, Adam Gabry´s, Georgi Tinchev, Bartosz  Putrycz, Daniel Korzekwa, and Viacheslav Klimkov,  “Universal neural vocoding with parallel wavenet,” in  ICASSP 2021-2021 IEEE International Conference on  Acoustics, Speech and Signal Processing (ICASSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 6044–6048.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [31] Recommendation BS ITU-R, “1534-1,“method for the  subjective assessment of intermediate quality levels of  coding systems (mushra)”,” International Telecommu-  nication Union, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [32] Robert AJ Clark, Monika Podsiadlo, Mark Fraser,  Catherine Mayo, and Simon King, “Statistical analy-  sis of the blizzard challenge 2007 listening test results,”  in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' Blizzard Challenge Workshop, 2007, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [33] Maximilian Bisani and Hermann Ney, “Bootstrap esti-  mates for confidence intervals in asr performance eval-  uation,”  in 2004 IEEE International Conference on  Acoustics, Speech, and Signal Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE, 2004,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' I–409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [34] David Talkin and W Bastiaan Kleijn, “A robust algo-  rithm for pitch tracking (rapt),” Speech coding and syn-  thesis, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 495, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 518, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [35] Berrak Sisman, Junichi Yamagishi, Simon King, and  Haizhou Li, “An overview of voice conversion and its  challenges: From statistical modeling to deep learning,”  IEEE/ACM Transactions on Audio, Speech, and Lan-  guage Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 29, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 132–157, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [36] Evelina Bakhturina, Vitaly Lavrukhin, Boris Ginsburg,  and Yang Zhang,  “Hi-fi multi-speaker english tts  dataset,” arXiv preprint arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='01497, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [37] Yi Ren, Ming Lei, Zhiying Huang, Shiliang Zhang, Qian  Chen, Zhijie Yan, and Zhou Zhao, “Prosospeech: En-  hancing prosody with quantized vector pre-training in  text-to-speech,” in ICASSP 2022-2022 IEEE Interna-  tional Conference on Acoustics, Speech and Signal Pro-  cessing (ICASSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 7577–7581.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content='  [38] Yiwei Guo, Chenpeng Du, and Kai Yu, “Unsupervised  word-level prosody tagging for controllable speech syn-  thesis,” in ICASSP 2022-2022 IEEE International Con-  ference on Acoustics, Speech and Signal Processing  (ICASSP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' IEEE, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
+page_content=' 7597–7601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/I9FJT4oBgHgl3EQfGCzl/content/2301.11446v1.pdf'}
diff --git a/KdE2T4oBgHgl3EQfpgjD/content/tmp_files/2301.04030v1.pdf.txt b/KdE2T4oBgHgl3EQfpgjD/content/tmp_files/2301.04030v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3b8d734618a09df4d4f6df2a488f4fa36d70311b
--- /dev/null
+++ b/KdE2T4oBgHgl3EQfpgjD/content/tmp_files/2301.04030v1.pdf.txt
@@ -0,0 +1,802 @@
+Conversational Turn-taking as a Stochastic Process
+on Networks
+Lisa O’Bryan1, Santiago Segarra2, Jensine Paoletti1, Stephanie Zajac1, Margaret E. Beier1,
+Ashutosh Sabharwal2, Matthew Wettergreen3, and Eduardo Salas1
+Abstract—Understanding why certain individuals work well
+(or poorly) together as a team is a key research focus in
+the psychological and behavioral sciences and a fundamental
+problem for team-based organizations. Nevertheless, we have a
+limited ability to predict the social and work-related dynamics
+that will emerge from a given combination of team members.
+In this work, we model vocal turn-taking behavior within
+conversations as a parametric stochastic process on a network
+composed of the team members. More precisely, we model
+the dynamic of exchanging the ‘speaker token’ among team
+members as a random walk in a graph that is driven by both
+individual level features and the conversation history. We fit our
+model to conversational turn-taking data extracted from audio
+recordings of multinational student teams during undergraduate
+engineering design internships. Through this real-world data we
+validate the explanatory power of our model and we unveil
+statistically significant differences in speaking behaviors between
+team members of different nationalities.
+I. INTRODUCTION
+Data consisting of entities in interconnected systems are
+ubiquitous in multiple fields. Thus, network structures are
+commonly used across many disciplines for representation and
+analysis of complex information [1], from neuroscience [2]
+to wireless communications [3]. In this work, we represent
+interactions within teams as small in-person social networks.
+Computational models can be an effective way to study
+the social dynamics that emerge from individuals interact-
+ing within groups [4]. In particular, a variety of modeling
+approaches have been used to try to replicate natural turn-
+taking behaviors observed in conversation [5]–[8]. Many of
+these models have been successful in replicating realistic
+patterns of conversational turn-taking. However, the ability to
+understand the driving mechanisms underlying these patterns
+and generalize to novel team compositions is lacking. As
+a step towards this goal, we develop a stochastic model of
+conversations that can be used to explore how individual dif-
+ferences impact the emergence of turn-taking patterns within
+teams. More precisely, we propose a parametric model that
+captures the individuals’ innate tendency to speak as well
+as the effect that having spoken recently has on speaking
+again. At every point in time, the next speaker is drawn
+1Department of Psychological Sciences, Rice University, Houston, TX,
+USA. 2Department of Electrical and Computer Engineering, Rice University,
+Houston, TX, USA. 3Department of Bioengineering, Rice University, Hous-
+ton, TX, USA. Subsets of the team data used in this manuscript have been
+previously published as part of dissertations by Stephanie Zajac, Department
+of Psychological Sciences, Rice University and Jian Cao, Department of
+Electrical and Computer Engineering, Rice University. Funding for this project
+was provided by a Microsoft Productivity Research Grant, the National
+Science Foundation (Award Number: 1910117), and the Army Research
+Institute (Grant Number: W911NF-22-1-0226).
+from a probability distribution determined by the history
+of speakers and the aforementioned parameters. The model
+replicates the majority of conversational turn-taking patterns
+observed in our real-world data, and our results highlight the
+important role the memory function plays in replicating these
+patterns. Furthermore, our results indicate that differences in
+team member nationality can play a strong role in shaping
+communication patterns within multinational teams.
+Contributions. The contributions of our work are twofold:
+i) We propose a simple parametric stochastic process that can
+capture complex behaviors observed in real data.
+ii) We present a novel dataset of conversational turn-taking
+in undergraduate teams and we apply our model to reveal
+significant differences in speaking behavior between student
+nationalities.
+II. CONVERSATION MODEL
+Inspired by a model by Stasser and Taylor [7], our model
+incorporates two key notions: i) the relative likelihood πi that
+team member i speaks on a given turn independent of their
+speaking history and ii) the effect mi that an individual’s
+current speaking turn has on their likelihood of speaking
+on subsequent turns. We consider the inherent likelihood of
+speaking πi of each member i as independent of the history
+of exchanges and, thus, a constant throughout the conversation.
+In contrast, we encode dependencies within a conversation
+through the (turn-dependent) memory function mi(t). More
+precisely, for a given member i and a turn t, the memory
+value is given by
+mi(t) = di e−0.5 (t−tlast
+i
+),
+(1)
+where di is a learnable parameter that controls the scale of the
+memory effect for each individual and tlast
+i
+denotes the last
+turn on which member i spoke. The negative exponential form
+in (1) reveals that the memory value asymptotically decreases
+to 0 as (t − tlast
+i
+) increases, i.e., as more turns occur since
+the last time that member i spoke. This encodes the natural
+assumption that whether or not an individual spoke many turns
+ago is inconsequential to their likelihood of speaking next. The
+memory function in (1) is combined with the innate speaking
+tendencies πi to compute the likelihood ℓi(t) that member i
+speaks at turn t as follows
+ℓi(t) =
+�
+0,
+if tlast
+i
+= t − 1,
+πi + mi(t),
+otherwise.
+(2)
+Speakers are not allowed to speak on two consecutive turns
+since these would simply be considered part of the same turn.
+arXiv:2301.04030v1  [cs.SI]  10 Jan 2023
+
+This is enforced in (2) by setting the likelihood to zero for the
+member that has just spoken. Lastly, denoting by N the total
+number of team members, the likelihoods ℓi(t) are normalized
+to sum up to 1 so that they define bona fide probabilities pi(t)
+as follows
+pi(t) =
+ℓi(t)
+�N
+j=1 ℓj(t)
+.
+(3)
+The speaker at turn t is then drawn from this probability
+distribution across team members.
+In summary, the conversational behavior of each individual
+i within our model is given by two parameters (πi, di). Given
+these parameters for every team member, the model provides
+a well-defined stochastic process to generate conversations
+by the team. More precisely, to determine the speaker at
+turn t, we first compute the memory values of each member
+following (1), we then compute likelihoods and transform
+those into probabilities following (2) and (3), respectively,
+and we finally draw the next speaker from that probability
+distribution.
+Our main departure from Stasser and Taylor [7] is that
+our model is based on individual-level parameters whereas
+theirs is based on team-level parameters. Specifically, Stasser
+and Taylor’s [7] model depends on a single parameter r
+that determines the inherent speaking probability of every
+individual (what we denote by πi) as well as a single parameter
+d that determines the scale of the memory function for every
+team member. This fundamental difference is a key enabler for
+our study of how individual traits relate to each team member’s
+conversational behavior since, given observed conversations of
+a team, our model enables the estimation of the parameters
+(πi, di) for every team member.
+Given observed turn-taking data, we can fit our model by
+selecting the parameters (πi, di) for every team member that
+maximize the probability of generating the observed data.
+More precisely, if we denote by Ht−1 the history of turn-
+taking up to turn t − 1 in the observed data for a given
+team, and by ht the speaker at turn t, we can compute the
+probability that our model selects that true speaker ht [cf. (3)].
+Following the notation in (3), we denote this probability by
+pht(t | Ht−1, {(πi, di)}n
+i=1), i.e., the probability of selecting
+the true speaker ht at turn t but where we have now made
+explicit that this value depends on the past history Ht−1 and
+the parameters (πi, di) for each of the n members in the team.
+With this notation in place, the log-likelihood of observing the
+true history of T turns is given by
+L(HT | {(πi, di)}n
+i=1) =
+T
+�
+t=1
+log pht(t | Ht−1, {(πi, di)}n
+i=1).
+(4)
+We fit our model by finding the parameters {(πi, di)}n
+i=1
+that maximize (4). We also fit a reduced model that does
+not contain the memory parameters {di}n
+i=1 or, equivalently,
+where di = 0 for all i. We did this to determine the minimal
+viable model that can explain our observed data.
+III. DATASET
+In 2016 and 2017, we collected data on team interactions
+in student engineering design teams during 7-week internships
+at a private university in the southern United States. The first
+week of the internship consisted of a condensed course on
+the engineering design process, which helped to ensure all
+participants had a similar baseline level of knowledge. During
+the remaining six weeks, team members worked together to
+plan and execute their project which sought to meet a real-
+world need. We collected data from 7 multi-national teams
+with team members from the United States (n = 13), Malawi
+(n = 7), and Brazil (n = 4), with equal numbers of female and
+male participants. After consenting to the study, participants
+completed a self-report survey of their personality traits,
+attitudes, and demographic information. From these data we
+extracted five features for each individual that we hypothesized
+could relate to individual differences in speaking patterns,
+namely, extraversion, agreeableness, conscientiousness, sex
+(male, female), and nationality (American, Non-American).
+Our dataset includes multiple meetings from throughout the
+internships for all teams. Audio streams were processed by
+annotating the start and end times of speaking turns by each
+team member during the meetings. Overall, we extracted a
+mean (SD) of 1941 (1416.5) speaking turns per team.
+IV. NUMERICAL EXPERIMENTS
+To assess the predictive power of the full and reduced
+(i.e., without the memory component) models, we perform the
+following three classes of experiments.
+Predicting the next speaker. For each team, we split their
+turn-taking history into a training and a testing set. The
+training data contains the first 80 percent of the total turns
+whereas the testing data contains the remaining turns. As
+previously explained, we compute the maximum likelihood
+estimates of the model parameters but this time based only
+on maximizing the probability of observing the history of
+the training dataset. We then compute the log-likelihood of
+observing the history of the testing dataset, as in (4), for
+both the full and reduced fitted models. The larger (less
+negative) the attained value, the better predictive power of the
+corresponding model.
+Overall, the full simulation model (i.e., with memory pa-
+rameter) predicts the observed data better than the reduced
+simulation model. Table I shows the log-likelihoods attained
+for the testing dataset (last 20 percent of speaking turns)
+for each team and simulation model. The full simulation
+model consistently yields larger (less negative) log-likelihoods,
+indicating a better predictive performance.
+Reproducing relevant conversation patterns.
+We test the fit of both the full and reduced simulation
+models by comparing three measures between our observed
+and simulated datasets: 1) the proportion of time in which each
+team member spoke, 2) the proportion of a given speaker’s
+speaking turns following an ABA format in which there was
+one turn by a different speaker between a given speaker’s
+sequential turns (reflecting the proportion of turns that were
+part of dyadic exchanges), and 3) the proportion of turns that
+
+TABLE I
+LOG-LIKELIHOOD ATTAINED BY BOTH MODELS
+Team
+No Memory
+Memory
+Team 1
+-159.1586
+-154.4533
+Team 2
+-45.3267
+-43.2123
+Team 3
+-196.5418
+-188.6291
+Team 4
+-278.8524
+-255.2545
+Team 5
+-909.8953
+-617.3478
+Team 6
+-623.9848
+-589.0674
+Team 7
+-105.8199
+-104.0864
+were part of long dyadic exchanges (4 or more consecutive
+speaking turns (e.g. ABAB) between two team members).
+We calculate these measures for each of 10,000 replications
+of our simulation models and compare them to the values
+found in our observed data from each team. For each of our
+three measures, we find the proportion of model replications
+in which the observed value in the real data fell within the
+95 percent confidence interval for values produced by each
+simulation model. For each of the three speaking patterns of
+interest, we use chi-squared tests to compare the number of
+individuals or dyads across teams whose behaviors are not
+significantly different from those displayed by the full and
+reduced simulation models.
+The full simulation model matches the patterns displayed
+by significantly more individuals and dyads across teams
+than the reduced simulation model. The full simulation model
+correctly estimates the proportion of speaking turns spoken
+by each team member for 100% (24/24) of team members
+whereas the reduced simulation model correctly estimates the
+proportion for 70.8% (17/24) of team members (χ2 = 6.0, p
+= 0.014; Figure 1(a)). Moreover, the full simulation model
+correctly estimates the proportion of each team member’s
+speaking turns with an ABA format for 87.5% (21/24) of team
+members, but the reduced simulation model correctly estimates
+the proportion for 29.2% (7/24) of team members, with the
+tendency to underestimate the proportion of turns (χ2 = 14.5,
+p = 0.00014; Figure 1(b)). Finally, the full simulation model
+correctly estimates the proportion of speaking turns that were
+part of dyadic exchanges of length 4 turns or greater for 86.7%
+(26/30) of team member dyads, and the reduced simulation
+model correctly estimates the proportion for 36.7% (11/30) of
+team member dyads, with the tendency to underestimate the
+proportion of turns (χ2 = 13.8, p = 0.00020; Figure 1(c)).
+Relating individual traits and speaking behavior. To gain
+insight into the relative importance of different individual traits
+in understanding speaking behaviors, we use an information-
+theoretic approach [9] to determine which trait(s) best explain
+between-individual variation in model parameters πi (baseline
+likelihood of speaking) and di (likelihood of speaking again
+after speaking recently). Using the MuMIn function [10] in
+R, we examine which linear model (i.e., a null model and 5
+uni-variate models consisting of each of our individual-level
+predictor variables; see Section III) best explains variation in
+each parameter value across team members. We group-mean
+center our three continuous variables (extraversion, agreeable-
+ness, conscientiousness) to reflect the relative values of these
+personality traits among team members. We limit the number
+of variables per linear model to one to avoid overfitting. We
+rank our linear models according to the Akaike information
+criterion adjusted for small sample sizes (AICc) [9]. We con-
+sider top-performing linear models to be the best performing
+model (i.e. the model with the lowest AICc value) in our model
+set and any model less than 2 AICc points greater than the
+best performing linear model [9]. We examine the correlation
+between individual traits and simulation model parameters for
+all top-performing linear models to determine how these traits
+shape speaking behaviors.
+Tables II and III display the results of our model selection
+analysis that compares the relative ability of each of our five
+univariate models to explain between-individual variation in
+πi and di. The tables display the AICc values for each model
+as well as the ∆AICc values (relative to the best model)
+and corresponding model weights. Model weights reflect the
+relative support for a given linear model compared to the other
+candidate models, with 1 indicating full support.
+TABLE II
+MODEL SELECTION FOR BASELINE LIKELIHOOD OF SPEAKING πi
+model
+df
+AICc
+∆
+wt
+Nationality
+3
+-19.6
+0.0
+0.94
+Null
+2
+-12.4
+7.2
+0.025
+Agreeableness
+3
+-11.4
+8.2
+0.015
+Sex
+3
+-10.3
+9.3
+0.010
+Extraversion
+3
+-10.0
+9.6
+0.010
+Conscientiousness
+3
+-9.9
+9.7
+0.010
+TABLE III
+MODEL SELECTION FOR SHAPE OF MEMORY FUNCTION di
+model
+df
+AICc
+∆
+wt
+Null
+2
+105.2
+0.0
+0.42
+Extraversion
+3
+107.5
+2.4
+0.13
+Nationality
+3
+107.7
+2.5
+0.12
+Conscientiousness
+3
+107.8
+2.6
+0.11
+Sex
+3
+107.8
+2.6
+0.11
+Agreeableness
+3
+107.8
+2.6
+0.11
+The linear model that best explains between-individual dif-
+ferences in πi, the parameter reflecting the baseline likelihood
+of initiating a speaking turn, has nationality as the predictor
+variable. This linear model has a cumulative model weight
+of 93.5%. The second best linear model is the null model,
+which has a ∆AICc value 7.2 higher than the best model
+(Table II). Since this ∆AICc value is greater than our criterion
+of ∆AICc = 2 [9], we only consider the linear model with
+nationality as a predictor variable as a top-performing model
+within our model set. Overall, this model is supported 37.6
+times more strongly (evidence ratio = wi/wj = 0.94/0.025 =
+37.6) than the null model. When we analyze our top model,
+we find that Americans have significantly higher likelihoods
+of initiating speaking turns than non-Americans (β = 0.20, p
+< 0.01, Figure 2).
+The linear model that best explains between-individual
+differences in di, the change in likelihood of speaking after
+having just spoken, is the null model. This linear model has
+a cumulative model weight of 41.6%. The second best linear
+
+Fig. 1. Black points represent a) observed proportion of speaking turns by each team member, b) observed proportion of speaking turns
+with one turn in between (e.g. ABA) for each team member, c) observed proportion of speaking turns that were part of consecutive dyadic
+exchanges of length 4 turns or greater. Error bars represent the 95 percent confidence intervals for the proportions estimated by the reduced
+simulation model (i.e., without memory parameter) (red) and full simulation model (blue). Y-axis scale varies by team to improve visibility
+Fig. 2. Boxplot of baseline likelihood of speaking (parameter πi) by
+nationality across all teams.
+model has extraversion as a predictor variable and a ∆AICc
+value of 2.4 (Table III). Thus, only the null model is con-
+sidered a top-performing linear model within our model set,
+indicating that none of the predictor variables we considered
+explain between-individual variation in di. Overall, the null
+model is supported approximately 3.2 times more strongly
+(evidence ratio = wi/wj = 0.42/0.13 = 3.2) than the model
+with extraversion as a predictor.
+V. DISCUSSION
+The presence of the memory parameter is important in
+simulating the patterns of vocal turn-taking we observed in
+our study. Compared to the reduced simulation model with no
+memory parameter, the full simulation model more accurately
+predicts future speaking turns and better captures individual
+and dyadic speaking patterns. This result supports the findings
+by Stasser and Taylor [7] and Parker [5] that an individual’s
+current likelihood of speaking is impacted by their recent
+speaking behaviors. Nevertheless, our results differ from those
+of Stasser and Taylor in that we find different parameter values
+controlling memory function shape for different individuals.
+Our study finds evidence for consistent between-individual
+differences in speaking behaviors supporting previous find-
+ings that individual traits can correlate with communication
+behaviors [11]–[13]. Our finding that non-Americans initiate
+speaking turns less frequently than Americans is consistent
+with a recent study by Li et al. [11] which found that Chinese
+team members, who tended to be less proficient in English, ini-
+tiated fewer speaking turns than the American team members.
+Although we did not measure English language proficiency in
+our study, our finding could be related to language proficiency
+since the non-American students in our study were non-native
+English speakers. Another reason why non-Americans may not
+have initiated speaking turns as frequently could be that they
+had a perceived lower status than American team members.
+Social status may be awarded to the ethnic subgroup with
+the greatest numerical majority [14]. Since both the Brazilian
+and Malawian students were completing the internship at
+
+a)
+Team 1
+Team 2
+Team 3
+Team 4
+Team 5
+Team 6
+Team 7
+王
+王
+工工
+0.40-
+王
+0.32
+0.4-
+0.4 -
+0.40
+工
+0.4 
+0.35
+0.28
+工
+0.35
+工
+1
+0.3-
+0.3
+0.3 -
+0.30
+0.30
+0.24 -
+0.32
+0.25
+T
+0.2
+0.2 -
+0.25
+0.2
+主
+0.20-
+0.20-
+0.30
+工
+1
+土
+0.16 -
+土
+0.1 -
+0.1-
+2
+0.15-
+0.20-
+2
+3
+4
+3
+4
+2
+3
+4
+1
+2
+3
+A
+2
+3
+4
+1
+2
+3
+4
+1
+2
+3
+4
+Team Member
+b)
+0.8-
+工王
+0.8-
+0.8-
+工
+0.7-
+土
+0.75
+工
+0.6
+0.6
+:
+Proportion
+0.6
+0.6
+T
+0.6
+0.5
+0.50
+T
+0.4 
+0.4
+工
+0.4
+0.4
+P
+0.25
+0.4 
+0.3
+0.2
+0.2-
+工
+0.2-
+工
+0.4 
+0.2
+1
+2
+3
+1
+2
+3
+4
+1
+2
+3
+4
+1
+3
+4
+1
+2
+3
+1
+3
+1
+2
+3
+4
+TeamMember
+(2
+0.3
+0.8
+0.6 -
+FI
+T
+0.4
+0.5
+Exchanges
+0.5-
+工
+Long
+0.20
+0.6
+0.4 
+0.4-
+0.3-
+0.2
+0.4 
+0.15
+0.3
+0.4
+0.3
+0.2-
+0.10
+0.2
+0.2
+0.2
+0.2
+.
+0.1-
+0.05
+0.1
+王工
+0.1-
+I 
+1
+王
+工
+工
+工
+工
+工
+王王
+0.0
+0.0-
+0.0 -
+0.00
+0.0 -
+2.3.4.3.4
+2.3.
+4
+2. 3.
+3
+3
+2'2'
+3
+Dyad0.6
+Baseline Likelihood
+0.4
+0.2
+American
+Nonamerican
+Nationalityan American university and were outnumbered by American
+students, they may have demonstrated lower status behaviors
+like speaking up less frequently [12].
+Although nationality best explained differences in baseline
+frequency of speaking turn initiation, none of our predictor
+variables explained variation in memory function shape. Future
+studies are needed to determine whether other traits may
+explain the observed variation in this speaking tendency.
+Nevertheless, since Americans were more likely to initiate
+speaking turns, the broad tendency to speak again after hav-
+ing recently spoken further enhanced individual differences
+in speaking frequency across team members. Overall, these
+results help expand knowledge of the impact cultural diversity
+can have on team processes [15].
+A limitation of our study was that we only had data on a
+relatively small number of teams and team members. This
+lack of power prevented us from exploring more complex
+relationships between individual traits and their impacts on
+speaking behaviors. For example, Neubert and Tagger [16]
+found that gender moderated the relationship between indi-
+vidual traits and leadership, with certain traits being more
+important for leadership in males than females and vice
+versa. Since we tested each of our predictor variables on its
+own, the strong effect of nationality may have overpowered
+more subtle or complicated effects of other variables, such as
+personality and gender. This could be a reason why individual
+traits like extraversion, which can be strongly correlated with
+communication tendencies [17]–[19], did not correspond to
+individual differences in speaking behaviors in our study.
+Extending our study to more teams would enable a greater
+understanding of how multiple traits may interact to impact
+speaking behaviors.
+VI. CONCLUSION AND FUTURE WORK
+Our study develops a model of conversational turn-taking
+that can provide a mechanistic understanding of how patterns
+of communication emerge within teams and can be used to
+investigate the relationship between team member traits and
+specific speaking behaviors. Future extensions of our model
+could integrate more fine-grained speaking behaviors such as
+the timing between turns and turn overlap, which may enable
+the study of more complex or subtle turn-taking dynamics. For
+example, individuals higher in dominance have been found
+to interrupt more often, which can have a suppressive effect
+on the speaking behaviors of others [20]. Ultimately, through
+extensions of our modeling approach, it could be possible to
+predict the conversational interactions among team members
+based on their trait composition alone. This ability could
+enable the anticipation of undesirable team outcomes (e.g., de-
+velopment of subgroups) so that interventions could be applied
+ahead of time. Similarly, for established teams, it could also be
+possible to predict the effects team composition changes may
+have on communication patterns, thus providing guidelines for
+restaffing or retraining team members. Such predictive models
+would represent a significant advancement in teams research,
+enabling a more mechanistic understanding of the connection
+between team composition and team processes [21], [22].
+REFERENCES
+[1] I. Brugere, B. Gallagher, and T. Y. Berger-Wolf, “Network structure
+inference, a survey: Motivations, methods, and applications,” ACM
+Computing Surveys (CSUR), vol. 51, no. 2, pp. 1–39, 2018.
+[2] J. D. Medaglia, W. Huang, S. Segarra, C. Olm, J. Gee, M. Grossman,
+A. Ribeiro, C. T. McMillan, and D. S. Bassett, “Brain network
+efficiency is influenced by the pathologic source of corticobasal
+syndrome,” Neurology, vol. 89, no. 13, pp. 1373–1381, 2017. [Online].
+Available: https://n.neurology.org/content/89/13/1373
+[3] A. Chowdhury, G. Verma, C. Rao, A. Swami, and S. Segarra, “Unfolding
+wmmse using graph neural networks for efficient power allocation,”
+IEEE Trans. Wireless Commun., vol. 20, no. 9, pp. 6004–6017, 2021.
+[4] J. E. McGrath, H. Arrow, and J. L. Berdahl, “The study of groups: Past,
+present, and future,” Personality and Social Psychology Review, vol. 4,
+no. 1, pp. 95–105, 2000.
+[5] K. C. H. Parker, “Speaking Turns in Small Group Interaction: A
+Context-Free Event Sequence Model,” Journal of Personality and Social
+Psychology, vol. 54, no. 6, pp. 965–971, 1988.
+[6] S. Basu, T. Choudhury, B. Clarkson, and A. Pentland, “Learning
+human interactions with the influence model,” MIT Media Laboratory,
+Cambridge, MA, Tech. Rep., 2001.
+[7] G. Stasser and L. A. Taylor, “Speaking turns in face-to-face discussions.”
+Journal of Personality and Social Psychology, vol. 60, no. 5, pp. 675–
+684, 1991.
+[8] E. Padilha and J. Carletta, “A simulation of small group discussion,”
+in Workshop on the Semantics and Pragmatics of Dialogue, 2002, pp.
+117–124.
+[9] K. P. Burnham and D. R. Anderson, Model Selection and Multimodel
+Inference: A Practical Information-Theoretic Approach, 2nd ed. Berlin:
+Springer, 2002.
+[10] K. Barton, “MuMIn: Multi-model inference,” 2013. [Online]. Available:
+http://cran.r-project.org/package=MuMIn
+[11] H. Li, Y. C. Yuan, N. N. Bazarova, and B. S. Bell, “Talk and let talk:
+The effects of language proficiency on speaking up and competence per-
+ceptions in multinational teams,” Group and Organization Management,
+vol. 44, no. 5, pp. 953–989, 2019.
+[12] M. S. Mast, “Dominance as expressed and inferred through speaking
+time,” Human Communication Research, vol. 28, no. 3, pp. 420–450,
+2002.
+[13] C. E. Kimble and J. I. Musgrove, “Dominance in arguing mixed-sex
+dyads: Visual dominance patterns, talking time, and speech loudness,”
+Journal of Research in Personality, vol. 22, no. 1, pp. 1–16, 1988.
+[14] A. D. Bellmore, A. Nishina, M. R. Witkow, S. Graham, and J. Juvonen,
+“The influence of classroom ethnic composition on same- and other-
+ethnicity peer nominations in middle school,” Social Development,
+vol. 16, no. 4, pp. 720–740, 2007.
+[15] G. K. Stahl, M. L. Maznevski, A. Voigt, and K. Jonsen, “Unraveling
+the effects of cultural diversity in teams: A meta-analysis of research on
+multicultural work groups,” Journal of International Business Studies,
+vol. 41, no. 4, pp. 690–709, 2010.
+[16] M. J. Neubert and S. Taggar, “Pathways to informal leadership: The
+moderating role of gender on the relationship of individual differences
+and team member network centrality to informal leadership emergence,”
+Leadership Quarterly, vol. 15, no. 2, pp. 175–194, 2004.
+[17] K. C. McLean and M. Pasupathi, “Collaborative narration of the past
+and extraversion,” Journal of Research in Personality, vol. 40, no. 6, pp.
+1219–1231, 2006.
+[18] S. K. Leung and M. H. Bond, “Interpersonal communication and person-
+ality: Self and other perspectives,” Asian Journal of Social Psychology,
+vol. 4, no. 1, pp. 69–86, 2001.
+[19] G. A. Macht, D. A. Nembhard, J. H. Kim, and L. Rothrock, “Structural
+models
+of
+extraversion,
+communication,
+and
+team
+performance,”
+International Journal of Industrial Ergonomics, vol. 44, no. 1, pp. 82–91,
+2014. [Online]. Available: http://dx.doi.org/10.1016/j.ergon.2013.10.007
+[20] E. M. Rogers and D. K. Bhowmik, “Homophily-heterophily: Rela-
+tional concepts for communication research,” Public Opinion Quarterly,
+vol. 34, no. 4, pp. 523–538, 1970.
+[21] S. T. Bell, S. G. Brown, A. Colaneri, and N. Outland, “Team composition
+and the ABCs of teamwork,” American Psychologist, vol. 73, no. 4, pp.
+349–362, 2018.
+[22] L. O’Bryan, M. Beier, and E. Salas, “How approaches to animal swarm
+intelligence can improve the study of collective intelligence in human
+teams,” Journal of Intelligence, vol. 8, no. 1, 2020.
+
diff --git a/KdE2T4oBgHgl3EQfpgjD/content/tmp_files/load_file.txt b/KdE2T4oBgHgl3EQfpgjD/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..83ea351bc6bd2fb680cc8e8666c8e2a2c2cc8553
--- /dev/null
+++ b/KdE2T4oBgHgl3EQfpgjD/content/tmp_files/load_file.txt
@@ -0,0 +1,540 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf,len=539
+page_content='Conversational Turn-taking as a Stochastic Process  on Networks  Lisa O’Bryan1, Santiago Segarra2, Jensine Paoletti1, Stephanie Zajac1, Margaret E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Beier1,  Ashutosh Sabharwal2, Matthew Wettergreen3, and Eduardo Salas1  Abstract—Understanding why certain individuals work well  (or poorly) together as a team is a key research focus in  the psychological and behavioral sciences and a fundamental  problem for team-based organizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Nevertheless, we have a  limited ability to predict the social and work-related dynamics  that will emerge from a given combination of team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  In this work, we model vocal turn-taking behavior within  conversations as a parametric stochastic process on a network  composed of the team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' More precisely, we model  the dynamic of exchanging the ‘speaker token’ among team  members as a random walk in a graph that is driven by both  individual level features and the conversation history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We fit our  model to conversational turn-taking data extracted from audio  recordings of multinational student teams during undergraduate  engineering design internships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Through this real-world data we  validate the explanatory power of our model and we unveil  statistically significant differences in speaking behaviors between  team members of different nationalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' INTRODUCTION  Data consisting of entities in interconnected systems are  ubiquitous in multiple fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Thus, network structures are  commonly used across many disciplines for representation and  analysis of complex information [1], from neuroscience [2]  to wireless communications [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' In this work, we represent  interactions within teams as small in-person social networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Computational models can be an effective way to study  the social dynamics that emerge from individuals interact-  ing within groups [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' In particular, a variety of modeling  approaches have been used to try to replicate natural turn-  taking behaviors observed in conversation [5]–[8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Many of  these models have been successful in replicating realistic  patterns of conversational turn-taking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' However, the ability to  understand the driving mechanisms underlying these patterns  and generalize to novel team compositions is lacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' As  a step towards this goal, we develop a stochastic model of  conversations that can be used to explore how individual dif-  ferences impact the emergence of turn-taking patterns within  teams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' More precisely, we propose a parametric model that  captures the individuals’ innate tendency to speak as well  as the effect that having spoken recently has on speaking  again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' At every point in time, the next speaker is drawn  1Department of Psychological Sciences, Rice University, Houston, TX,  USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 2Department of Electrical and Computer Engineering, Rice University,  Houston, TX, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 3Department of Bioengineering, Rice University, Hous-  ton, TX, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Subsets of the team data used in this manuscript have been  previously published as part of dissertations by Stephanie Zajac, Department  of Psychological Sciences, Rice University and Jian Cao, Department of  Electrical and Computer Engineering, Rice University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Funding for this project  was provided by a Microsoft Productivity Research Grant, the National  Science Foundation (Award Number: 1910117), and the Army Research  Institute (Grant Number: W911NF-22-1-0226).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  from a probability distribution determined by the history  of speakers and the aforementioned parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The model  replicates the majority of conversational turn-taking patterns  observed in our real-world data, and our results highlight the  important role the memory function plays in replicating these  patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Furthermore, our results indicate that differences in  team member nationality can play a strong role in shaping  communication patterns within multinational teams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The contributions of our work are twofold:  i) We propose a simple parametric stochastic process that can  capture complex behaviors observed in real data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  ii) We present a novel dataset of conversational turn-taking  in undergraduate teams and we apply our model to reveal  significant differences in speaking behavior between student  nationalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' CONVERSATION MODEL  Inspired by a model by Stasser and Taylor [7], our model  incorporates two key notions: i) the relative likelihood πi that  team member i speaks on a given turn independent of their  speaking history and ii) the effect mi that an individual’s  current speaking turn has on their likelihood of speaking  on subsequent turns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We consider the inherent likelihood of  speaking πi of each member i as independent of the history  of exchanges and, thus, a constant throughout the conversation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  In contrast, we encode dependencies within a conversation  through the (turn-dependent) memory function mi(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' More  precisely, for a given member i and a turn t, the memory  value is given by  mi(t) = di e−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5 (t−tlast  i  ),  (1)  where di is a learnable parameter that controls the scale of the  memory effect for each individual and tlast  i  denotes the last  turn on which member i spoke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The negative exponential form  in (1) reveals that the memory value asymptotically decreases  to 0 as (t − tlast  i  ) increases, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=', as more turns occur since  the last time that member i spoke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' This encodes the natural  assumption that whether or not an individual spoke many turns  ago is inconsequential to their likelihood of speaking next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The  memory function in (1) is combined with the innate speaking  tendencies πi to compute the likelihood ℓi(t) that member i  speaks at turn t as follows  ℓi(t) =  �  0,  if tlast  i  = t − 1,  πi + mi(t),  otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  (2)  Speakers are not allowed to speak on two consecutive turns  since these would simply be considered part of the same turn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='04030v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='SI]  10 Jan 2023  This is enforced in (2) by setting the likelihood to zero for the  member that has just spoken.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Lastly, denoting by N the total  number of team members, the likelihoods ℓi(t) are normalized  to sum up to 1 so that they define bona fide probabilities pi(t)  as follows  pi(t) =  ℓi(t)  �N  j=1 ℓj(t)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  (3)  The speaker at turn t is then drawn from this probability  distribution across team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  In summary, the conversational behavior of each individual  i within our model is given by two parameters (πi, di).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Given  these parameters for every team member, the model provides  a well-defined stochastic process to generate conversations  by the team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' More precisely, to determine the speaker at  turn t, we first compute the memory values of each member  following (1), we then compute likelihoods and transform  those into probabilities following (2) and (3), respectively,  and we finally draw the next speaker from that probability  distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Our main departure from Stasser and Taylor [7] is that  our model is based on individual-level parameters whereas  theirs is based on team-level parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Specifically, Stasser  and Taylor’s [7] model depends on a single parameter r  that determines the inherent speaking probability of every  individual (what we denote by πi) as well as a single parameter  d that determines the scale of the memory function for every  team member.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' This fundamental difference is a key enabler for  our study of how individual traits relate to each team member’s  conversational behavior since, given observed conversations of  a team, our model enables the estimation of the parameters  (πi, di) for every team member.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Given observed turn-taking data, we can fit our model by  selecting the parameters (πi, di) for every team member that  maximize the probability of generating the observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  More precisely, if we denote by Ht−1 the history of turn-  taking up to turn t − 1 in the observed data for a given  team, and by ht the speaker at turn t, we can compute the  probability that our model selects that true speaker ht [cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' (3)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Following the notation in (3), we denote this probability by  pht(t | Ht−1, {(πi, di)}n  i=1), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=', the probability of selecting  the true speaker ht at turn t but where we have now made  explicit that this value depends on the past history Ht−1 and  the parameters (πi, di) for each of the n members in the team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  With this notation in place, the log-likelihood of observing the  true history of T turns is given by  L(HT | {(πi, di)}n  i=1) =  T  �  t=1  log pht(t | Ht−1, {(πi, di)}n  i=1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  (4)  We fit our model by finding the parameters {(πi, di)}n  i=1  that maximize (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We also fit a reduced model that does  not contain the memory parameters {di}n  i=1 or, equivalently,  where di = 0 for all i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We did this to determine the minimal  viable model that can explain our observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' DATASET  In 2016 and 2017, we collected data on team interactions  in student engineering design teams during 7-week internships  at a private university in the southern United States.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The first  week of the internship consisted of a condensed course on  the engineering design process, which helped to ensure all  participants had a similar baseline level of knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' During  the remaining six weeks, team members worked together to  plan and execute their project which sought to meet a real-  world need.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We collected data from 7 multi-national teams  with team members from the United States (n = 13), Malawi  (n = 7), and Brazil (n = 4), with equal numbers of female and  male participants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' After consenting to the study, participants  completed a self-report survey of their personality traits,  attitudes, and demographic information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' From these data we  extracted five features for each individual that we hypothesized  could relate to individual differences in speaking patterns,  namely, extraversion, agreeableness, conscientiousness, sex  (male, female), and nationality (American, Non-American).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Our dataset includes multiple meetings from throughout the  internships for all teams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Audio streams were processed by  annotating the start and end times of speaking turns by each  team member during the meetings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Overall, we extracted a  mean (SD) of 1941 (1416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5) speaking turns per team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' NUMERICAL EXPERIMENTS  To assess the predictive power of the full and reduced  (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=', without the memory component) models, we perform the  following three classes of experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Predicting the next speaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' For each team, we split their  turn-taking history into a training and a testing set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The  training data contains the first 80 percent of the total turns  whereas the testing data contains the remaining turns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' As  previously explained, we compute the maximum likelihood  estimates of the model parameters but this time based only  on maximizing the probability of observing the history of  the training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We then compute the log-likelihood of  observing the history of the testing dataset, as in (4), for  both the full and reduced fitted models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The larger (less  negative) the attained value, the better predictive power of the  corresponding model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Overall, the full simulation model (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=', with memory pa-  rameter) predicts the observed data better than the reduced  simulation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Table I shows the log-likelihoods attained  for the testing dataset (last 20 percent of speaking turns)  for each team and simulation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The full simulation  model consistently yields larger (less negative) log-likelihoods,  indicating a better predictive performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Reproducing relevant conversation patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  We test the fit of both the full and reduced simulation  models by comparing three measures between our observed  and simulated datasets: 1) the proportion of time in which each  team member spoke,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 2) the proportion of a given speaker’s  speaking turns following an ABA format in which there was  one turn by a different speaker between a given speaker’s  sequential turns (reflecting the proportion of turns that were  part of dyadic exchanges),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' and 3) the proportion of turns that  TABLE I  LOG-LIKELIHOOD ATTAINED BY BOTH MODELS  Team  No Memory  Memory  Team 1  159.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='1586  154.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4533  Team 2  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3267  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2123  Team 3  196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5418  188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6291  Team 4  278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8524  255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2545  Team 5  909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8953  617.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3478  Team 6  623.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='9848  589.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0674  Team 7  105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8199  104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0864  were part of long dyadic exchanges (4 or more consecutive  speaking turns (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' ABAB) between two team members).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  We calculate these measures for each of 10,000 replications  of our simulation models and compare them to the values  found in our observed data from each team.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' For each of our  three measures, we find the proportion of model replications  in which the observed value in the real data fell within the  95 percent confidence interval for values produced by each  simulation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' For each of the three speaking patterns of  interest, we use chi-squared tests to compare the number of  individuals or dyads across teams whose behaviors are not  significantly different from those displayed by the full and  reduced simulation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  The full simulation model matches the patterns displayed  by significantly more individuals and dyads across teams  than the reduced simulation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The full simulation model  correctly estimates the proportion of speaking turns spoken  by each team member for 100% (24/24) of team members  whereas the reduced simulation model correctly estimates the  proportion for 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8% (17/24) of team members (χ2 = 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0, p  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Figure 1(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Moreover, the full simulation model  correctly estimates the proportion of each team member’s  speaking turns with an ABA format for 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5% (21/24) of team  members, but the reduced simulation model correctly estimates  the proportion for 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2% (7/24) of team members, with the  tendency to underestimate the proportion of turns (χ2 = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5,  p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='00014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Figure 1(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Finally, the full simulation model  correctly estimates the proportion of speaking turns that were  part of dyadic exchanges of length 4 turns or greater for 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='7%  (26/30) of team member dyads, and the reduced simulation  model correctly estimates the proportion for 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='7% (11/30) of  team member dyads, with the tendency to underestimate the  proportion of turns (χ2 = 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8, p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='00020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Figure 1(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Relating individual traits and speaking behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' To gain  insight into the relative importance of different individual traits  in understanding speaking behaviors, we use an information-  theoretic approach [9] to determine which trait(s) best explain  between-individual variation in model parameters πi (baseline  likelihood of speaking) and di (likelihood of speaking again  after speaking recently).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Using the MuMIn function [10] in  R, we examine which linear model (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=', a null model and 5  uni-variate models consisting of each of our individual-level  predictor variables;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' see Section III) best explains variation in  each parameter value across team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We group-mean  center our three continuous variables (extraversion, agreeable-  ness, conscientiousness) to reflect the relative values of these  personality traits among team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We limit the number  of variables per linear model to one to avoid overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We  rank our linear models according to the Akaike information  criterion adjusted for small sample sizes (AICc) [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We con-  sider top-performing linear models to be the best performing  model (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' the model with the lowest AICc value) in our model  set and any model less than 2 AICc points greater than the  best performing linear model [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' We examine the correlation  between individual traits and simulation model parameters for  all top-performing linear models to determine how these traits  shape speaking behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Tables II and III display the results of our model selection  analysis that compares the relative ability of each of our five  univariate models to explain between-individual variation in  πi and di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The tables display the AICc values for each model  as well as the ∆AICc values (relative to the best model)  and corresponding model weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Model weights reflect the  relative support for a given linear model compared to the other  candidate models, with 1 indicating full support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  TABLE II  MODEL SELECTION FOR BASELINE LIKELIHOOD OF SPEAKING πi  model  df  AICc  ∆  wt  Nationality  3  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='94  Null  2  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='025  Agreeableness  3  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='015  Sex  3  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='010  Extraversion  3  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='010  Conscientiousness  3  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='9  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='010  TABLE III  MODEL SELECTION FOR SHAPE OF MEMORY FUNCTION di  model  df  AICc  ∆  wt  Null  2  105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='42  Extraversion  3  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='13  Nationality  3  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='12  Conscientiousness  3  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='11  Sex  3  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='11  Agreeableness  3  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='11  The linear model that best explains between-individual dif-  ferences in πi, the parameter reflecting the baseline likelihood  of initiating a speaking turn, has nationality as the predictor  variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' This linear model has a cumulative model weight  of 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The second best linear model is the null model,  which has a ∆AICc value 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2 higher than the best model  (Table II).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Since this ∆AICc value is greater than our criterion  of ∆AICc = 2 [9], we only consider the linear model with  nationality as a predictor variable as a top-performing model  within our model set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Overall, this model is supported 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  times more strongly (evidence ratio = wi/wj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='94/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='025 =  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6) than the null model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' When we analyze our top model,  we find that Americans have significantly higher likelihoods  of initiating speaking turns than non-Americans (β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='20, p  < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='01, Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  The linear model that best explains between-individual  differences in di, the change in likelihood of speaking after  having just spoken, is the null model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' This linear model has  a cumulative model weight of 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' The second best linear  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Black points represent a) observed proportion of speaking turns by each team member, b) observed proportion of speaking turns  with one turn in between (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' ABA) for each team member, c) observed proportion of speaking turns that were part of consecutive dyadic  exchanges of length 4 turns or greater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Error bars represent the 95 percent confidence intervals for the proportions estimated by the reduced  simulation model (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=', without memory parameter) (red) and full simulation model (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Y-axis scale varies by team to improve visibility  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Boxplot of baseline likelihood of speaking (parameter πi) by  nationality across all teams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  model has extraversion as a predictor variable and a ∆AICc  value of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4 (Table III).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Thus, only the null model is con-  sidered a top-performing linear model within our model set,  indicating that none of the predictor variables we considered  explain between-individual variation in di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Overall, the null  model is supported approximately 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2 times more strongly  (evidence ratio = wi/wj = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='42/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='13 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2) than the model  with extraversion as a predictor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' DISCUSSION  The presence of the memory parameter is important in  simulating the patterns of vocal turn-taking we observed in  our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Compared to the reduced simulation model with no  memory parameter, the full simulation model more accurately  predicts future speaking turns and better captures individual  and dyadic speaking patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' This result supports the findings  by Stasser and Taylor [7] and Parker [5] that an individual’s  current likelihood of speaking is impacted by their recent  speaking behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Nevertheless, our results differ from those  of Stasser and Taylor in that we find different parameter values  controlling memory function shape for different individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Our study finds evidence for consistent between-individual  differences in speaking behaviors supporting previous find-  ings that individual traits can correlate with communication  behaviors [11]–[13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Our finding that non-Americans initiate  speaking turns less frequently than Americans is consistent  with a recent study by Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' [11] which found that Chinese  team members, who tended to be less proficient in English, ini-  tiated fewer speaking turns than the American team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Although we did not measure English language proficiency in  our study, our finding could be related to language proficiency  since the non-American students in our study were non-native  English speakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Another reason why non-Americans may not  have initiated speaking turns as frequently could be that they  had a perceived lower status than American team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Social status may be awarded to the ethnic subgroup with  the greatest numerical majority [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Since both the Brazilian  and Malawian students were completing the internship at  a)  Team 1  Team 2  Team 3  Team 4  Team 5  Team 6  Team 7  王  王  工工  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='40-  王  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='40  工  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='28  工  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='35  工  1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='24 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='32  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='25  T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  主  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='20-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='20-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='30  工  1  土  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='16 -  土  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='1 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='1-  2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='15-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='20-  2  3  4  3  4  2  3  4  1  2  3  A  2  3  4  1  2  3  4  1  2  3  4  Team Member  b)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8-  工王  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8-  工  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='7-  土  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='75  工  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  :  Proportion  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='50  T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  工  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  P  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2-  工  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2-  工  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  1  2  3  1  2  3  4  1  2  3  4  1  3  4  1  2  3  1  3  1  2  3  4  TeamMember  (2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6 -  FI  T  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5  Exchanges  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='5-  工  Long  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='1-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='1  王工  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='1-  I  1  王  工  工  工  工  工  王王  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0 -  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='0 -  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content="  3  3  2'2'  3  Dyad0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='6  Baseline Likelihood  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2  American  Nonamerican  Nationalityan American university and were outnumbered by American  students, they may have demonstrated lower status behaviors  like speaking up less frequently [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Although nationality best explained differences in baseline  frequency of speaking turn initiation, none of our predictor  variables explained variation in memory function shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Future  studies are needed to determine whether other traits may  explain the observed variation in this speaking tendency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Nevertheless, since Americans were more likely to initiate  speaking turns, the broad tendency to speak again after hav-  ing recently spoken further enhanced individual differences  in speaking frequency across team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Overall, these  results help expand knowledge of the impact cultural diversity  can have on team processes [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  A limitation of our study was that we only had data on a  relatively small number of teams and team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' This  lack of power prevented us from exploring more complex  relationships between individual traits and their impacts on  speaking behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' For example, Neubert and Tagger [16]  found that gender moderated the relationship between indi-  vidual traits and leadership, with certain traits being more  important for leadership in males than females and vice  versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Since we tested each of our predictor variables on its  own, the strong effect of nationality may have overpowered  more subtle or complicated effects of other variables, such as  personality and gender.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' This could be a reason why individual  traits like extraversion, which can be strongly correlated with  communication tendencies [17]–[19], did not correspond to  individual differences in speaking behaviors in our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Extending our study to more teams would enable a greater  understanding of how multiple traits may interact to impact  speaking behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' CONCLUSION AND FUTURE WORK  Our study develops a model of conversational turn-taking  that can provide a mechanistic understanding of how patterns  of communication emerge within teams and can be used to  investigate the relationship between team member traits and  specific speaking behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Future extensions of our model  could integrate more fine-grained speaking behaviors such as  the timing between turns and turn overlap, which may enable  the study of more complex or subtle turn-taking dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' For  example, individuals higher in dominance have been found  to interrupt more often, which can have a suppressive effect  on the speaking behaviors of others [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Ultimately, through  extensions of our modeling approach, it could be possible to  predict the conversational interactions among team members  based on their trait composition alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' This ability could  enable the anticipation of undesirable team outcomes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=', de-  velopment of subgroups) so that interventions could be applied  ahead of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Similarly, for established teams, it could also be  possible to predict the effects team composition changes may  have on communication patterns, thus providing guidelines for  restaffing or retraining team members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Such predictive models  would represent a significant advancement in teams research,  enabling a more mechanistic understanding of the connection  between team composition and team processes [21], [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  REFERENCES  [1] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Brugere, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Gallagher, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Berger-Wolf, “Network structure  inference, a survey: Motivations, methods, and applications,” ACM  Computing Surveys (CSUR), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 51, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 1–39, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Medaglia, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Huang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Segarra, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Olm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Gee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Grossman,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Ribeiro, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' McMillan, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Bassett, “Brain network  efficiency is influenced by the pathologic source of corticobasal  syndrome,” Neurology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 89, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 13, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 1373–1381, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  Available: https://n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='neurology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='org/content/89/13/1373  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Chowdhury, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Verma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Rao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Swami, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Segarra, “Unfolding  wmmse using graph neural networks for efficient power allocation,”  IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 6004–6017, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' McGrath, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Arrow, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Berdahl, “The study of groups: Past,  present, and future,” Personality and Social Psychology Review, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 4,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 95–105, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [5] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Parker, “Speaking Turns in Small Group Interaction: A  Context-Free Event Sequence Model,” Journal of Personality and Social  Psychology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 54, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 965–971, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Basu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Choudhury, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Clarkson, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Pentland, “Learning  human interactions with the influence model,” MIT Media Laboratory,  Cambridge, MA, Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=', 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [7] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Stasser and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Taylor, “Speaking turns in face-to-face discussions.”  Journal of Personality and Social Psychology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 60, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 675–  684, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [8] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Padilha and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Carletta, “A simulation of small group discussion,”  in Workshop on the Semantics and Pragmatics of Dialogue, 2002, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  117–124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [9] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Burnham and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Anderson, Model Selection and Multimodel  Inference: A Practical Information-Theoretic Approach, 2nd ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Berlin:  Springer, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [10] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Barton, “MuMIn: Multi-model inference,” 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Available:  http://cran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='r-project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='org/package=MuMIn  [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Yuan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Bazarova, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Bell, “Talk and let talk:  The effects of language proficiency on speaking up and competence per-  ceptions in multinational teams,” Group and Organization Management,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 44, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 953–989, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Mast, “Dominance as expressed and inferred through speaking  time,” Human Communication Research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 28, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 420–450,  2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [13] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Kimble and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Musgrove, “Dominance in arguing mixed-sex  dyads: Visual dominance patterns, talking time, and speech loudness,”  Journal of Research in Personality, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 1–16, 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Bellmore, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Nishina, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Witkow, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Graham, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Juvonen,  “The influence of classroom ethnic composition on same- and other-  ethnicity peer nominations in middle school,” Social Development,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 720–740, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [15] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Stahl, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Maznevski, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Voigt, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Jonsen, “Unraveling  the effects of cultural diversity in teams: A meta-analysis of research on  multicultural work groups,” Journal of International Business Studies,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 41, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 690–709, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Neubert and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Taggar, “Pathways to informal leadership: The  moderating role of gender on the relationship of individual differences  and team member network centrality to informal leadership emergence,”  Leadership Quarterly, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 175–194, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [17] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' McLean and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Pasupathi, “Collaborative narration of the past  and extraversion,” Journal of Research in Personality, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 40, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  1219–1231, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Leung and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Bond, “Interpersonal communication and person-  ality: Self and other perspectives,” Asian Journal of Social Psychology,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 69–86, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [19] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Macht, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Nembhard, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Kim, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Rothrock, “Structural  models  of  extraversion,  communication,  and  team  performance,”  International Journal of Industrial Ergonomics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 44, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 82–91,  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Available: http://dx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='ergon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='007  [20] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Rogers and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Bhowmik, “Homophily-heterophily: Rela-  tional concepts for communication research,” Public Opinion Quarterly,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 523–538, 1970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Bell, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Brown, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Colaneri, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Outland, “Team composition  and the ABCs of teamwork,” American Psychologist, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 73, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  349–362, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content='  [22] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' O’Bryan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Beier, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' Salas, “How approaches to animal swarm  intelligence can improve the study of collective intelligence in human  teams,” Journal of Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
+page_content=' 1, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KdE2T4oBgHgl3EQfpgjD/content/2301.04030v1.pdf'}
diff --git a/L9E3T4oBgHgl3EQfYgo-/content/tmp_files/2301.04488v1.pdf.txt b/L9E3T4oBgHgl3EQfYgo-/content/tmp_files/2301.04488v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..366d2175f1dd420041ad8feec364b0de733a4390
--- /dev/null
+++ b/L9E3T4oBgHgl3EQfYgo-/content/tmp_files/2301.04488v1.pdf.txt
@@ -0,0 +1,1527 @@
+WuYun: Exploring hierarchical skeleton-guided
+melody generation using knowledge-enhanced deep
+learning
+Kejun Zhang1,2,3,∗,
+Xinda Wu1,∗,
+Tieyao Zhang1,
+Zhijie Huang1,
+Xu Tan4,
+Qihao Liang1,
+Songruoyao Wu1,
+Lingyun Sun1,2,†
+1College of Computer Science and Technology, Zhejiang University, China.
+2Alibaba-Zhejiang University Joint Institute of Frontier Technologies, China.
+3Innovation Center of Yangtze River Delta, China.
+4Microsoft Research Asia
+{zhangkejun, wuxinda, kreutzer0421, zj_huang,
+qhliang, 12221193, sunly}@zju.edu.cn
+xuta@microsoft.com
+Abstract
+Although deep learning has revolutionized music generation, existing methods
+for structured melody generation follow an end-to-end left-to-right note-by-note
+generative paradigm and treat each note equally. Here, we present WuYun, a
+knowledge-enhanced deep learning architecture for improving the structure of
+generated melodies, which first generates the most structurally important notes to
+construct a melodic skeleton and subsequently infills it with dynamically decorative
+notes into a full-fledged melody. Specifically, we use music domain knowledge
+to extract melodic skeletons and employ sequence learning to reconstruct them,
+which serve as additional knowledge to provide auxiliary guidance for the melody
+generation process. We demonstrate that WuYun can generate melodies with better
+long-term structure and musicality and outperforms other state-of-the-art methods
+by 0.51 on average on all subjective evaluation metrics. Our study provides a
+multidisciplinary lens to design melodic hierarchical structures and bridge the
+gap between data-driven and knowledge-based approaches for numerous music
+generation tasks.
+1
+Introduction
+Automatic music generation is one of the popular multidisciplinary research topics in generative
+art and computational creativity (1), which has achieved revolutionary advances in various artificial
+intelligence-generated content applications by utilizing deep learning techniques (2, 3), including
+interactive music production collaboration tools (4, 5), video background music generation (6), music
+education (7), and music therapy (8). As one of the crucial components of music generation, melody
+generation has drawn much attention from both the academic and industrial fields. Although melodies
+appear to be a simple linear succession of notes unfolding over time, the organizational structure of
+the melodic notes is hierarchical, like a tree resulting in intricate long-distance dependencies (9, 10).
+Hence, the complex long-distance dependencies make it difficult for neural networks to discover and
+learn the hierarchical structure relationships among these musical elements and generate long-term
+structured melodies. In recent years, language models in natural language processing (NLP) have
+∗Equal contribution.
+†Corresponding author.
+Preprint. Under review.
+arXiv:2301.04488v1  [cs.SD]  11 Jan 2023
+
+been employed to capture long-distance dependencies for structured melody generation with the
+advantages of an easy-to-use end-to-end deep learning framework, effective representation learning,
+and arbitrary sequence length generation. Their powerful ability to automatically learn the latent
+knowledge from big data, without explicitly codifying the domain-specific rules, has been proved and
+applied in multiple disciplines (11–14).
+Numerous specialized architectures of the language model for music generation have demonstrated
+promising performance in generating long-range coherent melodies, including effective attention
+mechanisms (15, 16), enhanced memory networks (17–19), large-scale deep neural networks (20),
+and explicit musicality regularization (21). Furthermore, various MIDI-derived symbolic music
+representation methods designed auxiliary musical spatiotemporal symbols (e.g., BAR, POSITION,
+and CHORD) for the input symbolic music data to help music generation models learn the long-
+distance dependencies better, longer, and faster (17–19, 22, 23). However, the scarcity of publicly
+available melody data limits the usage of the power of language-based music generation models.
+Moreover, the process of melody generation still lacks controllability. These models are trained in the
+dominant end-to-end and data-driven learning paradigms, which optimize the network’s large-scale
+parameters via learning to map the input data to output data, thus occasionally resulting in excessive
+repetition or boring sounds in the generated music (21).
+Recent studies used a deep learning-based hierarchical generation strategy to first hallucinate or
+predict the object’s structure and then use it to constrain downstream generation tasks (e.g., protein,
+font, or music) (24–33), which enables the neural networks to learn from the limited data far
+more efficiently and improves the controllability of the generation process. For structured melody
+generation, some scholars first generate a melody’s hierarchical music structure representation (31)
+or bar-level musical structure relationship graph (32, 33) and then generate melodies conditioned
+on the generated parallel structure information as additional knowledge. Such a strategy requires
+recognizing the group structure of the musical syntax in a melodic surface (e.g., phrases and sections)
+to extract music features for building a structure generation model. Nonetheless, inadequate music
+structure boundary detection algorithms hinder the extraction of accurate melodic group structure.
+Conversely, little attention has been paid to the organizational logic of the deep structure beneath
+the melodic surface, organized by different levels of structural importance among various musical
+events (34–36) with the potential to enhance structured melody generation. Typically, the majority
+of existing melody generation methods for pursuing long-term structure follow an end-to-end left-
+to-right note-by-note generative paradigm and treat each note equally. So far, however, there is still
+an insufficient investigation into an alternative order of melody generation and the difference in the
+relative structural importance among musical notes.
+In this study, we propose WuYun, a hierarchical skeleton-guided melody generation architecture
+based on knowledge-enhanced deep learning that incorporates the melodic skeleton as deep structural
+support to provide explicit guidance on the development direction of melody generation (Fig. 1A).
+WuYun follows the hierarchical organization principle of structure and prolongation (35, 37), thus
+dividing traditional single-stage end-to-end melody generation into two stages: melodic skeleton
+construction and melody inpainting (Fig. 1B). At the stage of melodic skeleton construction, we first
+extract the most structurally important notes in a musical piece from rhythm and pitch dimensions
+as melodic skeletons on the basis of the music domain knowledge. We then train an autoregressive
+decoder-only Transformer-based network (38) on the collected melodic skeleton data to construct
+new melodic skeletons (Fig. 1C, a). We treat the melodic skeleton as the underlying framework of the
+final generated melody. At the stage of melody inpainting, we adopt a Transformer encoder–decoder
+architecture (39) to elaborate the melodic skeleton into a full-fledged melody by encoding the melodic
+skeleton as additional knowledge into the decoder to guide the melody generation process (Fig. 1C,
+b). To prove the effectiveness of the architecture, we evaluate WuYun on a publicly available melody
+dataset. Experimental results show that the generated melodic skeleton has comparable quality with
+the real one extracted by our proposed melodic skeleton extraction framework. The hierarchical
+skeleton-guided melody generation architecture effectively improves generated melodies’ long-term
+structure and musicality and outperforms other state-of-the-art methods by 0.51 on average on all
+subjective evaluation metrics.
+2
+
+Melodic skeleton
+Melody
+Melody
+Database
+Melodic Skeleton Extraction
+Framework
+Pairing
+B
+Stage 1: melodic skeleton construction
+Stage 2: melody inpainting
+Melodic
+Skeleton
+Database
+Hierarchical structure analysis in music
+(Music domain knowledge)
+Input Module
+(Embedding)
+Positional 
+Encoding
+Transformer-XL
+（4 blocks）
+Output Module
+(Classifier)
+C
+a) Melodic Skeleton Generation Module
+Input
+(Melodic skeleton)
+Representation
+Input Module
+(Embedding)
+Encoder
+（4 blocks）
+Decoder
+（4 blocks）
+Recurrent Transformer
+b) Melodic Prolongation Generation Module
+Representation
+Input Module
+(Embedding)
+Input
+(Melody)
+Representation
+Input
+(Melodic skeleton)
+Output Module
+(Classifier)
+Train
+A
+Melodic Skeleton
+Melody (example)
+Melodic skeleton
+Sequence learning model
+Y1
+Y2
+Yn
+···
+···
+X1
+X2
+Xn
+···
+···
+Partial sequence
+Melodic skeleton
+···
+X1
+X2
+Xn
+···
+Encoder
+Y2
+Y3
+Yn
+···
+Y1
+Y2
+Yn-1
+···
+···
+Decoder
+…
+Predicted tokens
+Predicted tokens
+···
+···
+···
+···
+···
+···
+···
+···
+···
+···
+···
+···
+···
+···
+···
+···
+Sequence-to-sequence
+learning model
+Melody
+Figure 1: Architecture of WuYun. (A) The first eight bars of the melody of “Hey Jude” from The Beatles
+(excluding anacrusis). The upper part of the figure shows the basic shape of the melodic motion, and the low
+part of the figure shows the melodic skeleton in the rhythm dimension. Every melody has an underlying melodic
+skeleton that provides structural support and connections among musical elements to guide the melodic motion.
+(B) Hierarchical melody generation process. WuYun divides the melody generation process into melodic skeleton
+construction and melody inpainting stages following the hierarchical organization principle of structure and
+prolongation. At the melodic skeleton construction stage, the melodic skeleton extraction framework is proposed
+to extract the melodic skeleton in the rhythm and pitch dimensions by the hierarchical structure theory from
+music domain knowledge. A neural network for sequence learning trained on melodic skeletons can generate
+novel ones. At the melody inpainting stage, another neural network for sequence-to-sequence learning would
+fill the generated melodic skeleton into a full-fledged melody. (C) Architecture details of WuYun. WuYun is
+composed of a melodic skeleton generation module and a melodic prolongation generation module; the former
+is used for the melodic skeleton construction stage, and the latter is used for the melody inpainting stage with the
+guidance of the melodic skeleton.
+3
+
+OO4车
+42
+Result
+2.1
+Hierarchical organization principle of structure and prolongation
+Most AI artistic generative models differ significantly from humans in their artistic creation process,
+especially in music generation. For example, a typical music generation model generates music
+content sequentially from left to right at once (40). However, human artworks tend to develop
+iteratively from a basic underlying idea or structure through elaboration, expansion, and individual
+shaping. Human artistic creation follows an age-old fundamental principle of creative thinking,
+namely, structure and prolongation, which has significantly contributed to human thinking and
+creativity. In the art of music, this principle governs the underlying logic in musical composition
+and makes musical reasoning and explanation comprehensible and acceptable (37). It conforms
+to the brain’s cognitive processing mechanism of structurally organizing sequential information
+(41–44), which makes the brain encode and process information more efficiently and improves
+musical memories (45, 46). For example, musicians use this principle, consciously or unconsciously,
+to study, organize, and perform their musical works.
+The hierarchical structure is a key feature of the tonal musical syntax system, where musical elements
+are almost always hierarchically organized by strict rules at a fundamental level rather than unlimited
+creative expression (36). Some researchers have investigated the patterns of structural organization
+and generalized them into music theories regarding the hierarchical structure in music from the
+perspective of the structure and prolongation principle. Schenker (47) was the first to introduce this
+principle to describe the musical structure in a hierarchically organized way. The central idea of
+Schenkerian theory about the hierarchical structure is that some musical events are elaborated by
+other musical events in a recursive and embedded fashion (9, 34). That is, not all musical events
+are equally important. Some musical events have structural importance as stable factors in music,
+whereas others are more decorative as dynamic factors. Therefore, Schenker proposed different
+levels of structure hierarchy to organize tonal music and analyze its motion. Based on Schenker’s
+ideas, the generative theory of tonal music (GTTM), proposed by Lerdahl and Jackendoff (34), is
+one of the most influential theories in current music theory and music psychology. GTTM provides
+a systematic analysis and description of the hierarchical structure in music. Based on the listeners’
+perception of tonal music, GTTM lists four hierarchical structure relationships from rhythm and pitch
+dimensions: grouping structure, metrical structure, time span reduction, and prolongational reduction.
+The term “reduction” refers to the stepwise reduction of less important musical events from the
+musical surface, revealing the underlying framework or skeleton that plays an essential role in the
+music’s qualities and developmental direction. In summary, under the surface of the music, musical
+events are hierarchically organized based on the structural stability in rhythm and pitch dimensions
+(48, 49).
+Inspired by the iterative mode of human composition guided by the principles of structure and
+prolongation, the whole process of melody creation can be seen as progressively filling individual
+decorative notes among the melodic skeleton; it is an effective modern composition technique that
+perfectly combines rules and composers’ personality (35). This composition technique has been
+developed and applied in music teaching for a long history. In the following, we elaborate on the
+melodic skeleton extraction framework from rhythm and pitch dimensions and introduce the design of
+WuYun melody generation architecture that first constructs the melodic skeleton and then completes
+the melody instead of sequentially generating a melody note-by-note at once. The manner of WuYun’s
+melody generation process is more musically meaningful than the dominant end-to-end left-to-right
+note-by-note melody generation paradigm.
+2.2
+Melodic skeleton extraction framework
+Music theories present that there is an underlying identifiable framework beneath the melody surface
+called the melodic skeleton (35, 50). The melodic skeleton is composed of certain notes, which
+sound more structurally important from rhythm and pitch dimensions (34, 48) and are called the
+skeleton notes. The skeleton note attracts the audience’s attention and makes a deeper impression
+on them. By contrast, the remaining part of the notes plays a decorative role, giving the melody
+personalities or styles, and are called the decorative notes or prolongation notes. The melodic skeleton
+serves as the crucial structural support of rhythm and harmony, indicating the direction of melody
+development. Knowledge of melodic skeleton information can help humans and machines better
+4
+
+Figure 2: Melodic skeleton extraction framework. (A) Rhythm pattern of strong and weak beat distribution
+in the 4/4 time signature with different note resolutions. (B) Rhythmic skeleton extraction. The rhythmic
+skeleton consists of the metrical accents, agogic accents on metrical accents, and agogic accents on syncopations
+in each measure. (C) Illustration of the tension measure in the pitch class helix of the spiral array with a C major
+chord. The right part of the figure presents the tension value of the notes in the first eight bars of the melody of
+“Hey Jude.” (D) Tonal skeleton extraction. The tonal skeleton consists of the notes with the minimum tension
+value in the rhythm cell.
+5
+
+A
+ Strong
+4th
+Weak
+Sub.
+Weak
+ Strong
+Strong
+8th
+Weak
+Weak
+Weak
+Strong
+Strong
+Weak
+Weak
+ Strong
+Weak
+ Strong
+Weak
+Weak
+Weak
+Weak
+ Strong
+ Strong
+Weak
+16th
+Weak
+Sub.
+Sub.
+Sub.
+Sub.
+Grid
+1
+2 
+3
+5
+6
+7
+8
+9
+10
+11
+12 
+13
+14
+15
+16
+4
+B
+Original
+Metrical Accent
+Agogic
+Synopation
+Rhythmic skeleton
+c
+1.9
+A#
+D#
+○ Tonal Skeleton Note
+1.8
+ Prolongation Note
+1.7
+G#
+F#
+B
+1.6
+C#
+1.5
+AD
+V
+D
+1.4
+G
+E
+E
+A
+E-
+B-
+C
+1.1
+IV
+F
+G-
+0.9
+G
+A-
+0.8
+D.
+0.7
+12
+14
+24
+26
+28
+30
+32
+40
+0
+16
+20
+22
+38
+Note Sequence
+D
+Rhythm Cell
+Tonal Skeletonanalyze, understand, and learn the logic of melodic hierarchy organization from surface to deep
+layers.
+Here, we introduce a framework for melodic skeleton extraction based on the knowledge of music
+theory (34, 35, 50–53) and music psychology (48, 49) to identify the dominant and subordinate
+relationship of structural importance from rhythm and pitch dimensions between melody notes. The
+theoretical basis and implementation details are described briefly below.
+2.2.1
+Rhythmic skeleton extraction
+Before describing the theoretical basis of this work, we would have to cover some basic musical
+terms and concepts regarding meter and rhythm in the time aspect of music. In music theory, the
+pulse splits time into a series of uniformly spaced chunks called beats. Not all beats are created equal,
+and certain beats are felt stronger than others. The first beat of each measure is a downbeat, and the
+one that follows is an upbeat. The meter measures the number of beats in the regular and repeated
+pattern of the downbeat. For example, the most common meter in music is 4/4; each measure has
+four quarter note beats. The distribution pattern of strong and weak beats is “strong weak sub-strong
+weak,” as shown in Fig. 2A. Rhythm can be defined as the organization pattern of one downbeat with
+one or more upbeat (54). Therefore, the meter provides the temporal framework for organizing music
+rhythm.
+To draw listeners’ attention, musicians often use accents in musical compositions or performances
+to emphasize a particular note. Accents can be expressed in various ways to increase musical
+expressiveness and add character to the movement of music. Metrical and rhythmic accents are the
+two main accents in the symbolic melody data. A metrical accent is an accent that falls on the strong
+beat position within a measure. The metrical accent is periodic and cyclic, whose distribution pattern
+depends on the type of meter. A rhythmic accent is an accent in a strong position within the rhythm,
+which emphasizes a point that is not constrained by the meter’s structure. Consequently, it is flexible
+and changeable rather than static and fixed. Rhythmic accents can be created by increasing the notes’
+dynamic (i.e., dynamic accent), extending the notes’ duration (agogic accent), using syncopation,
+and so forth. The agogic accent can be easily distinguished by comparing the surrounding notes on
+duration. Additionally, the musician can use syncopation to change the normal rhythm pattern by
+extending the duration of notes from the weak beat or weak beat part to the subsequent strong beat
+or strong beat part. Note that a note cannot be both a metrical accent and a syncopation, which are
+conflicted with each other. The dynamic accent is not used since it has no obvious changes in most
+symbolic melody data.
+In this study, we extract the metrical accents, the agogic accents falling on the metrical accent, and
+the agogic accents falling on the syncopation as the rhythmic skeleton notes, as illustrated in Fig.
+2B. Metrical accents are the foundation of other types of accent (34). When two or more different
+types of accents work together, the listener will experience a particularly more prominent accent.
+Therefore, when a rhythmic accent and a metrical accent overlap, the rhythmic accent is generally
+more perceptible and is the one that is preferred. If there were continuous rhythmic skeleton notes,
+we chose the most structurally important note as the rhythmic skeleton note according to the intensity
+of the accent.
+2.2.2
+Tonal skeleton extraction
+In tonal music, the pitch of the melody moves around a centrally stable note (i.e., the tonal center or
+tonic), repeatedly moving away from it and back to it. Pitches are essentially organized into a distinct
+hierarchy scale based on tonal stability. There is a mutual attraction between pitches with different
+stable levels, which can stimulate different emotional experiences (47). Specifically, an unstable
+pitch tends to be a stable pitch, which would make the listeners feel relaxed or dismissed. Moving
+from a stable to an unstable pitch would increase the listener’s sense of tension. The prolongational
+reduction theory of GTTM suggests that the more important music event has less tension and vice
+versa (53). Note that the same tone may have different feelings in different contexts, which may be
+pleasant or anxious.
+For the tonal skeleton extraction method, we use the tension level as a metric to quantify the relative
+importance of the pitch. The specific recognition procedure is as follows.
+6
+
+• First, we used the position of the rhythmic skeleton notes as the boundary of the individual
+context because the metrical structure is the important basis of all hierarchical structure
+types (34).
+• Second, we combined two or three successive notes as the minimum rhythmic cell in each
+segment, according to the repetition frequency in the melody (55) and the number of notes
+of this rhythmic cell. The term “rhythmic cell” defines as a “small rhythmic and melodic
+design that can be isolated or can make up one part of a thematic context” (56). Therefore,
+each rhythmic cell can be seen as an isolated thematic context for calculating the tension
+profile.
+• Finally, we adopted a mathematical tonal tension model to quantify each note’s tension
+value by calculating the distance between every single tone and global key in the spiral array
+(57–59), as shown in Fig. 2C. We selected the note with the minimum tension value in each
+rhythmic cell as the tonal skeleton note. For example, Fig. 2D shows the tonal skeleton of
+the first eight bars from the song “Hey Jude.”
+2.3
+Design of WuYun
+Figure 1C shows the diagram of the proposed hierarchical melody generation architecture called
+WuYun. First, we convert the melody MIDI files and their melodic skeletons into musical event
+sequences as the input data for model training using the MeMIDI symbolic music representation
+method. Then, we design a hierarchical melody generation architecture with two generative modules
+responsible for melodic skeleton construction and melody inpainting, respectively. In this subsection,
+we will introduce the hierarchical melody generation architecture about how we generate the melodic
+skeleton and incorporate it to guide the melody generation process. The details about the MeMIDI
+symbolic music representation method and the word embedding technique used in this architecture’s
+input module are described in the Materials and Methods section.
+WuYun is designed to generate melodies in two stages hierarchically: melodic skeleton construc-
+tion and melody inpainting, instead of the dominant end-to-end left-to-right note-by-note melody
+generation paradigm. At the stage of melodic skeleton construction, we use the Transformer-XL
+model with only the decoder as the melodic skeleton generation module (19), which has the ad-
+vantage of remarkable performance in capturing long-term dependence. To develop the capacity
+of melodic skeleton construction, we trained the Transformer-XL model on the extracted melodic
+skeleton database. At the stage of melody inpainting, we employ the recurrent Transformer-based
+encoder–decoder architecture (18) in a sequence-to-sequence setup as the melody inpainting module
+to complete the melody conditioned on the melodic skeleton, i.e., filling the missing information
+between the melodic skeleton notes. In this work, the melody inpainting problem can be defined as
+follows: given a melodic skeleton sequence Cs, generate an inpainted melody sequence Cm. The
+encoder maps the discrete input symbols of the melodic skeleton sequence Cs to a high-dimensional
+continuous vector as conditional input into the decoder, and the decoder then generates an output
+sequence Cm in an autoregressive manner. The melodic skeleton sequence will be saved in the final
+generated melody. This method provides users an entry point to interact with the melody generation
+model by adjusting melodic skeleton notes between two stages to control the melodic motion.
+In this work, we focus on designing a hierarchical skeleton-guided melody generation architecture
+based on knowledge-enhanced deep learning, following the hierarchical organization principle of
+structure and prolongation. Therefore, we used common language models in NLP to make the WuYun
+architecture accessible. The capacity of these two generative modules may be further optimized;
+however, the goal of this study is not to find the most optimal neural network.
+2.4
+Evaluation metrics
+Subjective and objective evaluations are the two essential aspects of evaluating the performance of
+music generation systems. The human listening test is currently an indispensable and viable method
+for subjective evaluation to measure the quality of the generated musical pieces. However, for the
+objective evaluation, many efforts have been made to design quantitative metrics; there is not a set of
+convincing and unified metrics. Although the research field of music generation is multidisciplinary,
+most researchers mainly focus on generative models with different improvement goals rather than
+their contribution to quantifying music complexity. Consequently, almost all the proposed objective
+7
+
+evaluation metrics are difficult to apply for comparing different music creation systems and lack
+sustainability for future development demands. We tried to calculate the averaging overlapped area
+of some musical feature distributions between generated musical pieces and ground-truth musical
+pieces as the objective evaluation metrics like (18, 60) using the public evaluation toolbox. We
+arrived at a similar conclusion as PopMNet (32) that a better result of objective evaluation does not
+mean better structure and musicality of generated music. The same objective evaluation result can be
+calculated and verified with the provided melody MIDI files of this study’s next two experiments.
+Therefore, we conducted two subjective evaluation experiments to evaluate the performance of our
+proposed WuYun, including different melodic skeleton settings in rhythm and pitch dimensions and
+comparisons with public state-of-the-art (SOTA) music generation models.
+We randomly selected ten melodies from the evaluation dataset for the listening materials. Similar to
+previous studies (15, 17, 19), we took the first four bars as prompt and set the maximum number of
+generated bars to 28. We assigned a random order for all musical pieces as the file name, including
+the generated and ground-truth musical pieces. All melody MIDI files were rendered into audio via a
+piano MIDI synthesizer. In the blind listening test, participants were asked to rate each melody on a
+five-point Likert scale (i.e., 1 for bad and 5 for excellent) on five dimensions:
+• Rhythm: Whether the brain can feel the regular accents and rhythm patterns.
+• Richness: Whether the melody sounds rich and interesting in the rhythm and pitch dimen-
+sions.
+• Structure: Whether the brain can feel the boundary of melodic phrases and the balance
+among melodic phrases’ length.
+• Expectation: Whether the direction of melody development meets the audience’s expecta-
+tions for melody development (61).
+• Overall: Overall quality.
+We found that most nonmusicians had heard technical music terms but did not understand what
+they meant. Therefore, before formal experiments, we conducted multiple rounds of discussions,
+testing, and validation with musicians and nonmusicians regarding the above subjective evaluation
+metrics and their descriptions until they could easily understand and grasp them. To ensure that
+the recruited subjects have a common understanding of the metrics and scales in the questionnaire,
+we also conducted evaluation training for them, including the explanation of subjective evaluation
+metrics and preliminary experiments. All audio and MIDI files for evaluation can be found in
+Acknowledgments.
+2.5
+Model performance based on different melodic skeleton settings
+To compare the effectiveness of variants of melodic skeleton extracted from rhythm and pitch
+dimensions, we comprehensively evaluated the performance of WuYun based on different settings of
+the melodic skeleton. Furthermore, we added three control group settings of randomly selected notes
+with different percentages as the melodic skeleton in order to verify the effectiveness of the proposed
+melodic skeleton extraction method based on music domain knowledge. All experimental settings
+and the proportion of melodic skeleton notes in the melody are described below:
+1. Downbeat only uses metrical accents as the melodic skeleton (32.8%).
+2. Long Note only uses agogic accents as the melodic skeleton (27.4%).
+3. Rhythm uses rhythmic skeleton notes as the melodic skeleton (33.8%).
+4. Tonic uses tonal skeleton notes as the melodic skeleton (43.2%).
+5. Interaction uses the intersection of rhythmic skeleton notes and tonal skeleton notes as the
+melodic skeleton (14.2%).
+6. Union uses the union of rhythmic skeleton notes and tonal skeleton notes as the melodic
+skeleton (62.8%).
+7. Random25% randomly selects 25% of melody notes as the melodic skeleton (25%).
+8. Random50% randomly selects 50% of melody notes as the melodic skeleton (50%).
+9. Random75% randomly selects 75% of melody notes as the melodic skeleton (75%).
+8
+
+In this experiment, we obtained 90 musical pieces for rating. We recruited 30 subjects (13 females
+and 17 males, ages 18 and 30 years) from Zhejiang University and Zhejiang Conservatory of Music
+to evaluate the musical pieces with payment. Fifteen subjects among them were professional music
+practitioners with an average of 9 years of music training and 4 years of music performance experience.
+The rest of the subjects have little professional music training or performance experience. Each
+musical piece was assigned to three professionals and three nonprofessional subjects. Each subject
+was required to rate 18 musical pieces, which cost approximately 25 min.
+Figure 3A shows the mean opinion scores of WuYun architecture’s melody generation performances
+with nine different settings on the five subjective evaluation metrics from all subjects in the form of
+histograms. The detailed experimental result is shown in Table S1. Generally, among all melodic
+skeleton settings, the proposed rhythmic and tonal skeleton based on music theory and psychological
+study performs better than other skeletons. The rhythmic skeleton setting (No. 3) achieved the best
+result on all subjective evaluation metrics, followed by the tonal skeleton setting (No. 4). Among
+the three types of melodic skeletons associated with rhythm (Nos. 1, 2, and 3), the melodic skeleton
+composed of a single type of accent (e.g., metrical accents or agogic accents (31)) has a large gap with
+the rhythmic skeleton in richness, expectation, and overall quality and even surpassed by the random
+melodic skeletons (Nos. 7, 8, and 9) on most subjective evaluation metrics. This result indicates that
+a flexible rhythmic skeleton (i.e., including several kinds of musical accents) is essential for melody
+composition to improve musicality. In contrast, a rigid melodic skeleton (i.e., including only one type
+of accent, especially metrical accents) reduces the quality of the generated melody and limits the
+models’ performance. Likewise, as depicted in the right part of Fig. 2C, the pitch classes of the tonal
+skeleton notes are mostly C, D, and E, which also lead to the rigidity of the generated tonal skeletons.
+Additionally, compared to the rhythmic and tonal skeleton settings, the intersection (No.5) and union
+(No. 6) skeleton settings led to a distinct degradation of the melody generation performance. For
+instance, the intersection (No. 5) skeleton setting received the worst scores in most evaluation aspects,
+even worse than the random sampling skeleton settings. This phenomenon can be explained by
+the structure and prolongation proportion tradeoffs in the design of two-stage melody generation
+architecture using an end-to-end learning framework. We can preliminarily see that with the increased
+percentage of melodic skeleton notes, the performance of the two-stage melody generation went up
+first but then down. On the one hand, a low proportion of melodic skeleton notes makes it easier
+to train the melodic skeleton construction model in the first stage. However, the generated skeleton
+notes will be too sparse to guide the second stage of melodic inpainting (such as the intersection
+skeleton setting, only 14.2%). On the other hand, if the proportion of melodic skeleton notes is too
+large, the training difficulty and data dependency of the melodic skeleton construction model will
+increase. Besides, from the perspective of the gestalt theory (62) about the law of the figure–ground
+relationship, during the perception of music, a person’s attention constantly switches between different
+musical elements; sometimes, he/she may be attracted to the rhythm, whereas at other times, to
+the pitch. Therefore, the extraction of the hierarchical dependency structural relationship between
+musical elements is affected by multiple musical dimensions; it will not be like a simple addition or
+subtraction operation but a complex organic combination (63).
+In this study, we chose the setting of the rhythmic skeleton (No. 3) that performed best on all
+subjective evaluation metrics in this experiment as the default skeleton configuration (denoted as
+WuYun-RS) for the next experiment to compare with other melody generation models.
+2.6
+Comparisons with other melody generation methods
+To prove the effectiveness of the proposed hierarchical skeleton-guided melody generation architecture
+based on knowledge-enhanced deep learning, we compared WuYun-RS (i.e., using the rhythmic
+skeleton setting) to five public SOTA Transformer-based melody generation models, namely, Music
+Transformer (15), Pop Music Transformer (17), Compound Word Transformer (19), Melons (33)
+and MeMIDI, that follow an end-to-end left-to-right note-by-note generative paradigm and treat
+each note equally. The MeMIDI setting uses the MeMIDI data representation method like WuYun-
+RS and employs the Transformer-XL model without using the melodic skeleton for the melody
+generation task. Moreover, to prove the effectiveness of the generated melodic skeleton, we added
+the setting of WuYun-RRS, skipped the melodic skeleton construction in the first stage, and directly
+used the real rhythmic skeleton as additional knowledge to guide the melody generation process
+of melody inpainting in the second stage. However, the original music representation of Music
+9
+
+Figure 3: Subjective evaluation results of the WuYun melody generation architecture based on different
+melodic skeleton settings, and the other public melody generation models. (A) Subjective comparison of the
+performance of the WuYun architecture based on different melodic skeleton settings in Experiment 1. Data is the
+mean opinion score. The WuYun architecture with the rhythmic skeleton setting achieves the best performance in
+all melodic skeleton settings on all subjective evaluation metrics. (B) Subjective comparison of the performance
+of different music generation models in Experiment 2. Violin plots show the kernel density estimate of rating
+distribution, the larger the area of the area graph, the greater the probability of the value distribution. The
+black dot within the violin plots indicates the mean; the black line within the violin plot indicates the standard
+deviation. Statistical analyses are done between WuYun-RS and the rest of the models using the one-tailed
+t-test (N = 130). P values of statistical significance are represented as *P < 0.05, **P < 0.01, ***P < 0.001,
+and ****P < 0.0001; ns, insignificant. The subjective comparison results’ data are in Tables S1, 1, and S2,
+respectively.
+Transformer does not include chord progressions. For a fair comparison, we added the CHORD
+events proposed in this work into the MIDI-Like music representation of Music Transformer. Each
+CHORD event was followed by a TIME-SHIFT event and had a higher sorting priority than NOTE-
+related events. Additionally, the MIDI quantization level of the Pop MusicTransformer, Compound
+Word Transformer, and Melons only considered the 16th note time grid. Therefore, in this experiment,
+we applied the 16th note time grid as the MIDI quantization level to the melody dataset for all music
+generation models.
+In this experiment, we obtained 80 musical pieces for rating. Since the second subjective evaluation
+experiment relies on the result of the first subjective evaluation experiment and requires some time to
+collect, process, and analyze, we recruited 13 participants again (i.e., six females and seven males,
+ages 18 and 25 years) to evaluate the musical pieces with payment. Six subjects among them were
+professional music practitioners with an average of 8 years of music training and 4 years of music
+performance experience. Each subject was required to rate all musical pieces. After rating 20 musical
+pieces, subjects were asked to rest for 5 min against hearing fatigue. The average experiment time
+cost each subject about 2 h.
+Figure 3B shows the mean opinion scores and one-tailed t-test results of the different music generation
+systems on the five evaluation metrics in the form of violin plots. The detailed experimental results are
+shown in Tables 1 and S2. Overall, WuYun-RS (No. 6) and WuYun-RRS (No. 7) outperformed the
+other five current SOTA end-to-end left-to-right note-by-note melody generation models on all metrics,
+including MusicTransformer (No. 1), Pop Music Transformer (No. 2), Compound Word Transformer
+(No. 4), Melons (No. 5), and MeMIDI (No. 3). Besides, except for WuYun-RRS, there is a significant
+10
+
+A
+3.25
+ Downbeat  Long Note
+ Rhythm  Tonic Intersection
+ Union  Random25%  Random50%
+■ Random75%
+Mean opinion score (MoS)
+3.00
+2.75
+2.50
+2.25
+2.00
+Rhythm
+Richness
+Structure
+Expectation
+Overall
+Subjective Evaluation Metrics
+B
+Music Transformer
+ Pop Music Transformer
+MeMIDI
+ Compound Word Transformer
+■ Melons
+-WuYun-Rs
+WuYun-RRS
+Mean opinion score(MOS)
+****
+****
+****
+****
+****
+****
+****
+**
+***
+**
+ns
+ns 
+ns
+ns
+5
+3 -
+Richness
+Structure
+Rhythm
+Expectation
+Overall
+Subjective Evaluation MetricsTable 1: Subjective evaluation scores of generated melodies based on different melody generation models in
+Experiment 2 (mean ± standard deviation).
+No.
+Model
+Rhythm
+Richness
+Structure
+Expectation
+Overall
+1
+MT
+2.52 ± 0.93
+2.34 ± 0.83
+2.28 ± 0.86
+2.47 ± 1.01
+2.25 ± 0.88
+2
+PMT
+2.57 ± 0.88
+2.43 ± 0.99
+2.54 ± 1.11
+2.50 ± 1.16
+2.39 ± 1.12
+3
+MeMIDI
+2.61 ± 0.91
+2.55 ± 0.95
+2.53 ± 1.00
+2.51 ± 0.97
+2.42 ± 0.96
+4
+CWT
+2.77 ± 0.83
+2.72 ± 0.85
+2.74 ± 0.81
+2.70 ± 0.83
+2.65 ± 0.90
+5
+Melons
+2.84 ± 0.89
+2.68 ± 0.95
+2.75 ± 0.87
+2.67 ± 0.87
+2.71 ± 0.88
+6
+WuYun-RS
+3.13 ± 0.88
+3.07 ± 0.87
+3.13 ± 0.86
+3.02 ± 0.92
+3.00 ± 0.87
+7
+WuYun-RRS
+3.20 ± 0.81
+3.11 ± 0.85
+3.15 ± 0.88
+3.00 ± 0.96
+3.02 ± 0.88
+8
+Human
+3.54 ± 0.82
+3.65 ± 0.76
+3.68 ± 0.89
+3.55 ± 0.92
+3.57 ± 0.84
+MT, PMT, and CWT stand for Music Transformer, Pop Music Transformer, and Compound Word Trans-
+former, respectively.
+difference (P < 0.01) between WuYun-RS and the other melody generation systems. This result
+demonstrates that WuYun-RS and WuYun-RRS are able to generate melodies with improved long-
+term structure and musicality, which benefit from the rhythmic skeleton as a deep structure to guide
+the melody generation process. Furthermore, WuYun-RS and WuYun-RRS demonstrate highly similar
+performances in terms of the quality of generated melodies on all evaluation metrics. This result
+indicates the effectiveness of the melodic skeletons generated via the melodic skeleton construction
+module. However, there is still an obvious gap between the WuYun melody generation architecture
+and human-composed music, leaving room for improvement. This also shows that designing clever
+decorations for melodic skeletons is another difficult research problem, even for human composers.
+Additionally, when using the same symbolic music representation method, the knowledge-enhanced
+hierarchical skeleton-guided melody generation model of WuYun-RS greatly outperformed the single-
+stage end-to-end left-to-right note-by-note melody generation model of MeMIDI (No. 3). On the one
+hand, this demonstrates that our proposed hierarchical melody generation paradigm can be applied to
+empower the dominant end-to-end left-to-right note-by-note melody generation paradigm. On the
+other hand, although the Compound Word Transformer and Melons (Nos. 4 and 5) were inferior to
+WuYun-RS, their effective compound word representation and the linear Transformer as the backbone
+architecture enable it to process multidimensional music information in one step simultaneously and
+obtain a better result among these five public SOTA melody generation models. Thus, combining the
+proposed knowledge-enhanced hierarchical skeleton-guided music generation architecture with more
+efficient music representation methods and advanced language models can bring a better result for
+melody generation tasks.
+3
+Discussion
+The methodology we have taken in designing WuYun, a hierarchical skeleton-guided melody genera-
+tion architecture based on knowledge-enhanced deep learning, combines music analysis theory and
+musical psychology. Unlike the dominant end-to-end left-to-right note-by-note melody generation
+paradigm, we use the hierarchical organization principle of structure and prolongation to decompose
+the melody generation process into melodic skeleton construction and melody inpainting stages. We
+extract the most structurally important notes based on hearing sensitivity as melodic skeletons and
+incorporate them into the melody generation process as a deep structure to guide the model to learn
+the hierarchical dependency structures among musical event sequences from the limited melody data
+without music boundary detection (31). The human evaluation results demonstrated that our model
+exhibits significant improvement in both long-term structure and musicality across the structured
+melody generation task.
+In practical application scenarios, the ability to obtain real feedback from human users for improving
+the performance and interaction experience of the system is essential for the next generation of
+iterative and interactive music generation systems. In general, WuYun allows human users to edit the
+generated melodic skeleton and adjust its shape to guide and constrain the range of the decorative
+notes at the next stage of melody inpainting. Thus, the proposed generation strategy based on the
+11
+
+hierarchical organization principle of structure and prolongation not only can maintain the long-range
+tonal coherence of generated melodies but also achieve control over the target of melodic motion by
+human users. Additionally, with WuYun and its melodic skeleton analysis framework, human users
+can directly extract the skeleton from existing music compositions for music composition analysis or
+re-creation.
+Our study has some limitations, notably the performance of the melody inpainting model, except
+that the quality of generated melodic skeleton may be poor; even if an original rhythmic skeleton
+is provided, the quality of the completed melody is still far from the real one. Further performance
+improvements could be achieved using pretrained masked language models (23) for music generation,
+especially for the melody inpainting task. Another issue is how to effectively extract an organic
+melodic skeleton from hierarchical musical structures combining two or more musical dimensions
+(e.g., rhythm and pitch) to further improve the structure of generated melodies. According to the
+research in the cognitive psychology in music, while listening to music, only by combining the tonal
+and rhythmic structures can we form a more coherent musical representation and create a complete
+sense of melody (34, 48, 49). However, the brain’s processing mechanism of the hierarchical musical
+structure remains a fundamental research problem in the field of music cognitive psychology (64–66).
+With the help of advanced electroencephalography devices, cognitive musicology can break through
+the human cognition of hierarchical musical structure and apply it to music generation. Additionally,
+we expect to investigate other systematic music analysis theories and gain further psychological
+knowledge to analyze and compare the hierarchical levels of important musical events along different
+musical dimensions for designing a more effective melodic skeleton extraction framework. Another
+direction is to explore explainable AI for music generation to assist end users in making better
+decisions since deep learning methods lack physical transparency of methods. With these potential
+future improvements in mind, we hope that our findings for structured melody generation will optimize
+the dominant melody generation paradigms to improve long-term structure and musicality and provide
+a new lens to develop multidisciplinary research via combining data-driven and knowledge-based
+approaches.
+4
+Materials and Methods
+4.1
+Details of dataset preprocessing
+We evaluate the effectiveness of WuYun architecture on a commonly used and publicly available
+symbolic melody dataset of Wikifonia (32, 33, 67). The Wikifonia dataset contains thousands of
+lead sheets in MusicXML format. It covers various music genres, composed of melody and the
+accompanying chord progression and tonality labels. Here, we describe the procedure below to clean
+up noisy data and artificial errors since the dataset is user-generated.
+• Data Segmentation: To simplify rhythm modeling, we only keep those segments from
+MIDI files with the most commonly used 4/4 time signature (18).
+• MIDI Quantization: For a more beat-accurate timing of sounds, quantization is a useful
+digital music processing of setting MIDI data on beats or exact fractions of beats to eliminate
+some imprecise timing because of expressive musical performance or mistake record. We
+contend that a more precise and adaptable time grid is required to model a more expressive
+metrical context, including the 32nd (18), 64th note, and even triplets. By contrast, most
+prior works only use the 16-note time grid for quantification (17, 19, 31–33); each bar
+is quantized into 16 intervals. In this study, we propose a self-adaptive mixed precision
+quantization method to reduce quantization errors (Fig. 4). This method can automatically
+choose a suitable quantize grid for every single note based on its duration, including straight
+notes and triplets. The difference between straight notes and triplets is dividing the musical
+beat evenly in half or third. First, the notes shorter than a 64th note are discarded, whereas
+notes longer than one bar are saved into the whole note. Second, according to the note
+duration, the rest notes are classified into straight or triplets. However, triplets do not always
+have to have three notes. There are only two notes in triplets is quite common, such as in
+Swing. Additionally, in theory, every note in triplets has an equal rhythm value. However, in
+practice, most notes are slightly different from each other in musical performance. Therefore,
+two or three consecutive notes with approximately the same duration and consistent with
+the duration of triplets are considered as triplets. Based on our experimental statistical
+12
+
+A
+1
+2
+4
+8
+16
+1
+2
+4
+8
+16
+2
+4
+8
+16
+2
+4
+8
+16
+1
+2
+4
+8
+16
+2
+4
+8
+16
+1
+2
+4
+8
+16
+4
+8
+16
+4
+8
+16
+4
+8
+16
+4
+8
+16
+4
+8
+16
+4
+8
+16
+4
+8
+16
+16
+16 16 16
+8
+16 16 16
+8
+16 16 16
+8
+16 16 16
+8
+16
+16
+8
+16 16 16
+8
+16 16 16
+8
+16 16 16
+8
+16
+16 16
+8
+16 16 16
+8
+16 16 16
+8
+16 16 16
+8
+16 16 16
+8
+16
+4
+4
+4
+4
+Basic Note
+Quantization Error
+Shift Backward
+Shift Forward
+Selected Grids
+Standard Grids
+Standard Duration
+Triplet Grids
+Time Signature
+Triplet
+Time 
+Grid
+4
+Whole Note
+16
+16
+16
+16
+8
+16
+16
+16
+8
+8
+8
+16
+8
+16
+16
+16
+16
+32
+64
+Triplet
+Triplet
+16
+16
+16
+8
+16
+16
+16
+64
+Triplet
+Triplet
+Shorter than 64th Note
+16
+16
+16
+16
+32
+8
+8
+16
+4
+16
+8
+8
+Longer than a whole note
+16
+❌
+Figure 4: Illustration of the self-adaptive mixed precision MIDI quantization. The MIDI quantization
+method would automatically choose a suitable quantize grid for every note according to its note length to
+eliminate imprecise timing, including straight notes (minimum 64th note) and triplets (minimum 48th note).
+results, we set the acceptable duration error ratio between the actual triplet and the standard
+triplet to within 20%. Last, the method automatically selects a proper quantize grid for
+every note. In terms of straight notes, the granularity of the time grid depends on the note
+duration. Particularly, the note onset is aligned to its closest 16th note time grid when the
+note duration is greater than or equal to a 16th note, to its closest 32nd note time grid when
+the note duration is between a 16nd and 32th note, and to its closest 64th note time grid
+when the note duration is between a 32nd and 64th note. Moreover, the straight note offset
+is aligned to the 64th note time grid. In terms of triplets, the note onset and offset time is
+aligned to the 48th note time grid.
+• Tonality Unification: For simplicity, the tonalities and chord progressions of those MIDI
+files are transposed to “C major” and “A minor” tonalities (68). We set one chord per beat
+and unify the chord representation of the Wikifonia dataset using the chord dictionary as
+described in the following subsection.
+• Octave Transposition: All melodies are applied octave transposition to shift the pitch into
+the range from C3 to C5 or are removed, which are out of the regular melodic pitch range
+(32).
+After data cleaning, we get 2,921 musical pieces in Wikifonia, including 116,935 bars and 425,223
+notes. Finally, randomly hold out 50 songs for testing and use the remaining for training.
+4.2
+Symbolic melody representation
+In this work, we adopted a modified version of the “MuMIDI” symbolic music representation (18)
+to encode a piece of monophonic melody into discrete musical event sequences. We refer to it as
+MeMIDI. Following is a description of the MeMIDI extensive symbols information, which includes
+bar, position, note, chord, and tempo symbols.
+• Bar and Position
+We use a bar symbol to represent a bar line and a position symbol to represent the onset
+of a note or a chord event. Since the minimum time grids of the straight and triplet note
+are 64th and 48th notes, respectively, and the MIDI files’ time resolution is 480 ticks per
+beat; thus we merge these two kinds of minimum time grids values ({0, 30, 60, ..., 1890} ∪
+{0, 40, 80, ..., 1880}) and use the <Pos_Value> symbol to represent 96 kinds of starting
+positions, such as <Pos_30>. We assign a position symbol for every chord and note music
+event.
+13
+
+Table 2: List of chord events.
+Chord
+Content
+Chord root
+C, Db, D, Eb, E, F, F#, G, Ab, A, Bb, B
+Triad
+M, m, o, +
+Seventh chord
+MM7, Mm7, mM7, mm7, o7, %7, +7, +M7
+Chord quality
+Suspension
+Sus.
+• Note
+A note has three basic attributes: pitch, duration, and velocity. Here, the value of the note
+pitch attribute ranges from 48 (C3) to 83 (C5). The value of the note velocity attribute
+ranges from 0 to 127. Considering both straight notes and triplet notes, the value range of
+the note duration attribute is {30, 60, 90, ..., 1920} ∪ {40, 80, 160, 320, 640} ticks. We use
+a compound word <Pitch_Value, Velocity_Value, Duration_Value> to compress these three
+attributes of one note in one token to shorten the length of the melody events sequence.
+• Chord
+To cover the chord types in the Wikifonia dataset, we use a more comprehensive chord
+event list. As shown in Table 2, we consider 12 chord roots and 13 chord qualities, yielding
+156 possible chord events. We use a chord symbol <Root_Quality> to represent a chord
+musical event. To reduce repetition, we use the same position symbol for Note and Chord,
+which start at the same time. For simplicity, we do not use the Chord symbol in the melodic
+skeleton event sequence.
+• Tempo
+We divide the tempo into three categories: low (below 90), medium (90 to 160), and high
+(above 160).
+4.3
+WuYun architecture
+Here, we briefly elaborate on the configuration details of the two Transformer-based generative
+modules of WuYun architecture, i.e., the melodic skeleton generation module for the melodic skeleton
+construction stage and the melodic prolongation generation module for the melody inpainting stage.
+We refer readers to (17–19) for more details. For reproducibility, we do not tweak the architecture of
+referenced models so that our music generation architecture can be easily assembled with the public
+implementation of Transformers.
+We use an unconditional sequence learning model Transformer-XL for the melodic skeleton genera-
+tion module. We use four self-attention layers, each with eight attention heads. The model hidden
+size and the inner layer of the feed-forward part are set to 512 and 2,048, respectively. All token
+embedding sizes are set to 512, following (19). We use the compound word embedding (Fig. S1) and
+token attribute prediction method for the input and output modules, repectively (18). We employed
+the top-k temperature-controlled stochastic sampling method (k = 10, temperature = 0.9) during
+inference. The length of training input tokens and the memory length are also 512. Here, we used the
+melodic skeleton data extracted from the training part of the Wikifonia dataset to train the melodic
+skeleton generation module.
+We use a conditional sequence-to-sequence model based on Transformer-based recurrent en-
+coder–decoder neural networks for the melodic prolongation generation module (18). We set the
+number of encoder layers, decoder layers, encoder heads, and decoder heads to 4. The size of hidden
+layers and the dimension of token embeddings are set to 256. We keep the same input module, output
+module, sampling method, length of training input tokens, and memory as same as the melodic
+skeleton generation module. For training the melodic prolongation generation module, we use the
+MeMIDI representations of the paired melodic skeleton and melody data as the encoder and decoder
+input data, respectively.
+14
+
+4.4
+Training
+We implemented the WuYun architecture with Pytorch (v1.7.1) (69). The parameters of the WuYun
+architecture were optimized by minimizing the cross-entropy loss on a single NVIDIA GTX 2080-Ti
+GPU with 11 GB memory. Specifically, the training loss was minimized with the Adam optimizer
+(β1 = 0.9, β2 = 0.98), a learning rate of ε = 10−3 , and dropout was applied with a ratio of 0.1.
+The mini-batches of the input data for the melodic skeleton generation module and the melodic
+prolongation generation module were 20 and 44, respectively. It took nearly 2 days to train the two
+modules until training convergence.
+4.5
+Statistical analysis
+All subjective evaluation results were expressed as mean ± standard deviation. The statistical
+significance of the performance difference in WuYun-RS and other melody generation methods
+was analyzed using the one-tailed t-test. Asterisk indicates significant difference at *P < 0.05,
+**P < 0.01, ***P < 0.001, ****P < 0.0001, and ns, not significant.
+Acknowledgements
+Thanks to Huawei Technologies Co., Ltd for the help in dataset collection and comments. We
+thank Jiaxing Yu, Chongjun Zhong, Ruiyuan Tang, and Jiaqi Wang for insightful discussions and
+visualizations.
+Funding:
+This work is supported by the National Natural Science Foundation of China
+(No.62272409), the Key R&D Program of Zhejiang Province (No.2022C03126), the Project of
+Key Laboratory of Intelligent Processing Technology for Digital Music (Zhejiang Conservatory of
+Music), and the Ministry of Culture and Tourism (No.2022DMKLB001).
+Author contributions: Conceptualization: K.Z., L.S. Methodology: X.W., T.Z., Z.H., K.Z. Investi-
+gation: T.Z., Z.H., Q.L. Visualization: S.W., Q.L. Supervision: L.S., K.Z., X.T. Writing—original
+draft: X.W., K.Z., Q.L. Writing—review & editing: K.Z., X.T., X.W., L.S.
+Competing interests: K.Z., X.W., and T.Z. are inventors on a patent application related to this work
+filed by Zhejiang University. The authors declare that they have no other competing interests.
+Data and materials availability: All data needed to evaluate the conclusions in the paper are present
+in the paper and/or the Supplementary Materials. Raw experimental data and the generated symbolic
+melody files are available on Zenodo at DOI 10.5281/zenodo.7480957
+under a Creative Commons Attribution 4.0 International license. The code of the WuYun music
+generation framework is available at https://github.com/NEXTLab-ZJU/wuyun.
+References
+[1] F. Carnovalini, A. Rodà, Computational creativity and music generation systems: An introduction to the state
+of the art. Front. Artif. Intell. Appl. 3, 14 (2020).
+[2] Y. LeCun, Y. Bengio, G. Hinton, Deep learning. Nature 521, 436–444 (2015).
+[3] J. Briot, G. Hadjeres, F. Pachet, Deep Learning Techniques for Music Generation (Springer, 2020).
+[4] E. Frid, C. Gomes, Z. Jin, Music creation by example, in Proceedings of the 2020 CHI conference on human
+factors in computing systems (CHI, 2020), pp. 1–13.
+[5] C. Yu, Z. Qin, F. J. Martín-Martínez, M. Buehler, A Self-Consistent Sonification Method to Translate Amino
+Acid Sequences into Musical Compositions and Application in Protein Design Using Artificial Intelligence. ACS
+Nano 13, 7471–7482 (2019).
+[6] S. Di, Z. Jiang, S. Liu, Z. Wang, L. Zhu, Z. He, Z. He, H. Liu, S. Yan, Video background music generation
+with controllable music transformer, in Proceedings of the 29th ACM International Conference on Multimedia
+(MM, 2021), pp. 2037–2045.
+[7] L.W. Wesseldijk, M. A. Mosing, F. Ullén,. Why Is an Early Start of Training Related to Musical Skills in
+Adulthood? A Genetically Informative Study. Psychol. Sci. 32, 3–13 (2020).
+15
+
+[8] W. Zhou, C. Ye, H. Wang, Y. Mao, W. Zhang, A. Liu, C. Yang, T. Li, L. Hayashi, W. Zhao, L. Chen, Y. Liu,
+W. Tao, Z. Zhang, Sound induces analgesia through corticothalamic circuits. Science 377, 198–204 (2022).
+[9] S. Koelsch, M. A. Rohrmeier, R. A. Torrecuso, S. Jentschke, Processing of hierarchical syntactic structure in
+music. Proc. Natl. Acad. Sci. 110, 15443–15448 (2013).
+[10] A. D. Patel, Language, music, syntax and the brain. Nat. Neurosci. 6, 674–681 (2003).
+[11] J. M. J. Valanarasu, P. Oza, I. Hacihaliloglu, V. M. Patel, Medical Transformer: Gated Axial-Attention for
+Medical Image Segmentation, in International Conference on Medical Image Computing and Computer-Assisted
+Intervention (Cham, 2021), pp. 36–46.
+[12] N. Li, S. Liu, Y. Liu, S. Zhao, M. Liu, M. T. Zhou, Neural speech synthesis with transformer network, in
+Proceedings of the AAAI Conference on Artificial Intelligence (AAAI, 2019), pp. 6706–6713.
+[13] P. Schwaller, B. Hoover, J. L. Reymond, H. Strobelt, T. Laino, Extraction of organic chemistry grammar
+from unsupervised learning of chemical reactions. Sci. Adv. 7, eabe4166 (2021).
+[14] J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, A.
+Žídek, A. Potapenko, A. Bridgland, C. Meyer, S. A. A. Kohl, A. J. Ballard, A. Cowie, B. Romera-Paredes, S.
+Nikolov, R. Jain, J. Adler, T. Back, S. Petersen, D. Reiman, E. Clancy, M. Zielinski, M. Steinegger, M. Pacholska,
+T. Berghammer, S. Bodenstein, D. Silver, O. Vinyals, A. W. Senior, K. Kavukcuoglu, P. Kohli, D. Hassabis,
+Highly accurate protein structure prediction with AlphaFold. Nature 596, 583–589 (2021).
+[15] C. A. Huang, A. Vaswani, J. Uszkoreit, I. Simon, C. Hawthorne, N. Shazeer, A. M. Dai, M. D. Hoffman,
+M. Dinculescu, D. Eck, Music Transformer: Generating music with long-term structure, in 7th International
+Conference on Learning Representations (ICLR, 2018).
+[16] B. Yu, P. Lu, R. Wang, W. Hu, X. Tan, W. Ye, S. Zhang, T. Qin, T. Liu, Museformer: Transformer with
+fine-and coarse-grained attention for music generation, in Advances in Neural Information Processing Systems
+(NeurIPS, 2022).
+[17] Y. Huang, Y. Yang, Pop music transformer: Beat-based modeling and generation of expressive pop piano
+compositions, in Proceedings of the 28th ACM International Conference on Multimedia (MM, 2020), pp.
+1180–1188.
+[18] Y. Ren, J. He, X. Tan, T. Qin, Z. Zhao, T. Liu, Popmag: Pop music accompaniment generation, in
+Proceedings of the 28th ACM International Conference on Multimedia (MM, 2020), pp. 1198–1206.
+[19] W. Hsiao, J. Liu, Y. Yeh, Y. Yang, Compound word transformer: Learning to compose full-song music over
+dynamic directed hypergraphs, in Proceedings of the AAAI Conference on Artificial Intelligence (AAAI, 2021),
+pp. 178–186.
+[20] C. Payne. 2019. “Musenet.” OpenAI, July 21, 2022. http://openai.com/blog/musenet.
+[21] N. Zhang, Learning adversarial transformer for symbolic music generation. IEEE Trans. Neural Netw.
+Learn. Syst. 1–10 (2020).
+[22] O. Sageev, S. Ian, D. Sander, E. Douglas, S. Karen, This time with feeling: Learning expressive musical
+performance. Neural. Comput. Appl. 32, 955–967 (2020).
+[23] M. Zeng, X. Tan, R. Wang, Z. Ju, T. Qin, T. Liu, MusicBERT: Symbolic music understanding with
+large-scale pre-training, in Findings of the ACL: ACL-IJCNLP 2021 (ACL, 2021), pp. 791–800.
+[24] I. V. Anishchenko, T. M. Chidyausiku, S. Ovchinnikov, S. J. Pellock, D. Baker, De novo protein design by
+deep network hallucination. Nature 600, 547–552 (2020).
+[25] R. Chowdhury, N. Bouatta, S. Biswas, C. Floristean, A. Kharkare, K. Roye, C. Rochereau, G. Ahdritz,
+J. Zhang, G. M. Church, P. K. Sorger, M. AlQuraishi, Single-sequence protein structure prediction using a
+language model and deep learning. Nat. Biotechnol. 40, 1617–1623 (2022).
+[26] J. Dauparas, I. V. Anishchenko, N. Bennett, H. Bai, R. J. Ragotte, L. F. Milles, B. I. M. Wicky, A. Courbet,
+R. Haas, N. Bethel, P. J. Y. Leung, T. F. Huddy, S. J. Pellock, D. Tischer, F. Chan, B. Koepnick, H. Nguyen, A.
+Kang, B. Sankaran, A. K. Bera, N. P. King, D. Baker, Robust deep learning-based protein sequence design using
+ProteinMPNN. Science 378, 49–56 (2022).
+[27] J. Tang, X. Han, M. Tan, X. Tong, K. Jia, SkeletonNet: A Topology-Preserving Solution for Learning Mesh
+Reconstruction of Object Surfaces From RGB Images. IEEE Trans. Pattern Anal. Mach. Intell. 44, 6454–6471
+(2020).
+[28] D. Shi, X. Diao, H. Tang, X. Li, H. Xing, H. Xu, RCRN: Real-world Character Image Restoration Network
+via Skeleton Extraction. In Proceedings of the 30th ACM International Conference on Multimedia (MM, 2022),
+pp. 1177–1185.
+16
+
+[29] K. Zhang, R. Zhang, Y. Yin, Y. Li, W. Wu, L. Sun, F. Wu, H. Deng, Y. Pan, Visual knowledge guided
+intelligent generation of Chinese seal carving. Front. Inf. Technol. Electron. Eng. 23, 1479–1493 (2022).
+[30] J. Wu, C. Hu, Y. Wang, X. Hu, J. Zhu, A hierarchical recurrent neural network for symbolic melody
+generation. IEEE Trans. Cybern. 50, 2749–2757 (2019).
+[31] S. Dai, Z. Jin, C. Gomes, R. B. Dannenberg, Controllable deep melody generation via hierarchical music
+structure representation, in Proceedings of the 22nd International Society for Music Information Retrieval
+Conference (ISMIR, 2021), pp. 143–150.
+[32] J. Wu, X. Liu, X. Hu, J. Zhu, Popmnet: Generating structured pop music melodies using neural networks.
+Artif. Intell. 286, 103303 (2020).
+[33]Y. Zou, P. Zou, Y. Zhao, K. Zhang, R. Zhang, X. Wang, MELONS: generating melody with long-term
+structure using transformers and structure graph, in ICASSP 2022-2022 IEEE International Conference on
+Acoustics, Speech and Signal Processing (ICASSP, 2022), pp. 191–195.
+[34] F. Lerdahl, R. Jackendoff, A Generative Theory of Tonal Music (MIT Press, Cambridge, MA, 1983).
+[35] B. M. K. Ayotte, Heinrich Schenker: A Guide to Research (Routledge, 2020).
+[36] J. Berezovsky, The structure of musical harmony as an ordered phase of sound: A statistical mechanics
+approach to music theory. Sci. Adv. 5, eaav8490 (2019).
+[37] F. Salzer, Structural Hearing: Tonal Coherence in Music (Courier Corporation, 1962).
+[38] Z. Dai, Z. L. Yang, Y. M. Yang, J. Carbonell, Q. Le, R. Salakhutdinov, Transformer-XL: Attentive language
+models beyond a fixed-length context, in Proceedings of the 57th Annual Meeting of the ACL (ACL, 2019), pp.
+2978–2988.
+[39] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, I. Polosukhin, Attention
+is all you need, in Proceedings of the 31st Conference on Neural Information Processing Systems (NIPS, 2017).
+[40] G. Hadjeres, F. Nielsen, Anticipation-RNN: enforcing unary constraints in sequence generation, with
+application to interactive music generation. Neural. Comput. Appl. 32, 995–1005 (2020).
+[41] B. Maess, S. Koelsch, T. C. Gunter, A. D. Friederici, Musical syntax is processed in Broca’s area: An MEG
+study. Nat. Neurosci. 4, 540–545 (2001).
+[42] M. D. Hauser, N. Chomsky, W. T. Fitch, The faculty of language: What is it, who has it, and how did it
+evolve. Science 298, 1569–1579 (2002).
+[43] W. T. Fitch, M. D. Hauser, Computational constraintson syntactic processing in a nonhuman primate.
+Science 303, 377–380 (2004). [44]A. D. Friederici, J. Bahlmann, S. Heim, R. I. Schubotz, A. Anwander, The
+brain differentiates human and non-human grammars: Functional localization and structural connectivity. Proc.
+Natl. Acad. Sci. 103, 2458–2463 (2006).
+[45] R. Näätänen, L. Anne, L. Mietta, C. Marie, H. Minna, I. Antti, V. Martti, Alku, Paavo, I. Risto, L. Aavo,
+Language-specific phoneme representations revealed by electric and magnetic brain responses. Nature 385,
+432–434 (1997).
+[46] A. Baddeley, Working memory: Looking back and looking forward. Nat. Rev. Neurosci 4, 829–839 (2003).
+[47] H. Schenker, Neue Musikalische Theorien und Phantasien: Der Freie Satz (Universal Edition, 1956).
+[48] D. Hodges, Music in the Human Experience: An Introduction to Music Psychology (Routledge, 2010).
+[49] A. D. Patel, Music, Language, and the Brain (Oxford University Press, 2010).
+[50] D. Povel, Melody generator: a device for algorithmic music construction. J. Softw. Eng. Appl 3, 683 (2010).
+[51] S. G. Laitz, The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening
+(Oxford University Press, 2012).
+[52] F. Lerdahl, Tonal Pitch Space (Oxford University Press, 2001).
+[53] F. Lerdahl, C. Krumhansl, Modeling tonal tension. Music Percept. 24, 329–366 (2007).
+[54] G. W. Cooper, L. B. Meyer, The Rhythmic Structure of Music (Chicago University Press, 1963).
+[55] C. L. Krumhansl, L. L. Cuddy, A theory of tonal hierarchies in music. Music Percept. 36, 51–87 (2010).
+[56] Nattiez, J. J., Music and Discourse: Toward a Semiology of Music (Princeton University Press, 1990).
+[57] E. Chew, Mathematical and computational modeling of tonality, AMC 10, 141 (2014).
+17
+
+[58] D. Herremans, E. Chew, Tension ribbons: Quantifying and visualising tonal tension, in Proceedings of the
+Second International Conference on Technologies for Music Notation and Representation (TENSOR, 2016), pp.
+8–18.
+[59] H. Dorien, E. Chew, MorpheuS: generating structured music with constrained patterns and tension. IEEE
+Trans. Affect. Comput. 10, 510–523 (2017).
+[60] L. C. Yang, A. Lerch, On the evaluation of generative models in music. Neural. Comput. Appl. 32,
+4773–4784 (2020).
+[61] D. B. Huron, Sweet Anticipation: Music and the Psychology of Expectation (MIT Press, Cambridge, MA,
+2006).
+[62] K. Koffka, Principles of Gestalt Psychology (Routledge, 2013).
+[63] A. M. Treisman, G. Gelade, A feature-integration theory of attention. Cogn. Psychol. 12, 97–136 (1980).
+[64] R. M. Brown, J. L. Chen, A. Hollinger, V. B. Penhune, C. Palmer, R. J. Zatorre, Repetition suppression in
+auditory-motor regions to pitch and temporal structure in music. J. Cogn. Neurosci. 25, 313328 (2013).
+[65] I. Peretz, M. Coltheart, Modularity of music processing. Nat. Neurosci. 6, 688–691 (2003).
+[66] G. R. Kuperberg, T. F. Jaeger, What do we mean by prediction in language comprehension? Lang. Cogn.
+Neurosci. 31, 32–59 (2016).
+[67] P. E. Hutchings, J. McCormack, Adaptive music composition for games. IEEE Trans. Games 12, 270–280
+(2019).
+[68] Z. Ju, P. Lu, X. Tan, R. Wang, C. Zhang, S. Wu, K. Zhang, X. Li, T. Qin, T. Liu, TeleMelody: Lyric-
+to-Melody generation with a template-based two-stage method, in Proceedings of the 2022 Conference on
+Empirical Methods in Natural Language Processing (EMNLP, 2022), pp. 5426–5437.
+[69] A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L.
+Antiga, A. Desmaison, A. Kopf, E. Yang, Z. De Vito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L.
+Fang, J. Bai, S. Chintala, PyTorch: An imperative style, high-performance deep learning library. Adv. Neural Inf.
+Process. Syst. 32, 8026–8037 (2019).
+18
+
+A
+Appendix
+A.1
+Additional Supplementary Figure
+···
+TempM
+Velocity Embeddings
+Duration Embeddings
+Token Embeddings
+Position Embeddings
+Bar Embeddings
+Tempo Embeddings
+Timestep
+A
+➕
+➕
+➕
+➕
+➕
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+11
+12
+13
+14
+15
+16
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+TempM
+Bar1
+Bar1
+Bar1
+Bar1
+Bar1
+Bar1
+Bar1
+Bar1
+Bar1
+Bar1
+Bar2
+Bar2
+Bar1
+Bar1
+Bar1
+Bar2
+Pos0
+Pos0
+Pos720
+Pos720
+Pos960
+Pos960
+Pos960
+Pos1440
+Pos1440
+Pos0
+Pos0
+Pos480
+Pos480
+Pos0
+Bar
+Pos0
+ChC_M
+Pos720
+Pitch62
+Pos960
+ChC_M
+Pitch63
+ChC_M
+Pitch60
+Bar
+Pos0
+Pitch60
+Pos480
+ChD_M
+ChC_M
+Dur240
+Dur480
+Dur480
+Dur720
+Vel127
+Vel127
+Vel127
+Vel127
+Figure S1: MeMIDI encoding method for MIDI sequences (example). The input embedding in each timestep
+of the MeMIDI event sequence is the sum of the event embeddings, including tempo embedding, bar embedding,
+position embedding, token embedding, duration embedding, and velocity embedding in this timestep.
+A.2
+Additional Supplementary Tables
+Table S1: Subjective evaluation scores of generated melodies based on different melodic skeleton settings in
+Experiment 1 (mean ± standard deviation).
+No.
+Settings
+Rhythm
+Richness
+Structure
+Expectation
+Overall
+1
+Downbeat
+2.75 ± 0.96
+2.50 ± 0.98
+2.63 ± 1.13
+2.45 ± 1.03
+2.52 ± 1.03
+2
+Long Note
+2.70 ± 1.03
+2.57 ± 1.17
+2.77 ± 1.21
+2.47 ± 1.27
+2.67 ± 1.26
+3
+Rhythm
+3.02 ± 1.01
+3.10 ± 0.89
+2.88 ± 1.02
+2.82 ± 0.81
+2.93 ± 0.97
+4
+Tonic
+2.95 ± 1.11
+2.80 ± 1.09
+2.87 ± 0.95
+2.65 ± 1.01
+2.80 ± 1.06
+5
+Intersection
+2.60 ± 0.85
+2.52 ± 0.87
+2.53 ± 0.83
+2.28 ± 0.98
+2.43 ± 0.83
+6
+Union
+2.95 ± 0.95
+2.57 ± 1.05
+2.62 ± 1.09
+2.43 ± 1.05
+2.60 ± 1.04
+7
+Random25%
+2.80 ± 1.11
+2.78 ± 0.98
+2.67 ± 1.07
+2.62 ± 0.95
+2.65 ± 1.12
+8
+Random50%
+2.92 ± 0.98
+2.82 ± 0.89
+2.70 ± 1.01
+2.68 ± 1.03
+2.73 ± 0.95
+9
+Random75%
+2.82 ± 0.95
+2.58 ± 1.12
+2.50 ± 1.11
+2.45 ± 1.04
+2.53 ± 1.08
+Table S2: One-tailed t-test results between WuYun-RS and other music generation models on the five evaluation
+metrics in experiment 2.
+Model
+Rhythm
+Richness
+Structure
+Expectation
+Overall
+MT
+3.43 × 10−7
+5.37 × 10−9
+2.44 × 10−12
+6.50 × 10−6
+2.21 × 10−10
+PMT
+2.18 × 10−8
+1.21 × 10−9
+1.20 × 10−6
+2.55 × 10−6
+1.13 × 10−7
+MeMIDI
+1.88 × 10−6
+3.09 × 10−6
+6.86 × 10−7
+2.31 × 10−5
+6.29 × 10−7
+CWT
+3.31 × 10−4
+8.47 × 10−4
+3.02 × 10−4
+2.03 × 10−3
+1.69 × 10−3
+Melons
+4.60 × 10−3
+1.54 × 10−3
+8.02 × 10−4
+2.12 × 10−3
+7.41 × 10−3
+WuYun-RRS
+0.26
+0.36
+0.42
+0.42
+0.41
+MT, PMT, and CWT stand for Music Transformer, Pop Music Transformer, and Compound Word Trans-
+former, respectively.
+19
+
diff --git a/L9E3T4oBgHgl3EQfYgo-/content/tmp_files/load_file.txt b/L9E3T4oBgHgl3EQfYgo-/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5efb962259d3661193113db128462fb927fd561d
--- /dev/null
+++ b/L9E3T4oBgHgl3EQfYgo-/content/tmp_files/load_file.txt
@@ -0,0 +1,1747 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf,len=1746
+page_content='WuYun: Exploring hierarchical skeleton-guided  melody generation using knowledge-enhanced deep  learning  Kejun Zhang1,2,3,∗,  Xinda Wu1,∗,  Tieyao Zhang1,  Zhijie Huang1,  Xu Tan4,  Qihao Liang1,  Songruoyao Wu1,  Lingyun Sun1,2,†  1College of Computer Science and Technology, Zhejiang University, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2Alibaba-Zhejiang University Joint Institute of Frontier Technologies, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  3Innovation Center of Yangtze River Delta, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  4Microsoft Research Asia  {zhangkejun, wuxinda, kreutzer0421, zj_huang,  qhliang, 12221193, sunly}@zju.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='cn  xuta@microsoft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='com  Abstract  Although deep learning has revolutionized music generation, existing methods  for structured melody generation follow an end-to-end left-to-right note-by-note  generative paradigm and treat each note equally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Here, we present WuYun, a  knowledge-enhanced deep learning architecture for improving the structure of  generated melodies, which first generates the most structurally important notes to  construct a melodic skeleton and subsequently infills it with dynamically decorative  notes into a full-fledged melody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Specifically, we use music domain knowledge  to extract melodic skeletons and employ sequence learning to reconstruct them,  which serve as additional knowledge to provide auxiliary guidance for the melody  generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We demonstrate that WuYun can generate melodies with better  long-term structure and musicality and outperforms other state-of-the-art methods  by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='51 on average on all subjective evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Our study provides a  multidisciplinary lens to design melodic hierarchical structures and bridge the  gap between data-driven and knowledge-based approaches for numerous music  generation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  1  Introduction  Automatic music generation is one of the popular multidisciplinary research topics in generative  art and computational creativity (1), which has achieved revolutionary advances in various artificial  intelligence-generated content applications by utilizing deep learning techniques (2, 3), including  interactive music production collaboration tools (4, 5), video background music generation (6), music  education (7), and music therapy (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' As one of the crucial components of music generation, melody  generation has drawn much attention from both the academic and industrial fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Although melodies  appear to be a simple linear succession of notes unfolding over time, the organizational structure of  the melodic notes is hierarchical, like a tree resulting in intricate long-distance dependencies (9, 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Hence, the complex long-distance dependencies make it difficult for neural networks to discover and  learn the hierarchical structure relationships among these musical elements and generate long-term  structured melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In recent years, language models in natural language processing (NLP) have  ∗Equal contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  †Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Preprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Under review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='04488v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='SD]  11 Jan 2023  been employed to capture long-distance dependencies for structured melody generation with the  advantages of an easy-to-use end-to-end deep learning framework, effective representation learning,  and arbitrary sequence length generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Their powerful ability to automatically learn the latent  knowledge from big data, without explicitly codifying the domain-specific rules, has been proved and  applied in multiple disciplines (11–14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Numerous specialized architectures of the language model for music generation have demonstrated  promising performance in generating long-range coherent melodies, including effective attention  mechanisms (15, 16), enhanced memory networks (17–19), large-scale deep neural networks (20),  and explicit musicality regularization (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Furthermore, various MIDI-derived symbolic music  representation methods designed auxiliary musical spatiotemporal symbols (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', BAR, POSITION,  and CHORD) for the input symbolic music data to help music generation models learn the long-  distance dependencies better, longer, and faster (17–19, 22, 23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' However, the scarcity of publicly  available melody data limits the usage of the power of language-based music generation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Moreover, the process of melody generation still lacks controllability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' These models are trained in the  dominant end-to-end and data-driven learning paradigms, which optimize the network’s large-scale  parameters via learning to map the input data to output data, thus occasionally resulting in excessive  repetition or boring sounds in the generated music (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Recent studies used a deep learning-based hierarchical generation strategy to first hallucinate or  predict the object’s structure and then use it to constrain downstream generation tasks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', protein,  font, or music) (24–33), which enables the neural networks to learn from the limited data far  more efficiently and improves the controllability of the generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For structured melody  generation, some scholars first generate a melody’s hierarchical music structure representation (31)  or bar-level musical structure relationship graph (32, 33) and then generate melodies conditioned  on the generated parallel structure information as additional knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Such a strategy requires  recognizing the group structure of the musical syntax in a melodic surface (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', phrases and sections)  to extract music features for building a structure generation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nonetheless, inadequate music  structure boundary detection algorithms hinder the extraction of accurate melodic group structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Conversely, little attention has been paid to the organizational logic of the deep structure beneath  the melodic surface, organized by different levels of structural importance among various musical  events (34–36) with the potential to enhance structured melody generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Typically, the majority  of existing melody generation methods for pursuing long-term structure follow an end-to-end left-  to-right note-by-note generative paradigm and treat each note equally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' So far, however, there is still  an insufficient investigation into an alternative order of melody generation and the difference in the  relative structural importance among musical notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  In this study, we propose WuYun, a hierarchical skeleton-guided melody generation architecture  based on knowledge-enhanced deep learning that incorporates the melodic skeleton as deep structural  support to provide explicit guidance on the development direction of melody generation (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  WuYun follows the hierarchical organization principle of structure and prolongation (35, 37), thus  dividing traditional single-stage end-to-end melody generation into two stages: melodic skeleton  construction and melody inpainting (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' At the stage of melodic skeleton construction, we first  extract the most structurally important notes in a musical piece from rhythm and pitch dimensions  as melodic skeletons on the basis of the music domain knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We then train an autoregressive  decoder-only Transformer-based network (38) on the collected melodic skeleton data to construct  new melodic skeletons (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1C, a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We treat the melodic skeleton as the underlying framework of the  final generated melody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' At the stage of melody inpainting, we adopt a Transformer encoder–decoder  architecture (39) to elaborate the melodic skeleton into a full-fledged melody by encoding the melodic  skeleton as additional knowledge into the decoder to guide the melody generation process (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1C,  b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' To prove the effectiveness of the architecture, we evaluate WuYun on a publicly available melody  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Experimental results show that the generated melodic skeleton has comparable quality with  the real one extracted by our proposed melodic skeleton extraction framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The hierarchical  skeleton-guided melody generation architecture effectively improves generated melodies’ long-term  structure and musicality and outperforms other state-of-the-art methods by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='51 on average on all  subjective evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melodic skeleton  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melody  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melody  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Database  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melodic Skeleton Extraction  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Framework  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pairing  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='B  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Stage 1: melodic skeleton construction  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Stage 2: melody inpainting  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melodic  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Skeleton  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Database  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Hierarchical structure analysis in music  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='(Music domain knowledge)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Input Module  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='(Embedding)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Positional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Encoding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Transformer-XL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='（4 blocks）  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Output Module  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='(Classifier)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='C  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='a) Melodic Skeleton Generation Module  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Input  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='(Melodic skeleton)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Representation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Input Module  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='(Embedding)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Encoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='（4 blocks）  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='（4 blocks）  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Recurrent Transformer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='b) Melodic Prolongation Generation Module  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Representation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Input Module  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='(Embedding)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Input  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='(Melody)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Representation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Input  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='(Melodic skeleton)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Output Module  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='(Classifier)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Train  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='A  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melodic Skeleton  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melody (example)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melodic skeleton  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Sequence learning model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Y1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Y2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Yn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='X1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='X2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Xn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Partial sequence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melodic skeleton  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='X1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='X2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Xn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Encoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Y2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Y3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Yn  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Y1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Y2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Yn-1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Decoder  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='…  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Predicted tokens  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Predicted tokens  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Sequence-to-sequence  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='learning model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Melody  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Figure 1: Architecture of WuYun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' (A) The first eight bars of the melody of “Hey Jude” from The Beatles  (excluding anacrusis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The upper part of the figure shows the basic shape of the melodic motion, and the low  part of the figure shows the melodic skeleton in the rhythm dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Every melody has an underlying melodic  skeleton that provides structural support and connections among musical elements to guide the melodic motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  (B) Hierarchical melody generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' WuYun divides the melody generation process into melodic skeleton  construction and melody inpainting stages following the hierarchical organization principle of structure and  prolongation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' At the melodic skeleton construction stage, the melodic skeleton extraction framework is proposed  to extract the melodic skeleton in the rhythm and pitch dimensions by the hierarchical structure theory from  music domain knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A neural network for sequence learning trained on melodic skeletons can generate  novel ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' At the melody inpainting stage, another neural network for sequence-to-sequence learning would  fill the generated melodic skeleton into a full-fledged melody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' (C) Architecture details of WuYun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' WuYun is  composed of a melodic skeleton generation module and a melodic prolongation generation module;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' the former  is used for the melodic skeleton construction stage, and the latter is used for the melody inpainting stage with the  guidance of the melodic skeleton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  3  OO4车  42  Result  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  Hierarchical organization principle of structure and prolongation  Most AI artistic generative models differ significantly from humans in their artistic creation process,  especially in music generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For example, a typical music generation model generates music  content sequentially from left to right at once (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' However, human artworks tend to develop  iteratively from a basic underlying idea or structure through elaboration, expansion, and individual  shaping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Human artistic creation follows an age-old fundamental principle of creative thinking,  namely, structure and prolongation, which has significantly contributed to human thinking and  creativity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In the art of music, this principle governs the underlying logic in musical composition  and makes musical reasoning and explanation comprehensible and acceptable (37).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' It conforms  to the brain’s cognitive processing mechanism of structurally organizing sequential information  (41–44), which makes the brain encode and process information more efficiently and improves  musical memories (45, 46).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For example, musicians use this principle, consciously or unconsciously,  to study, organize, and perform their musical works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  The hierarchical structure is a key feature of the tonal musical syntax system, where musical elements  are almost always hierarchically organized by strict rules at a fundamental level rather than unlimited  creative expression (36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Some researchers have investigated the patterns of structural organization  and generalized them into music theories regarding the hierarchical structure in music from the  perspective of the structure and prolongation principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Schenker (47) was the first to introduce this  principle to describe the musical structure in a hierarchically organized way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The central idea of  Schenkerian theory about the hierarchical structure is that some musical events are elaborated by  other musical events in a recursive and embedded fashion (9, 34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' That is, not all musical events  are equally important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Some musical events have structural importance as stable factors in music,  whereas others are more decorative as dynamic factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Therefore, Schenker proposed different  levels of structure hierarchy to organize tonal music and analyze its motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Based on Schenker’s  ideas, the generative theory of tonal music (GTTM), proposed by Lerdahl and Jackendoff (34), is  one of the most influential theories in current music theory and music psychology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' GTTM provides  a systematic analysis and description of the hierarchical structure in music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Based on the listeners’  perception of tonal music, GTTM lists four hierarchical structure relationships from rhythm and pitch  dimensions: grouping structure, metrical structure, time span reduction, and prolongational reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  The term “reduction” refers to the stepwise reduction of less important musical events from the  musical surface, revealing the underlying framework or skeleton that plays an essential role in the  music’s qualities and developmental direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In summary, under the surface of the music, musical  events are hierarchically organized based on the structural stability in rhythm and pitch dimensions  (48, 49).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Inspired by the iterative mode of human composition guided by the principles of structure and  prolongation, the whole process of melody creation can be seen as progressively filling individual  decorative notes among the melodic skeleton;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' it is an effective modern composition technique that  perfectly combines rules and composers’ personality (35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' This composition technique has been  developed and applied in music teaching for a long history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In the following, we elaborate on the  melodic skeleton extraction framework from rhythm and pitch dimensions and introduce the design of  WuYun melody generation architecture that first constructs the melodic skeleton and then completes  the melody instead of sequentially generating a melody note-by-note at once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The manner of WuYun’s  melody generation process is more musically meaningful than the dominant end-to-end left-to-right  note-by-note melody generation paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  Melodic skeleton extraction framework  Music theories present that there is an underlying identifiable framework beneath the melody surface  called the melodic skeleton (35, 50).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The melodic skeleton is composed of certain notes, which  sound more structurally important from rhythm and pitch dimensions (34, 48) and are called the  skeleton notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The skeleton note attracts the audience’s attention and makes a deeper impression  on them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' By contrast, the remaining part of the notes plays a decorative role, giving the melody  personalities or styles, and are called the decorative notes or prolongation notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The melodic skeleton  serves as the crucial structural support of rhythm and harmony, indicating the direction of melody  development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Knowledge of melodic skeleton information can help humans and machines better  4  Figure 2: Melodic skeleton extraction framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' (A) Rhythm pattern of strong and weak beat distribution  in the 4/4 time signature with different note resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' (B) Rhythmic skeleton extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The rhythmic  skeleton consists of the metrical accents, agogic accents on metrical accents, and agogic accents on syncopations  in each measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' (C) Illustration of the tension measure in the pitch class helix of the spiral array with a C major  chord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The right part of the figure presents the tension value of the notes in the first eight bars of the melody of  “Hey Jude.” (D) Tonal skeleton extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The tonal skeleton consists of the notes with the minimum tension  value in the rhythm cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  5  A  Strong  4th  Weak  Sub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Weak  Strong  Strong  8th  Weak  Weak  Weak  Strong  Strong  Weak  Weak  Strong  Weak  Strong  Weak  Weak  Weak  Weak  Strong  Strong  Weak  16th  Weak  Sub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Sub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Sub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Sub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Grid  1  2  3  5  6  7  8  9  10  11  12  13  14  15  16  4  B  Original  Metrical Accent  Agogic  Synopation  Rhythmic skeleton  c  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='9  A#  D#  Tonal Skeleton Note  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  Prolongation Note  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='7  G#  F#  B  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='6  C#  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='5  AD  V  D  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  G  E  E  A  E-  B-  C  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  IV  F  G-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='9  G  A-  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='7  12  14  24  26  28  30  32  40  0  16  20  22  38  Note Sequence  D  Rhythm Cell  Tonal Skeletonanalyze, understand, and learn the logic of melodic hierarchy organization from surface to deep  layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Here, we introduce a framework for melodic skeleton extraction based on the knowledge of music  theory (34, 35, 50–53) and music psychology (48, 49) to identify the dominant and subordinate  relationship of structural importance from rhythm and pitch dimensions between melody notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The  theoretical basis and implementation details are described briefly below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  Rhythmic skeleton extraction  Before describing the theoretical basis of this work, we would have to cover some basic musical  terms and concepts regarding meter and rhythm in the time aspect of music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In music theory, the  pulse splits time into a series of uniformly spaced chunks called beats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Not all beats are created equal,  and certain beats are felt stronger than others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The first beat of each measure is a downbeat, and the  one that follows is an upbeat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The meter measures the number of beats in the regular and repeated  pattern of the downbeat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For example, the most common meter in music is 4/4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' each measure has  four quarter note beats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The distribution pattern of strong and weak beats is “strong weak sub-strong  weak,” as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 2A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Rhythm can be defined as the organization pattern of one downbeat with  one or more upbeat (54).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Therefore, the meter provides the temporal framework for organizing music  rhythm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  To draw listeners’ attention, musicians often use accents in musical compositions or performances  to emphasize a particular note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Accents can be expressed in various ways to increase musical  expressiveness and add character to the movement of music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Metrical and rhythmic accents are the  two main accents in the symbolic melody data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A metrical accent is an accent that falls on the strong  beat position within a measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The metrical accent is periodic and cyclic, whose distribution pattern  depends on the type of meter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A rhythmic accent is an accent in a strong position within the rhythm,  which emphasizes a point that is not constrained by the meter’s structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Consequently, it is flexible  and changeable rather than static and fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Rhythmic accents can be created by increasing the notes’  dynamic (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', dynamic accent), extending the notes’ duration (agogic accent), using syncopation,  and so forth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The agogic accent can be easily distinguished by comparing the surrounding notes on  duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Additionally, the musician can use syncopation to change the normal rhythm pattern by  extending the duration of notes from the weak beat or weak beat part to the subsequent strong beat  or strong beat part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Note that a note cannot be both a metrical accent and a syncopation, which are  conflicted with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The dynamic accent is not used since it has no obvious changes in most  symbolic melody data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  In this study, we extract the metrical accents, the agogic accents falling on the metrical accent, and  the agogic accents falling on the syncopation as the rhythmic skeleton notes, as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Metrical accents are the foundation of other types of accent (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' When two or more different  types of accents work together, the listener will experience a particularly more prominent accent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Therefore, when a rhythmic accent and a metrical accent overlap, the rhythmic accent is generally  more perceptible and is the one that is preferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' If there were continuous rhythmic skeleton notes,  we chose the most structurally important note as the rhythmic skeleton note according to the intensity  of the accent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  Tonal skeleton extraction  In tonal music, the pitch of the melody moves around a centrally stable note (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', the tonal center or  tonic), repeatedly moving away from it and back to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Pitches are essentially organized into a distinct  hierarchy scale based on tonal stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' There is a mutual attraction between pitches with different  stable levels, which can stimulate different emotional experiences (47).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Specifically, an unstable  pitch tends to be a stable pitch, which would make the listeners feel relaxed or dismissed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Moving  from a stable to an unstable pitch would increase the listener’s sense of tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The prolongational  reduction theory of GTTM suggests that the more important music event has less tension and vice  versa (53).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Note that the same tone may have different feelings in different contexts, which may be  pleasant or anxious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  For the tonal skeleton extraction method, we use the tension level as a metric to quantify the relative  importance of the pitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The specific recognition procedure is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  6  First, we used the position of the rhythmic skeleton notes as the boundary of the individual  context because the metrical structure is the important basis of all hierarchical structure  types (34).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Second, we combined two or three successive notes as the minimum rhythmic cell in each  segment, according to the repetition frequency in the melody (55) and the number of notes  of this rhythmic cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The term “rhythmic cell” defines as a “small rhythmic and melodic  design that can be isolated or can make up one part of a thematic context” (56).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Therefore,  each rhythmic cell can be seen as an isolated thematic context for calculating the tension  profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Finally, we adopted a mathematical tonal tension model to quantify each note’s tension  value by calculating the distance between every single tone and global key in the spiral array  (57–59), as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 2C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We selected the note with the minimum tension value in each  rhythmic cell as the tonal skeleton note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For example, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 2D shows the tonal skeleton of  the first eight bars from the song “Hey Jude.”  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='3  Design of WuYun  Figure 1C shows the diagram of the proposed hierarchical melody generation architecture called  WuYun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' First, we convert the melody MIDI files and their melodic skeletons into musical event  sequences as the input data for model training using the MeMIDI symbolic music representation  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Then, we design a hierarchical melody generation architecture with two generative modules  responsible for melodic skeleton construction and melody inpainting, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In this subsection,  we will introduce the hierarchical melody generation architecture about how we generate the melodic  skeleton and incorporate it to guide the melody generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The details about the MeMIDI  symbolic music representation method and the word embedding technique used in this architecture’s  input module are described in the Materials and Methods section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  WuYun is designed to generate melodies in two stages hierarchically: melodic skeleton construc-  tion and melody inpainting, instead of the dominant end-to-end left-to-right note-by-note melody  generation paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' At the stage of melodic skeleton construction, we use the Transformer-XL  model with only the decoder as the melodic skeleton generation module (19), which has the ad-  vantage of remarkable performance in capturing long-term dependence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' To develop the capacity  of melodic skeleton construction, we trained the Transformer-XL model on the extracted melodic  skeleton database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' At the stage of melody inpainting, we employ the recurrent Transformer-based  encoder–decoder architecture (18) in a sequence-to-sequence setup as the melody inpainting module  to complete the melody conditioned on the melodic skeleton, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', filling the missing information  between the melodic skeleton notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In this work, the melody inpainting problem can be defined as  follows: given a melodic skeleton sequence Cs, generate an inpainted melody sequence Cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The  encoder maps the discrete input symbols of the melodic skeleton sequence Cs to a high-dimensional  continuous vector as conditional input into the decoder, and the decoder then generates an output  sequence Cm in an autoregressive manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The melodic skeleton sequence will be saved in the final  generated melody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' This method provides users an entry point to interact with the melody generation  model by adjusting melodic skeleton notes between two stages to control the melodic motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  In this work, we focus on designing a hierarchical skeleton-guided melody generation architecture  based on knowledge-enhanced deep learning, following the hierarchical organization principle of  structure and prolongation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Therefore, we used common language models in NLP to make the WuYun  architecture accessible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The capacity of these two generative modules may be further optimized;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  however, the goal of this study is not to find the most optimal neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  Evaluation metrics  Subjective and objective evaluations are the two essential aspects of evaluating the performance of  music generation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The human listening test is currently an indispensable and viable method  for subjective evaluation to measure the quality of the generated musical pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' However, for the  objective evaluation, many efforts have been made to design quantitative metrics;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' there is not a set of  convincing and unified metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Although the research field of music generation is multidisciplinary,  most researchers mainly focus on generative models with different improvement goals rather than  their contribution to quantifying music complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Consequently, almost all the proposed objective  7  evaluation metrics are difficult to apply for comparing different music creation systems and lack  sustainability for future development demands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We tried to calculate the averaging overlapped area  of some musical feature distributions between generated musical pieces and ground-truth musical  pieces as the objective evaluation metrics like (18, 60) using the public evaluation toolbox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We  arrived at a similar conclusion as PopMNet (32) that a better result of objective evaluation does not  mean better structure and musicality of generated music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The same objective evaluation result can be  calculated and verified with the provided melody MIDI files of this study’s next two experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Therefore, we conducted two subjective evaluation experiments to evaluate the performance of our  proposed WuYun, including different melodic skeleton settings in rhythm and pitch dimensions and  comparisons with public state-of-the-art (SOTA) music generation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  We randomly selected ten melodies from the evaluation dataset for the listening materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Similar to  previous studies (15, 17, 19), we took the first four bars as prompt and set the maximum number of  generated bars to 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We assigned a random order for all musical pieces as the file name, including  the generated and ground-truth musical pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' All melody MIDI files were rendered into audio via a  piano MIDI synthesizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In the blind listening test, participants were asked to rate each melody on a  five-point Likert scale (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', 1 for bad and 5 for excellent) on five dimensions:  Rhythm: Whether the brain can feel the regular accents and rhythm patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Richness: Whether the melody sounds rich and interesting in the rhythm and pitch dimen-  sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Structure: Whether the brain can feel the boundary of melodic phrases and the balance  among melodic phrases’ length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Expectation: Whether the direction of melody development meets the audience’s expecta-  tions for melody development (61).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Overall: Overall quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  We found that most nonmusicians had heard technical music terms but did not understand what  they meant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Therefore, before formal experiments, we conducted multiple rounds of discussions,  testing, and validation with musicians and nonmusicians regarding the above subjective evaluation  metrics and their descriptions until they could easily understand and grasp them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' To ensure that  the recruited subjects have a common understanding of the metrics and scales in the questionnaire,  we also conducted evaluation training for them, including the explanation of subjective evaluation  metrics and preliminary experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' All audio and MIDI files for evaluation can be found in  Acknowledgments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='5  Model performance based on different melodic skeleton settings  To compare the effectiveness of variants of melodic skeleton extracted from rhythm and pitch  dimensions, we comprehensively evaluated the performance of WuYun based on different settings of  the melodic skeleton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Furthermore, we added three control group settings of randomly selected notes  with different percentages as the melodic skeleton in order to verify the effectiveness of the proposed  melodic skeleton extraction method based on music domain knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' All experimental settings  and the proportion of melodic skeleton notes in the melody are described below:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Downbeat only uses metrical accents as the melodic skeleton (32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Long Note only uses agogic accents as the melodic skeleton (27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Rhythm uses rhythmic skeleton notes as the melodic skeleton (33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tonic uses tonal skeleton notes as the melodic skeleton (43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Interaction uses the intersection of rhythmic skeleton notes and tonal skeleton notes as the  melodic skeleton (14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Union uses the union of rhythmic skeleton notes and tonal skeleton notes as the melodic  skeleton (62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Random25% randomly selects 25% of melody notes as the melodic skeleton (25%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Random50% randomly selects 50% of melody notes as the melodic skeleton (50%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Random75% randomly selects 75% of melody notes as the melodic skeleton (75%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  8  In this experiment, we obtained 90 musical pieces for rating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We recruited 30 subjects (13 females  and 17 males, ages 18 and 30 years) from Zhejiang University and Zhejiang Conservatory of Music  to evaluate the musical pieces with payment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Fifteen subjects among them were professional music  practitioners with an average of 9 years of music training and 4 years of music performance experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  The rest of the subjects have little professional music training or performance experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Each  musical piece was assigned to three professionals and three nonprofessional subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Each subject  was required to rate 18 musical pieces, which cost approximately 25 min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Figure 3A shows the mean opinion scores of WuYun architecture’s melody generation performances  with nine different settings on the five subjective evaluation metrics from all subjects in the form of  histograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The detailed experimental result is shown in Table S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Generally, among all melodic  skeleton settings, the proposed rhythmic and tonal skeleton based on music theory and psychological  study performs better than other skeletons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The rhythmic skeleton setting (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 3) achieved the best  result on all subjective evaluation metrics, followed by the tonal skeleton setting (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Among  the three types of melodic skeletons associated with rhythm (Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1, 2, and 3), the melodic skeleton  composed of a single type of accent (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', metrical accents or agogic accents (31)) has a large gap with  the rhythmic skeleton in richness, expectation, and overall quality and even surpassed by the random  melodic skeletons (Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 7, 8, and 9) on most subjective evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' This result indicates that  a flexible rhythmic skeleton (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', including several kinds of musical accents) is essential for melody  composition to improve musicality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In contrast, a rigid melodic skeleton (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', including only one type  of accent, especially metrical accents) reduces the quality of the generated melody and limits the  models’ performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Likewise, as depicted in the right part of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 2C, the pitch classes of the tonal  skeleton notes are mostly C, D, and E, which also lead to the rigidity of the generated tonal skeletons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Additionally, compared to the rhythmic and tonal skeleton settings, the intersection (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='5) and union  (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 6) skeleton settings led to a distinct degradation of the melody generation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For  instance, the intersection (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 5) skeleton setting received the worst scores in most evaluation aspects,  even worse than the random sampling skeleton settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' This phenomenon can be explained by  the structure and prolongation proportion tradeoffs in the design of two-stage melody generation  architecture using an end-to-end learning framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We can preliminarily see that with the increased  percentage of melodic skeleton notes, the performance of the two-stage melody generation went up  first but then down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' On the one hand, a low proportion of melodic skeleton notes makes it easier  to train the melodic skeleton construction model in the first stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' However, the generated skeleton  notes will be too sparse to guide the second stage of melodic inpainting (such as the intersection  skeleton setting, only 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' On the other hand, if the proportion of melodic skeleton notes is too  large, the training difficulty and data dependency of the melodic skeleton construction model will  increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Besides, from the perspective of the gestalt theory (62) about the law of the figure–ground  relationship, during the perception of music, a person’s attention constantly switches between different  musical elements;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' sometimes, he/she may be attracted to the rhythm, whereas at other times, to  the pitch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Therefore, the extraction of the hierarchical dependency structural relationship between  musical elements is affected by multiple musical dimensions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' it will not be like a simple addition or  subtraction operation but a complex organic combination (63).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  In this study, we chose the setting of the rhythmic skeleton (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 3) that performed best on all  subjective evaluation metrics in this experiment as the default skeleton configuration (denoted as  WuYun-RS) for the next experiment to compare with other melody generation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='6  Comparisons with other melody generation methods  To prove the effectiveness of the proposed hierarchical skeleton-guided melody generation architecture  based on knowledge-enhanced deep learning, we compared WuYun-RS (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', using the rhythmic  skeleton setting) to five public SOTA Transformer-based melody generation models, namely, Music  Transformer (15), Pop Music Transformer (17), Compound Word Transformer (19), Melons (33)  and MeMIDI, that follow an end-to-end left-to-right note-by-note generative paradigm and treat  each note equally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The MeMIDI setting uses the MeMIDI data representation method like WuYun-  RS and employs the Transformer-XL model without using the melodic skeleton for the melody  generation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Moreover, to prove the effectiveness of the generated melodic skeleton, we added  the setting of WuYun-RRS, skipped the melodic skeleton construction in the first stage, and directly  used the real rhythmic skeleton as additional knowledge to guide the melody generation process  of melody inpainting in the second stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' However, the original music representation of Music  9  Figure 3: Subjective evaluation results of the WuYun melody generation architecture based on different  melodic skeleton settings, and the other public melody generation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' (A) Subjective comparison of the  performance of the WuYun architecture based on different melodic skeleton settings in Experiment 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Data is the  mean opinion score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The WuYun architecture with the rhythmic skeleton setting achieves the best performance in  all melodic skeleton settings on all subjective evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' (B) Subjective comparison of the performance  of different music generation models in Experiment 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Violin plots show the kernel density estimate of rating  distribution, the larger the area of the area graph, the greater the probability of the value distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The  black dot within the violin plots indicates the mean;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' the black line within the violin plot indicates the standard  deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Statistical analyses are done between WuYun-RS and the rest of the models using the one-tailed  t-test (N = 130).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' P values of statistical significance are represented as *P < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='05, **P < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='01, ***P < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='001,  and ****P < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='0001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' ns, insignificant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The subjective comparison results’ data are in Tables S1, 1, and S2,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Transformer does not include chord progressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For a fair comparison, we added the CHORD  events proposed in this work into the MIDI-Like music representation of Music Transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Each  CHORD event was followed by a TIME-SHIFT event and had a higher sorting priority than NOTE-  related events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Additionally, the MIDI quantization level of the Pop MusicTransformer, Compound  Word Transformer, and Melons only considered the 16th note time grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Therefore, in this experiment,  we applied the 16th note time grid as the MIDI quantization level to the melody dataset for all music  generation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  In this experiment, we obtained 80 musical pieces for rating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Since the second subjective evaluation  experiment relies on the result of the first subjective evaluation experiment and requires some time to  collect, process, and analyze, we recruited 13 participants again (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', six females and seven males,  ages 18 and 25 years) to evaluate the musical pieces with payment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Six subjects among them were  professional music practitioners with an average of 8 years of music training and 4 years of music  performance experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Each subject was required to rate all musical pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' After rating 20 musical  pieces, subjects were asked to rest for 5 min against hearing fatigue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The average experiment time  cost each subject about 2 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Figure 3B shows the mean opinion scores and one-tailed t-test results of the different music generation  systems on the five evaluation metrics in the form of violin plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The detailed experimental results are  shown in Tables 1 and S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Overall, WuYun-RS (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 6) and WuYun-RRS (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 7) outperformed the  other five current SOTA end-to-end left-to-right note-by-note melody generation models on all metrics,  including MusicTransformer (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1), Pop Music Transformer (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 2), Compound Word Transformer  (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 4), Melons (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 5), and MeMIDI (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Besides, except for WuYun-RRS, there is a significant  10  A  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='25  Downbeat  Long Note  Rhythm  Tonic Intersection  Union  Random25%  Random50%  ■ Random75%  Mean opinion score (MoS)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='75  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='50  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='25  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='00  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Rhythm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Richness  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Structure  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Expectation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Overall  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Subjective Evaluation Metrics  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='B  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Music Transformer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pop Music Transformer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='MeMIDI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Compound Word Transformer  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='■ Melons  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='WuYun-Rs  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='WuYun-RRS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Mean opinion score(MOS)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='****  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='****  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='****  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='****  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='****  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='****  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='****  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='**  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='***  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='**  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='ns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='ns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='ns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='ns  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='3 -  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Richness  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Structure  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Rhythm  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Expectation  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Overall  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Subjective Evaluation MetricsTable 1: Subjective evaluation scores of generated melodies based on different melody generation models in  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Experiment 2 (mean ± standard deviation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Model  Rhythm  Richness  Structure  Expectation  Overall  1  MT  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='93  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='34 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='83  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='86  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='47 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='88  2  PMT  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='88  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='99  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='54 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='50 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='39 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='12  3  MeMIDI  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='61 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='91  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='95  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='53 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='51 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='97  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='42 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='96  4  CWT  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='77 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='83  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='72 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='85  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='74 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='81  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='70 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='83  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='65 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='90  5  Melons  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='84 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='89  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='95  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='87  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='87  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='71 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='88  6  WuYun-RS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='13 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='88  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='07 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='87  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='13 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='86  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='02 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='92  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='87  7  WuYun-RRS  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='20 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='81  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='85  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='15 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='88  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='00 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='96  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='02 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='88  8  Human  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='54 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='82  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='65 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='76  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='68 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='89  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='92  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='84  MT, PMT, and CWT stand for Music Transformer, Pop Music Transformer, and Compound Word Trans-  former, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  difference (P < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='01) between WuYun-RS and the other melody generation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' This result  demonstrates that WuYun-RS and WuYun-RRS are able to generate melodies with improved long-  term structure and musicality, which benefit from the rhythmic skeleton as a deep structure to guide  the melody generation process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Furthermore, WuYun-RS and WuYun-RRS demonstrate highly similar  performances in terms of the quality of generated melodies on all evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' This result  indicates the effectiveness of the melodic skeletons generated via the melodic skeleton construction  module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' However, there is still an obvious gap between the WuYun melody generation architecture  and human-composed music, leaving room for improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' This also shows that designing clever  decorations for melodic skeletons is another difficult research problem, even for human composers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Additionally, when using the same symbolic music representation method, the knowledge-enhanced  hierarchical skeleton-guided melody generation model of WuYun-RS greatly outperformed the single-  stage end-to-end left-to-right note-by-note melody generation model of MeMIDI (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' On the one  hand, this demonstrates that our proposed hierarchical melody generation paradigm can be applied to  empower the dominant end-to-end left-to-right note-by-note melody generation paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' On the  other hand, although the Compound Word Transformer and Melons (Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 4 and 5) were inferior to  WuYun-RS, their effective compound word representation and the linear Transformer as the backbone  architecture enable it to process multidimensional music information in one step simultaneously and  obtain a better result among these five public SOTA melody generation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Thus, combining the  proposed knowledge-enhanced hierarchical skeleton-guided music generation architecture with more  efficient music representation methods and advanced language models can bring a better result for  melody generation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  3  Discussion  The methodology we have taken in designing WuYun, a hierarchical skeleton-guided melody genera-  tion architecture based on knowledge-enhanced deep learning, combines music analysis theory and  musical psychology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Unlike the dominant end-to-end left-to-right note-by-note melody generation  paradigm, we use the hierarchical organization principle of structure and prolongation to decompose  the melody generation process into melodic skeleton construction and melody inpainting stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We  extract the most structurally important notes based on hearing sensitivity as melodic skeletons and  incorporate them into the melody generation process as a deep structure to guide the model to learn  the hierarchical dependency structures among musical event sequences from the limited melody data  without music boundary detection (31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The human evaluation results demonstrated that our model  exhibits significant improvement in both long-term structure and musicality across the structured  melody generation task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  In practical application scenarios, the ability to obtain real feedback from human users for improving  the performance and interaction experience of the system is essential for the next generation of  iterative and interactive music generation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In general, WuYun allows human users to edit the  generated melodic skeleton and adjust its shape to guide and constrain the range of the decorative  notes at the next stage of melody inpainting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Thus, the proposed generation strategy based on the  11  hierarchical organization principle of structure and prolongation not only can maintain the long-range  tonal coherence of generated melodies but also achieve control over the target of melodic motion by  human users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Additionally, with WuYun and its melodic skeleton analysis framework, human users  can directly extract the skeleton from existing music compositions for music composition analysis or  re-creation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Our study has some limitations, notably the performance of the melody inpainting model, except  that the quality of generated melodic skeleton may be poor;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' even if an original rhythmic skeleton  is provided, the quality of the completed melody is still far from the real one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Further performance  improvements could be achieved using pretrained masked language models (23) for music generation,  especially for the melody inpainting task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Another issue is how to effectively extract an organic  melodic skeleton from hierarchical musical structures combining two or more musical dimensions  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', rhythm and pitch) to further improve the structure of generated melodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' According to the  research in the cognitive psychology in music, while listening to music, only by combining the tonal  and rhythmic structures can we form a more coherent musical representation and create a complete  sense of melody (34, 48, 49).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' However, the brain’s processing mechanism of the hierarchical musical  structure remains a fundamental research problem in the field of music cognitive psychology (64–66).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  With the help of advanced electroencephalography devices, cognitive musicology can break through  the human cognition of hierarchical musical structure and apply it to music generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Additionally,  we expect to investigate other systematic music analysis theories and gain further psychological  knowledge to analyze and compare the hierarchical levels of important musical events along different  musical dimensions for designing a more effective melodic skeleton extraction framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Another  direction is to explore explainable AI for music generation to assist end users in making better  decisions since deep learning methods lack physical transparency of methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' With these potential  future improvements in mind, we hope that our findings for structured melody generation will optimize  the dominant melody generation paradigms to improve long-term structure and musicality and provide  a new lens to develop multidisciplinary research via combining data-driven and knowledge-based  approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  4  Materials and Methods  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  Details of dataset preprocessing  We evaluate the effectiveness of WuYun architecture on a commonly used and publicly available  symbolic melody dataset of Wikifonia (32, 33, 67).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The Wikifonia dataset contains thousands of  lead sheets in MusicXML format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' It covers various music genres, composed of melody and the  accompanying chord progression and tonality labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Here, we describe the procedure below to clean  up noisy data and artificial errors since the dataset is user-generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Data Segmentation: To simplify rhythm modeling, we only keep those segments from  MIDI files with the most commonly used 4/4 time signature (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  MIDI Quantization: For a more beat-accurate timing of sounds, quantization is a useful  digital music processing of setting MIDI data on beats or exact fractions of beats to eliminate  some imprecise timing because of expressive musical performance or mistake record.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We  contend that a more precise and adaptable time grid is required to model a more expressive  metrical context, including the 32nd (18), 64th note, and even triplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' By contrast, most  prior works only use the 16-note time grid for quantification (17, 19, 31–33);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' each bar  is quantized into 16 intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In this study, we propose a self-adaptive mixed precision  quantization method to reduce quantization errors (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' This method can automatically  choose a suitable quantize grid for every single note based on its duration, including straight  notes and triplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The difference between straight notes and triplets is dividing the musical  beat evenly in half or third.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' First, the notes shorter than a 64th note are discarded, whereas  notes longer than one bar are saved into the whole note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Second, according to the note  duration, the rest notes are classified into straight or triplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' However, triplets do not always  have to have three notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' There are only two notes in triplets is quite common, such as in  Swing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Additionally, in theory, every note in triplets has an equal rhythm value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' However, in  practice, most notes are slightly different from each other in musical performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Therefore,  two or three consecutive notes with approximately the same duration and consistent with  the duration of triplets are considered as triplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Based on our experimental statistical  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='A  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16 16 16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Basic Note  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Quantization Error  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Shift Backward  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Shift Forward  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Selected Grids  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Standard Grids  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Standard Duration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Triplet Grids  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Time Signature  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Triplet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Time  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Grid  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Whole Note  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='64  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Triplet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Triplet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='64  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Triplet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Triplet  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Shorter than 64th Note  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='32  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Longer than a whole note  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='❌  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Figure 4: Illustration of the self-adaptive mixed precision MIDI quantization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The MIDI quantization  method would automatically choose a suitable quantize grid for every note according to its note length to  eliminate imprecise timing, including straight notes (minimum 64th note) and triplets (minimum 48th note).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  results, we set the acceptable duration error ratio between the actual triplet and the standard  triplet to within 20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Last, the method automatically selects a proper quantize grid for  every note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In terms of straight notes, the granularity of the time grid depends on the note  duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Particularly, the note onset is aligned to its closest 16th note time grid when the  note duration is greater than or equal to a 16th note, to its closest 32nd note time grid when  the note duration is between a 16nd and 32th note, and to its closest 64th note time grid  when the note duration is between a 32nd and 64th note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Moreover, the straight note offset  is aligned to the 64th note time grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In terms of triplets, the note onset and offset time is  aligned to the 48th note time grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Tonality Unification: For simplicity, the tonalities and chord progressions of those MIDI  files are transposed to “C major” and “A minor” tonalities (68).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We set one chord per beat  and unify the chord representation of the Wikifonia dataset using the chord dictionary as  described in the following subsection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Octave Transposition: All melodies are applied octave transposition to shift the pitch into  the range from C3 to C5 or are removed, which are out of the regular melodic pitch range  (32).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  After data cleaning, we get 2,921 musical pieces in Wikifonia, including 116,935 bars and 425,223  notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Finally, randomly hold out 50 songs for testing and use the remaining for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  Symbolic melody representation  In this work, we adopted a modified version of the “MuMIDI” symbolic music representation (18)  to encode a piece of monophonic melody into discrete musical event sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We refer to it as  MeMIDI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Following is a description of the MeMIDI extensive symbols information, which includes  bar, position, note, chord, and tempo symbols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Bar and Position  We use a bar symbol to represent a bar line and a position symbol to represent the onset  of a note or a chord event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Since the minimum time grids of the straight and triplet note  are 64th and 48th notes, respectively, and the MIDI files’ time resolution is 480 ticks per  beat;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' thus we merge these two kinds of minimum time grids values ({0, 30, 60, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', 1890} ∪  {0, 40, 80, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', 1880}) and use the <Pos_Value> symbol to represent 96 kinds of starting  positions, such as <Pos_30>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We assign a position symbol for every chord and note music  event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  13  Table 2: List of chord events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Chord  Content  Chord root  C, Db, D, Eb, E, F, F#, G, Ab, A, Bb, B  Triad  M, m, o, +  Seventh chord  MM7, Mm7, mM7, mm7, o7, %7, +7, +M7  Chord quality  Suspension  Sus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Note  A note has three basic attributes: pitch, duration, and velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Here, the value of the note  pitch attribute ranges from 48 (C3) to 83 (C5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The value of the note velocity attribute  ranges from 0 to 127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Considering both straight notes and triplet notes, the value range of  the note duration attribute is {30, 60, 90, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', 1920} ∪ {40, 80, 160, 320, 640} ticks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We use  a compound word <Pitch_Value, Velocity_Value, Duration_Value> to compress these three  attributes of one note in one token to shorten the length of the melody events sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Chord  To cover the chord types in the Wikifonia dataset, we use a more comprehensive chord  event list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' As shown in Table 2, we consider 12 chord roots and 13 chord qualities, yielding  156 possible chord events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We use a chord symbol <Root_Quality> to represent a chord  musical event.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' To reduce repetition, we use the same position symbol for Note and Chord,  which start at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For simplicity, we do not use the Chord symbol in the melodic  skeleton event sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Tempo  We divide the tempo into three categories: low (below 90), medium (90 to 160), and high  (above 160).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='3  WuYun architecture  Here, we briefly elaborate on the configuration details of the two Transformer-based generative  modules of WuYun architecture, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', the melodic skeleton generation module for the melodic skeleton  construction stage and the melodic prolongation generation module for the melody inpainting stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  We refer readers to (17–19) for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For reproducibility, we do not tweak the architecture of  referenced models so that our music generation architecture can be easily assembled with the public  implementation of Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  We use an unconditional sequence learning model Transformer-XL for the melodic skeleton genera-  tion module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We use four self-attention layers, each with eight attention heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The model hidden  size and the inner layer of the feed-forward part are set to 512 and 2,048, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' All token  embedding sizes are set to 512, following (19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We use the compound word embedding (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' S1) and  token attribute prediction method for the input and output modules, repectively (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We employed  the top-k temperature-controlled stochastic sampling method (k = 10, temperature = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='9) during  inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The length of training input tokens and the memory length are also 512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Here, we used the  melodic skeleton data extracted from the training part of the Wikifonia dataset to train the melodic  skeleton generation module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  We use a conditional sequence-to-sequence model based on Transformer-based recurrent en-  coder–decoder neural networks for the melodic prolongation generation module (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We set the  number of encoder layers, decoder layers, encoder heads, and decoder heads to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The size of hidden  layers and the dimension of token embeddings are set to 256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We keep the same input module, output  module, sampling method, length of training input tokens, and memory as same as the melodic  skeleton generation module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' For training the melodic prolongation generation module, we use the  MeMIDI representations of the paired melodic skeleton and melody data as the encoder and decoder  input data, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  14  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  Training  We implemented the WuYun architecture with Pytorch (v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1) (69).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The parameters of the WuYun  architecture were optimized by minimizing the cross-entropy loss on a single NVIDIA GTX 2080-Ti  GPU with 11 GB memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Specifically, the training loss was minimized with the Adam optimizer  (β1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='9, β2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='98), a learning rate of ε = 10−3 , and dropout was applied with a ratio of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  The mini-batches of the input data for the melodic skeleton generation module and the melodic  prolongation generation module were 20 and 44, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' It took nearly 2 days to train the two  modules until training convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='5  Statistical analysis  All subjective evaluation results were expressed as mean ± standard deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The statistical  significance of the performance difference in WuYun-RS and other melody generation methods  was analyzed using the one-tailed t-test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Asterisk indicates significant difference at *P < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='05,  **P < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='01, ***P < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='001, ****P < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='0001, and ns, not significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Acknowledgements  Thanks to Huawei Technologies Co.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', Ltd for the help in dataset collection and comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' We  thank Jiaxing Yu, Chongjun Zhong, Ruiyuan Tang, and Jiaqi Wang for insightful discussions and  visualizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Funding:  This work is supported by the National Natural Science Foundation of China  (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='62272409), the Key R&D Program of Zhejiang Province (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2022C03126), the Project of  Key Laboratory of Intelligent Processing Technology for Digital Music (Zhejiang Conservatory of  Music), and the Ministry of Culture and Tourism (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2022DMKLB001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Author contributions: Conceptualization: K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Methodology: X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Investi-  gation: T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Visualization: S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Supervision: L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Writing—original  draft: X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Writing—review & editing: K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Competing interests: K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' are inventors on a patent application related to this work  filed by Zhejiang University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The authors declare that they have no other competing interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Data and materials availability: All data needed to evaluate the conclusions in the paper are present  in the paper and/or the Supplementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Raw experimental data and the generated symbolic  melody files are available on Zenodo at DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='5281/zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='7480957  under a Creative Commons Attribution 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='0 International license.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The code of the WuYun music  generation framework is available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='com/NEXTLab-ZJU/wuyun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  References  [1] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Carnovalini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Rodà, Computational creativity and music generation systems: An introduction to the state  of the art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Front.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Artif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 3, 14 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [2] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' LeCun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bengio, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hinton, Deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nature 521, 436–444 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Briot, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hadjeres, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Pachet, Deep Learning Techniques for Music Generation (Springer, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [4] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Frid, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Gomes, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jin, Music creation by example, in Proceedings of the 2020 CHI conference on human  factors in computing systems (CHI, 2020), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Qin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Martín-Martínez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Buehler, A Self-Consistent Sonification Method to Translate Amino  Acid Sequences into Musical Compositions and Application in Protein Design Using Artificial Intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' ACS  Nano 13, 7471–7482 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Di, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jiang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' He, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' He, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yan, Video background music generation  with controllable music transformer, in Proceedings of the 29th ACM International Conference on Multimedia  (MM, 2021), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 2037–2045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [7] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wesseldijk, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Mosing, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ullén,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Why Is an Early Start of Training Related to Musical Skills in  Adulthood?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A Genetically Informative Study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Psychol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 32, 3–13 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  15  [8] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ye, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Mao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hayashi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, Sound induces analgesia through corticothalamic circuits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Science 377, 198–204 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Koelsch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Rohrmeier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Torrecuso, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jentschke, Processing of hierarchical syntactic structure in  music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 110, 15443–15448 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Patel, Language, music, syntax and the brain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neurosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 6, 674–681 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Valanarasu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Oza, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hacihaliloglu, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Patel, Medical Transformer: Gated Axial-Attention for  Medical Image Segmentation, in International Conference on Medical Image Computing and Computer-Assisted  Intervention (Cham, 2021), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 36–46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [12] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhou, Neural speech synthesis with transformer network, in  Proceedings of the AAAI Conference on Artificial Intelligence (AAAI, 2019), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 6706–6713.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [13] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Schwaller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hoover, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Reymond, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Strobelt, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Laino, Extraction of organic chemistry grammar  from unsupervised learning of chemical reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 7, eabe4166 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [14] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jumper, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Evans, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Pritzel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Green, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Figurnov, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ronneberger, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tunyasuvunakool, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bates, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Žídek, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Potapenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bridgland, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Meyer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Kohl, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ballard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Cowie, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Romera-Paredes, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Nikolov, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jain, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Adler, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Back, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Petersen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Reiman, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Clancy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zielinski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Steinegger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Pacholska,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Berghammer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bodenstein, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Silver, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Vinyals, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Senior, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Kavukcuoglu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Kohli, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hassabis,  Highly accurate protein structure prediction with AlphaFold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nature 596, 583–589 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [15] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Huang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Vaswani, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Uszkoreit, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Simon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hawthorne, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Shazeer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Dai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hoffman,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Dinculescu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Eck, Music Transformer: Generating music with long-term structure, in 7th International  Conference on Learning Representations (ICLR, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [16] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Lu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ye, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Qin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, Museformer: Transformer with  fine-and coarse-grained attention for music generation, in Advances in Neural Information Processing Systems  (NeurIPS, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [17] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yang, Pop music transformer: Beat-based modeling and generation of expressive pop piano  compositions, in Proceedings of the 28th ACM International Conference on Multimedia (MM, 2020), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  1180–1188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Qin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, Popmag: Pop music accompaniment generation, in  Proceedings of the 28th ACM International Conference on Multimedia (MM, 2020), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1198–1206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [19] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hsiao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yeh, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yang, Compound word transformer: Learning to compose full-song music over  dynamic directed hypergraphs, in Proceedings of the AAAI Conference on Artificial Intelligence (AAAI, 2021),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 178–186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [20] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Payne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' “Musenet.” OpenAI, July 21, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' http://openai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='com/blog/musenet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [21] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, Learning adversarial transformer for symbolic music generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neural Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1–10 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [22] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sageev, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ian, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sander, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Douglas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Karen, This time with feeling: Learning expressive musical  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neural.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 32, 955–967 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zeng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ju, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Qin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, MusicBERT: Symbolic music understanding with  large-scale pre-training, in Findings of the ACL: ACL-IJCNLP 2021 (ACL, 2021), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 791–800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [24] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Anishchenko, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chidyausiku, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ovchinnikov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Pellock, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Baker, De novo protein design by  deep network hallucination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nature 600, 547–552 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [25] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chowdhury, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bouatta, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Biswas, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Floristean, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Kharkare, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Roye, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Rochereau, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ahdritz,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Church, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sorger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' AlQuraishi, Single-sequence protein structure prediction using a  language model and deep learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Biotechnol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 40, 1617–1623 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Dauparas, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Anishchenko, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bennett, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bai, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ragotte, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Milles, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wicky, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Courbet,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Haas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bethel, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Leung, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Huddy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Pellock, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tischer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Koepnick, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nguyen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Kang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sankaran, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bera, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' King, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Baker, Robust deep learning-based protein sequence design using  ProteinMPNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Science 378, 49–56 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Han, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tong, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jia, SkeletonNet: A Topology-Preserving Solution for Learning Mesh  Reconstruction of Object Surfaces From RGB Images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Pattern Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 44, 6454–6471  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [28] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Shi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Diao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Xing, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Xu, RCRN: Real-world Character Image Restoration Network  via Skeleton Extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' In Proceedings of the 30th ACM International Conference on Multimedia (MM, 2022),  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 1177–1185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  16  [29] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sun, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Deng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Pan, Visual knowledge guided  intelligent generation of Chinese seal carving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Front.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 23, 1479–1493 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [30] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhu, A hierarchical recurrent neural network for symbolic melody  generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Cybern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 50, 2749–2757 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [31] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Dai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Gomes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Dannenberg, Controllable deep melody generation via hierarchical music  structure representation, in Proceedings of the 22nd International Society for Music Information Retrieval  Conference (ISMIR, 2021), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 143–150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [32] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhu, Popmnet: Generating structured pop music melodies using neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Artif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 286, 103303 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [33]Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zou, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wang, MELONS: generating melody with long-term  structure using transformers and structure graph, in ICASSP 2022-2022 IEEE International Conference on  Acoustics, Speech and Signal Processing (ICASSP, 2022), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 191–195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [34] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Lerdahl, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jackendoff, A Generative Theory of Tonal Music (MIT Press, Cambridge, MA, 1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [35] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ayotte, Heinrich Schenker: A Guide to Research (Routledge, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [36] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Berezovsky, The structure of musical harmony as an ordered phase of sound: A statistical mechanics  approach to music theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 5, eaav8490 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [37] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Salzer, Structural Hearing: Tonal Coherence in Music (Courier Corporation, 1962).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [38] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Dai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Carbonell, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Le, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Salakhutdinov, Transformer-XL: Attentive language  models beyond a fixed-length context, in Proceedings of the 57th Annual Meeting of the ACL (ACL, 2019), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  2978–2988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [39] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Vaswani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Shazeer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Parmar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Uszkoreit, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jones, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Gomez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Kaiser, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Polosukhin, Attention  is all you need, in Proceedings of the 31st Conference on Neural Information Processing Systems (NIPS, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [40] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hadjeres, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nielsen, Anticipation-RNN: enforcing unary constraints in sequence generation, with  application to interactive music generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neural.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 32, 995–1005 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [41] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Maess, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Koelsch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Gunter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Friederici, Musical syntax is processed in Broca’s area: An MEG  study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neurosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 4, 540–545 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [42] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hauser, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chomsky, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Fitch, The faculty of language: What is it, who has it, and how did it  evolve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Science 298, 1569–1579 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [43] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Fitch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hauser, Computational constraintson syntactic processing in a nonhuman primate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Science 303, 377–380 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' [44]A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Friederici, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bahlmann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Heim, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Schubotz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Anwander, The  brain differentiates human and non-human grammars: Functional localization and structural connectivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 103, 2458–2463 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [45] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Näätänen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Anne, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Mietta, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Marie, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Minna, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Antti, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Martti, Alku, Paavo, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Risto, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Aavo,  Language-specific phoneme representations revealed by electric and magnetic brain responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nature 385,  432–434 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [46] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Baddeley, Working memory: Looking back and looking forward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neurosci 4, 829–839 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [47] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Schenker, Neue Musikalische Theorien und Phantasien: Der Freie Satz (Universal Edition, 1956).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [48] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hodges, Music in the Human Experience: An Introduction to Music Psychology (Routledge, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [49] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Patel, Music, Language, and the Brain (Oxford University Press, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [50] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Povel, Melody generator: a device for algorithmic music construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Softw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Appl 3, 683 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [51] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Laitz, The Complete Musician: An Integrated Approach to Tonal Theory, Analysis, and Listening  (Oxford University Press, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [52] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Lerdahl, Tonal Pitch Space (Oxford University Press, 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [53] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Lerdahl, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Krumhansl, Modeling tonal tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Music Percept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 24, 329–366 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [54] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Cooper, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Meyer, The Rhythmic Structure of Music (Chicago University Press, 1963).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [55] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Krumhansl, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Cuddy, A theory of tonal hierarchies in music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Music Percept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 36, 51–87 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [56] Nattiez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=', Music and Discourse: Toward a Semiology of Music (Princeton University Press, 1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [57] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chew, Mathematical and computational modeling of tonality, AMC 10, 141 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  17  [58] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Herremans, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chew, Tension ribbons: Quantifying and visualising tonal tension, in Proceedings of the  Second International Conference on Technologies for Music Notation and Representation (TENSOR, 2016), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  8–18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [59] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Dorien, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chew, MorpheuS: generating structured music with constrained patterns and tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' IEEE  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Affect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 10, 510–523 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [60] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Lerch, On the evaluation of generative models in music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neural.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 32,  4773–4784 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [61] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Huron, Sweet Anticipation: Music and the Psychology of Expectation (MIT Press, Cambridge, MA,  2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [62] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Koffka, Principles of Gestalt Psychology (Routledge, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [63] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Treisman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Gelade, A feature-integration theory of attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Cogn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Psychol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 12, 97–136 (1980).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [64] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Brown, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hollinger, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Penhune, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Palmer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zatorre, Repetition suppression in  auditory-motor regions to pitch and temporal structure in music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Cogn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neurosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 25, 313328 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [65] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Peretz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Coltheart, Modularity of music processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neurosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 6, 688–691 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [66] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Kuperberg, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Jaeger, What do we mean by prediction in language comprehension?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Lang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Cogn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Neurosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 31, 32–59 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [67] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Hutchings, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' McCormack, Adaptive music composition for games.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Games 12, 270–280  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [68] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Ju, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Wu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Qin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Liu, TeleMelody: Lyric-  to-Melody generation with a template-based two-stage method, in Proceedings of the 2022 Conference on  Empirical Methods in Natural Language Processing (EMNLP, 2022), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 5426–5437.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  [69] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Paszke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Gross, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Massa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Lerer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bradbury, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chanan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Killeen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Lin, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Gimelshein, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Antiga, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Desmaison, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Kopf, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' De Vito, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Raison, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Tejani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chilamkurthy, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Steiner, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Fang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Bai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Chintala, PyTorch: An imperative style, high-performance deep learning library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Neural Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' 32, 8026–8037 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  18  A  Appendix  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Additional Supplementary Figure  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='···  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Velocity Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Duration Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Token Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Position Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Tempo Embeddings  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Timestep  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='A  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='➕  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='➕  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='➕  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='➕  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='➕  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='8  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='9  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='13  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='16  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='TempM  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos720  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos720  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos960  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos960  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos960  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos1440  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos1440  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos480  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos480  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='ChC_M  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos720  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pitch62  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos960  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='ChC_M  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pitch63  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='ChC_M  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pitch60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Bar  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pitch60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Pos480  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='ChD_M  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='ChC_M  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Dur240  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Dur480  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Dur480  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Dur720  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Vel127  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Vel127  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Vel127  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Vel127  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='Figure S1: MeMIDI encoding method for MIDI sequences (example).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content=' The input embedding in each timestep  of the MeMIDI event sequence is the sum of the event embeddings, including tempo embedding, bar embedding,  position embedding, token embedding, duration embedding, and velocity embedding in this timestep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='2  Additional Supplementary Tables  Table S1: Subjective evaluation scores of generated melodies based on different melodic skeleton settings in  Experiment 1 (mean ± standard deviation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Settings  Rhythm  Richness  Structure  Expectation  Overall  1  Downbeat  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='75 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='96  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='98  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='63 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='13  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='45 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='03  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='52 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='03  2  Long Note  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='70 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='03  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='57 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='17  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='77 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='21  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='47 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='27  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='67 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='26  3  Rhythm  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='02 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='01  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='10 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='89  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='88 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='02  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='81  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='93 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='97  4  Tonic  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='95 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='80 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='87 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='95  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='65 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='80 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='06  5  Intersection  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='60 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='85  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='52 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='87  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='53 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='83  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='98  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='43 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='83  6  Union  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='95 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='95  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='57 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='62 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='09  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='43 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='05  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='60 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='04  7  Random25%  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='80 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='78 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='98  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='67 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='07  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='62 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='95  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='65 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='12  8  Random50%  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='92 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='98  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='89  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='70 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='01  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='68 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='03  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='95  9  Random75%  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='82 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='95  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='58 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='50 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='11  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='45 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='04  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='53 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='08  Table S2: One-tailed t-test results between WuYun-RS and other music generation models on the five evaluation  metrics in experiment 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  Model  Rhythm  Richness  Structure  Expectation  Overall  MT  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='43 × 10−7  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='37 × 10−9  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='44 × 10−12  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='50 × 10−6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='21 × 10−10  PMT  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='18 × 10−8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='21 × 10−9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='20 × 10−6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='55 × 10−6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='13 × 10−7  MeMIDI  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='88 × 10−6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='09 × 10−6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='86 × 10−7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='31 × 10−5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='29 × 10−7  CWT  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='31 × 10−4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='47 × 10−4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='02 × 10−4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='03 × 10−3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='69 × 10−3  Melons  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='60 × 10−3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='54 × 10−3  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='02 × 10−4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='12 × 10−3  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='41 × 10−3  WuYun-RRS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='26  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='41  MT, PMT, and CWT stand for Music Transformer, Pop Music Transformer, and Compound Word Trans-  former, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
+page_content='  19' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/L9E3T4oBgHgl3EQfYgo-/content/2301.04488v1.pdf'}
diff --git a/OtFKT4oBgHgl3EQffy6V/content/2301.11831v1.pdf b/OtFKT4oBgHgl3EQffy6V/content/2301.11831v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..2446ce4051013ea74a5c523b222b0c5eae88974e
--- /dev/null
+++ b/OtFKT4oBgHgl3EQffy6V/content/2301.11831v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:16ca724abca29ed93b2f0ad54b5c68316d85a00744af463df29437f180ee0be4
+size 346643
diff --git a/PdE3T4oBgHgl3EQfCglF/content/tmp_files/2301.04276v1.pdf.txt b/PdE3T4oBgHgl3EQfCglF/content/tmp_files/2301.04276v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..608eae697e1bd15dd91d310c00a524e24924c48b
--- /dev/null
+++ b/PdE3T4oBgHgl3EQfCglF/content/tmp_files/2301.04276v1.pdf.txt
@@ -0,0 +1,902 @@
+Performance Analysis of Superconductor-constriction-Superconductor Transmon
+Qubits
+Mingzhao Liu∗ and Charles T. Black†
+Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA
+This work presents a computational analysis of a superconducting transmon qubit design, in which
+the superconductor-insulator-superconductor (SIS) Josephson junction is replaced by a co-planar,
+superconductor-constriction-superconductor (ScS) junction.
+For short junctions having a Kulik-
+Omelyanchuk current-phase relationship, we find that the ScS transmon has an improved charge
+dispersion compared to the SIS transmon, with a tradeoff of 50% smaller anharmonicity. These
+calculations provide a framework for estimating the superconductor material properties and junction
+dimensions needed to provide proper ScS transmon operation at typical gigahertz frequencies.
+I.
+INTRODUCTION
+The transmon has become an enabling superconduct-
+ing qubit device architecture, with primary advantages of
+immunity to charge noise and longer coherence lifetimes
+achieved by designing the device to have Josephson en-
+ergy far exceeding the charging energy. Similar to other
+superconducting qubit architectures, the transmon core
+consists of one or more Josephson junctions (JJs), which
+are exclusively superconductor-insulator-superconductor
+tunnel junctions (SIS) — typically a thin film sand-
+wich structure of aluminum/aluminum oxide/aluminum
+(Al/AlOx/Al), in which AlOx is the tunnel barrier (Fig-
+ure 1a).
+Fabrication of Al/AlOx/Al SIS JJs typically involves
+physical vapor deposition of the top and bottom Al lay-
+ers from two different angles relative to the substrate,
+through a common mask [1]. After depositing the first
+Al layer, the sample is exposed to a controlled level of
+oxygen to form the thin AlOx barrier. This ingenious
+fabrication method has been refined over many years but
+will nevertheless be highly challenging to implement at
+the manufacturing scale required for larger-scale quan-
+tum computers. The exponential dependence of the JJ
+critical supercurrent (Ic) on tunnel barrier width also re-
+sults in a typical few percent variation in Ic across devices
+Al
+Al
+AlOx
+Superconductor
+Constriction
+a
+b
+Figure 1. (a) Schematic of an Al/AlOx/Al superconductor-
+insulator-superconductor (SIS) Josephson junction. For clar-
+ity, the native oxide covering both Al electrodes is omitted.
+(b) Schematic of a co-planar superconductor-constriction-
+superconductor (ScS) Josephson junction.
+∗ mzliu@bnl.gov
+† ctblack@bnl.gov
+fabricated within a few centimeters, even when oxidation
+conditions are tightly controlled.[2–5] Since the Joseph-
+son energy is directly proportional to Ic, this variation
+presents an additional design and manufacturing chal-
+lenge.
+In a transmon, the SIS JJ is shunted by a large capac-
+itor to minimize the charging energy and thus provide
+immunity to charge noise. Further, the qubit is coupled
+to a high-Q microwave resonator for readout. Typically,
+the shunting capacitor and the resonator are fabricated
+separately from the SIS JJ, using a superconductor with
+higher Tc and better chemical robustness compared to Al
+(e.g., niobium (Tc = 9.2 K)[6], tantalum (Tc = 4.4 K)[7],
+and titanium nitride (Tc = 5.6 K)[8]). The improved ro-
+bustness allows post-fabrication chemical treatments to
+remove surface contaminants, which contribute to TLS
+loss. However, most of these treatments are not possible
+after Al/AlOx/Al junction fabrication, due to the junc-
+tion’s fragile nature [9].
+In this work we analyze the performance impact
+of replacing the transmon SIS tunnel junction with
+a co-planar superconductor-constriction-superconductor
+(ScS) Josephson junction. A ScS JJ is comprised of two
+superconductors separated by a thin neck of the same
+superconductor (Figure 1b), with the constriction estab-
+lishing the superconducting phase difference that enables
+Josephson behavior. ScS JJs are co-planar (unlike SIS
+tunnel junctions) and can be fabricated using conven-
+tional lithography and metallization. Here, we follow the
+formalism established by Koch et al.
+in [10] to deter-
+mine the electrical properties of ScS transmons, which
+are shown to be different from SIS transmons, stemming
+from a different ScS JJ current-phase relationship (CPR
+or CΦR) compared to that of a SIS JJ.[11–13]. Compar-
+ing the two device architectures, we show that the ScS
+transmon has 50% less anharmonicity than the SIS trans-
+mon, for devices with the same Josephson energy and
+capacitive energy. However, the smaller anharmonicity
+is accompanied by a significantly smaller charge disper-
+sion, giving the ScS transmon stronger immunity against
+charge noise.
+arXiv:2301.04276v1  [cond-mat.supr-con]  11 Jan 2023
+
+2
+II.
+RESULTS AND DISCUSSION
+II.1.
+Current-phase relation of a short ScS junction
+Consider a ScS Josephson junction comprised of two
+large superconductors connected by a diffusive quasi-one-
+dimensional wire with length d ≪ √ξ0l and width w ≪
+d, where ξ0 is the Pippard superconducting coherence
+length, and l ≪ ξ0 is the dirty-limit electron mean free
+path. In this case, Kulik and Omelyanchuk showed that
+the CPR for the ScS junction (KO-1) at T = 0 K is:
+IScS(ϕ) = π∆
+eRn
+cos ϕ
+2 tanh−1 �
+sin ϕ
+2
+�
+,
+(1)
+in which ∆ is the superconducting energy gap and Rn
+is the normal state resistance of the junction.[11, 12]
+The junction critical current Ic,ScS = 0.662π∆/(eRn) is
+achieved at ϕ = (2k ± 0.627)π to satisfy dI(ϕ)/dϕ ∝
+1 − sin(ϕ/2) tanh−1 [sin(ϕ/2)] = 0. Given the Maclau-
+rin series tanh−1(x) = x + x3/3 + O(x5), Eq.
+1 may
+be rewritten to a form that resembles the CPR of a SIS
+Josephson junction, as
+IScS(ϕ) = 0.755Ic,ScS sin ϕ
+�
+1 + 1
+3 sin2 ϕ
+2 + O
+�
+sin4 ϕ
+2
+� �
+,
+which shows that the CPR of a ScS junction distorts
+from the conventional sinusoidal form, but still bears odd
+parity and a 2π periodicity (Figure 2a).
+II.2.
+Josephson energy of a ScS transmon
+The potential energy of a Josephson junction is given
+by the integral
+EJ(ϕ) =
+�
+IJV dt =
+�
+IJ
+Φ0
+2π
+dϕ
+dt dt =
+�
+IJ
+Φ0
+2π dϕ.
+(2)
+−2
+−1
+0
+1
+2
+φ/π
+−1.0
+−0.5
+0.0
+0.5
+1.0
+I(φ)/Ic
+ScS
+SIS
+−1.0
+−0.5
+0.0
+0.5
+1.0
+φ/π
+0
+1
+2
+3
+EJ(φ)/EJ
+ScS
+SIS
+φ2/2
+a
+b
+Figure 2. (a) The CPR of a ScS Josephson junction in the
+KO-1 limit (solid red) is distorted from the sinusoidal form
+of a SIS junction (dashed black). (b) The Josephson energy
+of a ScS transmon (solid red) deviates from the cosine form
+of a SIS transmon (dashed black) and has 50% smaller an-
+harmonicity at its lowest order (ϕ4). A harmonic parabola,
+ϕ2/2, is displayed (dotted cyan) for reference.
+−1.0
+−0.5
+0.0
+0.5
+1.0
+φ/π
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+EJ(φ)/EJ
+−1.0
+−0.5
+0.0
+0.5
+1.0
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+φ/π
+EJ(φ)/EJ
+a
+b
+SIS
+ScS
+0.3031
+0.8800
+1.3993
+1.7751
+0.3096
+0.9145
+1.4896
+2.0077
+Figure 3. The eigenenergies (blue lines and numbers) and the
+probability densities (∥Ψ∥2) of the first 4 eigenstates of (a) a
+SIS transmon and (b) a ScS transmon, both with EJ/EC = 20
+and ng = 1/2. The corresponding potential energies, normal-
+ized by EJ, are plotted in red lines for both transmons.
+For a KO-1 junction defined by Eq. 1, the integral in Eq.
+2 leads to
+EJ,ScS(ϕ) = ∆Φ0
+2eRn
+�
+ln
+�
+cos2 ϕ
+2
+�
++ 2 sin ϕ
+2 tanh−1 �
+sin ϕ
+2
+� �
+.
+(3)
+Although this form appears very different from the po-
+tential energy of a SIS junction, EJ,SIS(ϕ) = EJ,SIS(1 −
+cos ϕ), with EJ,SIS = Ic,SISΦ0/2π, Maclaurin expansions
+of EJ,ScS and EJ,SIS make their similarities apparent:
+EJ,ScS(ϕ) = ∆Φ0
+4eRn
+�1
+2ϕ2 − 1
+48ϕ4 + O(ϕ6)
+�
+EJ,SIS(ϕ) = EJ,SIS
+�1
+2ϕ2 − 1
+24ϕ4 + O(ϕ6)
+�
+.
+(4)
+Comparing the coefficients of the harmonic (ϕ2) term,
+we observe that the Josephson energy of a ScS transmon
+can be defined as:
+EJ,ScS = ∆Φ0
+4eRn
+= 0.755Ic,ScSΦ0/(2π) ,
+(5)
+where
+the
+last
+equality
+recognizes
+that
+Ic,ScS
+=
+0.662π∆/(eRn). Eq. 5 shows that both potential ener-
+gies contain anharmonicity led by a ϕ4 term, from which
+we estimate that the anharmonicity of a ScS transmon
+is about one half that of a SIS transmon, for devices
+with the same EJ. This difference is clear when compar-
+ing normalized EJ(ϕ) of ScS and SIS transmons with a
+harmonic parabolic potential ϕ2/2 (Figure 2b). A more
+precise evaluation of the anharmonicity is given in II.3,
+by computing the ScS transmon eigenenergies.
+II.3.
+Eigenenergies and eigenstates of a ScS
+transmon
+A conventional SIS transmon has a Hamiltonian of the
+form:
+ˆHSIS = 4Ec(ˆn − ng)2 + EJ(1 − cos ˆϕ),
+(6)
+
+3
+0
+20
+40
+60
+80
+100
+0
+20
+40
+60
+80
+E0m/EC
+0
+20
+40
+60
+80
+100
+−1
+0
+1
+2
+3
+4
+5
+(E12 - E01)/EC
+ScS
+SIS
+a
+b
+EJ/EC
+EJ/EC
+ScS
+SIS
+m = 0
+1
+2
+3
+0
+20
+40
+60
+80
+100
+100
+τp (ns)
+SIS
+ScS
+EJ/EC
+10-1
+10-2
+c
+Figure 4. (a) Transition energy E0m = Em − E0 at ng = 1/2 and (b) oscillator anharmonicity (E12 − E01) at ng = 1/2, as
+functions of EJ/EC for ScS transmon (solid lines) and SIS transmon (dashed lines). (c) The minimal pulse duration (τp) of
+ScS (solid line) and SIS transmons (dashed line) vs. EJ/EC, all operated at ω01 = 2π × 10 GHz.
+where ng is the offset charge. The wave equation for a
+SIS transmon can be solved analytically.[10]
+In the ScS transmon, the potential energy is given by
+Eq. 3, so that the Hamiltonian becomes,
+ˆHScS = 4EC(ˆn − ng)2 + EJ
+�
+2 ln
+�
+cos2 ˆϕ
+2
+�
++ 4 sin ˆϕ
+2 tanh−1
+�
+sin ˆϕ
+2
+� �
+.
+(7)
+The wave equation of a ScS transmon can be solved nu-
+merically using the finite difference method, in which the
+Hamiltonian is expressed in a discretized space of phase
+ϕ ∈ [−π, π), with the periodic boundary condition ap-
+plied to both ends. The validity of the computation is
+confirmed by comparing a similar numerical solution of
+the wave equation for a SIS transmon with the analytical
+solutions presented by Koch et al.[10] Figure 3 compares
+the first 4 eigenstates of a SIS transmon and a ScS trans-
+mon, both with EJ/EC = 20 and ng = 1/2. Although
+the lower level eigenenergies and eigenfunctions are sim-
+ilar, the differences become more apparent at higher en-
+ergies. This trend is more clearly observed for the transi-
+tion energies E0m = Em − E0 calculated for both trans-
+mon types, across a range of EJ/EC from 1 and 100
+(Figure 4a). This difference reflects the smaller anhar-
+monicity of the ScS transmon, compared to the SIS trans-
+mon. By treating the leading anharmonic term (−ϕ4/24)
+in Eq.
+4 as a perturbation to the harmonic potential
+and applying the first-order perturbation theory, the mth
+eigenenergy of a SIS transmon is approximated by [10]
+Em,SIS ≈ ℏωp
+�
+m + 1
+2
+�
+− EC
+4
+�
+2m2 + 2m + 1
+�
+,
+(8)
+in which ℏωp = √8EJEC is the Josephson plasma energy.
+The transition energy between the (m − 1)th and mth
+levels is therefore
+Em−1,m,SIS ≈ ℏωp − mEC.
+(9)
+From Eq.
+9, we find that the anharmonicity of SIS
+transmon αSIS ≡ E12,SIS−E01,SIS is approximately −EC.
+By applying the same first-order perturbation theory cal-
+culation but realizing that the perturbation term is half
+as a SIS transmon (Eq. 4), the mth eigenenergy of a ScS
+transmon can be approximated by
+Em,ScS ≈ ℏωp
+�
+m + 1
+2
+�
+− EC
+8
+�
+2m2 + 2m + 1
+�
+,
+(10)
+so that its anharmonicity, αScS, is approximately −EC/2,
+or half the anharmonicity of a SIS transmon. We can vi-
+sualize this finding in a plot of numerical results, looking
+at transmons with EJ/EC ≥ 20 (Figure 4b).
+The smaller anharmonicity of a ScS transmon means
+that the transitions E01 and E12 lie closer in energy, so
+that a longer RF pulse is needed to correctly excite the
+desired transition E01. The minimal pulse duration can
+be estimated as τp ≈ ℏ|α|−1.
+As shown in Figure 4c,
+despite its lower anharmonicity, τp of the ScS transmon
+remains below 1 ns even for EJ/EC = 100, when the
+qubit operates at 10 GHz. Because typical qubit pulse
+durations are ∼10 ns, we may conclude that the lower
+anharmonicity will not inhibit normal operation of a ScS
+transmon.
+II.4.
+Charge dispersion of a ScS transmon
+A primary benefit of the transmon architecture is its
+relative immunity to charge noise, when designed to op-
+erate in the regime of EJ ≫ EC. In a SIS transmon, the
+charge dispersion of the mth level decreases exponentially
+with
+�
+8EJ/EC, following [10]
+ϵm ≡ Em(ng = 1/2) − Em(ng = 0)
+≈ EC
+24m+5
+(−1)mm!
+�
+2
+π
+� EJ
+2EC
+� m
+2 + 3
+4
+e−√
+8EJ/EC.
+(11)
+Intuitively, the charge dispersion is related to the
+tunneling probability between neighboring potential en-
+ergy valleys (Figure 3), e.g., when ϕ makes a full 2π
+
+4
+−2
+−1
+0
+1
+2
+ng
+0.5
+1.0
+1.5
+2.0
+Em/EJ
+SIS
+ScS
+SIS
+ScS
+|ϵm|/E01(ng = 1/2)
+101
+10-3
+10-7
+10-1
+10-5
+10-9
+10-11
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+(EJ/EC)1/2
+10
+20
+30
+40
+50 60 70 80 90 100
+EJ/EC
+a
+b
+m = 0
+1
+2
+m = 0
+1
+2
+0
+20
+40
+60
+80
+100
+SIS
+ScS
+T2 (ns)
+EJ/EC
+100
+10-2
+104
+102
+106
+108
+c
+Figure 5. (a) The eigenenergies Em of the lowest 3 eigenstates (m = 0, 1, 2) of a ScS transmon (solid line) and a SIS transmon
+(dashed lines), both with EJ/EC = 10, as functions of the offset charge ng. (b) The charge dispersion ϵm of the lowest 3
+eigenstates of a ScS transmon (solid line) and a SIS transmon (dashed lines), as functions of EJ/EC. (c) The dephasing time
+T2 of ScS (solid line) and SIS transmons (dashed line) vs. EJ/EC, all operated at ω01 = 2π × 10 GHz.
+rotation.[10] By this reasoning, we may expect the higher
+barrier height of a ScS transmon (∼ 2.8EJ vs.
+2EJ)
+to better suppress the tunneling probability and provide
+lower charge dispersion, compared to a SIS transmon.
+Figure 5a plots the first three eigenenergies Em (m =
+0, 1, 2) versus the effective offset charge ng for both SIS
+(dashed) and ScS (solid) transmons, with EJ/EC = 10.
+Clearly, the ScS transmon eigenenergies are more weakly
+perturbed by ng. Calculations of the charge dispersion,
+ϵm = Em(ng = 1/2) − Em(ng = 0), across a wide range
+of 1 ≤ EJ/EC ≤ 100 show that suppression of charge dis-
+persion in the ScS transmon becomes more effective for
+larger EJ/EC ratios (Figure 5b). When EJ/EC = 100,
+the charge dispersion of the first excited state of a ScS
+transmon, ϵ1,ScS, is over one order of magnitude less than
+the corresponding SIS transmon. It is noted that com-
+putation on SIS transmon matches the analytical result
+very well[10], again demonstrating the high numerical
+precision of our finite difference computation.
+Never-
+theless, the computational error becomes significant as
+the normalized charge dispersion, |ϵm|/E01, approaches
+10−11 and smaller. This is due to the accumulation of
+floating-point error that eventually shows up for evaluat-
+ing the vanishing difference between the two eigenener-
+gies at ng = 0 and 1/2.
+In Figure 5b, the y−axis is presented in the logarith-
+mic scale and the x−axis is presented in the scale of
+�
+EJ/EC, so that all curves take a linear form approach-
+ing large EJ/EC values. For the SIS transmon, the slope
+matches the expected exp(−
+�
+8EJ/EC) dependence in
+Eq. 11. For the ScS transmon, the slope is larger, and is
+best described by:
+ϵm ∝ exp
+�
+−
+�
+1.16 × 8EJ/EC
+�
+.
+The improved charge dispersion makes the ScS trans-
+mon both less sensitive to charge noise and, in turn, gives
+it a longer dephasing time T2.
+For dephasing caused
+by slow charge fluctuations of large amplitude, Koch et
+al[10] has found an upper limit of T2 given by
+T2 ≈
+4ℏ
+e2π|ϵ1|.
+Using this relation, we compare T2 for both SIS and ScS
+transmons for EJ/EC between 1 and 100 (Figure 5c).
+The ScS transmon improves T2 across the entire range of
+EJ/EC and especially at higher ratios. At EJ/EC = 100,
+the SIS transmon has a T2 ceiling of about 3 ms, com-
+pared to about 50 ms for the ScS transmon, an over 10
+fold increase. At present, because the T1 lifetime of SIS
+transmon qubits is still beyond 1 ms and not limited by
+the charge noise, this benefit of the ScS transmon archi-
+tecture will have little performance benefit. However, be-
+cause we expect the lifetimes of superconducting qubits
+to continue improving (Schoelkopf’s Law) [14], we an-
+ticipate a point when charge noise dephasing becomes a
+bottleneck, and the ScS transmon architecture can offer
+effective mitigation.
+II.5.
+ScS transmon design parameters
+The operational behavior of a ScS transmon is deter-
+mined by its EJ and EC, which define the operating fre-
+quency ω01, the relative immunity to charge noise (ϵ1),
+and the minimum excitation pulse duration (τp).
+Be-
+cause these three quantities are determined by EJ and
+EC, they are not independent. We can visualize this in-
+terdependence with three sets contour lines plotted in the
+plane of EJ versus EC in Figure 6. These contours rep-
+resent: (1) a transmon operating frequency (ω01/(2π))
+between 1 and 10 GHz (set of red, descending diagonal
+lines), (2) ratios of EJ/EC from 10, 100, and 1000 (set
+of blue, ascending diagonal lines), and the minimum ex-
+citation pulse duration τp between 0.32 and 10 ns (set of
+dashed, predominantly vertical lines). Selecting two of
+these defines the third one. For example, a ScS trans-
+mon designed to operate at ω01/(2π) = 5 GHz and with
+
+5
+EC/(2�ħ) (GHz)
+102
+EJ/(2�ħ) (GHz)
+101
+100
+10-2
+10-1
+100
+EJ/EC=103
+EJ/EC=102
+EJ/EC=101
+ω01/(2�) = 1 GHz
+2 GHz
+3 GHz
+4 GHz
+5 GHz
+6 GHz
+7 GHz
+8 GHz
+9 GHz
+10 GHz
+τp = 10 ns
+7.94 ns
+6.31 ns
+5.01 ns
+1.58 ns
+1.26 ns
+1.00 ns
+0.79 ns
+0.63 ns
+0.50 ns
+0.40 ns
+3.98 ns
+0.32 ns
+104
+105
+2
+3
+4
+5
+6
+7
+8
+9
+2
+3
+4
+5
+6
+7
+8
+9
+103
+2
+3
+4
+5
+6
+7
+8
+9
+2
+3
+4
+5
+6
+7
+8
+9
+3.16 ns
+2.51 ns
+2.00 ns
+Rn/Tc (Ω K-1)
+102
+103
+2x101
+2
+3
+4
+5
+6
+7 8 9
+2
+3
+4
+5
+6
+7 8 9
+2
+3
+4
+5
+6
+7
+8
+9
+3
+4
+5
+6
+7
+8
+9
+CΣ (fF)
+Figure 6. A graphical guide for designing ScS transmon with required EJ and EC to match desired transmon frequency ω01
+and minimum pulse duration τp. The red lines are contours lines for transmon frequencies set at values between 1 and 10 GHz.
+The dashed black lines are contours lines for τp set at a few values between 0.32 and 10 ns. The blue lines are contours lines
+for EJ/EC ratios set at 10, 100, and 1000. A second x-axis that is parallel to EC is presented for CΣ, following CΣ = e2/2EC.
+Simlarly, a second y-axis that is parallel to EJ is presented for Rn/Tc, following Rn/Tc = 1.76kBΦ0/(4eEJ).
+a readout pulse of τp = 4 ns (green dot in Figure 6) will
+have a EJ/EC ratio of about 600.
+Instead, a shorter
+excitation pulse of τp = 1 ns (purple dot in Figure 6)
+requires a tradeoff of smaller EJ/EC ≈ 40, and thus less
+immunity against charge noise.
+Importantly, EJ and EC of a ScS transmon are set by
+the physical device dimensions and fundamental prop-
+erties of the materials composing it. EJ is determined
+by the superconducting energy gap of the material (∆)
+and the normal state resistance of the junction (Rn) (Eq.
+5).
+For a BCS superconductor where ∆ = 1.76kBTc,
+we can express EJ in terms of the material properties
+Rn/Tc = 1.76kBΦ0/(4eEJ,ScS), which is shown as the
+second (right) y-axis in Figure 6. Similarly, because EC
+is set by the total capacitance (CΣ = e2/2EC,ScS) which
+depends on device geometry and dielectric properties, we
+can express EC as a capacitance, shown as a second (top)
+x-axis in Figure 6.
+Returning to the example, we can now see from Figure
+6 that designing a ScS transmon with ω01/(2π) = 5 GHz,
+τp = 4 ns, and EJ/EC ratio of about 600 (green dot) re-
+quires a junction with Rn/Tc ≈ 3 kΩ · K−1 and capacitor
+with CΣ ≈ 250 fF. The properties can be realized by a
+constriction junction fabricated from a thin film super-
+conductor that has both a relatively high normal state
+resistivity and a long superconducting coherence length.
+As one example, a 10-nm-thick PtSi film was reported
+has normal-state sheet resistance Rs = 67 Ω/□, super-
+conducting Tc = 0.63 K, and Pippard coherence length
+ξ = 440 nm.[15] Using these material parameters, we can
+meet the ScS transmon design criteria using a constric-
+tion junction with physical length of 440 nm and width of
+
+6
+16 nm. The qubit capacitor physical dimensions should
+be designed for CΣ ≈ 250 fF, according to Figure 6. If one
+instead desires the shorter readout pulse time of τp = 1
+ns (purple dot), the constriction must have Rn/Tc ≈ 10
+kΩ · K−1 and CΣ ≈ 70 fF. For the same PtSi supercon-
+ductor, these values can be met with physical length of
+440 nm and width of 5 nm. which are more challenging
+dimensions to fabricate.
+III.
+CONCLUSION
+In summary, we have demonstrated through computa-
+tion that a short ScS Josephson junction can be used as
+a drop-in replacement for the SIS tunnel junction in a
+transmon qubit. In the transmon regime (EJ ≫ EC), a
+ScS transmon has 50% smaller anharmonicity than a SIS
+transmon, but is compensated by its appreciably lower
+charge dispersion that provides a significantly higher T2
+ceiling. Using this analysis, we estimate that high per-
+formance ScS transmons can be achieved with constric-
+tions having a normal state resistance of a few kiloohms,
+which can be made from a thin nanobridge formed in low
+Tc superconductors using conventional, high-resolution
+nanofabrication techniques.
+The ScS transmon design
+allows all components, including constriction junction,
+capacitor, and resonator, to be fabricated in a single
+lithography step. This is a significant simplification com-
+pared to multistep SIS transmon fabrication, and also
+provides an robust architecture amenable to device post-
+processing, cleaning, and encapsulation.
+ACKNOWLEDGMENTS
+This material is based upon work supported by the
+U.S. Department of Energy, Office of Science, National
+Quantum Information Science Research Centers, Co-
+design Center for Quantum Advantage (C2QA) under
+contract number DE-SC0012704.
+This research used
+computational resources of the Center for Functional
+Nanomaterials (CFN), which is a U.S. Department of
+Energy Office of Science User Facility, at Brookhaven Na-
+tional Laboratory under Contract No. DE-SC0012704.
+[1] G. J. Dolan, Offset masks for lift-off photoprocessing,
+Appl. Phys. Lett. 31, 337 (1977).
+[2] J. M. Kreikebaum, K. P. O’Brien, A. Morvan, and I. Sid-
+diqi, Improving wafer-scale Josephson junction resistance
+variation in superconducting quantum coherent circuits,
+Supercond. Sci. Technol. 33, 06LT02 (2020).
+[3] J. B. Hertzberg, E. J. Zhang, S. Rosenblatt, E. Mage-
+san, J. A. Smolin, J.-B. Yau, V. P. Adiga, M. Sandberg,
+M. Brink, J. M. Chow, and J. S. Orcutt, Laser-annealing
+Josephson junctions for yielding scaled-up superconduct-
+ing quantum processors, npj Quantum Inf. 7, 129 (2021).
+[4] A. Osman, J. Simon, A. Bengtsson, S. Kosen, P. Krantz,
+D. P. Lozano, M. Scigliuzzo, P. Delsing, J. Bylander, and
+A. Fadavi Roudsari, Simplified Josephson-junction fabri-
+cation process for reproducibly high-performance super-
+conducting qubits, Appl. Phys. Lett. 118, 064002 (2021).
+[5] H. Kim, C. J¨unger, A. Morvan, E. S. Barnard, W. P.
+Livingston, M. V. P. Alto´e, Y. Kim, C. Song, L. Chen,
+J. M. Kreikebaum, D. F. Ogletree, D. I. Santiago, and
+I. Siddiqi, Effects of laser-annealing on fixed-frequency
+superconducting qubits, Appl. Phys. Lett. 121, 142601
+(2022).
+[6] A. Premkumar, C. Weiland, S. Hwang, B. J¨ack, A. P. M.
+Place, I. Waluyo, A. Hunt, V. Bisogni, J. Pelliciari,
+A. Barbour,
+M. S. Miller,
+P. Russo,
+F. Camino,
+K. Kisslinger, X. Tong, M. S. Hybertsen, A. A. Houck,
+and I. Jarrige, Microscopic relaxation channels in mate-
+rials for superconducting qubits, Commun. Mater. 2, 72
+(2021).
+[7] A. P. M. Place, L. V. H. Rodgers, P. Mundada, B. M.
+Smitham, M. Fitzpatrick, Z. Leng, A. Premkumar,
+J. Bryon, A. Vrajitoarea, S. Sussman, G. Cheng, T. Mad-
+havan, H. K. Babla, X. H. Le, Y. Gang, B. J¨ack, A. Gye-
+nis, N. Yao, R. J. Cava, N. P. de Leon, and A. A. Houck,
+New material platform for superconducting transmon
+qubits with coherence times exceeding 0.3 milliseconds,
+Nature Commun. 12, 1779 (2021).
+[8] J. B. Chang, M. R. Vissers, A. D. C´orcoles, M. Sandberg,
+J. Gao, D. W. Abraham, J. M. Chow, J. M. Gambetta,
+M. B. Rothwell, G. A. Keefe, M. Steffen, and D. P. Pap-
+pas, Improved superconducting qubit coherence using ti-
+tanium nitride, Appl. Phys. Lett. 103, 012602 (2013).
+[9] K. Williams, K. Gupta, and M. Wasilik, Etch rates for
+micromachining processing-part ii, J. Microelectromech.
+Syst. 12, 761 (2003).
+[10] J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I.
+Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin,
+and R. J. Schoelkopf, Charge-insensitive qubit design de-
+rived from the Cooper pair box, Phys. Rev. A 76, 042319
+(2007).
+[11] I. O. Kulik and A. N. Omel’yanchuk, Contribution to the
+microscopic theory of the Josephson effect in supercon-
+ducting bridges, JETP Lett. 21, 96 (1975).
+[12] A. A. Golubov, M. Y. Kupriyanov, and E. Il’ichev, The
+current-phase relation in Josephson junctions, Rev. Mod.
+Phys. 76, 411 (2004).
+[13] R. Vijay, E. M. Levenson-Falk, D. H. Slichter, and I. Sid-
+diqi, Approaching ideal weak link behavior with three di-
+mensional aluminum nanobridges, Appl. Phys. Lett. 96,
+223112 (2010).
+[14] M.
+Kjaergaard,
+M.
+E.
+Schwartz,
+J.
+Braum¨uller,
+P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D.
+Oliver, Superconducting qubits: Current state of play,
+Annu. Rev. Condens. Matter Phys. 11, 369 (2020).
+[15] K. Oto, S. Takaoka, K. Murase, and S. Ishida, Supercon-
+ductivity in PtSi ultrathin films, J. Appl. Phys. 76, 5339
+(1994).
+
diff --git a/PdE3T4oBgHgl3EQfCglF/content/tmp_files/load_file.txt b/PdE3T4oBgHgl3EQfCglF/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8d507e0f734eccc76bceebcbec6c031b8cd1d7b5
--- /dev/null
+++ b/PdE3T4oBgHgl3EQfCglF/content/tmp_files/load_file.txt
@@ -0,0 +1,477 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf,len=476
+page_content='Performance Analysis of Superconductor-constriction-Superconductor Transmon  Qubits  Mingzhao Liu∗ and Charles T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Black†  Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA  This work presents a computational analysis of a superconducting transmon qubit design, in which  the superconductor-insulator-superconductor (SIS) Josephson junction is replaced by a co-planar,  superconductor-constriction-superconductor (ScS) junction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  For short junctions having a Kulik-  Omelyanchuk current-phase relationship, we find that the ScS transmon has an improved charge  dispersion compared to the SIS transmon, with a tradeoff of 50% smaller anharmonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' These  calculations provide a framework for estimating the superconductor material properties and junction  dimensions needed to provide proper ScS transmon operation at typical gigahertz frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  INTRODUCTION  The transmon has become an enabling superconduct-  ing qubit device architecture, with primary advantages of  immunity to charge noise and longer coherence lifetimes  achieved by designing the device to have Josephson en-  ergy far exceeding the charging energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Similar to other  superconducting qubit architectures, the transmon core  consists of one or more Josephson junctions (JJs), which  are exclusively superconductor-insulator-superconductor  tunnel junctions (SIS) — typically a thin film sand-  wich structure of aluminum/aluminum oxide/aluminum  (Al/AlOx/Al), in which AlOx is the tunnel barrier (Fig-  ure 1a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Fabrication of Al/AlOx/Al SIS JJs typically involves  physical vapor deposition of the top and bottom Al lay-  ers from two different angles relative to the substrate,  through a common mask [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' After depositing the first  Al layer, the sample is exposed to a controlled level of  oxygen to form the thin AlOx barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' This ingenious  fabrication method has been refined over many years but  will nevertheless be highly challenging to implement at  the manufacturing scale required for larger-scale quan-  tum computers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The exponential dependence of the JJ  critical supercurrent (Ic) on tunnel barrier width also re-  sults in a typical few percent variation in Ic across devices  Al  Al  AlOx  Superconductor  Constriction  a  b  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' (a) Schematic of an Al/AlOx/Al superconductor-  insulator-superconductor (SIS) Josephson junction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' For clar-  ity, the native oxide covering both Al electrodes is omitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  (b) Schematic of a co-planar superconductor-constriction-  superconductor (ScS) Josephson junction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  ∗ mzliu@bnl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='gov  † ctblack@bnl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='gov  fabricated within a few centimeters, even when oxidation  conditions are tightly controlled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' [2–5] Since the Joseph-  son energy is directly proportional to Ic, this variation  presents an additional design and manufacturing chal-  lenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  In a transmon, the SIS JJ is shunted by a large capac-  itor to minimize the charging energy and thus provide  immunity to charge noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Further, the qubit is coupled  to a high-Q microwave resonator for readout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Typically,  the shunting capacitor and the resonator are fabricated  separately from the SIS JJ, using a superconductor with  higher Tc and better chemical robustness compared to Al  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=', niobium (Tc = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='2 K)[6], tantalum (Tc = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='4 K)[7],  and titanium nitride (Tc = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='6 K)[8]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The improved ro-  bustness allows post-fabrication chemical treatments to  remove surface contaminants, which contribute to TLS  loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' However, most of these treatments are not possible  after Al/AlOx/Al junction fabrication, due to the junc-  tion’s fragile nature [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  In this work we analyze the performance impact  of replacing the transmon SIS tunnel junction with  a co-planar superconductor-constriction-superconductor  (ScS) Josephson junction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A ScS JJ is comprised of two  superconductors separated by a thin neck of the same  superconductor (Figure 1b), with the constriction estab-  lishing the superconducting phase difference that enables  Josephson behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' ScS JJs are co-planar (unlike SIS  tunnel junctions) and can be fabricated using conven-  tional lithography and metallization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Here, we follow the  formalism established by Koch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  in [10] to deter-  mine the electrical properties of ScS transmons, which  are shown to be different from SIS transmons, stemming  from a different ScS JJ current-phase relationship (CPR  or CΦR) compared to that of a SIS JJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='[11–13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Compar-  ing the two device architectures, we show that the ScS  transmon has 50% less anharmonicity than the SIS trans-  mon, for devices with the same Josephson energy and  capacitive energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' However, the smaller anharmonicity  is accompanied by a significantly smaller charge disper-  sion, giving the ScS transmon stronger immunity against  charge noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='04276v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='supr-con]  11 Jan 2023  2  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  RESULTS AND DISCUSSION  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Current-phase relation of a short ScS junction  Consider a ScS Josephson junction comprised of two  large superconductors connected by a diffusive quasi-one-  dimensional wire with length d ≪ √ξ0l and width w ≪  d, where ξ0 is the Pippard superconducting coherence  length, and l ≪ ξ0 is the dirty-limit electron mean free  path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' In this case, Kulik and Omelyanchuk showed that  the CPR for the ScS junction (KO-1) at T = 0 K is:  IScS(ϕ) = π∆  eRn  cos ϕ  2 tanh−1 �  sin ϕ  2  �  ,  (1)  in which ∆ is the superconducting energy gap and Rn  is the normal state resistance of the junction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' [11, 12]  The junction critical current Ic,ScS = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='662π∆/(eRn) is  achieved at ϕ = (2k ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='627)π to satisfy dI(ϕ)/dϕ ∝  1 − sin(ϕ/2) tanh−1 [sin(ϕ/2)] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Given the Maclau-  rin series tanh−1(x) = x + x3/3 + O(x5), Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  1 may  be rewritten to a form that resembles the CPR of a SIS  Josephson junction, as  IScS(ϕ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='755Ic,ScS sin ϕ  �  1 + 1  3 sin2 ϕ  2 + O  �  sin4 ϕ  2  � �  ,  which shows that the CPR of a ScS junction distorts  from the conventional sinusoidal form, but still bears odd  parity and a 2π periodicity (Figure 2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Josephson energy of a ScS transmon  The potential energy of a Josephson junction is given  by the integral  EJ(ϕ) =  �  IJV dt =  �  IJ  Φ0  2π  dϕ  dt dt =  �  IJ  Φ0  2π dϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  (2)  −2  −1  0  1  2  φ/π  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  I(φ)/Ic  ScS  SIS  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  φ/π  0  1  2  3  EJ(φ)/EJ  ScS  SIS  φ2/2  a  b  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' (a) The CPR of a ScS Josephson junction in the  KO-1 limit (solid red) is distorted from the sinusoidal form  of a SIS junction (dashed black).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' (b) The Josephson energy  of a ScS transmon (solid red) deviates from the cosine form  of a SIS transmon (dashed black) and has 50% smaller an-  harmonicity at its lowest order (ϕ4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A harmonic parabola,  ϕ2/2, is displayed (dotted cyan) for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  φ/π  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  EJ(φ)/EJ  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  φ/π  EJ(φ)/EJ  a  b  SIS  ScS  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='3031  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='8800  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='3993  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='7751  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='3096  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='9145  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='4896  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0077  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The eigenenergies (blue lines and numbers) and the  probability densities (∥Ψ∥2) of the first 4 eigenstates of (a) a  SIS transmon and (b) a ScS transmon, both with EJ/EC = 20  and ng = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The corresponding potential energies, normal-  ized by EJ, are plotted in red lines for both transmons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  For a KO-1 junction defined by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 1, the integral in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  2 leads to  EJ,ScS(ϕ) = ∆Φ0  2eRn  �  ln  �  cos2 ϕ  2  �  + 2 sin ϕ  2 tanh−1 �  sin ϕ  2  � �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  (3)  Although this form appears very different from the po-  tential energy of a SIS junction, EJ,SIS(ϕ) = EJ,SIS(1 −  cos ϕ), with EJ,SIS = Ic,SISΦ0/2π, Maclaurin expansions  of EJ,ScS and EJ,SIS make their similarities apparent:  EJ,ScS(ϕ) = ∆Φ0  4eRn  �1  2ϕ2 − 1  48ϕ4 + O(ϕ6)  �  EJ,SIS(ϕ) = EJ,SIS  �1  2ϕ2 − 1  24ϕ4 + O(ϕ6)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  (4)  Comparing the coefficients of the harmonic (ϕ2) term,  we observe that the Josephson energy of a ScS transmon  can be defined as:  EJ,ScS = ∆Φ0  4eRn  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='755Ic,ScSΦ0/(2π) ,  (5)  where  the  last  equality  recognizes  that  Ic,ScS  =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='662π∆/(eRn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 5 shows that both potential ener-  gies contain anharmonicity led by a ϕ4 term, from which  we estimate that the anharmonicity of a ScS transmon  is about one half that of a SIS transmon, for devices  with the same EJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' This difference is clear when compar-  ing normalized EJ(ϕ) of ScS and SIS transmons with a  harmonic parabolic potential ϕ2/2 (Figure 2b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A more  precise evaluation of the anharmonicity is given in II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='3,  by computing the ScS transmon eigenenergies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Eigenenergies and eigenstates of a ScS  transmon  A conventional SIS transmon has a Hamiltonian of the  form:  ˆHSIS = 4Ec(ˆn − ng)2 + EJ(1 − cos ˆϕ),  (6)  3  0  20  40  60  80  100  0  20  40  60  80  E0m/EC  0  20  40  60  80  100  −1  0  1  2  3  4  5  (E12 - E01)/EC  ScS  SIS  a  b  EJ/EC  EJ/EC  ScS  SIS  m = 0  1  2  3  0  20  40  60  80  100  100  τp (ns)  SIS  ScS  EJ/EC  10-1  10-2  c  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' (a) Transition energy E0m = Em − E0 at ng = 1/2 and (b) oscillator anharmonicity (E12 − E01) at ng = 1/2, as  functions of EJ/EC for ScS transmon (solid lines) and SIS transmon (dashed lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' (c) The minimal pulse duration (τp) of  ScS (solid line) and SIS transmons (dashed line) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' EJ/EC, all operated at ω01 = 2π × 10 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  where ng is the offset charge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The wave equation for a  SIS transmon can be solved analytically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' [10]  In the ScS transmon, the potential energy is given by  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 3, so that the Hamiltonian becomes,  ˆHScS = 4EC(ˆn − ng)2 + EJ  �  2 ln  �  cos2 ˆϕ  2  �  + 4 sin ˆϕ  2 tanh−1  �  sin ˆϕ  2  � �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  (7)  The wave equation of a ScS transmon can be solved nu-  merically using the finite difference method, in which the  Hamiltonian is expressed in a discretized space of phase  ϕ ∈ [−π, π), with the periodic boundary condition ap-  plied to both ends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The validity of the computation is  confirmed by comparing a similar numerical solution of  the wave equation for a SIS transmon with the analytical  solutions presented by Koch et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' [10] Figure 3 compares  the first 4 eigenstates of a SIS transmon and a ScS trans-  mon, both with EJ/EC = 20 and ng = 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Although  the lower level eigenenergies and eigenfunctions are sim-  ilar, the differences become more apparent at higher en-  ergies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' This trend is more clearly observed for the transi-  tion energies E0m = Em − E0 calculated for both trans-  mon types, across a range of EJ/EC from 1 and 100  (Figure 4a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' This difference reflects the smaller anhar-  monicity of the ScS transmon, compared to the SIS trans-  mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' By treating the leading anharmonic term (−ϕ4/24)  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  4 as a perturbation to the harmonic potential  and applying the first-order perturbation theory, the mth  eigenenergy of a SIS transmon is approximated by [10]  Em,SIS ≈ ℏωp  �  m + 1  2  �  − EC  4  �  2m2 + 2m + 1  �  ,  (8)  in which ℏωp = √8EJEC is the Josephson plasma energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  The transition energy between the (m − 1)th and mth  levels is therefore  Em−1,m,SIS ≈ ℏωp − mEC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  (9)  From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  9, we find that the anharmonicity of SIS  transmon αSIS ≡ E12,SIS−E01,SIS is approximately −EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  By applying the same first-order perturbation theory cal-  culation but realizing that the perturbation term is half  as a SIS transmon (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 4), the mth eigenenergy of a ScS  transmon can be approximated by  Em,ScS ≈ ℏωp  �  m + 1  2  �  − EC  8  �  2m2 + 2m + 1  �  ,  (10)  so that its anharmonicity, αScS, is approximately −EC/2,  or half the anharmonicity of a SIS transmon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' We can vi-  sualize this finding in a plot of numerical results, looking  at transmons with EJ/EC ≥ 20 (Figure 4b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  The smaller anharmonicity of a ScS transmon means  that the transitions E01 and E12 lie closer in energy, so  that a longer RF pulse is needed to correctly excite the  desired transition E01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The minimal pulse duration can  be estimated as τp ≈ ℏ|α|−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  As shown in Figure 4c,  despite its lower anharmonicity, τp of the ScS transmon  remains below 1 ns even for EJ/EC = 100, when the  qubit operates at 10 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Because typical qubit pulse  durations are ∼10 ns, we may conclude that the lower  anharmonicity will not inhibit normal operation of a ScS  transmon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Charge dispersion of a ScS transmon  A primary benefit of the transmon architecture is its  relative immunity to charge noise, when designed to op-  erate in the regime of EJ ≫ EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' In a SIS transmon, the  charge dispersion of the mth level decreases exponentially  with  �  8EJ/EC, following [10]  ϵm ≡ Em(ng = 1/2) − Em(ng = 0)  ≈ EC  24m+5  (−1)mm!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  �  2  π  � EJ  2EC  � m  2 + 3  4  e−√  8EJ/EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  (11)  Intuitively, the charge dispersion is related to the  tunneling probability between neighboring potential en-  ergy valleys (Figure 3), e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=', when ϕ makes a full 2π  4  −2  −1  0  1  2  ng  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='0  Em/EJ  SIS  ScS  SIS  ScS  |ϵm|/E01(ng = 1/2)  101  10-3  10-7  10-1  10-5  10-9  10-11  1  2  3  4  5  6  7  8  9  10  (EJ/EC)1/2  10  20  30  40  50 60 70 80 90 100  EJ/EC  a  b  m = 0  1  2  m = 0  1  2  0  20  40  60  80  100  SIS  ScS  T2 (ns)  EJ/EC  100  10-2  104  102  106  108  c  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' (a) The eigenenergies Em of the lowest 3 eigenstates (m = 0, 1, 2) of a ScS transmon (solid line) and a SIS transmon  (dashed lines), both with EJ/EC = 10, as functions of the offset charge ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' (b) The charge dispersion ϵm of the lowest 3  eigenstates of a ScS transmon (solid line) and a SIS transmon (dashed lines), as functions of EJ/EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' (c) The dephasing time  T2 of ScS (solid line) and SIS transmons (dashed line) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' EJ/EC, all operated at ω01 = 2π × 10 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' [10] By this reasoning, we may expect the higher  barrier height of a ScS transmon (∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='8EJ vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  2EJ)  to better suppress the tunneling probability and provide  lower charge dispersion, compared to a SIS transmon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Figure 5a plots the first three eigenenergies Em (m =  0, 1, 2) versus the effective offset charge ng for both SIS  (dashed) and ScS (solid) transmons, with EJ/EC = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Clearly, the ScS transmon eigenenergies are more weakly  perturbed by ng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Calculations of the charge dispersion,  ϵm = Em(ng = 1/2) − Em(ng = 0), across a wide range  of 1 ≤ EJ/EC ≤ 100 show that suppression of charge dis-  persion in the ScS transmon becomes more effective for  larger EJ/EC ratios (Figure 5b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' When EJ/EC = 100,  the charge dispersion of the first excited state of a ScS  transmon, ϵ1,ScS, is over one order of magnitude less than  the corresponding SIS transmon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' It is noted that com-  putation on SIS transmon matches the analytical result  very well[10], again demonstrating the high numerical  precision of our finite difference computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Never-  theless, the computational error becomes significant as  the normalized charge dispersion, |ϵm|/E01, approaches  10−11 and smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' This is due to the accumulation of  floating-point error that eventually shows up for evaluat-  ing the vanishing difference between the two eigenener-  gies at ng = 0 and 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  In Figure 5b, the y−axis is presented in the logarith-  mic scale and the x−axis is presented in the scale of  �  EJ/EC, so that all curves take a linear form approach-  ing large EJ/EC values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' For the SIS transmon, the slope  matches the expected exp(−  �  8EJ/EC) dependence in  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' For the ScS transmon, the slope is larger, and is  best described by:  ϵm ∝ exp  �  −  �  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='16 × 8EJ/EC  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  The improved charge dispersion makes the ScS trans-  mon both less sensitive to charge noise and, in turn, gives  it a longer dephasing time T2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  For dephasing caused  by slow charge fluctuations of large amplitude, Koch et  al[10] has found an upper limit of T2 given by  T2 ≈  4ℏ  e2π|ϵ1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Using this relation, we compare T2 for both SIS and ScS  transmons for EJ/EC between 1 and 100 (Figure 5c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  The ScS transmon improves T2 across the entire range of  EJ/EC and especially at higher ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' At EJ/EC = 100,  the SIS transmon has a T2 ceiling of about 3 ms, com-  pared to about 50 ms for the ScS transmon, an over 10  fold increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' At present, because the T1 lifetime of SIS  transmon qubits is still beyond 1 ms and not limited by  the charge noise, this benefit of the ScS transmon archi-  tecture will have little performance benefit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' However, be-  cause we expect the lifetimes of superconducting qubits  to continue improving (Schoelkopf’s Law) [14], we an-  ticipate a point when charge noise dephasing becomes a  bottleneck, and the ScS transmon architecture can offer  effective mitigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  ScS transmon design parameters  The operational behavior of a ScS transmon is deter-  mined by its EJ and EC, which define the operating fre-  quency ω01, the relative immunity to charge noise (ϵ1),  and the minimum excitation pulse duration (τp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Be-  cause these three quantities are determined by EJ and  EC, they are not independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' We can visualize this in-  terdependence with three sets contour lines plotted in the  plane of EJ versus EC in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' These contours rep-  resent: (1) a transmon operating frequency (ω01/(2π))  between 1 and 10 GHz (set of red, descending diagonal  lines), (2) ratios of EJ/EC from 10, 100, and 1000 (set  of blue, ascending diagonal lines), and the minimum ex-  citation pulse duration τp between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='32 and 10 ns (set of  dashed, predominantly vertical lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Selecting two of  these defines the third one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' For example, a ScS trans-  mon designed to operate at ω01/(2π) = 5 GHz and with  5  EC/(2�ħ) (GHz)  102  EJ/(2�ħ) (GHz)  101  100  10-2  10-1  100  EJ/EC=103  EJ/EC=102  EJ/EC=101  ω01/(2�) = 1 GHz  2 GHz  3 GHz  4 GHz  5 GHz  6 GHz  7 GHz  8 GHz  9 GHz  10 GHz  τp = 10 ns  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='94 ns  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='31 ns  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='01 ns  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='58 ns  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='26 ns  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='00 ns  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='79 ns  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='63 ns  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='50 ns  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='40 ns  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='98 ns  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='32 ns  104  105  2  3  4  5  6  7  8  9  2  3  4  5  6  7  8  9  103  2  3  4  5  6  7  8  9  2  3  4  5  6  7  8  9  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='16 ns  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='51 ns  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='00 ns  Rn/Tc (Ω K-1)  102  103  2x101  2  3  4  5  6  7 8 9  2  3  4  5  6  7 8 9  2  3  4  5  6  7  8  9  3  4  5  6  7  8  9  CΣ (fF)  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A graphical guide for designing ScS transmon with required EJ and EC to match desired transmon frequency ω01  and minimum pulse duration τp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The red lines are contours lines for transmon frequencies set at values between 1 and 10 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  The dashed black lines are contours lines for τp set at a few values between 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='32 and 10 ns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The blue lines are contours lines  for EJ/EC ratios set at 10, 100, and 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A second x-axis that is parallel to EC is presented for CΣ, following CΣ = e2/2EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Simlarly, a second y-axis that is parallel to EJ is presented for Rn/Tc, following Rn/Tc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='76kBΦ0/(4eEJ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  a readout pulse of τp = 4 ns (green dot in Figure 6) will  have a EJ/EC ratio of about 600.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Instead, a shorter  excitation pulse of τp = 1 ns (purple dot in Figure 6)  requires a tradeoff of smaller EJ/EC ≈ 40, and thus less  immunity against charge noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Importantly, EJ and EC of a ScS transmon are set by  the physical device dimensions and fundamental prop-  erties of the materials composing it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' EJ is determined  by the superconducting energy gap of the material (∆)  and the normal state resistance of the junction (Rn) (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  For a BCS superconductor where ∆ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='76kBTc,  we can express EJ in terms of the material properties  Rn/Tc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='76kBΦ0/(4eEJ,ScS), which is shown as the  second (right) y-axis in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Similarly, because EC  is set by the total capacitance (CΣ = e2/2EC,ScS) which  depends on device geometry and dielectric properties, we  can express EC as a capacitance, shown as a second (top)  x-axis in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Returning to the example, we can now see from Figure  6 that designing a ScS transmon with ω01/(2π) = 5 GHz,  τp = 4 ns, and EJ/EC ratio of about 600 (green dot) re-  quires a junction with Rn/Tc ≈ 3 kΩ · K−1 and capacitor  with CΣ ≈ 250 fF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The properties can be realized by a  constriction junction fabricated from a thin film super-  conductor that has both a relatively high normal state  resistivity and a long superconducting coherence length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  As one example, a 10-nm-thick PtSi film was reported  has normal-state sheet resistance Rs = 67 Ω/□, super-  conducting Tc = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='63 K, and Pippard coherence length  ξ = 440 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' [15] Using these material parameters, we can  meet the ScS transmon design criteria using a constric-  tion junction with physical length of 440 nm and width of  6  16 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' The qubit capacitor physical dimensions should  be designed for CΣ ≈ 250 fF, according to Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' If one  instead desires the shorter readout pulse time of τp = 1  ns (purple dot), the constriction must have Rn/Tc ≈ 10  kΩ · K−1 and CΣ ≈ 70 fF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' For the same PtSi supercon-  ductor, these values can be met with physical length of  440 nm and width of 5 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' which are more challenging  dimensions to fabricate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  CONCLUSION  In summary, we have demonstrated through computa-  tion that a short ScS Josephson junction can be used as  a drop-in replacement for the SIS tunnel junction in a  transmon qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' In the transmon regime (EJ ≫ EC), a  ScS transmon has 50% smaller anharmonicity than a SIS  transmon, but is compensated by its appreciably lower  charge dispersion that provides a significantly higher T2  ceiling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Using this analysis, we estimate that high per-  formance ScS transmons can be achieved with constric-  tions having a normal state resistance of a few kiloohms,  which can be made from a thin nanobridge formed in low  Tc superconductors using conventional, high-resolution  nanofabrication techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  The ScS transmon design  allows all components, including constriction junction,  capacitor, and resonator, to be fabricated in a single  lithography step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' This is a significant simplification com-  pared to multistep SIS transmon fabrication, and also  provides an robust architecture amenable to device post-  processing, cleaning, and encapsulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  This material is based upon work supported by the  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Department of Energy, Office of Science, National  Quantum Information Science Research Centers, Co-  design Center for Quantum Advantage (C2QA) under  contract number DE-SC0012704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  This research used  computational resources of the Center for Functional  Nanomaterials (CFN), which is a U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Department of  Energy Office of Science User Facility, at Brookhaven Na-  tional Laboratory under Contract No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' DE-SC0012704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [1] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Dolan, Offset masks for lift-off photoprocessing,  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 31, 337 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Kreikebaum, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' O’Brien, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Morvan, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Sid-  diqi, Improving wafer-scale Josephson junction resistance  variation in superconducting quantum coherent circuits,  Supercond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 33, 06LT02 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Hertzberg, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Rosenblatt, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Mage-  san, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Smolin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Yau, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Adiga, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Sandberg,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Brink, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Chow, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Orcutt, Laser-annealing  Josephson junctions for yielding scaled-up superconduct-  ing quantum processors, npj Quantum Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 7, 129 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Osman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Simon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Bengtsson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Kosen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Krantz,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Lozano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Scigliuzzo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Delsing, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Bylander, and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Fadavi Roudsari, Simplified Josephson-junction fabri-  cation process for reproducibly high-performance super-  conducting qubits, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 118, 064002 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [5] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Kim, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' J¨unger, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Morvan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Barnard, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Livingston, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Alto´e, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Kim, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Song, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Chen,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Kreikebaum, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Ogletree, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Santiago, and  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Siddiqi, Effects of laser-annealing on fixed-frequency  superconducting qubits, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 121, 142601  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [6] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Premkumar, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Weiland, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Hwang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' J¨ack, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Place, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Waluyo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Hunt, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Bisogni, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Pelliciari,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Barbour,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Miller,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Russo,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Camino,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Kisslinger, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Tong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Hybertsen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Houck,  and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Jarrige, Microscopic relaxation channels in mate-  rials for superconducting qubits, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 2, 72  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [7] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Place, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Rodgers, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Mundada, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Smitham, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Fitzpatrick, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Leng, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Premkumar,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Bryon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Vrajitoarea, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Sussman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Cheng, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Mad-  havan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Babla, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Le, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Gang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' J¨ack, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Gye-  nis, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Yao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Cava, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' de Leon, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Houck,  New material platform for superconducting transmon  qubits with coherence times exceeding 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='3 milliseconds,  Nature Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 12, 1779 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Chang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Vissers, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' C´orcoles, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Sandberg,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Gao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Abraham, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Chow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Gambetta,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Rothwell, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Keefe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Steffen, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Pap-  pas, Improved superconducting qubit coherence using ti-  tanium nitride, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 103, 012602 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [9] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Williams, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Gupta, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Wasilik, Etch rates for  micromachining processing-part ii, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Microelectromech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 12, 761 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Koch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Gambetta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Houck, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Schuster, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Majer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Blais, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Devoret, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Girvin,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Schoelkopf, Charge-insensitive qubit design de-  rived from the Cooper pair box, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A 76, 042319  (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [11] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Kulik and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Omel’yanchuk, Contribution to the  microscopic theory of the Josephson effect in supercon-  ducting bridges, JETP Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 21, 96 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Golubov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Kupriyanov, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Il’ichev, The  current-phase relation in Josephson junctions, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 76, 411 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [13] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Vijay, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Levenson-Falk, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Slichter, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Sid-  diqi, Approaching ideal weak link behavior with three di-  mensional aluminum nanobridges, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 96,  223112 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Kjaergaard,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Schwartz,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Braum¨uller,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Krantz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Gustavsson, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  Oliver, Superconducting qubits: Current state of play,  Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Matter Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 11, 369 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content='  [15] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Oto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Takaoka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Murase, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Ishida, Supercon-  ductivity in PtSi ultrathin films, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
+page_content=' 76, 5339  (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdE3T4oBgHgl3EQfCglF/content/2301.04276v1.pdf'}
diff --git a/PdFKT4oBgHgl3EQfgi6G/content/tmp_files/2301.11834v1.pdf.txt b/PdFKT4oBgHgl3EQfgi6G/content/tmp_files/2301.11834v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8803f19b8bfdc055c7cc873b4c347df08983019d
--- /dev/null
+++ b/PdFKT4oBgHgl3EQfgi6G/content/tmp_files/2301.11834v1.pdf.txt
@@ -0,0 +1,1274 @@
+arXiv:2301.11834v1  [cond-mat.soft]  27 Jan 2023
+Gas Diffusion in Cement Pastes: An Analysis using a
+Fluctuating Diffusivity Model
+Fumiaki Nakai1, Takato Ishida1,∗
+Department of Materials Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa,
+Nagoya 464-8603, Japan
+Abstract
+This work propose an application of the concept of fluctuating diffusivity to the dif-
+fusion of gas molecules in cementitious materials, particularly through a two-state
+fluctuating diffusivity (2SFD) model. The 2SFD model is utilized to investigate the
+diffusion of oxygen in cement pastes. The analysis provides a reasonable description
+of the diffusion coefficient of oxygen in cement pastes, and highlights the presence of
+non-Gaussian diffusion, which can be attributed to the heterogeneous microstructure.
+The presence of non-Gaussianity in the probability density of the molecule’s displace-
+ment, characterized by heavier tails than those of the Gaussian distribution, may have
+a significant impact on the durability assessments of concrete structures.
+1. Introduction
+Since the invention of Portland cement by Joseph Aspdin in 1824, cementitious ma-
+terials have been widely utilized in the construction of infrastructure. In recent decades,
+there has been a growing emphasis on assessing the long-term performance of rein-
+forced concrete structures, with a focus on reducing carbon emissions and preserving
+resources. The durability of concrete structures can be compromised by the penetration
+of aggressive lightweight molecules (causing chemical degradation [1] such as carbon-
+ation [2, 3, 4], corrosion [5, 6], sulphate attack [7], calcium leaching [8, 9]), making
+the examination of transport phenomena in cementitious materials a vital subject in the
+field of cement and concrete research. It is an undeniable fact that cementitious ma-
+terials are inherently porous in nature, possessing pores of various scales. Diffusion,
+the primary mode of mass transport, has been comprehended by devising effective dif-
+fusion coefficients which properly reflect the characteristics of the pore network struc-
+ture (tortuosity, connectivity, constrictivity, formation factor [10, 11, 12, 13, 14, 15])
+and by utilizing them to solve the diffusion equation. It is obvious that the probabilis-
+tic displacement distribution is Gaussian when the conventional diffusion equation is
+∗Corresponding author
+Email addresses: nakai.fumiaki.c7@s.mail.nagoya-u.ac.jp (Fumiaki Nakai),
+ishida@mp.pse.nagoya-u.ac.jp (Takato Ishida )
+
+resolved [16, 17]. However, recent research in the field of theoretical physics has high-
+lighted the existence of cases in which the displacement distribution deviates from a
+Gaussian distribution, depending on the spatio-temporal scale of interest. Such non-
+Gaussianity may have a significant impact on the long-term reliability probability as-
+sessment of reinforced concrete structures. We have effectively formulated the concept
+in a form that is applicable to diffusion in cementitious materials.
+A microstructure of cementitious materials inherently exhibits a heterogeneous
+composition, which can result in the non-Gaussian diffusion of gases. To effectively
+describe the diffusion in heterogeneous material, the concept of fluctuating diffusivity
+(FD) [18, 19, 20, 21, 22, 23, 24] has been demonstrated to be useful, as evidenced by
+the studies for the glass forming liquid [25], colloidal suspensions [26, 27], and bio-
+logical systems [28, 29]. The diffusion of a free molecule with fluctuating diffusivity
+is described by the equation
+∂G(x; t)
+∂t
+= D(t)∇2G(x; t)
+(1)
+where t denotes the time, x represents the displacement vector of the particle, G(x; t)
+is the probability density of x at time t, and D(t) represents the fluctuating diffusivity
+and is subject to a stochastic process. By providing a simple and physically reasonable
+rule for D(t), it is possible to theoretically analyze the dynamics of the diffusing par-
+ticles. The Fluctuating diffusivity is based on the idea that the diffusion environment
+experienced by the particle changes in time, either as a result of a temporal alteration
+in the environment or due to the migration of particles to a distinct milieu. Upon ini-
+tial inspection, one may think that the fluctuating diffusivity approach, expressed as
+Eq. (1), is similar to the time-dependent diffusivity models taking into account the
+long-term effects of changing diffusion media, such as prolonged hydration reactions
+and accumulated damages [30, 31, 32]. However, it is important to note that these
+two approaches are fundamentally distinct in terms of their concepts and underlying
+motivations. The fluctuating diffusivity approach posits that the diffusion coefficient
+changes stochastically over time, reflecting the temporal and spatial heterogeneity of
+the matrix. In contrast, the time-dependent diffusion coefficient varies deterministi-
+cally, reflecting the time evolution of internal microstructures caused by the long-term
+effects. In this paper, the latter approach, which is characterized by the deterministic
+variation of the diffusion coefficient, is referred to as deterministic drifting diffusiv-
+ity (DDD), and is distinguished from the fluctuating diffusivity. It is undeniable that
+the extensive research conducted on DDD has greatly enhanced our understanding of
+transport phenomena in cementitious materials and continues to be applied effectively
+in current studies. It is important to note that fluctuating diffusivity does not aim to
+replace or update DDD, but rather it takes a distinct physical perspective. In fact, the
+target timescale is significantly different between the fluctuating diffusivity and DDD
+approaches. Typically, the FD analyzes the particle diffusion on a timescale where the
+particle diffuses over the characteristic length of the heterogeneous environment, while
+the DDD approach focuses on the timescale where the state of the diffusion medium
+changes over a prolonged period. Here, it is important to note that some studies have
+employed DDD approach [30], which does not treat temporal and spatial fluctuations
+and is inadequate in describing diffusion in heterogeneous environments. The appli-
+2
+
+cation of the fluctuating diffusivity framework allows for an effective analysis of the
+phenomena of small molecule diffusion in cementitious materials, where the diffu-
+sivity may fluctuate spatio-temporally in response to the heterogeneous nature of the
+diffusion medium. In the context of diffusion in cementitious materials, it should be ef-
+fortless for researchers in the field of cement materials to envision diffusion phenomena
+that fall within the scope of such a framework, such as gas diffusion in a depercolated
+capillary pore network, cases of diffusion coupling with adsorption on the pore wall or
+dissolution in the pore solution. Additionally, phenomena such as the consumption of
+CO2 by carbonation and the immobilization of chloride ions through Friedel’s salt and
+calcium oxychlorides formation [33, 34], may also fall within the scope of this frame-
+work if these phenomena are regarded as trapping states with quite long time constants.
+When the timescale of observation is comparable to a timescale where the molecules
+diffuse over the characteristic length of the heterogeneous environment, non-Gaussian
+behavior of the displacement distribution is exhibited, i.e., the tails of the displacement
+distribution tend to be heavy).
+Let us herein present several sophisticated approaches for investigating diffusion
+in cementitious materials. There are two primary existing methods for understanding
+the diffusion phenomena of small molecules in cementitious materials: (i) numerical
+diffusion simulations on virtual microstructures that replicate the microstructural char-
+acteristics of cementitious materials, and (ii) empirical or semi-empirical modeling of
+effective diffusion coefficients through a process of homogenization. In recent years,
+the former approach of numerical diffusion simulations on virtual microstructures has
+made significant progress, successfully simulating the diffusion of various diffusants
+in cementitious materials of various types and compositions, both with and without
+interfacial transition zones (ITZs) [35, 36, 6, 37, 38, 39, 40, 41, 42, 43]. A particularly
+successful recent approach within this model has been the implementation of numerical
+diffusion models, such as those based on the Lattice Bolzmann method [37, 40, 41, 42],
+random walk method [6, 39, 44, 43], and finite element method [35], utilizing virtual
+3D microstructures generated by hydration models. Several hydration models have
+been previously proposed, such as CHEMHYD3D [45, 46, 47], HYMOSTRUC3D
+[48], THAMES [49, 50], DuCOM [51], IPKM [52], µic [53], which are widely used
+in the field of cement and concrete research. In such microstructure-guided diffusion
+models, the CHEMHYD3D model (a voxel-based approach) devised by Bentz and Gar-
+boczi [45, 46, 47] and the HYMOSTRUC3D (a vector-based approach) developed by
+van Breugel [48], are commonly utilized [35, 54, 40, 41]. Both CHEMHYD3D and
+HYMOSTRUC3D are founded upon Jennings’s colloidal model of Calcium-Silicate-
+Hydrates (CSH) morphology [55]. Recently, advancements in the force field of molec-
+ular dynamics in cementitious materials is becoming quite well-developed [56, 57, 58].
+Zhang et al. reported the modeling of diffusion simulations using the random walk
+method on structures generated by molecular dynamics [43]. The latter approach en-
+tails describing mass diffusion phenomena through empirically or semi-empirically
+modeling the effective diffusion coefficient in heterogeneous media and solving the
+standard diffusion equations utilizing that effective diffusion coefficient. The effec-
+tive diffusion coefficients are modeled in accordance with homogenization procedures
+commonly utilized in the field of composite materials, and are inferred to be in agree-
+ment with experimental observations and structural insights garnered from hydration
+3
+
+models [59, 60, 61, 62, 63, 14, 64, 65]. In the realm of finite element-based analysis
+utilizing representative elementary volume (REV) meshes (where the discretizing mesh
+size is generally greater than the discretization scale in microstructure-guided models),
+the identical homogenization procedure is applied to assign an effective diffusion co-
+efficient to each REV mesh [66, 15]. The empirical relationship linking the parameters
+of capillary pore and the effective diffusion coefficient is well organized in a critical
+review article by Patel et al [11]. When the porosity is known, the primary strategy is
+to attempt to express the effective diffusion coefficient through Archie’s law [67], and
+when porosity data is unavailable, the effective diffusion coefficient is frequently de-
+rived via the Powers model [68], which can link the hydration degree and water-cement
+ratio (w/c) to the capillary porosity. Yamaguchi et al. refined the empirical relationship
+by assessing the accessible capillary pores, and demonstrated that the modified model
+is efficacious in describing the effective diffusion coefficient of tritiated water [69].
+Furthermore, the empirical effective diffusive coefficient has been adapted to include
+semi-empirical parameters that characterize the morphology of the pore network (tor-
+tuosity, connectivity, constrictivity, formation factor) [10, 11, 12, 13, 14, 15]. There has
+been extensive research aimed at relating these parameters to the actual pore topology
+obtained from imaging techniques, rather than simply adjusting bulk diffusion coef-
+ficients to effective diffusion coefficients [70, 71, 10, 66, 72, 13, 15]. Recently, an
+attempt has been reported to construct a regression model for the diffusion of chloride
+ions in concrete using machine learning techniques [73]. It is important to note that
+none of the models presented in this paragraph, which express diffusion coefficients,
+can be considered universally applicable. For instance, the microstructure-based dif-
+fusion model in dry cement paste established by Liu et al., despite taking into account
+various factors related multi-scale properties, cannot perfectly explain the diffusion co-
+efficient in low w/c mixing cement pastes [40]. This discrepancy may be attributed to
+the structural fluctuations of the generated virtual microstructures, which have a greater
+impact on the apparent diffusivity in the regime of low w/c regime. Additionally, the
+empirical model also appears to exhibit a somewhat greater discrepancy between its
+predicted diffusion coefficients and those observed in the low w/c regime [11]. In this
+work, we introduce an up-to-date concept of theoretical physics, “fluctuating diffusiv-
+ity”, to the cement and concrete field. The proposed framework enables the incor-
+poration of morphological features of heterogeneous medias and the consideration of
+several types of diffusion as stochastic processes, without the requirement for detailed
+structural information or multiple empirical parameters.
+The paper is structured as follows: In Section 2.1, we present a comprehensive for-
+mulation of the fluctuating diffusivity using a general discretized state. In Section 2.2,
+we delve into a simplified two-state fluctuating diffusivity (2SFD) model, following
+the work by Uneyama et al [21] and Miyaguchi et al [74]. We analytically calculate
+the self-part of the intermediate scattering function and the second and fourth moments
+of the probability density of particle displacement, which are integral components for
+discussing the probability density of the displacement within the model. In Section 2.3,
+we apply the 2SFD model to a fundamental system, specifically the diffusion of O2 in
+cement pastes under standard temperatures and pressures as a preliminary test case.
+The subsequent Section 3 discusses the distinctions of the proposed model in com-
+parison to existing models, its scope of applicability and limitations, its potential for
+4
+
+generalization to cementitious systems, and the potential impact of the derived diffuse
+displacement distribution on the long-term durability assessment of future structures.
+The conclusion is provided in section 4.
+2. Theory
+2.1. Fluctuating diffusivity with n-states
+The fluctuating diffusivity can be represented by the diffusion equation, which in-
+cludes a fluctuating diffusivity term, D(t), as
+∂G(x; t)
+∂t
+= D(t)∇2G(x; t)
+(2)
+where x represents the tracer position, t denotes the time, G(x; t) is the probabil-
+ity density of x for a given t, and D(t) is the time-dependent fluctuating diffusivity.
+While this work analyzes the 2SFD model in the following subsections, the calcula-
+tion method is not restricted to the two-state. Thus, we here calculate for the general
+n-states case as
+D(t) = D⊤ξ(t)
+(3)
+where D⊤ = (D1, D2, · · · , Dn) is the vector of the diffusion coefficients and its
+component Di denotes the diffusion coefficient of the i-th state. ξ(t) indicates the state
+of the diffusivity at time t; ξi = 1 and the other components are zero.
+We here describe the probability density vector where the particle is in i-state at
+time t as P (t), and its stochastic process is described as:
+∂P (t)
+∂t
+= RP (t)
+(4)
+where R represents the transition matrix. From this expression, we can formally ex-
+press the probability density of P (t+ ∆) with the infinitesimal time step ∆ for a given
+P (t) as
+P (t + ∆) = exp (∆R) P (t)
+(5)
+From this expression, the transition probability where the state changes from ξ(t) to
+ξ(t + ∆) is
+P(ξ(t + ∆); ξ(t)) = ξ⊤(t + ∆) exp (∆R) ξ(t)
+(6)
+To proceed with the calculation of Eq. (2), the intermediate scattering function:
+F(k, t) =
+�
+e−ik·rG(x; t) is useful. By taking the Fourier-transform of Eq. 2, we
+obtain the differential equation with F(k, t) as follows.
+∂F(k; t)
+∂t
+= −D(t)k2F(k; t).
+(7)
+This differential equation is formally solved as [22, 24]
+F(k; t) =
+�
+exp
+�
+−k2
+� t
+0
+D(t′)dt′
+��
+D
+(8)
+5
+
+where ⟨· · · ⟩D denotes the ensemble average for D(t). Formally, Eq. (8) can be de-
+scribed as a discretized form as
+F(k; t) =
+�
+ξ(j∆t)
+exp
+
+−
+t/∆−1
+�
+j=0
+∆k2D⊤ξ(j∆)
+
+ ×
+t/∆−1
+�
+j=0
+[P(ξ((j + 1)∆); ξ(j∆))] ξ⊤(0)P (0)
+=
+�
+ξ(j∆)
+t/∆−1
+�
+j=0
+�
+exp
+�
+−∆k2D⊤ξ(j∆)
+�
+×
+ξ⊤((j + 1)∆) exp (∆R) ξ(j∆)
+�
+ξ⊤(0)P (0)
+(9)
+This equation is akin to that of the partition function of the Ising model under an exter-
+nal field. Then, we define the transfer matrix as
+ξ⊤T ξ(t) =ξ⊤(t + ∆) exp
+�
+∆R − ∆k2D⊤ [ξ(t + ∆) + ξ(t)]
+2
+�
+ξ(t)
+(10)
+Since ∆ is an infinitesimal quantity, the elements of the transfer matrix can be ex-
+pressed as:
+Tij = exp(∆R)ij exp(−∆k2Djδij) = δij + ∆(Rij − k2Djδij)
+(11)
+For the sake of brevity, we also define the matrix Qij as:
+Tij = δij + ∆Qij
+(12)
+By utilizing the transfer matrix, Eq. (9) can be reduced to
+F(k; t) =
+�
+ξ(j∆)
+e∆k2D⊤ξ(t)/2×
+t/∆−1
+�
+j=0
+ξ⊤((j + 1)∆)T ξ(j∆)e−∆k2D⊤ξ(0)/2ξ⊤(0)P (0)
+=
+�
+ξ(j∆)
+t/∆−1
+�
+j=0
+ξ⊤((j + 1)∆)T ξ(j∆)ξ⊤(0)P (0)
+=
+�
+ξ(t)
+ξ⊤(t)T t/∆P (0) =
+�
+ξ(t)
+ξ⊤(t)etQP (0)
+(13)
+This equation can be calculated when the initial probability density P (0), the i-th state
+diffusivity coefficient from Eq.(3), and the transition probability R from Eq.(4) are
+provided.
+6
+
+2.2. 2SFD model
+We here consider the two-state fluctuating diffusivity (2SFD) model following the
+literature by Uneyama et al [21] and Miyaguchi et al [74], which serves as a mathemati-
+cally tractable model. The diffusivity of the particle in the 2SFD model is characterized
+by distinct variables, D⊤ = (Df, Ds), and the transition probability matrix, R, which
+is represented as
+R =
+�−rf
+rs
+rf
+−rs
+�
+(14)
+In the equilibrium state, the initial probability density is given by
+P (0) =
+1
+rf + rs
+�
+rs
+rf
+�
+(15)
+Then, the matrix Q in Eq. (13) is presented as
+Q =
+�
+−rf − k2Df
+rs
+rf
+−rs − k2Ds
+�
+(16)
+For this Q, the eigenvalues and the corresponding eigenvectors are respectively given
+by:
+λ± = −rf + k2Df + rs + k2Ds ±
+�
+(rf + k2Df − rs − k2Ds)2 + 4rfrs
+2
+(17)
+v± =
+�
+−
+rf+k2Df −rs−k2Ds±√
+(rf+k2Df −rs−k2Ds)2+4rf rs
+2rf
+1
+�
+(18)
+Using λ± and v±, matrix Q can be described as
+Q = (v+, v−)
+�
+λ+
+0
+0
+λ−
+�
+(v+, v−)−1
+(19)
+Combining Eq. (13) and (19), we obtain
+F(k; t) =(1, 1)(v+, v−)
+�eλ+t
+0
+0
+eλ−t
+�
+(v+, v−)−1
+1
+rf + rs
+�rs
+rf
+�
+=χ+eλ+t + χ−eλ−t
+(20)
+where we defined χ± as
+χ± = 1
+2
+�
+1 ± (k2Df − k2Ds)(rf − rs) + (rs + rf)2
+(λ+ − λ−)(rf + rs)
+�
+(21)
+Eq. (20) includes all information for the probability density function G(x, t). From
+Eq. (20), we can calculate all moments of the probability density such as second and
+fourth moments (⟨x2(t)⟩ and ⟨x4(t)⟩), respectively, where the bracket ⟨· · · ⟩ denotes
+the statistical average. The utilization of higher moments serves to quantify the devi-
+ation of G(r; t) from the Gaussian distribution, as will be discussed subsequently. As
+7
+
+per the definition of the self-part of the intermediate scattering function, these moments
+are formally obtained in the isotropic system as
+⟨x2(t)⟩ = − ∂2
+∂k2 F(k, t)|k=0
+(22)
+⟨x4(t)⟩ = ∂2
+∂k2
+∂2F(k, t)
+∂k2
+|k=0
+(23)
+To assign Eq. (20) to Eq. (22), we obtain
+⟨x2(t)⟩ = 6Dfrs + Dsrf
+rf + rs
+t,
+(24)
+Using this relation, the average diffusion coefficient D can be determined through the
+relation ⟨x2(t)⟩ = 6Dt in a three-dimensional system as
+D = Dfrs + Dsrf
+rf + rs
+(25)
+This outcome indicates that the average diffusion coefficient in the present 2SFD model
+is the weighted average of Df and Ds with the transition rates rf and rs. Furthermore,
+by utilizing Eq.(23), we can obtain an analytical expression for the fourth moment of
+G(r; t) as
+⟨x4(t)⟩ =120
+�(Dfrs + Dsrf)2
+2(rf + rs)2
+t2−
+(Df − Ds)2rfrs
+(rf + rs)4
+�
+1 − (rf + rs)t − e−(rf+rs)t��
+,
+(26)
+which is used later.
+2.3. Application of 2SFD model to gas O2 in cement paste
+In this study, we address the fundamental problem of O2 diffusion, which is known
+to be one of the basic aggressive gases that can affect the long-term performance of
+reinforced concrete structures [75]. The diffusion of oxygen in dry cement paste (i.e.,
+the absence of free water in capillary pores), is chosen as the primary case study. This
+system was selected as it presents a relatively simple diffusion medium of cementi-
+tious materials, yet offers somewhat heterogeneity. We here focus on the O2 diffusion
+in dry cement paste consisting of the capillary pore phase and the colloidal CSH [55]
+phase under ambient temperature and pressure conditions T = 298 K, P = 1 atm.
+As depicted in Figure 1, the colloidal CSH consists of two different density phases in
+proximity to the surface and the hydration front, which are classified as LD-CSH (low-
+density CSH) and HD-CSH (high-density CSH), respectively [76, 77]. For simplicity,
+this study treats the capillary pore phase and the LD-CSH phase are considered as
+diffusive, while the HD-CSH and unhydrated clinker regions as non-diffusive phases.
+Given the non-negligible difference in density between the LD-CSH and HD-CSH, we
+tentatively assumed that O2 molecules cannot be able to penetrate into the HD-CSH
+8
+
+Capillary pore
+: O  molecule
+2
+(Fast diffusive phase; Df )
+(Slow diffusion phase; Ds )
+LD CSH
+HD CSH & clinker
+(Non-diffusive)
+Figure 1: Schematic diagram of O2 diffusion in a cement paste, consisting of three phases: capillary
+pore, low-density CSH (diffusive) phase and non-diffusive phase (high-density CSH and unhydrated cement
+clinker)
+Trapping at CSH phase
+Diffusion in capillary pores
+fast
+slow
+Figure 2: Schematic illustration of transitional process of diffusivity D(t). Df corresponds diffusivity of
+the fast diffusion in capillary pores, and Ds corresponds diffusivity of the slow diffusion at CSH phase.
+phase through the LD-CSH phase. This study regards the diffusion in the capillary
+void as a rapid diffusion process (diffusion coefficient Df), comprising both molecu-
+lar diffusion and Knudsen diffusion, while diffusion in the LD-CSH is considered as
+a slow diffusion process (diffusion coefficient Ds). They are used as the inputs for
+the 2SFD model, as illustrated in Figure 2. Note that the following analyses derive
+all characteristic values of the heterogeneous diffusion media through physically rea-
+sonable estimations. In our system, at ambient temperature and pressure, the impact
+of surface diffusion on the overall diffusion characteristics is possibly negligible (the
+coverage of O2 molecule is approximately 0.01 or less, it could be estimated by the
+similar way in Ref. [40]).
+From this point on, the system setup is described in detail. The size of the colloidal
+CSH is assumed to be l = 50 nm, which is determined based on the size of the globule
+floc in the CM-II model proposed by Jennings [78]. In this study, the thickness of the
+LD-CSH on colloidal CSH, which is treated as the diffusive phase, is assumed as 10 nm
+from the surface, in accordance with the value utilized in the previous microstructure-
+guided model [40]. The porosity is represented by φ, and the number density of the
+colloidal CSH is denoted by ρ. For simplicity, we assume that the colloidal CSH is
+spherical, and then the relation between φ and ρ is described as
+1 − φ = ρπl3
+6
+(27)
+With the parameters specified above, we describe the four input parameters, namely
+9
+
+Df, Ds, rf, and rs, in the 2SFD model. In the present model, the diffusion coefficient
+of the fast state, Df, can be considered as the harmonic average of the molecular and
+Knudsen diffusion coefficients, DM and DK, as follows:
+Df =
+DMDK
+DM + DK
+(28)
+In the ordinary pressure and temperature conditions, DM is estimated as [79]
+DM = 3kBT
+8Pσ2
+�
+kBT
+πm
+(29)
+where kB denotes the Boltzmann constant. σ and m represent the diameter and mass
+of the Oxygen, respectively. They are effectively given as σ = 3.46×10−10m [80, 81]
+and m = 5.31 × 10−26kg. From these variables, DM is estimated as DM = 1.99 ×
+10−5m2s−1. In a complex system such as cement materials, the estimation of DK
+is difficult. We roughly estimate DK by approximating the target cement system as a
+Lorentz gas, i.e. a single mobile particle in fixed spherical obstacles. An analogous
+postulation was utilized in the research examining gas diffusion in cement paste by Liu
+et al [40]. Under this assumption, the diffusion coefficient is determined as [82]
+DK = ¯v2τ
+3
+(30)
+where ¯v denotes the mean speed of the Oxygen, given as ¯v =
+�
+8kBT/πm, and τ
+represents the mean free time. The estimation of τ is a challenging task, however,
+it has been roughly estimated from the mean pore size [40]. In this study, a rough
+approximation of τ is made by considering the gas kinetics. When the colloidal CSH
+is dilute, the mean free time can be expressed as τ = 4/ρπl2¯v, where it is assumed
+that the interaction distance between O2 and the colloidal CSH is approximated as (l +
+σ)/2 ≃ l/2. This estimated τ is not adequate for the low porosity regime, for instance,
+τ should be 0 for φ = 0. To account for the case of small φ, a phenomenological
+description of τ as depicted in previous literature [83] is employed:
+τ =
+�
+1 − ρπl3
+6
+�
+4
+ρπl2¯v
+(31)
+Combining Eqs. (27), (30), and (31) we obtain
+DK =
+4lφ
+9(1 − φ)
+�
+2kBT
+πm
+(32)
+In this expression, DK becomes 0 for φ = 0 and diverges for φ = 1, this is in agree-
+ment with the intuitive representation of Knudsen diffusion. The slow diffusion state
+pertains to diffusion within the LD-CSH phase. The determination of diffusivity is
+not straightforward as the handling of diffusion within the LD-CSH phase is complex.
+Though this estimation remains an open problem, prior investigations suggest that there
+may exist two possible approaches, (i) consider it as surface diffusion and determining
+10
+
+the diffusion coefficient through Wu’s empirical equation [84] and the model of Chen
+and Yang [85], which are commonly employed in the context of shale gas, or (ii) by
+utilizing effective medium theory as demonstrated by Patel et al [61]. Here, we ten-
+tatively assume the slow diffusion coefficient as Ds = 10−8m2s−1. This value does
+not contradict with both estimations introduced above. The first approach necessitates
+the isosteric adsorption heat (∆H) as an input for Wu’s empirical equation [84]. If
+we adopt the isosteric adsorption heat of CO2 on the CSH surface, ∆H ∼ 10 kJ/mol
+is tentatively applied to O2 as the same procedure conducted by Liu et al. [40], the
+Ds would be of the order of 10−8m2s−1. Furthermore, Patel et al. also reported that
+the C-S-H diffusivity is three orders of magnitude lower than the bulk diffusivity for
+various diffusants [61]. Subsequently, the transition rates rf and rs are determined
+consistently with information on the pore structure. The rf corresponds to the transi-
+tion rate from the fast diffusion state at capillary pores to the slow diffusion state in
+the LD-CSH phase. In the dilute limit of the volume fraction of the CSH phase, the
+average capillary pore size, L, can be roughly approximated to be ρ−1/3. When the
+volume fraction of the CSH phase is not dilute, the effect of excluded volume must be
+taken into account, which can be phenomenologically estimated. As L approaches 0
+when the space is entirely occupied by the CSH phase and diverges when the CSH is
+absent, a possible relation between L and the CSH number density is
+L =
+�
+ρ
+(1 − ρπl3/6)
+�−1/3
+= l
+�
+πφ
+6(1 − φ)
+�1/3
+(33)
+If it is assumed that rf represents the rate of contact with the colloidal CSH from the
+capillary pore phase, rf can be estimated as
+Df = L2rf
+(34)
+The rs represents the transition rate from the slow diffusion state in the LD-CSH phase
+back to the fast diffusion state at capillary pores. Considering that the thickness of the
+LD-CSH phase is about lLD = 10nm and that it can escape from the surface by about
+10nm motion, the following estimation can be obtained.
+Ds = l2
+LDrs
+(35)
+By utilizing the relations of Df, Ds, rf, and rs as stated above, we can calculate the
+dynamics of the O2 in the 2SFD model.
+The representation of the trajectory may prove informative in providing an intu-
+itive understanding of the 2SFD model. Subsequently, utilizing a kinetic Monte Carlo
+scheme [86, 87] based on Equations (2) and (4), we numerically calculate the trajectory.
+Figure 3 illustrates a representative trajectory of an O2 molecule in the 2SFD model,
+depicted by the red curve with black dots indicating a time interval of (rf + rs)−1.
+For comparative purposes, the trajectory of an O2 molecule moving without fluctuat-
+ing diffusivity (diffusion coefficient kept constant as per Equation (25)) is presented
+by the yellow curve with black dots plotted at every time interval (rf + rs)−1. The
+red curve effectively captures the heterogeneous diffusivity, which can be interpreted
+as a reflection of the heterogeneous nature of the cement paste. In contrast, the yellow
+curve does not exhibit heterogeneity, of course.
+11
+
+x
+y
+2SFD model
+Constant diffusion coefficient
+100 nm
+Figure 3: The trajectory of O2 over the observed time duration 1000/(rf + rs) at a porosity φ = 0.5 is
+represented by the pink curve. For comparison, the trajectory of particle diffusion with a constant diffusion
+coefficient, as represented by equation (25), is depicted by the blue curve. Closed circle symbols are also
+displayed at the same time intervals of (rf + rs)−1.
+12
+
+From Equation (25), we depict the diffusion coefficient D as a function of porosity
+φ in Figure (4). For comparative purposes, data obtained in previous studies by Yio
+et al. [13], Boumaaza et al. [88], and Houst and Wittmann [89] are represented by
+blue, purple, and green symbols, respectively. Table 1 summarizes the detailed condi-
+tions of previous works that measured oxygen diffusion coefficients in cement pastes.
+In this study, the ideal comparison for the measured O2 diffusivity in cement pastes
+would have been to data obtained from completely dry cement pastes, as reported by
+Boumaaza et al. [88]. However, to the best of our knowledge, such data is quite scarce.
+Therefore, in order to provide a reasonable comparison, we have elected to include
+the results of previous studies that have measured O2 diffusivity in cement pastes un-
+der conditions of relatively low humidity, as suggested by the findings of Houst and
+Wittmann [89] that the effect of relative humidity on diffusivity is minimal below 55%.
+Specifically, we have included the results of Yio et al. [13], Houst and Wittmann [89]
+as comparable data for O2 diffusivity in cement pastes. However, we have not included
+the part of the results in Yio et al. where the hydration reaction was not fully completed
+in the comparison data. The size of the colloidal CSH changes as the hydration reaction
+progresses, which affects the estimated diffusion coefficient in this 2SFD model, as we
+will discuss later in the study (See discussion section). Our theoretical results exhibit
+a qualitative agreement with the data presented in these prior works. It is important to
+note that the four inputs, Df, Ds, rf, and rs, are derived from system parameters and
+can be determined through physical considerations.
+Porosity
+0.1
+0.2
+0.3
+0.4
+0.5
+0
+1
+2
+3
+4
+[m / s]
+2
+Yio et al. (2019)
+Boumaaza et al. (2018)
+Houst and Wittmann (1994)
+2SFD model
+Figure 4: Diffusion coefficient of the molecule O2 against the porosity φ.
+Gas diffusion in cementitious materials is often characterized by the diffusion coef-
+ficient, however, it may be insufficient to fully explore the corrosion of reinforcement.
+The tail of the probability density of the displacement G(r; t) should also be taken into
+account. We herein analyze the probability density of the displacement for a single de-
+13
+
+Table 1: Detail information of previous gas diffusion datasets.
+Ref.
+w/c ratio
+Curing
+Drying method
+Porosity
+Conditions
+Yio et al. [13]
+0.30
+Cured at 100% RH,
+Kept in 55% RH, 293 K
+0.133
+0.5 ∼ 2.5 atm
+0.45
+293 K for 90 days
+0.194
+and room temperature
+Boumaaza
+0.50
+Cured at 100% RH
+Oven-dried
+0.492
+1 atm and 293 K
+et al. [88]
+for 1 day, 2 months and 8 month
+0.455
+0.417
+0.60
+0.483
+0.454
+Houst and
+0.40
+Immersed in lime water
+Oven-dried
+0.110
+1 atm, room temperature
+Wittmann [89]
+0.80
+for 6 months or more
+0.390
+and 47 % RH
+gree of freedom, x, G(x; t), which is derived from the inverse Fourier transform of the
+self-part of the intermediate scattering function as G(x; t) =
+�
+eikxxF(kx; t). F(kx; t)
+can be computed from Eq.(2) by substituting x with x; as a result, Eq.(20) where k is
+substituted with kx is obtained. As the analytical calculation of the inverse transfor-
+mation of F(kx; t) is difficult, we perform the numerical integration. Fig. 5 illustrates
+the probability density of the O2 displacement for various time durations t at a typical
+porosity φ = 0.5. We scale the horizontal and vertical axes by the standard deviation of
+the displacement
+√
+2Dt and display the Gaussian distribution function as a reference.
+In the short time scale t ≤ 10−8s, clear deviations of G(x; t) from the Gaussian distri-
+bution are observed. These deviations gradually diminish with increasing observation
+time t. t ∼ 10−8s is comparable to the timescales of the inverse of rf or rs. This result
+suggests that the Gaussian approximation for G(x; t) may not be appropriate for the
+timescale over which O2 diffuses the lengths of colloidal CSH or the capillary pore.
+Our result is reasonable since non-Gaussian distributions, in fact, have been frequently
+observed at the microscopic scale in various heterogeneous systems such as confined
+water in CSH [90], glass-forming liquids [25], or colloidal suspensions [26, 27].
+To characterize non-Gaussian diffusion, the non-Gaussian parameter α is often em-
+ployed [91, 92, 93] and defined in three-dimensional systems as [94]
+α(t) = 3⟨r4(t)⟩
+5⟨r2(t)⟩2 − 1
+(36)
+where brackets denote the statistical average. α is equal to zero when the stochastic
+process of displacement conforms to a Gaussian distribution; if the dynamics of the
+particle can be described by the conventional diffusion equation with constant diffusiv-
+ity, α is equal to zero. Empirically, non-Gaussianity cannot be neglected for α > 0.1.
+We have obtained the second moment ⟨r2(t)⟩ and the fourth moment ⟨r4(t)⟩ as repre-
+sented by Equations (24) and (26), respectively. Consequently, we can determine α as
+the following expression:
+α(t) =
+2(Df − Ds)2rfrs
+(Dfrs + Dsrf)2(rf + rs)2
+e−(rf+rs)t + (rf + rs)t − 1
+t2
+(37)
+Fig. 6 displays α against time t with various porosity φ.
+α exhibits strong non-
+Gaussianity for the small-time regime t ≪ 10−9, and it non-monotonically changes
+with increasing porosity φ. This result may be reasonable since the heterogeneity of
+14
+
+ 
+ 
+ 
+ 
+ 
+0
+1
+2
+3
+4
+-1
+-2
+-3
+-4
+10
+-1
+10
+ 0
+10
+-2
+10
+-3
+=10
+-9
+=10
+-8
+=10
+-7
+=10
+-6
+Gaussian
+Figure 5: Probability density of O2 displacement for various time duration t at the porosity φ = 0.5. The
+horizontal and vertical axes are normalized by the standard deviation
+√
+2Dt. For comparison, the Gaussian
+distribution is also presented with the black curve.
+the diffusivity will disappear for φ = 0 and φ = 1. Additionally, the non-Gaussian
+parameter α exhibits a decrease from 10−9s < t < 10−8, indicating that diffusion in
+the timescale of t < 10−8 cannot be described by a Gaussian process or a conventional
+diffusion equation with constant diffusivity.
+3. Discussion
+In this study, we employed the 2SFD model for O2 diffusion in cement pastes,
+which constitutes a stochastic diffusion model comprising parameters that can be phys-
+ically inferred from an abundance of experimental studies on gas diffusivity in cemen-
+titious materials, while incorporating some crucial aspects of microstructures. This
+model effectively addresses stochastic processes involving transitions between multi-
+ple diffuse states, and is capable of analytically determining the probabilistic displace-
+ment distribution including the non-Gaussian parameter. Therefore, we posit that it
+constitutes a highly flexible framework that can be easily modified as long as the tran-
+sition rates between multiple diffuse states including additional states can be effectively
+assessed.
+In the above analysis, we tentatively assumed a colloidal CSH dimension of 50 nm.
+This is possibly acceptable since the Jennings’s CSH morphological model of CM-II
+[78], suggests that the size of globule flocs within the ranges from 30 to 60 nm. The
+estimated net diffusion coefficient, as one of the outputs of the 2SFD model increases
+as the assumed colloidal CSH size increases, as shown in Figure 7. This behavior is
+consistent with the experimental results reported by Bentz et al. [95] that the diffusion
+15
+
+Time
+10
+ 0
+10
+ 1
+10
+ -11
+10
+ -10
+10
+ -9
+10
+ -8
+=0.005
+=0.250
+=0.450
+=0.650
+=0.850
+Figure 6: Non-Gaussian parameter α against time t with various porosity φ.
+coefficient increases with the size of the cement particles used in the cement paste in
+the high-porosity region, while remaining largely independent of cement particle size
+in the low-porosity region.
+In this model, we have demonstrated that the assumed size of the colloidal CSH
+not only has an impact on the diffusion coefficient, but also influences the higher-
+order moments of the probability distribution of displacement, such as the shape of
+the distribution function and the non-Gaussian parameter. Besides the size effect of the
+colloidal CSH, the examination of the influence of the shape of the assumed CSH shape
+may also be significant. Zhang et al. [96] recently revealed that the effect of the shape
+of cement particles (elliptical or spherical) on the chloride diffusion behavior in cement
+paste is limited. However, it is feasible that the shape of cement particles might have
+an effect on the shape of the probabilistic distribution of diffusion displacement, even
+in the system studied by Zhang et al. If we adopt the Jennings’s CM-II model for the
+CSH morphology in modeling, the CSH should possess the shape of an ellipsoid, rather
+than perfectly spherical. This discussion is worth for further investigations. Hence, it
+can be inferred that some of the elements of the microstructure have an impact on the
+shape of the probabilistic distribution of diffusional displacement, despite their limited
+influence on the diffusion coefficient. Since the tail of the diffusion distribution has
+a significant influence on the reliability (durability) assessment of reinforced concrete
+structures, it should be quite important to consider not only the diffusion coefficient,
+but also the shape of the displacement distribution in any theoretical, numerical, or
+empirical approaches.
+Liu, Liu, and Zhang [40] conducted a study investigating the dynamics of CO2, O2,
+and H2 in dry cement paste using the lattice Boltzmann method. In their research, a
+heterogeneous structure of cement paste was phenomenologically constructed, within
+which gas diffused. They determined the diffusion coefficient as a function of porosity,
+however, the probability density of displacement G(x; t) or the non-Gaussian parame-
+16
+
+2.5
+[m / s]
+2
+2.0
+1.5
+1.0
+0.5
+[nm]
+30
+40
+50
+60
+=0.10
+=0.20
+=0.30
+=0.40
+=0.50
+Figure 7: Diffusion coefficient D against the colloidal CSH size l with various porosity φ.
+ter α were not examined. The theoretical model presented here is akin to their system,
+thus their system would exhibit similar non-Gaussianity of G(x; t) and a non-negligible
+non-Gaussian parameter. In other words, their simulation methodology could verify
+our theoretical results.
+The current study addresses O2 diffusion as a case in point, however, since oxygen
+is not highly soluble in water, the estimates can be readily extrapolated even if the ce-
+ment paste in a humid environment (i.e., non-negligible amount of free or physically
+adsorbed water in capillary pores). The correction could be accomplished by incorpo-
+rating the relationship between relative humidity and water adsorption layer thickness
+[97], and incorporating it into the estimation of the diffusion coefficient of Knudsen
+diffusion. However, to extend the 2SFD model to CO2 diffusion (another crucial ag-
+gressive gas species), a slight alteration of the model may be necessary. Due to its high
+solubility in water, CO2 must be addressed as a diffusion phenomenon in conjunction
+with local solubility equilibrium, or it may be immobilized through an in-situ carbon-
+ation reaction that occurs in the pore solution and/or inside the CSH gel. To take this
+into account, it is essential to additionally incorporate as a third state a stochastic pro-
+cess that transits on a time scale so long in comparison to the observation time that
+the diffusion coefficient is virtually zero, but the trapped time can be considered effec-
+tively infinite. A comparable methodology should be necessary when addressing the
+diffusion problem of chloride ions as it also necessitates consideration of the effects
+of chloride binding. Even when it is expanded to a three-state (even for the extension
+for a multi-state model), as long as the eigenvalues and eigenvectors of the matrix Q
+in Eq. (13) (case of the 2SFD model in Eq. (16))) are obtained, all other calculations
+can always be performed. The simplicity of its mathematical structure is also another
+benefit of this model. The application to the diffusion phenomenon of chemical species
+(CO2, Cl –), which is more critical and reactive for the durability of concrete structures,
+17
+
+will be discussed in a future publication as ongoing research in the near future.
+4. Conclusion
+In conclusion, this work presents an application of the analytic method of fluc-
+tuating diffusivity to the study of gas diffusion in cementitious materials. Note that
+the concept of fluctuating diffusivity is not in opposition to the time-dependent diffu-
+sivity approach reflecting the long-term effects of changing diffusion media, such as
+prolonged hydration reactions, pore closure due to carbonation, crackings, but rather
+the target timescale is significantly different between the two approaches The fluctu-
+ating diffusivity framework effectively analyzes the diffusion of small molecules in
+cementitious materials, where the diffusivity may fluctuate spatio-temporally due to
+the heterogeneous nature of the diffusion medium, and has potential applicability to
+various diffusion phenomena in these materials. Our theoretical results of the 2SFD
+model provide a reasonable description of the diffusion coefficient of O2 in colloidal
+CSH, as measured in previous studies, by estimating input parameters from the vari-
+ables in the target systems. Furthermore, the 2SFD model highlights the presence of
+non-Gaussian diffusion, which can be attributed to the heterogeneous microstructure of
+cement pastes. The presence of non-Gaussianity in the displacement distribution, char-
+acterized by heavier tails than those of the Gaussian distribution, is quite critical for
+the accurate evaluation of the long-term reliability probability of reinforced concrete
+structures. The deviation in the shape of the tail of the Gaussian distribution obtained
+when solving the diffusion equation using a comparable diffusion coefficient in the
+2SFD model may lead to an underestimation of the conventional method’s reliability.
+In addition, while some numerical approaches utilizing the lattice Boltzmann meth-
+ods and/or random walk methods on virtual microstructures generated by previously
+established hydration models, it is important to acknowledge that there is still ample
+scope for improvement. In this regard, the development of a more conceptual stochas-
+tic model, such as the 2SFD model rooted in statistical physics, for the examination of
+diffusion phenomena in cementitious materials from a micro-perspective, and which
+can be solved analytically owing to its straightforward theoretical framework, in addi-
+tion to the structure-based model, would be of great significance to the field of cement
+and concrete materials research. We are convinced that this work contributes novel in-
+sights into the comprehension of diffusion of small molecules in cement and concrete
+materials, and has potential for further applications in the field of cement and concrete
+research.
+References
+[1] Fredrik P Glasser, Jacques Marchand, and Eric Samson. Durability of concrete —
+Degradation phenomena involving detrimental chemical reactions. Cement and
+Concrete Research, 38(2):226–246, 2008.
+[2] Cheng-Feng Chang and Jing-Wen Chen. The experimental investigation of con-
+crete carbonation depth. Cement and Concrete Research, 36(9):1760–1767,2006.
+18
+
+[3] B Bary and A Sellier. Coupled moisture—carbon dioxide–calcium transfer model
+for carbonation of concrete. Cement and Concrete Research, 34(10):1859–1872,
+2004.
+[4] A Morandeau, M Thi´ery, and P Dangla. Investigation of the carbonation mecha-
+nism of CH and C-S-H in terms of kinetics, microstructure changes and moisture
+properties. Cement and Concrete Research, 56:153–170, 2014.
+[5] Ueli Angst, Bernhard Elsener, Claus K Larsen, and Øystein Vennesland. Criti-
+cal chloride content in reinforced concrete — A review. Cement and Concrete
+Research, 39(12):1122–1138, 2009.
+[6] Hongyan Ma, Dongshuai Hou, and Zongjin Li. Two-scale modeling of transport
+properties of cement paste: Formation factor, electrical conductivity and chloride
+diffusivity. Computational Materials Science, 110:270–280, 2015.
+[7] Adam Neville. The confused world of sulfate attack on concrete. Cement and
+Concrete Research, 34(8):1275–1296, 2004.
+[8] Christophe Carde, Raoul Franc¸ois, and Jean-Michel Torrenti. Leaching of both
+calcium hydroxide and C-S-H from cement paste: Modeling the mechanical be-
+havior. Cement and Concrete Research, 26(8):1257–1268, 1996.
+[9] Christophe Carde and Raoul Franc¸ois. Effect of the leaching of calcium hydrox-
+ide from cement paste on mechanical and physical properties. Cement and Con-
+crete Research, 27(4):539–550, 1997.
+[10] M A B Promentilla, T Sugiyama, T Hitomi, and N Takeda. Quantification of
+tortuosity in hardened cement pastes using synchrotron-based X-ray computed
+microtomography. Cement and Concrete Research, 39(6):548–557, 2009.
+[11] Ravi A Patel, Quoc Tri Phung, Suresh C Seetharam, Janez Perko, Diederik
+Jacques, Norbert Maes, Geert De Schutter, Guang Ye, and Klaas Van Breugel.
+Diffusivity of saturated ordinary Portland cement-based materials: A critical re-
+view of experimental and analytical modelling approaches. Cement and Concrete
+Research, 90:52–72, 2016.
+[12] Akira Hatanaka, Yogarajah Elakneswaran, Kiyofumi Kurumisawa, and Toyoharu
+Nawa. The Impact of Tortuosity on Chloride Ion Diffusion in Slag-Blended Ce-
+mentitious Materials. Journal of Advanced Concrete Technology, 15(8):426–439,
+2017.
+[13] M H N Yio, H S Wong, and N R Buenfeld. 3D pore structure and mass transport
+properties of blended cementitious materials. Cement and Concrete Research,
+117:23–37, 2019.
+[14] Jinbo Yang and Peng Zhang. A concise pore structure model for predicting the
+effective ion diffusion coefficients of cementitious materials. Construction and
+Building Materials, 265:120321, 2020.
+19
+
+[15] Yun Gao, Kai Wu, Zhidan Rong, and Qiang Yuan. A hybrid analytical-numerical
+algorithm based general modeling framework of molecular diffusivity in cement
+paste. International Journal of Heat and Mass Transfer, 180:121774, 2021.
+[16] Robert Zwanzig. Nonequilibrium Statistical Mechanics. Oxford university press,
+2001.
+[17] E Nelson. Dynamical Theories of Brownian Motion. Princeton University Press,
+2020.
+[18] Ralf Metzler. Superstatistics and non-gaussian diffusion. The European Physical
+Journal Special Topics, 229(5):711–728, 2020.
+[19] Aleksei V Chechkin, Flavio Seno, Ralf Metzler, and Igor M Sokolov. Brown-
+ian yet non-gaussian diffusion: from superstatistics to subordination of diffusing
+diffusivities. Physical Review X, 7(2):021002, 2017.
+[20] Mykyta V Chubynsky and Gary W Slater. Diffusing diffusivity: a model for
+anomalous, yet brownian, diffusion.
+Physical review letters, 113(9):098302,
+2014.
+[21] Takashi Uneyama, Tomoshige Miyaguchi, and Takuma Akimoto.
+Relaxation
+functions of the ornstein-uhlenbeck process with fluctuating diffusivity. Physi-
+cal Review E, 99(3):032127, 2019.
+[22] Takashi Uneyama, Tomoshige Miyaguchi, and Takuma Akimoto.
+Fluctu-
+ation analysis of time-averaged mean-square displacement for the langevin
+equation with time-dependent and fluctuating diffusivity.
+Physical Review E,
+92(3):032140, 2015.
+[23] Tomoshige Miyaguchi, Takuma Akimoto, and Eiji Yamamoto. Langevin equation
+with fluctuating diffusivity: A two-state model. Physical Review E, 94(1):012109,
+2016.
+[24] Tomoshige Miyaguchi. Elucidating fluctuating diffusivity in center-of-mass mo-
+tion of polymer models with time-averaged mean-square-displacement tensor.
+Physical Review E, 96(4):042501, 2017.
+[25] Francesco Rusciano,
+Raffaele Pastore,
+and Francesco Greco.
+Fickian
+non-gaussian diffusion in glass-forming liquids.
+Physical Review Letters,
+128(16):168001, 2022.
+[26] Raffaele Pastore, Antonio Ciarlo, Giuseppe Pesce, Francesco Greco, and Anto-
+nio Sasso. Rapid fickian yet non-gaussian diffusion after subdiffusion. Physical
+Review Letters, 126(15):158003, 2021.
+[27] Jeongmin Kim, Chanjoong Kim, and Bong June Sung. Simulation study of seem-
+ingly fickian but heterogeneous dynamics of two dimensional colloids. Physical
+review letters, 110(4):047801, 2013.
+20
+
+[28] Jae-Hyung Jeon, Matti Javanainen, Hector Martinez-Seara, Ralf Metzler, and
+Ilpo Vattulainen. Protein crowding in lipid bilayers gives rise to non-gaussian
+anomalous lateral diffusion of phospholipids and proteins. Physical Review X,
+6(2):021006, 2016.
+[29] Bo Wang, Stephen M Anthony, Sung Chul Bae, and Steve Granick. Anomalous
+yet brownian. Proceedings of the National Academy of Sciences, 106(36):15160–
+15164, 2009.
+[30] Jordan Hristov. On the diffusion with decaying time-dependent diffusivity: For-
+mulations and approximate solutions pertinent to diffusion in concretes. Methods
+of Mathematical Modelling and Computation for Complex Systems, pages 1–44,
+2022.
+[31] Lan-zhen Yu and Jian-kang Chen. A new evolution model of concrete porosity
+under continuous hydration. International Journal of Modelling, Identification
+and Control, 26(4):345–352, jan 2016.
+[32] Hui Xu and Jian-kang Chen. Coupling effect of corrosion damage on chloride
+ions diffusion in cement based materials. Construction and Building Materials,
+243:118225, 2020.
+[33] A K Suryavanshi, J D Scantlebury, and S B Lyon. Mechanism of Friedel’s salt for-
+mation in cements rich in tri-calcium aluminate. Cement and Concrete Research,
+26(5):717–727, 1996.
+[34] Paul Brown and James Bothe. The system CaO-Al2O3-CaCl2-H2O at 23±2 °C
+and the mechanisms of chloride binding in concrete. Cement and Concrete Re-
+search, 34(9):1549–1553, 2004.
+[35] Mingzhong Zhang, Guang Ye, and Klaas van Breugel.
+Microstructure-based
+modeling of water diffusivity in cement paste. Construction and Building Ma-
+terials, 25(4):2046–2052, 2011.
+[36] Qing-feng Liu, Jian Yang, Jin Xia, Dave Easterbrook, Long-yuan Li, and Xian-
+Yang Lu.
+A numerical study on chloride migration in cracked concrete us-
+ing multi-component ionic transport models. Computational Materials Science,
+99:396–416, 2015.
+[37] E Walther, M Bogdan, R Bennacer, and C De Sa. Cement paste morphologies
+and effective diffusivity: using the Lattice Boltzmann method. European Journal
+of Environmental and Civil Engineering, 20(6):667–679, jul 2016.
+[38] Qing-feng Liu, Gan-lin Feng, Jin Xia, Jian Yang, and Long-yuan Li. Ionic trans-
+port features in concrete composites containing various shaped aggregates: a nu-
+merical study. Composite Structures, 183:371–380, 2018.
+[39] Cheng Liu, Chen Qian, Rusheng Qian, Zhiyong Liu, Hongxia Qiao, and Yun-
+sheng Zhang. Numerical prediction of effective diffusivity in hardened cement
+paste between aggregates using different shapes of cement powder. Construction
+and Building Materials, 223:806–816, 2019.
+21
+
+[40] Cheng Liu, Zhiyong Liu, and Yunsheng Zhang. A multi-scale framework for
+modelling effective gas diffusivity in dry cement paste: Combined effects of
+surface, Knudsen and molecular diffusion.
+Cement and Concrete Research,
+131:106035, 2020.
+[41] Cheng Liu, Fazhou Wang, and Mingzhong Zhang. Modelling of 3D microstruc-
+ture and effective diffusivity of fly ash blended cement paste. Cement and Con-
+crete Composites, 110:103586, 2020.
+[42] Cheng Liu, Beatrice Baudet, and Mingzhong Zhang. Lattice Boltzmann mod-
+elling of ionic diffusivity in non-saturated limestone blended cement paste. Con-
+struction and Building Materials, 316:126060, 2022.
+[43] Wei Zhang, Dongshuai Hou, and Hongyan Ma.
+Multi-scale study water and
+ions transport in the cement-based materials:from molecular dynamics to random
+walk. Microporous and Mesoporous Materials, 325:111330, 2021.
+[44] Wang Hailong, Chen Zhiwei, Zhang Jian, Zheng Jianjun, Sun Xiaoyan, and
+Li Jianhua. Numerical Scheme for Predicting Chloride Diffusivity of Concrete.
+Journal of Materials in Civil Engineering, 33(9):4021237, sep 2021.
+[45] Percolation of phases in a three-dimensional cement paste microstructural model.
+Cement and Concrete Research, 21(2):325–344, 1991.
+[46] E J Garboczi and D P Bentz. Computer simulation of the diffusivity of cement-
+based materials. Journal of Materials Science, 27(8):2083–2092, 1992.
+[47] Dale Bentz. CEMHYD3D: A Three-Dimensional Cement Hydration and Mi-
+crostructure Development Modeling Package. Version 3.0., 2005.
+[48] K van Breugel. Numerical simulation of hydration and microstructural devel-
+opment in hardening cement-based materials (I) theory. Cement and Concrete
+Research, 25(2):319–331, 1995.
+[49] Jeffrey W Bullard, Barbara Lothenbach, Paul E Stutzman, and Kenneth A Sny-
+der. Coupling thermodynamics and digital image models to simulate hydration
+and microstructure development of portland cement pastes. Journal of Materials
+Research, 26(4):609–622, 2011.
+[50] Pan Feng, Changwen Miao, and Jeffrey W Bullard. A model of phase stability,
+microstructure and properties during leaching of portland cement binders. Cement
+and Concrete Composites, 49:9–19, 2014.
+[51] Koichi Maekawa, Tetsuya Ishida, and Toshiharu Kishi. Multi-scale Modeling of
+Concrete Performance. Journal of Advanced Concrete Technology, 1(2):91–126,
+2003.
+[52] C Pignat, P Navi, and K Scrivener. Simulation of cement paste microstructure
+hydration, pore space characterization and permeability determination. Materials
+and Structures, 38(4):459–466, 2005.
+22
+
+[53] Shashank Bishnoi and Karen L Scrivener. µic: A new platform for modelling the
+hydration of cements. Cement and Concrete Research, 39(4):266–274, 2009.
+[54] Mingzhong Zhang, Guang Ye, and Klaas van Breugel. Modeling of ionic diffu-
+sivity in non-saturated cement-based materials using lattice Boltzmann method.
+Cement and Concrete Research, 42(11):1524–1533, 2012.
+[55] Hamlin M Jennings. A model for the microstructure of calcium silicate hydrate
+in cement paste. Cement and Concrete Research, 30(1):101–116, 2000.
+[56] Roland J.-M. Pellenq, Akihiro Kushima, Rouzbeh Shahsavari, Krystyn J Van
+Vliet, Markus J Buehler, Sidney Yip, and Franz-Josef Ulm. A realistic molecular
+model of cement hydrates. Proceedings of the National Academy of Sciences,
+106(38):16102–16107, sep 2009.
+[57] Ratan K Mishra, Aslam Kunhi Mohamed, David Geissb¨uhler, Hegoi Manzano,
+Tariq Jamil, Rouzbeh Shahsavari, Andrey G Kalinichev, Sandra Galmarini, Lei
+Tao, Hendrik Heinz, Roland Pellenq, Adri C T van Duin, Stephen C Parker,
+Robert J Flatt, and Paul Bowen. cemff: A force field database for cementitious
+materials including validations, applications and opportunities. Cement and Con-
+crete Research, 102:68–89, 2017.
+[58] Masood Valavi, Ziga Casar, Aslam Kunhi Mohamed, Paul Bowen, and San-
+dra Galmarini. Molecular dynamic simulations of cementitious systems using
+a newly developed force field suite ERICA FF. Cement and Concrete Research,
+154:106712, 2022.
+[59] Byung Hwan Oh and Seung Yup Jang. Prediction of diffusivity of concrete based
+on simple analytic equations. Cement and Concrete Research, 34(3):463–480,
+2004.
+[60] Nattapong Damrongwiriyanupap, Stefan Scheiner, Bernhard Pichler, and Chris-
+tian Hellmich. Self-Consistent Channel Approach for Upscaling Chloride Diffu-
+sivity in Cement Pastes. Transport in Porous Media, 118(3):495–518, 2017.
+[61] Ravi A Patel, Janez Perko, Diederik Jacques, Geert De Schutter, Guang Ye, and
+Klaas Van Bruegel. Effective diffusivity of cement pastes from virtual microstruc-
+tures: Role of gel porosity and capillary pore percolation.
+Construction and
+Building Materials, 165:833–845, 2018.
+[62] S E Chidiac and M Shafikhani. Phenomenological model for quantifying concrete
+chloride diffusion coefficient. Construction and Building Materials, 224:773–
+784, 2019.
+[63] Mohamad Achour, Franc¸ois Bignonnet, Jean-Franc¸ois Barth´el´emy, Emmanuel
+Rozi`ere, and Ouali Amiri. Multi-scale modeling of the chloride diffusivity and
+the elasticity of Portland cement paste. Construction and Building Materials,
+234:117124, 2020.
+23
+
+[64] M Shafikhani and S E Chidiac. A holistic model for cement paste and concrete
+chloride diffusion coefficient. Cement and Concrete Research, 133:106049,2020.
+[65] Yushan Gu, Benoˆıt Bary, Alisa Machner, Klaartje De Weerdt, Gerd Bolte, and
+Mohsen Ben Haha. Multi-scale strategy to estimate the mechanical and diffusive
+properties of cementitious materials prepared with CEM II/C-M. Cement and
+Concrete Composites, 131:104537, 2022.
+[66] N Ukrainczyk and E A B Koenders. Representative elementary volumes for 3D
+modeling of mass transport in cementitious materials. Modelling and Simulation
+in Materials Science and Engineering, 22(3):35001, 2014.
+[67] Gustave E Archie. The electrical resistivity log as an aid in determining some
+reservoir characteristics. Transactions of the AIME, 146(01):54–62, 1942.
+[68] T C Powers Brownyard and T L. Studies of the Physical Properties of Hardened
+Portland Cement Paste. ACI Journal Proceedings, 43(9), 1946.
+[69] Tetsuji Yamaguchi, Kumi Negishi, Seiichi Hoshino, and Tadao Tanaka. Modeling
+of diffusive mass transport in micropores in cement based materials. Cement and
+Concrete Research, 39(12):1149–1155, 2009.
+[70] S Lu, E N Landis, and D T Keane. X-ray microtomographic studies of pore
+structure and permeability in Portland cement concrete. Materials and Structures,
+39(6):611–620, 2006.
+[71] H S Wong and N R Buenfeld. Patch microstructure in cement-based materials:
+Fact or artefact? Cement and Concrete Research, 36(5):990–997, 2006.
+[72] M H N Yio, H S Wong, and N R Buenfeld. Representative elementary volume
+(REV) of cementitious materials from three-dimensional pore structure analysis.
+Cement and Concrete Research, 102:187–202, 2017.
+[73] Qing-feng Liu, Muhammad Farjad Iqbal, Jian Yang, Xian-yang Lu, Peng Zhang,
+and Momina Rauf. Prediction of chloride diffusivity in concrete using artificial
+neural network: Modelling and performance evaluation. Construction and Build-
+ing Materials, 268:121082, 2021.
+[74] Tomoshige Miyaguchi, Takashi Uneyama, and Takuma Akimoto. Brownian mo-
+tion with alternately fluctuating diffusivity: Stretched-exponential and power-law
+relaxation. Physical Review E, 100(1):12116, jul 2019.
+[75] CD Lawrence. Transport of oxygen through concrete. In Proceedings of Concrete
+Society, Meeting on Chemistry and Chemically-Related Properties of Cement,
+Imperial College, London, pages 277–293, 1984.
+[76] Paul D Tennis and Hamlin M Jennings. A model for two types of calcium silicate
+hydrate in the microstructure of Portland cement pastes. Cement and Concrete
+Research, 30(6):855–863, 2000.
+24
+
+[77] Hamlin M Jennings, Jeffrey J Thomas, Julia S Gevrenov, Georgios Constan-
+tinides, and Franz-Josef Ulm. A multi-technique investigation of the nanoporosity
+of cement paste. Cement and Concrete Research, 37(3):329–336, 2007.
+[78] Hamlin M Jennings. Refinements to colloid model of C-S-H in cement: CM-II.
+Cement and Concrete Research, 38(3):275–289, 2008.
+[79] Sydney Chapman and Thomas George Cowling. The Mathematical Theory of
+Non-uniform Gases: an Account of the Kinetic Theory of Viscosity, Thermal Con-
+duction and Diffusion in Gases. Cambridge University Press, 3rd edition, 1990.
+[80] Won-Tae Koo, Shaopeng Qiao, Alana F Ogata, Gaurav Jha, Ji-Soo Jang, Vivian T
+Chen, Il-Doo Kim, and Reginald M Penner. Accelerating palladium nanowire h2
+sensors using engineered nanofiltration. ACS nano, 11(9):9276–9285, 2017.
+[81] Shuzhen Lv, Kangyao Zhang, Ling Zhu, Dianping Tang, Reinhard Niessner, and
+Dietmar Knopp. H2-based electrochemical biosensor with pd nanowires@ zif-67
+molecular sieve bilayered sensing interface for immunoassay. Analytical Chem-
+istry, 91(18):12055–12062, 2019.
+[82] J. R. Dorfman, Henk van Beijeren, and T. R. Kirkpatrick. Contemporary Kinetic
+Theory of Matter. Cambridge University Press, 2021.
+[83] Christoph Dellago, Henk v Beijeren, Debabrata Panja, and JR Dorfman. Field-
+dependent collision frequency of the two-dimensional driven random lorentz gas.
+Physical Review E, 64(3):036217, 2001.
+[84] Keliu Wu, Xiangfang Li, Chenchen Wang, Wei Yu, and Zhangxin Chen. Model
+for Surface Diffusion of Adsorbed Gas in Nanopores of Shale Gas Reservoirs.
+Industrial & Engineering Chemistry Research, 54(12):3225–3236, apr 2015.
+[85] Y D Chen and R T Yang. Concentration dependence of surface diffusion and
+zeolitic diffusion. AIChE Journal, 37(10):1579–1582, oct 1991.
+[86] Daniel T Gillespie. A general method for numerically simulating the stochastic
+time evolution of coupled chemical reactions. J. Comput. Phys., 22(4):403–434,
+1976.
+[87] Alfred B Bortz, Malvin H Kalos, and Joel L Lebowitz. A new algorithm for monte
+carlo simulation of ising spin systems. J. Comput. Phys., 17(1):10–18, 1975.
+[88] M Boumaaza, B Huet, G Pham, P Turcry, A A¨ıt-Mokhtar, and C Gehlen. A
+new test method to determine the gaseous oxygen diffusion coefficient of cement
+pastes as a function of hydration duration, microstructure, and relative humidity.
+Materials and Structures, 51(2):51, 2018.
+[89] Yves F Houst and Folker H Wittmann. Influence of porosity and water content
+on the diffusivity of CO2 and O2 through hydrated cement paste. Cement and
+Concrete Research, 24(6):1165–1176, 1994.
+25
+
+[90] Mohammad Javad Abdolhosseini Qomi, Mathieu Bauchy, Franz-Josef Ulm, and
+Roland J.-M. Pellenq. Anomalous composition-dependent dynamics of nanocon-
+fined water in the interlayer of disordered calcium-silicates. The Journal of Chem-
+ical Physics, 140(5):54515, feb 2014.
+[91] Walter Kob, Claudio Donati, Steven J Plimpton, Peter H Poole, and Sharon C
+Glotzer. Dynamical heterogeneities in a supercooled lennard-jones liquid. Phys-
+ical review letters, 79(15):2827, 1997.
+[92] Bart Vorselaars, Alexey V Lyulin, K Karatasos, and MAJ Michels.
+Non-
+gaussian nature of glassy dynamics by cage to cage motion. Physical Review
+E, 75(1):011504, 2007.
+[93] Fumiaki Nakai, Yuichi Masubuchi, Yuya Doi, Takato Ishida, and Takashi Un-
+eyama. Fluctuating diffusivity emerges even in binary gas mixtures. Physical
+Review E, 107(1):014605, 2023.
+[94] Aneesur Rahman. Correlations in the motion of atoms in liquid argon. Physical
+review, 136(2A):A405, 1964.
+[95] Dale P Bentz, Edward J Garboczi, Claus J Haecker, and Ole M Jensen. Effects of
+cement particle size distribution on performance properties of Portland cement-
+based materials. Cement and Concrete Research, 29(10):1663–1671, 1999.
+[96] Jian Zhang, Hai-long Wang, Zhi-wei Chen, Qing-feng Liu, Xiao-yan Sun, and
+Jian-jun Zheng. Experimental investigation and numerical simulation for chloride
+diffusivity of cement paste with elliptical cement particles. Construction and
+Building Materials, 337:127616, 2022.
+[97] Dale P Bentz, Daniel A Quenard, Veronique Baroghel-Bouny, Edward J Gar-
+boczi, and Hamlin M Jennings. Modelling drying shrinkage of cement paste and
+mortar Part 1. Structural models from nanometres to millimetres. Materials and
+Structures, 28(8):450–458, 1995.
+26
+
diff --git a/PdFKT4oBgHgl3EQfgi6G/content/tmp_files/load_file.txt b/PdFKT4oBgHgl3EQfgi6G/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d0f091c02f5a2174ec7693c5818895cecb1dabd8
--- /dev/null
+++ b/PdFKT4oBgHgl3EQfgi6G/content/tmp_files/load_file.txt
@@ -0,0 +1,676 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf,len=675
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='11834v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='soft]  27 Jan 2023  Gas Diffusion in Cement Pastes: An Analysis using a  Fluctuating Diffusivity Model  Fumiaki Nakai1, Takato Ishida1,∗  Department of Materials Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa,  Nagoya 464-8603, Japan  Abstract  This work propose an application of the concept of fluctuating diffusivity to the dif-  fusion of gas molecules in cementitious materials, particularly through a two-state  fluctuating diffusivity (2SFD) model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The 2SFD model is utilized to investigate the  diffusion of oxygen in cement pastes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The analysis provides a reasonable description  of the diffusion coefficient of oxygen in cement pastes, and highlights the presence of  non-Gaussian diffusion, which can be attributed to the heterogeneous microstructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  The presence of non-Gaussianity in the probability density of the molecule’s displace-  ment, characterized by heavier tails than those of the Gaussian distribution, may have  a significant impact on the durability assessments of concrete structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Introduction  Since the invention of Portland cement by Joseph Aspdin in 1824, cementitious ma-  terials have been widely utilized in the construction of infrastructure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In recent decades,  there has been a growing emphasis on assessing the long-term performance of rein-  forced concrete structures, with a focus on reducing carbon emissions and preserving  resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The durability of concrete structures can be compromised by the penetration  of aggressive lightweight molecules (causing chemical degradation [1] such as carbon-  ation [2, 3, 4], corrosion [5, 6], sulphate attack [7], calcium leaching [8, 9]), making  the examination of transport phenomena in cementitious materials a vital subject in the  field of cement and concrete research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' It is an undeniable fact that cementitious ma-  terials are inherently porous in nature, possessing pores of various scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Diffusion,  the primary mode of mass transport, has been comprehended by devising effective dif-  fusion coefficients which properly reflect the characteristics of the pore network struc-  ture (tortuosity, connectivity, constrictivity, formation factor [10, 11, 12, 13, 14, 15])  and by utilizing them to solve the diffusion equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' It is obvious that the probabilis-  tic displacement distribution is Gaussian when the conventional diffusion equation is  ∗Corresponding author  Email addresses: nakai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='fumiaki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='c7@s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='nagoya-u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='jp (Fumiaki Nakai),  ishida@mp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='pse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='nagoya-u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='jp (Takato Ishida )  resolved [16, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' However, recent research in the field of theoretical physics has high-  lighted the existence of cases in which the displacement distribution deviates from a  Gaussian distribution, depending on the spatio-temporal scale of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Such non-  Gaussianity may have a significant impact on the long-term reliability probability as-  sessment of reinforced concrete structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' We have effectively formulated the concept  in a form that is applicable to diffusion in cementitious materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  A microstructure of cementitious materials inherently exhibits a heterogeneous  composition, which can result in the non-Gaussian diffusion of gases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' To effectively  describe the diffusion in heterogeneous material, the concept of fluctuating diffusivity  (FD) [18, 19, 20, 21, 22, 23, 24] has been demonstrated to be useful, as evidenced by  the studies for the glass forming liquid [25], colloidal suspensions [26, 27], and bio-  logical systems [28, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The diffusion of a free molecule with fluctuating diffusivity  is described by the equation  ∂G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t)  ∂t  = D(t)∇2G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t)  (1)  where t denotes the time, x represents the displacement vector of the particle, G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t)  is the probability density of x at time t, and D(t) represents the fluctuating diffusivity  and is subject to a stochastic process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' By providing a simple and physically reasonable  rule for D(t), it is possible to theoretically analyze the dynamics of the diffusing par-  ticles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The Fluctuating diffusivity is based on the idea that the diffusion environment  experienced by the particle changes in time, either as a result of a temporal alteration  in the environment or due to the migration of particles to a distinct milieu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Upon ini-  tial inspection, one may think that the fluctuating diffusivity approach, expressed as  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (1), is similar to the time-dependent diffusivity models taking into account the  long-term effects of changing diffusion media, such as prolonged hydration reactions  and accumulated damages [30, 31, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' However, it is important to note that these  two approaches are fundamentally distinct in terms of their concepts and underlying  motivations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The fluctuating diffusivity approach posits that the diffusion coefficient  changes stochastically over time, reflecting the temporal and spatial heterogeneity of  the matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In contrast, the time-dependent diffusion coefficient varies deterministi-  cally, reflecting the time evolution of internal microstructures caused by the long-term  effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In this paper, the latter approach, which is characterized by the deterministic  variation of the diffusion coefficient, is referred to as deterministic drifting diffusiv-  ity (DDD), and is distinguished from the fluctuating diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' It is undeniable that  the extensive research conducted on DDD has greatly enhanced our understanding of  transport phenomena in cementitious materials and continues to be applied effectively  in current studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' It is important to note that fluctuating diffusivity does not aim to  replace or update DDD, but rather it takes a distinct physical perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In fact, the  target timescale is significantly different between the fluctuating diffusivity and DDD  approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Typically, the FD analyzes the particle diffusion on a timescale where the  particle diffuses over the characteristic length of the heterogeneous environment, while  the DDD approach focuses on the timescale where the state of the diffusion medium  changes over a prolonged period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Here, it is important to note that some studies have  employed DDD approach [30], which does not treat temporal and spatial fluctuations  and is inadequate in describing diffusion in heterogeneous environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The appli-  2  cation of the fluctuating diffusivity framework allows for an effective analysis of the  phenomena of small molecule diffusion in cementitious materials, where the diffu-  sivity may fluctuate spatio-temporally in response to the heterogeneous nature of the  diffusion medium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In the context of diffusion in cementitious materials, it should be ef-  fortless for researchers in the field of cement materials to envision diffusion phenomena  that fall within the scope of such a framework, such as gas diffusion in a depercolated  capillary pore network, cases of diffusion coupling with adsorption on the pore wall or  dissolution in the pore solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Additionally, phenomena such as the consumption of  CO2 by carbonation and the immobilization of chloride ions through Friedel’s salt and  calcium oxychlorides formation [33, 34], may also fall within the scope of this frame-  work if these phenomena are regarded as trapping states with quite long time constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  When the timescale of observation is comparable to a timescale where the molecules  diffuse over the characteristic length of the heterogeneous environment, non-Gaussian  behavior of the displacement distribution is exhibited, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=', the tails of the displacement  distribution tend to be heavy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Let us herein present several sophisticated approaches for investigating diffusion  in cementitious materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' There are two primary existing methods for understanding  the diffusion phenomena of small molecules in cementitious materials: (i) numerical  diffusion simulations on virtual microstructures that replicate the microstructural char-  acteristics of cementitious materials, and (ii) empirical or semi-empirical modeling of  effective diffusion coefficients through a process of homogenization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In recent years,  the former approach of numerical diffusion simulations on virtual microstructures has  made significant progress, successfully simulating the diffusion of various diffusants  in cementitious materials of various types and compositions, both with and without  interfacial transition zones (ITZs) [35, 36, 6, 37, 38, 39, 40, 41, 42, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A particularly  successful recent approach within this model has been the implementation of numerical  diffusion models, such as those based on the Lattice Bolzmann method [37, 40, 41, 42],  random walk method [6, 39, 44, 43], and finite element method [35], utilizing virtual  3D microstructures generated by hydration models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Several hydration models have  been previously proposed, such as CHEMHYD3D [45, 46, 47], HYMOSTRUC3D  [48], THAMES [49, 50], DuCOM [51], IPKM [52], µic [53], which are widely used  in the field of cement and concrete research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In such microstructure-guided diffusion  models, the CHEMHYD3D model (a voxel-based approach) devised by Bentz and Gar-  boczi [45, 46, 47] and the HYMOSTRUC3D (a vector-based approach) developed by  van Breugel [48], are commonly utilized [35, 54, 40, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Both CHEMHYD3D and  HYMOSTRUC3D are founded upon Jennings’s colloidal model of Calcium-Silicate-  Hydrates (CSH) morphology [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Recently, advancements in the force field of molec-  ular dynamics in cementitious materials is becoming quite well-developed [56, 57, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' reported the modeling of diffusion simulations using the random walk  method on structures generated by molecular dynamics [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The latter approach en-  tails describing mass diffusion phenomena through empirically or semi-empirically  modeling the effective diffusion coefficient in heterogeneous media and solving the  standard diffusion equations utilizing that effective diffusion coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The effec-  tive diffusion coefficients are modeled in accordance with homogenization procedures  commonly utilized in the field of composite materials, and are inferred to be in agree-  ment with experimental observations and structural insights garnered from hydration  3  models [59, 60, 61, 62, 63, 14, 64, 65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In the realm of finite element-based analysis  utilizing representative elementary volume (REV) meshes (where the discretizing mesh  size is generally greater than the discretization scale in microstructure-guided models),  the identical homogenization procedure is applied to assign an effective diffusion co-  efficient to each REV mesh [66, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The empirical relationship linking the parameters  of capillary pore and the effective diffusion coefficient is well organized in a critical  review article by Patel et al [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' When the porosity is known, the primary strategy is  to attempt to express the effective diffusion coefficient through Archie’s law [67], and  when porosity data is unavailable, the effective diffusion coefficient is frequently de-  rived via the Powers model [68], which can link the hydration degree and water-cement  ratio (w/c) to the capillary porosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Yamaguchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' refined the empirical relationship  by assessing the accessible capillary pores, and demonstrated that the modified model  is efficacious in describing the effective diffusion coefficient of tritiated water [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Furthermore, the empirical effective diffusive coefficient has been adapted to include  semi-empirical parameters that characterize the morphology of the pore network (tor-  tuosity, connectivity, constrictivity, formation factor) [10, 11, 12, 13, 14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' There has  been extensive research aimed at relating these parameters to the actual pore topology  obtained from imaging techniques, rather than simply adjusting bulk diffusion coef-  ficients to effective diffusion coefficients [70, 71, 10, 66, 72, 13, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Recently, an  attempt has been reported to construct a regression model for the diffusion of chloride  ions in concrete using machine learning techniques [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' It is important to note that  none of the models presented in this paragraph, which express diffusion coefficients,  can be considered universally applicable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' For instance, the microstructure-based dif-  fusion model in dry cement paste established by Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=', despite taking into account  various factors related multi-scale properties, cannot perfectly explain the diffusion co-  efficient in low w/c mixing cement pastes [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This discrepancy may be attributed to  the structural fluctuations of the generated virtual microstructures, which have a greater  impact on the apparent diffusivity in the regime of low w/c regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Additionally, the  empirical model also appears to exhibit a somewhat greater discrepancy between its  predicted diffusion coefficients and those observed in the low w/c regime [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In this  work, we introduce an up-to-date concept of theoretical physics, “fluctuating diffusiv-  ity”, to the cement and concrete field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The proposed framework enables the incor-  poration of morphological features of heterogeneous medias and the consideration of  several types of diffusion as stochastic processes, without the requirement for detailed  structural information or multiple empirical parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  The paper is structured as follows: In Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='1, we present a comprehensive for-  mulation of the fluctuating diffusivity using a general discretized state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='2,  we delve into a simplified two-state fluctuating diffusivity (2SFD) model, following  the work by Uneyama et al [21] and Miyaguchi et al [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' We analytically calculate  the self-part of the intermediate scattering function and the second and fourth moments  of the probability density of particle displacement, which are integral components for  discussing the probability density of the displacement within the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='3,  we apply the 2SFD model to a fundamental system, specifically the diffusion of O2 in  cement pastes under standard temperatures and pressures as a preliminary test case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  The subsequent Section 3 discusses the distinctions of the proposed model in com-  parison to existing models, its scope of applicability and limitations, its potential for  4  generalization to cementitious systems, and the potential impact of the derived diffuse  displacement distribution on the long-term durability assessment of future structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  The conclusion is provided in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Theory  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Fluctuating diffusivity with n-states  The fluctuating diffusivity can be represented by the diffusion equation, which in-  cludes a fluctuating diffusivity term, D(t), as  ∂G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t)  ∂t  = D(t)∇2G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t)  (2)  where x represents the tracer position, t denotes the time, G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) is the probabil-  ity density of x for a given t, and D(t) is the time-dependent fluctuating diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  While this work analyzes the 2SFD model in the following subsections, the calcula-  tion method is not restricted to the two-state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Thus, we here calculate for the general  n-states case as  D(t) = D⊤ξ(t)  (3)  where D⊤ = (D1, D2, · · · , Dn) is the vector of the diffusion coefficients and its  component Di denotes the diffusion coefficient of the i-th state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' ξ(t) indicates the state  of the diffusivity at time t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' ξi = 1 and the other components are zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  We here describe the probability density vector where the particle is in i-state at  time t as P (t), and its stochastic process is described as:  ∂P (t)  ∂t  = RP (t)  (4)  where R represents the transition matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' From this expression, we can formally ex-  press the probability density of P (t+ ∆) with the infinitesimal time step ∆ for a given  P (t) as  P (t + ∆) = exp (∆R) P (t)  (5)  From this expression, the transition probability where the state changes from ξ(t) to  ξ(t + ∆) is  P(ξ(t + ∆);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' ξ(t)) = ξ⊤(t + ∆) exp (∆R) ξ(t)  (6)  To proceed with the calculation of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (2), the intermediate scattering function:  F(k, t) =  �  e−ik·rG(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) is useful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' By taking the Fourier-transform of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' 2, we  obtain the differential equation with F(k, t) as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  ∂F(k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t)  ∂t  = −D(t)k2F(k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  (7)  This differential equation is formally solved as [22, 24]  F(k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) =  �  exp  �  −k2  � t  0  D(t′)dt′  ��  D  (8)  5  where ⟨· · · ⟩D denotes the ensemble average for D(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Formally, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (8) can be de-  scribed as a discretized form as  F(k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) =  �  ξ(j∆t)  exp  \uf8ee  \uf8f0−  t/∆−1  �  j=0  ∆k2D⊤ξ(j∆)  \uf8f9  \uf8fb ×  t/∆−1  �  j=0  [P(ξ((j + 1)∆);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' ξ(j∆))] ξ⊤(0)P (0)  =  �  ξ(j∆)  t/∆−1  �  j=0  �  exp  �  −∆k2D⊤ξ(j∆)  �  ×  ξ⊤((j + 1)∆) exp (∆R) ξ(j∆)  �  ξ⊤(0)P (0)  (9)  This equation is akin to that of the partition function of the Ising model under an exter-  nal field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Then, we define the transfer matrix as  ξ⊤T ξ(t) =ξ⊤(t + ∆) exp  �  ∆R − ∆k2D⊤ [ξ(t + ∆) + ξ(t)]  2  �  ξ(t)  (10)  Since ∆ is an infinitesimal quantity, the elements of the transfer matrix can be ex-  pressed as:  Tij = exp(∆R)ij exp(−∆k2Djδij) = δij + ∆(Rij − k2Djδij)  (11)  For the sake of brevity, we also define the matrix Qij as:  Tij = δij + ∆Qij  (12)  By utilizing the transfer matrix, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (9) can be reduced to  F(k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) =  �  ξ(j∆)  e∆k2D⊤ξ(t)/2×  t/∆−1  �  j=0  ξ⊤((j + 1)∆)T ξ(j∆)e−∆k2D⊤ξ(0)/2ξ⊤(0)P (0)  =  �  ξ(j∆)  t/∆−1  �  j=0  ξ⊤((j + 1)∆)T ξ(j∆)ξ⊤(0)P (0)  =  �  ξ(t)  ξ⊤(t)T t/∆P (0) =  �  ξ(t)  ξ⊤(t)etQP (0)  (13)  This equation can be calculated when the initial probability density P (0), the i-th state  diffusivity coefficient from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (3), and the transition probability R from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (4) are  provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' 2SFD model  We here consider the two-state fluctuating diffusivity (2SFD) model following the  literature by Uneyama et al [21] and Miyaguchi et al [74], which serves as a mathemati-  cally tractable model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The diffusivity of the particle in the 2SFD model is characterized  by distinct variables, D⊤ = (Df, Ds), and the transition probability matrix, R, which  is represented as  R =  �−rf  rs  rf  −rs  �  (14)  In the equilibrium state, the initial probability density is given by  P (0) =  1  rf + rs  �  rs  rf  �  (15)  Then, the matrix Q in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (13) is presented as  Q =  �  −rf − k2Df  rs  rf  −rs − k2Ds  �  (16)  For this Q, the eigenvalues and the corresponding eigenvectors are respectively given  by:  λ± = −rf + k2Df + rs + k2Ds ±  �  (rf + k2Df − rs − k2Ds)2 + 4rfrs  2  (17)  v± =  �  −  rf+k2Df −rs−k2Ds±√  (rf+k2Df −rs−k2Ds)2+4rf rs  2rf  1  �  (18)  Using λ± and v±, matrix Q can be described as  Q = (v+, v−)  �  λ+  0  0  λ−  �  (v+, v−)−1  (19)  Combining Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (13) and (19), we obtain  F(k;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) =(1, 1)(v+, v−)  �eλ+t  0  0  eλ−t  �  (v+, v−)−1  1  rf + rs  �rs  rf  �  =χ+eλ+t + χ−eλ−t  (20)  where we defined χ± as  χ± = 1  2  �  1 ± (k2Df − k2Ds)(rf − rs) + (rs + rf)2  (λ+ − λ−)(rf + rs)  �  (21)  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (20) includes all information for the probability density function G(x, t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' From  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (20), we can calculate all moments of the probability density such as second and  fourth moments (⟨x2(t)⟩ and ⟨x4(t)⟩), respectively, where the bracket ⟨· · · ⟩ denotes  the statistical average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The utilization of higher moments serves to quantify the devi-  ation of G(r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) from the Gaussian distribution, as will be discussed subsequently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' As  7  per the definition of the self-part of the intermediate scattering function, these moments  are formally obtained in the isotropic system as  ⟨x2(t)⟩ = − ∂2  ∂k2 F(k, t)|k=0  (22)  ⟨x4(t)⟩ = ∂2  ∂k2  ∂2F(k, t)  ∂k2  |k=0  (23)  To assign Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (20) to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (22), we obtain  ⟨x2(t)⟩ = 6Dfrs + Dsrf  rf + rs  t,  (24)  Using this relation, the average diffusion coefficient D can be determined through the  relation ⟨x2(t)⟩ = 6Dt in a three-dimensional system as  D = Dfrs + Dsrf  rf + rs  (25)  This outcome indicates that the average diffusion coefficient in the present 2SFD model  is the weighted average of Df and Ds with the transition rates rf and rs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Furthermore,  by utilizing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (23), we can obtain an analytical expression for the fourth moment of  G(r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) as  ⟨x4(t)⟩ =120  �(Dfrs + Dsrf)2  2(rf + rs)2  t2−  (Df − Ds)2rfrs  (rf + rs)4  �  1 − (rf + rs)t − e−(rf+rs)t��  ,  (26)  which is used later.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Application of 2SFD model to gas O2 in cement paste  In this study, we address the fundamental problem of O2 diffusion, which is known  to be one of the basic aggressive gases that can affect the long-term performance of  reinforced concrete structures [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The diffusion of oxygen in dry cement paste (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=',  the absence of free water in capillary pores), is chosen as the primary case study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This  system was selected as it presents a relatively simple diffusion medium of cementi-  tious materials, yet offers somewhat heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' We here focus on the O2 diffusion  in dry cement paste consisting of the capillary pore phase and the colloidal CSH [55]  phase under ambient temperature and pressure conditions T = 298 K, P = 1 atm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  As depicted in Figure 1, the colloidal CSH consists of two different density phases in  proximity to the surface and the hydration front, which are classified as LD-CSH (low-  density CSH) and HD-CSH (high-density CSH), respectively [76, 77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' For simplicity,  this study treats the capillary pore phase and the LD-CSH phase are considered as  diffusive, while the HD-CSH and unhydrated clinker regions as non-diffusive phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Given the non-negligible difference in density between the LD-CSH and HD-CSH, we  tentatively assumed that O2 molecules cannot be able to penetrate into the HD-CSH  8  Capillary pore  : O  molecule  2  (Fast diffusive phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Df )  (Slow diffusion phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Ds )  LD CSH  HD CSH & clinker  (Non-diffusive)  Figure 1: Schematic diagram of O2 diffusion in a cement paste, consisting of three phases: capillary  pore, low-density CSH (diffusive) phase and non-diffusive phase (high-density CSH and unhydrated cement  clinker)  Trapping at CSH phase  Diffusion in capillary pores  fast  slow  Figure 2: Schematic illustration of transitional process of diffusivity D(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Df corresponds diffusivity of  the fast diffusion in capillary pores, and Ds corresponds diffusivity of the slow diffusion at CSH phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  phase through the LD-CSH phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This study regards the diffusion in the capillary  void as a rapid diffusion process (diffusion coefficient Df), comprising both molecu-  lar diffusion and Knudsen diffusion, while diffusion in the LD-CSH is considered as  a slow diffusion process (diffusion coefficient Ds).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' They are used as the inputs for  the 2SFD model, as illustrated in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Note that the following analyses derive  all characteristic values of the heterogeneous diffusion media through physically rea-  sonable estimations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In our system, at ambient temperature and pressure, the impact  of surface diffusion on the overall diffusion characteristics is possibly negligible (the  coverage of O2 molecule is approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='01 or less, it could be estimated by the  similar way in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [40]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  From this point on, the system setup is described in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The size of the colloidal  CSH is assumed to be l = 50 nm, which is determined based on the size of the globule  floc in the CM-II model proposed by Jennings [78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In this study, the thickness of the  LD-CSH on colloidal CSH, which is treated as the diffusive phase, is assumed as 10 nm  from the surface, in accordance with the value utilized in the previous microstructure-  guided model [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The porosity is represented by φ, and the number density of the  colloidal CSH is denoted by ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' For simplicity, we assume that the colloidal CSH is  spherical, and then the relation between φ and ρ is described as  1 − φ = ρπl3  6  (27)  With the parameters specified above, we describe the four input parameters, namely  9  Df, Ds, rf, and rs, in the 2SFD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In the present model, the diffusion coefficient  of the fast state, Df, can be considered as the harmonic average of the molecular and  Knudsen diffusion coefficients, DM and DK, as follows:  Df =  DMDK  DM + DK  (28)  In the ordinary pressure and temperature conditions, DM is estimated as [79]  DM = 3kBT  8Pσ2  �  kBT  πm  (29)  where kB denotes the Boltzmann constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' σ and m represent the diameter and mass  of the Oxygen, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' They are effectively given as σ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='46×10−10m [80, 81]  and m = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='31 × 10−26kg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' From these variables, DM is estimated as DM = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='99 ×  10−5m2s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In a complex system such as cement materials, the estimation of DK  is difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' We roughly estimate DK by approximating the target cement system as a  Lorentz gas, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' a single mobile particle in fixed spherical obstacles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' An analogous  postulation was utilized in the research examining gas diffusion in cement paste by Liu  et al [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Under this assumption, the diffusion coefficient is determined as [82]  DK = ¯v2τ  3  (30)  where ¯v denotes the mean speed of the Oxygen, given as ¯v =  �  8kBT/πm, and τ  represents the mean free time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The estimation of τ is a challenging task, however,  it has been roughly estimated from the mean pore size [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In this study, a rough  approximation of τ is made by considering the gas kinetics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' When the colloidal CSH  is dilute, the mean free time can be expressed as τ = 4/ρπl2¯v, where it is assumed  that the interaction distance between O2 and the colloidal CSH is approximated as (l +  σ)/2 ≃ l/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This estimated τ is not adequate for the low porosity regime, for instance,  τ should be 0 for φ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' To account for the case of small φ, a phenomenological  description of τ as depicted in previous literature [83] is employed:  τ =  �  1 − ρπl3  6  �  4  ρπl2¯v  (31)  Combining Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (27), (30), and (31) we obtain  DK =  4lφ  9(1 − φ)  �  2kBT  πm  (32)  In this expression, DK becomes 0 for φ = 0 and diverges for φ = 1, this is in agree-  ment with the intuitive representation of Knudsen diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The slow diffusion state  pertains to diffusion within the LD-CSH phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The determination of diffusivity is  not straightforward as the handling of diffusion within the LD-CSH phase is complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Though this estimation remains an open problem, prior investigations suggest that there  may exist two possible approaches, (i) consider it as surface diffusion and determining  10  the diffusion coefficient through Wu’s empirical equation [84] and the model of Chen  and Yang [85], which are commonly employed in the context of shale gas, or (ii) by  utilizing effective medium theory as demonstrated by Patel et al [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Here, we ten-  tatively assume the slow diffusion coefficient as Ds = 10−8m2s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This value does  not contradict with both estimations introduced above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The first approach necessitates  the isosteric adsorption heat (∆H) as an input for Wu’s empirical equation [84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' If  we adopt the isosteric adsorption heat of CO2 on the CSH surface, ∆H ∼ 10 kJ/mol  is tentatively applied to O2 as the same procedure conducted by Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [40], the  Ds would be of the order of 10−8m2s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Furthermore, Patel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' also reported that  the C-S-H diffusivity is three orders of magnitude lower than the bulk diffusivity for  various diffusants [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Subsequently, the transition rates rf and rs are determined  consistently with information on the pore structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The rf corresponds to the transi-  tion rate from the fast diffusion state at capillary pores to the slow diffusion state in  the LD-CSH phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In the dilute limit of the volume fraction of the CSH phase, the  average capillary pore size, L, can be roughly approximated to be ρ−1/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' When the  volume fraction of the CSH phase is not dilute, the effect of excluded volume must be  taken into account, which can be phenomenologically estimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' As L approaches 0  when the space is entirely occupied by the CSH phase and diverges when the CSH is  absent,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' a possible relation between L and the CSH number density is  L =  �  ρ  (1 − ρπl3/6)  �−1/3  = l  �  πφ  6(1 − φ)  �1/3  (33)  If it is assumed that rf represents the rate of contact with the colloidal CSH from the  capillary pore phase,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' rf can be estimated as  Df = L2rf  (34)  The rs represents the transition rate from the slow diffusion state in the LD-CSH phase  back to the fast diffusion state at capillary pores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Considering that the thickness of the  LD-CSH phase is about lLD = 10nm and that it can escape from the surface by about  10nm motion, the following estimation can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Ds = l2  LDrs  (35)  By utilizing the relations of Df, Ds, rf, and rs as stated above, we can calculate the  dynamics of the O2 in the 2SFD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  The representation of the trajectory may prove informative in providing an intu-  itive understanding of the 2SFD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Subsequently, utilizing a kinetic Monte Carlo  scheme [86, 87] based on Equations (2) and (4), we numerically calculate the trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Figure 3 illustrates a representative trajectory of an O2 molecule in the 2SFD model,  depicted by the red curve with black dots indicating a time interval of (rf + rs)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  For comparative purposes, the trajectory of an O2 molecule moving without fluctuat-  ing diffusivity (diffusion coefficient kept constant as per Equation (25)) is presented  by the yellow curve with black dots plotted at every time interval (rf + rs)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The  red curve effectively captures the heterogeneous diffusivity, which can be interpreted  as a reflection of the heterogeneous nature of the cement paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In contrast, the yellow  curve does not exhibit heterogeneity, of course.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  11  x  y  2SFD model  Constant diffusion coefficient  100 nm  Figure 3: The trajectory of O2 over the observed time duration 1000/(rf + rs) at a porosity φ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='5 is  represented by the pink curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' For comparison, the trajectory of particle diffusion with a constant diffusion  coefficient, as represented by equation (25), is depicted by the blue curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Closed circle symbols are also  displayed at the same time intervals of (rf + rs)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  12  From Equation (25), we depict the diffusion coefficient D as a function of porosity  φ in Figure (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' For comparative purposes, data obtained in previous studies by Yio  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [13], Boumaaza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [88], and Houst and Wittmann [89] are represented by  blue, purple, and green symbols, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Table 1 summarizes the detailed condi-  tions of previous works that measured oxygen diffusion coefficients in cement pastes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  In this study, the ideal comparison for the measured O2 diffusivity in cement pastes  would have been to data obtained from completely dry cement pastes, as reported by  Boumaaza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [88].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' However, to the best of our knowledge, such data is quite scarce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Therefore, in order to provide a reasonable comparison, we have elected to include  the results of previous studies that have measured O2 diffusivity in cement pastes un-  der conditions of relatively low humidity, as suggested by the findings of Houst and  Wittmann [89] that the effect of relative humidity on diffusivity is minimal below 55%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Specifically, we have included the results of Yio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [13], Houst and Wittmann [89]  as comparable data for O2 diffusivity in cement pastes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' However, we have not included  the part of the results in Yio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' where the hydration reaction was not fully completed  in the comparison data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The size of the colloidal CSH changes as the hydration reaction  progresses, which affects the estimated diffusion coefficient in this 2SFD model, as we  will discuss later in the study (See discussion section).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Our theoretical results exhibit  a qualitative agreement with the data presented in these prior works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' It is important to  note that the four inputs, Df, Ds, rf, and rs, are derived from system parameters and  can be determined through physical considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Porosity  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='5  0  1  2  3  4  [m / s]  2  Yio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (2019)  Boumaaza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (2018)  Houst and Wittmann (1994)  2SFD model  Figure 4: Diffusion coefficient of the molecule O2 against the porosity φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Gas diffusion in cementitious materials is often characterized by the diffusion coef-  ficient, however, it may be insufficient to fully explore the corrosion of reinforcement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  The tail of the probability density of the displacement G(r;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) should also be taken into  account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' We herein analyze the probability density of the displacement for a single de-  13  Table 1: Detail information of previous gas diffusion datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  w/c ratio  Curing  Drying method  Porosity  Conditions  Yio et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [13]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='30  Cured at 100% RH,  Kept in 55% RH, 293 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='133  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='5 ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='5 atm  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='45  293 K for 90 days  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='194  and room temperature  Boumaaza  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='50  Cured at 100% RH  Oven-dried  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='492  1 atm and 293 K  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [88]  for 1 day, 2 months and 8 month  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='455  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='417  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='483  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='454  Houst and  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='40  Immersed in lime water  Oven-dried  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='110  1 atm, room temperature  Wittmann [89]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='80  for 6 months or more  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='390  and 47 % RH  gree of freedom, x, G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t), which is derived from the inverse Fourier transform of the  self-part of the intermediate scattering function as G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) =  �  eikxxF(kx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' F(kx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t)  can be computed from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (2) by substituting x with x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' as a result, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (20) where k is  substituted with kx is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' As the analytical calculation of the inverse transfor-  mation of F(kx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) is difficult, we perform the numerical integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' 5 illustrates  the probability density of the O2 displacement for various time durations t at a typical  porosity φ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' We scale the horizontal and vertical axes by the standard deviation of  the displacement  √  2Dt and display the Gaussian distribution function as a reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  In the short time scale t ≤ 10−8s, clear deviations of G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) from the Gaussian distri-  bution are observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' These deviations gradually diminish with increasing observation  time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t ∼ 10−8s is comparable to the timescales of the inverse of rf or rs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This result  suggests that the Gaussian approximation for G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) may not be appropriate for the  timescale over which O2 diffuses the lengths of colloidal CSH or the capillary pore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Our result is reasonable since non-Gaussian distributions, in fact, have been frequently  observed at the microscopic scale in various heterogeneous systems such as confined  water in CSH [90], glass-forming liquids [25], or colloidal suspensions [26, 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  To characterize non-Gaussian diffusion, the non-Gaussian parameter α is often em-  ployed [91, 92, 93] and defined in three-dimensional systems as [94]  α(t) = 3⟨r4(t)⟩  5⟨r2(t)⟩2 − 1  (36)  where brackets denote the statistical average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' α is equal to zero when the stochastic  process of displacement conforms to a Gaussian distribution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' if the dynamics of the  particle can be described by the conventional diffusion equation with constant diffusiv-  ity, α is equal to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Empirically, non-Gaussianity cannot be neglected for α > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  We have obtained the second moment ⟨r2(t)⟩ and the fourth moment ⟨r4(t)⟩ as repre-  sented by Equations (24) and (26), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Consequently, we can determine α as  the following expression:  α(t) =  2(Df − Ds)2rfrs  (Dfrs + Dsrf)2(rf + rs)2  e−(rf+rs)t + (rf + rs)t − 1  t2  (37)  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' 6 displays α against time t with various porosity φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  α exhibits strong non-  Gaussianity for the small-time regime t ≪ 10−9, and it non-monotonically changes  with increasing porosity φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This result may be reasonable since the heterogeneity of  14  0  1  2  3  4  1  2  3  4  10  1  10  0  10  2  10  3  =10  9  =10  8  =10  7  =10  6  Gaussian  Figure 5: Probability density of O2 displacement for various time duration t at the porosity φ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The  horizontal and vertical axes are normalized by the standard deviation  √  2Dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' For comparison, the Gaussian  distribution is also presented with the black curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  the diffusivity will disappear for φ = 0 and φ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Additionally, the non-Gaussian  parameter α exhibits a decrease from 10−9s < t < 10−8, indicating that diffusion in  the timescale of t < 10−8 cannot be described by a Gaussian process or a conventional  diffusion equation with constant diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Discussion  In this study, we employed the 2SFD model for O2 diffusion in cement pastes,  which constitutes a stochastic diffusion model comprising parameters that can be phys-  ically inferred from an abundance of experimental studies on gas diffusivity in cemen-  titious materials, while incorporating some crucial aspects of microstructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This  model effectively addresses stochastic processes involving transitions between multi-  ple diffuse states, and is capable of analytically determining the probabilistic displace-  ment distribution including the non-Gaussian parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Therefore, we posit that it  constitutes a highly flexible framework that can be easily modified as long as the tran-  sition rates between multiple diffuse states including additional states can be effectively  assessed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  In the above analysis, we tentatively assumed a colloidal CSH dimension of 50 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  This is possibly acceptable since the Jennings’s CSH morphological model of CM-II  [78], suggests that the size of globule flocs within the ranges from 30 to 60 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The  estimated net diffusion coefficient, as one of the outputs of the 2SFD model increases  as the assumed colloidal CSH size increases, as shown in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This behavior is  consistent with the experimental results reported by Bentz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [95] that the diffusion  15  Time  10  0  10  1  10  11  10  10  10  9  10  8  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='005  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='250  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='450  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='650  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='850  Figure 6: Non-Gaussian parameter α against time t with various porosity φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  coefficient increases with the size of the cement particles used in the cement paste in  the high-porosity region, while remaining largely independent of cement particle size  in the low-porosity region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  In this model, we have demonstrated that the assumed size of the colloidal CSH  not only has an impact on the diffusion coefficient, but also influences the higher-  order moments of the probability distribution of displacement, such as the shape of  the distribution function and the non-Gaussian parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Besides the size effect of the  colloidal CSH, the examination of the influence of the shape of the assumed CSH shape  may also be significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' [96] recently revealed that the effect of the shape  of cement particles (elliptical or spherical) on the chloride diffusion behavior in cement  paste is limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' However, it is feasible that the shape of cement particles might have  an effect on the shape of the probabilistic distribution of diffusion displacement, even  in the system studied by Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' If we adopt the Jennings’s CM-II model for the  CSH morphology in modeling, the CSH should possess the shape of an ellipsoid, rather  than perfectly spherical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' This discussion is worth for further investigations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Hence, it  can be inferred that some of the elements of the microstructure have an impact on the  shape of the probabilistic distribution of diffusional displacement, despite their limited  influence on the diffusion coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Since the tail of the diffusion distribution has  a significant influence on the reliability (durability) assessment of reinforced concrete  structures, it should be quite important to consider not only the diffusion coefficient,  but also the shape of the displacement distribution in any theoretical, numerical, or  empirical approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Liu, Liu, and Zhang [40] conducted a study investigating the dynamics of CO2, O2,  and H2 in dry cement paste using the lattice Boltzmann method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In their research, a  heterogeneous structure of cement paste was phenomenologically constructed, within  which gas diffused.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' They determined the diffusion coefficient as a function of porosity,  however, the probability density of displacement G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) or the non-Gaussian parame-  16  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='5  [m / s]  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='5  [nm]  30  40  50  60  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='10  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='20  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='30  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='40  =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='50  Figure 7: Diffusion coefficient D against the colloidal CSH size l with various porosity φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  ter α were not examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The theoretical model presented here is akin to their system,  thus their system would exhibit similar non-Gaussianity of G(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' t) and a non-negligible  non-Gaussian parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In other words, their simulation methodology could verify  our theoretical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  The current study addresses O2 diffusion as a case in point, however, since oxygen  is not highly soluble in water, the estimates can be readily extrapolated even if the ce-  ment paste in a humid environment (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=', non-negligible amount of free or physically  adsorbed water in capillary pores).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The correction could be accomplished by incorpo-  rating the relationship between relative humidity and water adsorption layer thickness  [97], and incorporating it into the estimation of the diffusion coefficient of Knudsen  diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' However, to extend the 2SFD model to CO2 diffusion (another crucial ag-  gressive gas species), a slight alteration of the model may be necessary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Due to its high  solubility in water, CO2 must be addressed as a diffusion phenomenon in conjunction  with local solubility equilibrium, or it may be immobilized through an in-situ carbon-  ation reaction that occurs in the pore solution and/or inside the CSH gel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' To take this  into account, it is essential to additionally incorporate as a third state a stochastic pro-  cess that transits on a time scale so long in comparison to the observation time that  the diffusion coefficient is virtually zero, but the trapped time can be considered effec-  tively infinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A comparable methodology should be necessary when addressing the  diffusion problem of chloride ions as it also necessitates consideration of the effects  of chloride binding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Even when it is expanded to a three-state (even for the extension  for a multi-state model), as long as the eigenvalues and eigenvectors of the matrix Q  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (13) (case of the 2SFD model in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' (16))) are obtained, all other calculations  can always be performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The simplicity of its mathematical structure is also another  benefit of this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The application to the diffusion phenomenon of chemical species  (CO2, Cl –), which is more critical and reactive for the durability of concrete structures,  17  will be discussed in a future publication as ongoing research in the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Conclusion  In conclusion, this work presents an application of the analytic method of fluc-  tuating diffusivity to the study of gas diffusion in cementitious materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Note that  the concept of fluctuating diffusivity is not in opposition to the time-dependent diffu-  sivity approach reflecting the long-term effects of changing diffusion media,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' such as  prolonged hydration reactions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' pore closure due to carbonation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' crackings,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' but rather  the target timescale is significantly different between the two approaches The fluctu-  ating diffusivity framework effectively analyzes the diffusion of small molecules in  cementitious materials,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' where the diffusivity may fluctuate spatio-temporally due to  the heterogeneous nature of the diffusion medium,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' and has potential applicability to  various diffusion phenomena in these materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Our theoretical results of the 2SFD  model provide a reasonable description of the diffusion coefficient of O2 in colloidal  CSH, as measured in previous studies, by estimating input parameters from the vari-  ables in the target systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Furthermore, the 2SFD model highlights the presence of  non-Gaussian diffusion, which can be attributed to the heterogeneous microstructure of  cement pastes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The presence of non-Gaussianity in the displacement distribution, char-  acterized by heavier tails than those of the Gaussian distribution, is quite critical for  the accurate evaluation of the long-term reliability probability of reinforced concrete  structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The deviation in the shape of the tail of the Gaussian distribution obtained  when solving the diffusion equation using a comparable diffusion coefficient in the  2SFD model may lead to an underestimation of the conventional method’s reliability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  In addition, while some numerical approaches utilizing the lattice Boltzmann meth-  ods and/or random walk methods on virtual microstructures generated by previously  established hydration models, it is important to acknowledge that there is still ample  scope for improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In this regard, the development of a more conceptual stochas-  tic model, such as the 2SFD model rooted in statistical physics, for the examination of  diffusion phenomena in cementitious materials from a micro-perspective, and which  can be solved analytically owing to its straightforward theoretical framework, in addi-  tion to the structure-based model, would be of great significance to the field of cement  and concrete materials research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' We are convinced that this work contributes novel in-  sights into the comprehension of diffusion of small molecules in cement and concrete  materials, and has potential for further applications in the field of cement and concrete  research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  References  [1] Fredrik P Glasser, Jacques Marchand, and Eric Samson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Durability of concrete —  Degradation phenomena involving detrimental chemical reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and  Concrete Research, 38(2):226–246, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [2] Cheng-Feng Chang and Jing-Wen Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The experimental investigation of con-  crete carbonation depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 36(9):1760–1767,2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  18  [3] B Bary and A Sellier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Coupled moisture—carbon dioxide–calcium transfer model  for carbonation of concrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 34(10):1859–1872,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [4] A Morandeau, M Thi´ery, and P Dangla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Investigation of the carbonation mecha-  nism of CH and C-S-H in terms of kinetics, microstructure changes and moisture  properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 56:153–170, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [5] Ueli Angst, Bernhard Elsener, Claus K Larsen, and Øystein Vennesland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Criti-  cal chloride content in reinforced concrete — A review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete  Research, 39(12):1122–1138, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [6] Hongyan Ma, Dongshuai Hou, and Zongjin Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Two-scale modeling of transport  properties of cement paste: Formation factor, electrical conductivity and chloride  diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Computational Materials Science, 110:270–280, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [7] Adam Neville.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The confused world of sulfate attack on concrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and  Concrete Research, 34(8):1275–1296, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [8] Christophe Carde, Raoul Franc¸ois, and Jean-Michel Torrenti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Leaching of both  calcium hydroxide and C-S-H from cement paste: Modeling the mechanical be-  havior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 26(8):1257–1268, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [9] Christophe Carde and Raoul Franc¸ois.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Effect of the leaching of calcium hydrox-  ide from cement paste on mechanical and physical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Con-  crete Research, 27(4):539–550, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [10] M A B Promentilla, T Sugiyama, T Hitomi, and N Takeda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Quantification of  tortuosity in hardened cement pastes using synchrotron-based X-ray computed  microtomography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 39(6):548–557, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [11] Ravi A Patel, Quoc Tri Phung, Suresh C Seetharam, Janez Perko, Diederik  Jacques, Norbert Maes, Geert De Schutter, Guang Ye, and Klaas Van Breugel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Diffusivity of saturated ordinary Portland cement-based materials: A critical re-  view of experimental and analytical modelling approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete  Research, 90:52–72, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [12] Akira Hatanaka, Yogarajah Elakneswaran, Kiyofumi Kurumisawa, and Toyoharu  Nawa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The Impact of Tortuosity on Chloride Ion Diffusion in Slag-Blended Ce-  mentitious Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Journal of Advanced Concrete Technology, 15(8):426–439,  2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [13] M H N Yio, H S Wong, and N R Buenfeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' 3D pore structure and mass transport  properties of blended cementitious materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research,  117:23–37, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [14] Jinbo Yang and Peng Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A concise pore structure model for predicting the  effective ion diffusion coefficients of cementitious materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Construction and  Building Materials, 265:120321, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  19  [15] Yun Gao, Kai Wu, Zhidan Rong, and Qiang Yuan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A hybrid analytical-numerical  algorithm based general modeling framework of molecular diffusivity in cement  paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' International Journal of Heat and Mass Transfer, 180:121774, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [16] Robert Zwanzig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Nonequilibrium Statistical Mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Oxford university press,  2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [17] E Nelson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Dynamical Theories of Brownian Motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Princeton University Press,  2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [18] Ralf Metzler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Superstatistics and non-gaussian diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The European Physical  Journal Special Topics, 229(5):711–728, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [19] Aleksei V Chechkin, Flavio Seno, Ralf Metzler, and Igor M Sokolov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Brown-  ian yet non-gaussian diffusion: from superstatistics to subordination of diffusing  diffusivities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physical Review X, 7(2):021002, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [20] Mykyta V Chubynsky and Gary W Slater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Diffusing diffusivity: a model for  anomalous, yet brownian, diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Physical review letters, 113(9):098302,  2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [21] Takashi Uneyama, Tomoshige Miyaguchi, and Takuma Akimoto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Relaxation  functions of the ornstein-uhlenbeck process with fluctuating diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physi-  cal Review E, 99(3):032127, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [22] Takashi Uneyama, Tomoshige Miyaguchi, and Takuma Akimoto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Fluctu-  ation analysis of time-averaged mean-square displacement for the langevin  equation with time-dependent and fluctuating diffusivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Physical Review E,  92(3):032140, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [23] Tomoshige Miyaguchi, Takuma Akimoto, and Eiji Yamamoto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Langevin equation  with fluctuating diffusivity: A two-state model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physical Review E, 94(1):012109,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [24] Tomoshige Miyaguchi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Elucidating fluctuating diffusivity in center-of-mass mo-  tion of polymer models with time-averaged mean-square-displacement tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Physical Review E, 96(4):042501, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [25] Francesco Rusciano,  Raffaele Pastore,  and Francesco Greco.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Fickian  non-gaussian diffusion in glass-forming liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Physical Review Letters,  128(16):168001, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [26] Raffaele Pastore, Antonio Ciarlo, Giuseppe Pesce, Francesco Greco, and Anto-  nio Sasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Rapid fickian yet non-gaussian diffusion after subdiffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physical  Review Letters, 126(15):158003, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [27] Jeongmin Kim, Chanjoong Kim, and Bong June Sung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Simulation study of seem-  ingly fickian but heterogeneous dynamics of two dimensional colloids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physical  review letters, 110(4):047801, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  20  [28] Jae-Hyung Jeon, Matti Javanainen, Hector Martinez-Seara, Ralf Metzler, and  Ilpo Vattulainen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Protein crowding in lipid bilayers gives rise to non-gaussian  anomalous lateral diffusion of phospholipids and proteins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physical Review X,  6(2):021006, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [29] Bo Wang, Stephen M Anthony, Sung Chul Bae, and Steve Granick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Anomalous  yet brownian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences, 106(36):15160–  15164, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [30] Jordan Hristov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' On the diffusion with decaying time-dependent diffusivity: For-  mulations and approximate solutions pertinent to diffusion in concretes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Methods  of Mathematical Modelling and Computation for Complex Systems, pages 1–44,  2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [31] Lan-zhen Yu and Jian-kang Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A new evolution model of concrete porosity  under continuous hydration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' International Journal of Modelling, Identification  and Control, 26(4):345–352, jan 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [32] Hui Xu and Jian-kang Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Coupling effect of corrosion damage on chloride  ions diffusion in cement based materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Construction and Building Materials,  243:118225, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [33] A K Suryavanshi, J D Scantlebury, and S B Lyon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Mechanism of Friedel’s salt for-  mation in cements rich in tri-calcium aluminate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research,  26(5):717–727, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [34] Paul Brown and James Bothe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The system CaO-Al2O3-CaCl2-H2O at 23±2 °C  and the mechanisms of chloride binding in concrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Re-  search, 34(9):1549–1553, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [35] Mingzhong Zhang, Guang Ye, and Klaas van Breugel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Microstructure-based  modeling of water diffusivity in cement paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Construction and Building Ma-  terials, 25(4):2046–2052, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [36] Qing-feng Liu, Jian Yang, Jin Xia, Dave Easterbrook, Long-yuan Li, and Xian-  Yang Lu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  A numerical study on chloride migration in cracked concrete us-  ing multi-component ionic transport models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Computational Materials Science,  99:396–416, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [37] E Walther, M Bogdan, R Bennacer, and C De Sa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement paste morphologies  and effective diffusivity: using the Lattice Boltzmann method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' European Journal  of Environmental and Civil Engineering, 20(6):667–679, jul 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [38] Qing-feng Liu, Gan-lin Feng, Jin Xia, Jian Yang, and Long-yuan Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Ionic trans-  port features in concrete composites containing various shaped aggregates: a nu-  merical study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Composite Structures, 183:371–380, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [39] Cheng Liu, Chen Qian, Rusheng Qian, Zhiyong Liu, Hongxia Qiao, and Yun-  sheng Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Numerical prediction of effective diffusivity in hardened cement  paste between aggregates using different shapes of cement powder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Construction  and Building Materials, 223:806–816, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  21  [40] Cheng Liu, Zhiyong Liu, and Yunsheng Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A multi-scale framework for  modelling effective gas diffusivity in dry cement paste: Combined effects of  surface, Knudsen and molecular diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Cement and Concrete Research,  131:106035, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [41] Cheng Liu, Fazhou Wang, and Mingzhong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Modelling of 3D microstruc-  ture and effective diffusivity of fly ash blended cement paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Con-  crete Composites, 110:103586, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [42] Cheng Liu, Beatrice Baudet, and Mingzhong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Lattice Boltzmann mod-  elling of ionic diffusivity in non-saturated limestone blended cement paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Con-  struction and Building Materials, 316:126060, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [43] Wei Zhang, Dongshuai Hou, and Hongyan Ma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Multi-scale study water and  ions transport in the cement-based materials:from molecular dynamics to random  walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Microporous and Mesoporous Materials, 325:111330, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [44] Wang Hailong, Chen Zhiwei, Zhang Jian, Zheng Jianjun, Sun Xiaoyan, and  Li Jianhua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Numerical Scheme for Predicting Chloride Diffusivity of Concrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Journal of Materials in Civil Engineering, 33(9):4021237, sep 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [45] Percolation of phases in a three-dimensional cement paste microstructural model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Cement and Concrete Research, 21(2):325–344, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [46] E J Garboczi and D P Bentz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Computer simulation of the diffusivity of cement-  based materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Journal of Materials Science, 27(8):2083–2092, 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [47] Dale Bentz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' CEMHYD3D: A Three-Dimensional Cement Hydration and Mi-  crostructure Development Modeling Package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Version 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=', 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [48] K van Breugel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Numerical simulation of hydration and microstructural devel-  opment in hardening cement-based materials (I) theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete  Research, 25(2):319–331, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [49] Jeffrey W Bullard, Barbara Lothenbach, Paul E Stutzman, and Kenneth A Sny-  der.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Coupling thermodynamics and digital image models to simulate hydration  and microstructure development of portland cement pastes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Journal of Materials  Research, 26(4):609–622, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [50] Pan Feng, Changwen Miao, and Jeffrey W Bullard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A model of phase stability,  microstructure and properties during leaching of portland cement binders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement  and Concrete Composites, 49:9–19, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [51] Koichi Maekawa, Tetsuya Ishida, and Toshiharu Kishi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Multi-scale Modeling of  Concrete Performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Journal of Advanced Concrete Technology, 1(2):91–126,  2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [52] C Pignat, P Navi, and K Scrivener.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Simulation of cement paste microstructure  hydration, pore space characterization and permeability determination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Materials  and Structures, 38(4):459–466, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  22  [53] Shashank Bishnoi and Karen L Scrivener.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' µic: A new platform for modelling the  hydration of cements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 39(4):266–274, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [54] Mingzhong Zhang, Guang Ye, and Klaas van Breugel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Modeling of ionic diffu-  sivity in non-saturated cement-based materials using lattice Boltzmann method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Cement and Concrete Research, 42(11):1524–1533, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [55] Hamlin M Jennings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A model for the microstructure of calcium silicate hydrate  in cement paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 30(1):101–116, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [56] Roland J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Pellenq, Akihiro Kushima, Rouzbeh Shahsavari, Krystyn J Van  Vliet, Markus J Buehler, Sidney Yip, and Franz-Josef Ulm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A realistic molecular  model of cement hydrates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences,  106(38):16102–16107, sep 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [57] Ratan K Mishra, Aslam Kunhi Mohamed, David Geissb¨uhler, Hegoi Manzano,  Tariq Jamil, Rouzbeh Shahsavari, Andrey G Kalinichev, Sandra Galmarini, Lei  Tao, Hendrik Heinz, Roland Pellenq, Adri C T van Duin, Stephen C Parker,  Robert J Flatt, and Paul Bowen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' cemff: A force field database for cementitious  materials including validations, applications and opportunities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Con-  crete Research, 102:68–89, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [58] Masood Valavi, Ziga Casar, Aslam Kunhi Mohamed, Paul Bowen, and San-  dra Galmarini.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Molecular dynamic simulations of cementitious systems using  a newly developed force field suite ERICA FF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research,  154:106712, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [59] Byung Hwan Oh and Seung Yup Jang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Prediction of diffusivity of concrete based  on simple analytic equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 34(3):463–480,  2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [60] Nattapong Damrongwiriyanupap, Stefan Scheiner, Bernhard Pichler, and Chris-  tian Hellmich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Self-Consistent Channel Approach for Upscaling Chloride Diffu-  sivity in Cement Pastes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Transport in Porous Media, 118(3):495–518, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [61] Ravi A Patel, Janez Perko, Diederik Jacques, Geert De Schutter, Guang Ye, and  Klaas Van Bruegel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Effective diffusivity of cement pastes from virtual microstruc-  tures: Role of gel porosity and capillary pore percolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Construction and  Building Materials, 165:833–845, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [62] S E Chidiac and M Shafikhani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Phenomenological model for quantifying concrete  chloride diffusion coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Construction and Building Materials, 224:773–  784, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [63] Mohamad Achour, Franc¸ois Bignonnet, Jean-Franc¸ois Barth´el´emy, Emmanuel  Rozi`ere, and Ouali Amiri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Multi-scale modeling of the chloride diffusivity and  the elasticity of Portland cement paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Construction and Building Materials,  234:117124, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  23  [64] M Shafikhani and S E Chidiac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A holistic model for cement paste and concrete  chloride diffusion coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 133:106049,2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [65] Yushan Gu, Benoˆıt Bary, Alisa Machner, Klaartje De Weerdt, Gerd Bolte, and  Mohsen Ben Haha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Multi-scale strategy to estimate the mechanical and diffusive  properties of cementitious materials prepared with CEM II/C-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and  Concrete Composites, 131:104537, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [66] N Ukrainczyk and E A B Koenders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Representative elementary volumes for 3D  modeling of mass transport in cementitious materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Modelling and Simulation  in Materials Science and Engineering, 22(3):35001, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [67] Gustave E Archie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The electrical resistivity log as an aid in determining some  reservoir characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Transactions of the AIME, 146(01):54–62, 1942.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [68] T C Powers Brownyard and T L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Studies of the Physical Properties of Hardened  Portland Cement Paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' ACI Journal Proceedings, 43(9), 1946.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [69] Tetsuji Yamaguchi, Kumi Negishi, Seiichi Hoshino, and Tadao Tanaka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Modeling  of diffusive mass transport in micropores in cement based materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and  Concrete Research, 39(12):1149–1155, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [70] S Lu, E N Landis, and D T Keane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' X-ray microtomographic studies of pore  structure and permeability in Portland cement concrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Materials and Structures,  39(6):611–620, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [71] H S Wong and N R Buenfeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Patch microstructure in cement-based materials:  Fact or artefact?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 36(5):990–997, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [72] M H N Yio, H S Wong, and N R Buenfeld.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Representative elementary volume  (REV) of cementitious materials from three-dimensional pore structure analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Cement and Concrete Research, 102:187–202, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [73] Qing-feng Liu, Muhammad Farjad Iqbal, Jian Yang, Xian-yang Lu, Peng Zhang,  and Momina Rauf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Prediction of chloride diffusivity in concrete using artificial  neural network: Modelling and performance evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Construction and Build-  ing Materials, 268:121082, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [74] Tomoshige Miyaguchi, Takashi Uneyama, and Takuma Akimoto.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Brownian mo-  tion with alternately fluctuating diffusivity: Stretched-exponential and power-law  relaxation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physical Review E, 100(1):12116, jul 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [75] CD Lawrence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Transport of oxygen through concrete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' In Proceedings of Concrete  Society, Meeting on Chemistry and Chemically-Related Properties of Cement,  Imperial College, London, pages 277–293, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [76] Paul D Tennis and Hamlin M Jennings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A model for two types of calcium silicate  hydrate in the microstructure of Portland cement pastes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete  Research, 30(6):855–863, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  24  [77] Hamlin M Jennings, Jeffrey J Thomas, Julia S Gevrenov, Georgios Constan-  tinides, and Franz-Josef Ulm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A multi-technique investigation of the nanoporosity  of cement paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 37(3):329–336, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [78] Hamlin M Jennings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Refinements to colloid model of C-S-H in cement: CM-II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Cement and Concrete Research, 38(3):275–289, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [79] Sydney Chapman and Thomas George Cowling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The Mathematical Theory of  Non-uniform Gases: an Account of the Kinetic Theory of Viscosity, Thermal Con-  duction and Diffusion in Gases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cambridge University Press, 3rd edition, 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [80] Won-Tae Koo, Shaopeng Qiao, Alana F Ogata, Gaurav Jha, Ji-Soo Jang, Vivian T  Chen, Il-Doo Kim, and Reginald M Penner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Accelerating palladium nanowire h2  sensors using engineered nanofiltration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' ACS nano, 11(9):9276–9285, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [81] Shuzhen Lv, Kangyao Zhang, Ling Zhu, Dianping Tang, Reinhard Niessner, and  Dietmar Knopp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' H2-based electrochemical biosensor with pd nanowires@ zif-67  molecular sieve bilayered sensing interface for immunoassay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Analytical Chem-  istry, 91(18):12055–12062, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [82] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Dorfman, Henk van Beijeren, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Kirkpatrick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Contemporary Kinetic  Theory of Matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cambridge University Press, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [83] Christoph Dellago, Henk v Beijeren, Debabrata Panja, and JR Dorfman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Field-  dependent collision frequency of the two-dimensional driven random lorentz gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Physical Review E, 64(3):036217, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [84] Keliu Wu, Xiangfang Li, Chenchen Wang, Wei Yu, and Zhangxin Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Model  for Surface Diffusion of Adsorbed Gas in Nanopores of Shale Gas Reservoirs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Industrial & Engineering Chemistry Research, 54(12):3225–3236, apr 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [85] Y D Chen and R T Yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Concentration dependence of surface diffusion and  zeolitic diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' AIChE Journal, 37(10):1579–1582, oct 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [86] Daniel T Gillespie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A general method for numerically simulating the stochastic  time evolution of coupled chemical reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=', 22(4):403–434,  1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [87] Alfred B Bortz, Malvin H Kalos, and Joel L Lebowitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A new algorithm for monte  carlo simulation of ising spin systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=', 17(1):10–18, 1975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [88] M Boumaaza, B Huet, G Pham, P Turcry, A A¨ıt-Mokhtar, and C Gehlen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' A  new test method to determine the gaseous oxygen diffusion coefficient of cement  pastes as a function of hydration duration, microstructure, and relative humidity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Materials and Structures, 51(2):51, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [89] Yves F Houst and Folker H Wittmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Influence of porosity and water content  on the diffusivity of CO2 and O2 through hydrated cement paste.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and  Concrete Research, 24(6):1165–1176, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  25  [90] Mohammad Javad Abdolhosseini Qomi, Mathieu Bauchy, Franz-Josef Ulm, and  Roland J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Pellenq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Anomalous composition-dependent dynamics of nanocon-  fined water in the interlayer of disordered calcium-silicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' The Journal of Chem-  ical Physics, 140(5):54515, feb 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [91] Walter Kob, Claudio Donati, Steven J Plimpton, Peter H Poole, and Sharon C  Glotzer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Dynamical heterogeneities in a supercooled lennard-jones liquid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Phys-  ical review letters, 79(15):2827, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [92] Bart Vorselaars, Alexey V Lyulin, K Karatasos, and MAJ Michels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  Non-  gaussian nature of glassy dynamics by cage to cage motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physical Review  E, 75(1):011504, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [93] Fumiaki Nakai, Yuichi Masubuchi, Yuya Doi, Takato Ishida, and Takashi Un-  eyama.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Fluctuating diffusivity emerges even in binary gas mixtures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physical  Review E, 107(1):014605, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [94] Aneesur Rahman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Correlations in the motion of atoms in liquid argon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Physical  review, 136(2A):A405, 1964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [95] Dale P Bentz, Edward J Garboczi, Claus J Haecker, and Ole M Jensen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Effects of  cement particle size distribution on performance properties of Portland cement-  based materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Cement and Concrete Research, 29(10):1663–1671, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [96] Jian Zhang, Hai-long Wang, Zhi-wei Chen, Qing-feng Liu, Xiao-yan Sun, and  Jian-jun Zheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Experimental investigation and numerical simulation for chloride  diffusivity of cement paste with elliptical cement particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Construction and  Building Materials, 337:127616, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  [97] Dale P Bentz, Daniel A Quenard, Veronique Baroghel-Bouny, Edward J Gar-  boczi, and Hamlin M Jennings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Modelling drying shrinkage of cement paste and  mortar Part 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Structural models from nanometres to millimetres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content=' Materials and  Structures, 28(8):450–458, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
+page_content='  26' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/PdFKT4oBgHgl3EQfgi6G/content/2301.11834v1.pdf'}
diff --git a/QNE0T4oBgHgl3EQfkQEN/vector_store/index.faiss b/QNE0T4oBgHgl3EQfkQEN/vector_store/index.faiss
new file mode 100644
index 0000000000000000000000000000000000000000..cd87e775d89deb94ff8e39267bb8ac2377b55234
--- /dev/null
+++ b/QNE0T4oBgHgl3EQfkQEN/vector_store/index.faiss
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:53859644ddcc4a399461b85c92aa960eba61e120300b097ddeaf1ad57f4703e0
+size 1245229
diff --git a/RtE2T4oBgHgl3EQfWQe7/content/tmp_files/2301.03832v1.pdf.txt b/RtE2T4oBgHgl3EQfWQe7/content/tmp_files/2301.03832v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e12f91c4683271501762c99bfbc0718dfbd4433e
--- /dev/null
+++ b/RtE2T4oBgHgl3EQfWQe7/content/tmp_files/2301.03832v1.pdf.txt
@@ -0,0 +1,1216 @@
+Video Semantic Segmentation with Inter-Frame Feature
+Fusion and Inner-Frame Feature Refinement
+Jiafan Zhuang, Zilei Wang∗, Junjie Li
+National Engineering Laboratory for Brain-inspired Intelligence Technology and
+Application, University of Science and Technology of China, Hefei 230027, China
+Abstract
+Video semantic segmentation aims to generate accurate semantic maps for each
+video frame. To this end, many works dedicate to integrate diverse information
+from consecutive frames to enhance the features for prediction, where a feature
+alignment procedure via estimated optical flow is usually required. However, the
+optical flow would inevitably suffer from inaccuracy, and then introduce noises
+in feature fusion and further result in unsatisfactory segmentation results. In
+this paper, to tackle the misalignment issue, we propose a spatial-temporal fu-
+sion (STF) module to model dense pairwise relationships among multi-frame
+features. Different from previous methods, STF uniformly and adaptively fuses
+features at different spatial and temporal positions, and avoids error-prone opti-
+cal flow estimation. Besides, we further exploit feature refinement within a sin-
+gle frame and propose a novel memory-augmented refinement (MAR) module to
+tackle difficult predictions among semantic boundaries. Specifically, MAR can
+store the boundary features and prototypes extracted from the training samples,
+which together form the task-specific memory, and then use them to refine the
+features during inference. Essentially, MAR can move the hard features closer to
+the most likely category and thus make them more discriminative. We conduct
+extensive experiments on Cityscapes and CamVid, and the results show that
+our proposed methods significantly outperform previous methods and achieves
+∗Corresponding author.
+Email addresses: jfzhuang@mail.ustc.edu.cn (Jiafan Zhuang), zlwang@ustc.edu.cn
+(Zilei Wang), hnljj@mail.ustc.edu.cn (Junjie Li)
+Preprint submitted to Pattern Recognition
+January 11, 2023
+arXiv:2301.03832v1  [cs.CV]  10 Jan 2023
+
+the state-of-the-art performance. Code and pretrained models are available at
+https://github.com/jfzhuang/ST Memory.
+Keywords:
+Video semantic segmentation, Spatial-temporal feature fusion,
+Memory mechanism, Feature refinement.
+1. Introduction
+Semantic segmentation targets to assign each pixel in scene images a se-
+mantic class, which is one of the fundamental tasks in computer vision.
+In
+recent years, image semantic segmentation has achieved unprecedented per-
+formance benefited from the great progress of deep convolutional neural net-
+work (DCNN) [1] and construction of various datasets (e.g.Cityscapes [2] and
+CamVid [3]). However, many real-world applications have strong demands for
+accurate video semantic segmentation, e.g., robotics, autonomous driving, and
+video surveillance. Actually, video data offer richer information than static im-
+ages, e.g., diverse presentations from multiple frames and temporal consistency
+prior. Thus video can provide good potential to achieve more accurate seman-
+tic segmentation. The key is how to produce more discriminative features by
+exploiting the characteristics of videos.
+A natural way to enhance video features is to integrate the diverse informa-
+tion of consecutive frames [4, 5]. Specifically, the feature alignment is commonly
+performed via the optical flow based feature warping, which ensures that pixel-
+level features at the same spatial position represent the identical object, and
+then the temporal feature fusion is conducted for each pixel. Evidently, the
+accurate optical flow is critical for feature fusion. However, the optical flow
+estimation inevitably suffers from inaccuracy in the boundary areas due to ob-
+ject occlusion and plain texture [6, 7]. If the features are not well-aligned, the
+noises would be introduced. Consequently, the quality of fused features would
+be reduced and the segmentation performance would be deteriorated.
+Besides, after aggregating information from consecutive frames, can we fur-
+ther refine the fused feature? Different from inter-frame feature fusion in video
+2
+
+(b)
+f
+f
+f𝑡−1
+f𝑡
+f𝑡
+f𝑡+1
+(a)
+f𝑡−1
+f𝑡
+f𝑡
+f𝑡+1
+f𝑡
+(c)
+Backbone
+Classifier
+Feature
+Fusion
+Feature
+Refinement
+Inter-Frame
+Feature
+Fusion
+Inner-Frame
+Feature
+Refinement
+Figure 1: Architecture illustrations for different methods. (a) Feature fusion in video
+segmentation methods (e.g., NetWarp [4] and GRFP [5]). (b) Feature refinement in image
+segmentation methods (e.g., DenseCRF [8] and SegFix [9]). (c) Our proposed method. Best
+viewed in color.
+segmentation methods, some image-based methods adopt the post-processing
+techniques to optimize the features for prediction. For example, DenseCRF [8]
+uses a graph structure to model pairwise potentials on all pixels and iteratively
+adjusts the feature by optimizing an energy function. Essentially, it uses simi-
+lar features to mutually enhance themselves. SegFix [9] proposes to replace the
+difficult boundary features with some better ones, whose locations are predicted
+by a network and often lie around the boundary areas in practice.
+Actually, feature fusion is proposed to aggregate useful information from
+different frames while feature refinement is designed for correcting error-prone
+features, which are potentially complementary. Based on this motivation, in
+this paper, we aim to improve the accuracy of video semantic segmentation by
+simultaneously considering inter-frame feature fusion and inner-frame feature
+refinement, as shown in Figure 1. For the inter-frame fusion, we need to tackle
+the feature misalignment issue.
+To this end, we propose a spatial-temporal
+fusion (STF) module that uniformly fuses the features at different spatial and
+temporal positions and does not require explicit feature alignment via error-
+prone optical flows. Here the transformer [10] is particularly adopted due to
+the power to model long-range dependencies.
+To be specific, the encoder is
+fed with the features extracted from consecutive frames, and the decoder is
+used to generate the prediction features by retrieving the current frame from
+3
+
+the encoded features. In particular, we utilize the self-attention mechanism in
+transformer to guide the feature fusion in latent space, in which more similar
+features are supposed to be more likely to represent the same object. For an
+image pixel, hence, STF would integrate multiple similar features at different
+temporal and spatial positions, rather than only the temporal-aligned features
+in the previous works [4, 5].
+In addition, an image with the resolution of (1024, 2048) would typically
+produce the features with the resolution of (128, 256). The transformer taking
+three frames needs to process 3 × 128 × 256 = 98304 pixel-level features, which
+results in unacceptable computation and memory cost with O(N 2) complexity
+when computing affinity matrix. Inspired by a recent work [11], we propose an
+interlaced cross-self attention (ICSA) attention mechanism to divide the dense
+affinity matrix computation in transformer as the product of a long-range cross-
+attention and a short-range self-attention, which can greatly reduce the memory
+consumption.
+On the other hand, we propose inner-frame feature refinement to further ad-
+just the fused features for better prediction without devising more complicated
+network structure. In this work, we focus on refining the hard features that are
+error-prone and always lie in the boundary areas of different classes [9]. To this
+end, we propose a novel memory-augmented refinement (MAR) module that
+uses the stored features in memory to augment the hard features. Actually, this
+is motivated by an intuitive observation that humans would retrieve memory to
+enhance the judgement when facing semantically ambiguous contents. Here the
+memory represents the experience from the training samples. For each semantic
+category, we particularly store the hard features and their corresponding class
+prototypes (refer to the mean feature representing a single category), which to-
+gether form a key-value memory bank. During inference, a hard feature would
+be refined by the class prototypes, where the weights of different classes are
+computed by comparing it with the stored hard features in the memory. In this
+way, the discriminativeness of boundary features would be enhanced since MAR
+would make them move closer to the most likely category. Evidently, MAR has
+4
+
+good interpretability and can be conveniently inserted into different models as
+an independent module.
+We experimentally evaluate the proposed method on the Cityscapes and
+CamVid datasets. The results validate the effectiveness of our STF and MAR
+to improve the quality of features, and their combination can achieve the state-
+of-the-art segmentation performance.
+The contributions of this work are summarized as
+• We design a novel video semantic segmentation framework by simultane-
+ously considering inter-frame feature fusion and inner-frame feature re-
+finement, which can take advantages from both two feature enhancement
+techniques and effectively improve segmentation accuracy.
+• We propose an effective spatial-temporal fusion module based on the trans-
+former, which can uniformly aggregate the features at different spatial and
+temporal positions and avoid error-prone temporal feature alignment.
+• We propose a novel memory-augmented refinement module to particularly
+refine hard features using the experience from training samples. In par-
+ticular, the key-value memory is stored to refine the hard features closer
+to the most likely category.
+• We experimentally evaluate the effectiveness of our proposed methods,
+and the results on Cityscapes and CamVid demonstrate the superiority of
+our methods to previous state-of-the-art methods.
+The rest of this paper is organized as follows. We review the related works on
+image and video semantic segmentation, transformer and memory mechanism
+in Section 2.
+Section 3 provides the details of our approach, and Section 4
+experimentally evaluates the proposed method. Finally, we conclude the work
+in Section 5.
+5
+
+2. Related Work
+2.1. Image Semantic Segmentation
+With the development of DCNN, more semantic segmentation networks
+spring up. Specifically, the fully convolutional networks (FCNs) [1] firstly uses
+the convolutional layers to replace fully-connected layers and can achieve better
+performance. Inspired by FCN, many extensions have been proposed to ad-
+vance image semantic segmentation. The dilated layers [12] are used to replace
+the pooling layers, which can better balance the computational cost and size
+of receptive fields. To further improve segmentation accuracy, spatial pyramid
+pooling and atrous spatial pyramid pooling (ASPP) are used in PSPNet [13]
+and DeepLab [12] to capture multi-scale contextual information.
+Mitivated
+by ASPP, Peng et al. [14] proposes a stride spatial pyramid pooling (SSPP)
+to capture multiscale semantic information from the high-level feature map,
+while Lian et al. [15] proposes a cascaded hierarchical atrous pyramid pooling
+module to simultaneously extract rich local detail characteristics and impor-
+tant global contextual information. CENet [16] aggregates contextual cues via
+densely usampling the convolutional features of deep layer to the shallow decon-
+volutional layers, which can fully explore multiple scale contextual information.
+GPNet [17] densely captures and filters the multi-scale information in a gated
+and pair-wise manner with a gated pyramid module and a cross-layer attention
+module. Marin et al. [18] propose a novel architecture based on shared pyrami-
+dal representation and fusion of heterogeneous features along the upsampling
+path, which is effective for dense inference in images with large scale. Different
+from enhancing features, EFNet [19] propose to produce multiple enhanced im-
+ages and fuses them to yield one new image, which can encourage the model to
+exploit complementary information.
+Differently, our proposed methods focus on exploiting both spatial and tem-
+poral contexts to further improve the performance and can build upon any
+existing image segmentation models.
+6
+
+2.2. Video Semantic Segmentation
+Different from static images, videos embody rich temporal information that
+can be exploited to improve the semantic segmentation performance. Existing
+video semantic segmentation methods mainly fall into two categories. The first
+category aims to accelerate inference speed by reusing the features in previous
+frames. DFF [20] estimates the optical flow fields [21] from the key frame to
+other frames and then propagates the high-level features using the predicted
+optical flows.
+Accel [22] proposes a reference branch to extract high-quality
+segmentation from the key frames and an update branch to efficiently extract
+low-quality segmentation from the current frames, and the fuses them to improve
+the segmentation accuracy. DAVSS [7] designs a feature correction mechanism
+to tackle distorted features after propagation due to inaccurate optical flows.
+LERNet [23] proposes to propagate multi-level features from the key frame via a
+temporal holistic attention module. TDNet [24] distributes several sub-networks
+over sequential frames and then recomposes the extracted features for segmen-
+tation via an attention propagation module. Differently, Liu et al. [25] designs
+a new temporal knowledge distillation methods to narrow the performance gap
+between compact models and large models.
+Another category focus on improving segmentation accuracy by modeling
+cross-frame relations to integrate information from consecutive frames. V2V [26]
+utilizes a 3D CNN to perform a voxel-level prediction. STFCN [27] utilizes a
+spatial-temporal LSTM over per-frame CNN features. However, these methods
+cannot achieve high performance due to rough processing of different frames.
+HDCNN [28] proposes a transition layer structure to make the pixel-wise label
+prediction consist with adjacent pixels across space and time domains. Recently,
+some works [4, 5] propose to fuse features from multiple frames to produce the
+better features for prediction. They usually adopt the optical flow to model
+cross-frame relationships and perform temporal alignment by warping features.
+In particular, NetWarp [4] uses a set of learnable weights to fuse multiple fea-
+tures, and GRFP [5] proposes the gated recurrent units STGRU to estimate the
+uncertainty of warped features and then conducts feature fusion on the areas
+7
+
+with high reliability. Obviously, the optical flow is critical for feature align-
+ment and would affect the final accuracy. However, the optical flow estimation
+inevitably suffers from inaccuracy, especially for the occlusion areas and small
+objects (e.g., pedestrian, pole) [7]. In this work, we follow the route of sec-
+ond category and focus on improving segmentation accuracy. Different from
+previous works, we propose to simultaneously model the spatial-temporal re-
+lationship without feature alignment, which can avoid error-prone optical-flow
+estimation. Furthermore, we propose to use memory to refine the prediction
+features.
+2.3. Transformer
+Transformer is originally proposed for the sequence-to-sequence machine
+translation [10], and currently has dominated various NLP tasks. As the core
+component of transformer, the self-attention is particularly suitable for mod-
+eling long-range dependencies. Due to the success of transformer in the NLP
+field, some works attempt to explore the benefits of transformer in computer
+vision. DETR [29] first builds an object detection system based on transformer,
+which can reason about relationships between objects and global context and
+directly output the final set of predictions. Swin Transformer [30] designs a
+novel shifted windowing scheme, which can limit attention computation to local
+windows while also allow for cross-window connection. It achieves an impressive
+performance on a broad range of vision tasks. In this paper, we propose STF by
+using transformer to model the spatial-temporal relationship among pixel-wise
+features extracted from consecutive frames. To our best knowledge, this is the
+first attempt to exploit the transformer in video semantic segmentation.
+Recently, Action Transformer [31] and Actor Transformer [32] also adopt
+transformer to model spatial-temporal relationship in action detection and group
+action recognition tasks, which are closely related to our proposed STF. They
+naturally adopt transformer for modeling proposal-context and proposal-proposal
+relationship. But our proposed STF is different from these two works. STF is
+designed for modeling pixel-wise relationship, which would involve huge memory
+8
+
+and computation overhead issues. In this work, we propose interlaced cross-self
+attention (ICSA) mechanism to tackle these issues and achieve efficient global
+relationship modeling.
+2.4. External Memory
+In DCNN, external memory is generally used to enhance feature represen-
+tations by storing history data, which is especially useful for the tasks without
+enough samples, e.g., life-long learning [33] and few-shot learning [34, 35]. For
+example, MM-Net [35] proposes to store the representative features in the sup-
+port set for one-shot learning, and then use them to predict the parameters of
+feature extraction network on query images. Actually, this can make the query
+features more relevant to the support features. In recent years, the memory
+mechanism is also exploited to store long-range temporal contexts for video
+tasks during inference. In video object detection, [36] proposes to store pixel-
+level and instance-level features extracted from previous frames and then use
+them to enhance the current frame.
+LFB [37] proposes a long-term feature
+bank for action localization to store supportive information extracted over the
+entire span of a video, and then uses them to enhance the short-term features
+extracted from short video clips. Different from the previous works that store
+temporal [36, 37] or sample [35] contexts, in this paper we propose to store
+the hard features and class prototypes from the training samples to form a
+task-specific memory, and then use them to refine the boundary features during
+inference.
+3. Our Approach
+In this work, we aim to boost the accuracy of video semantic segmenta-
+tion by enhancing the features for prediction. To this end, we first propose a
+spatial-temporal fusion (STF) module to perform inter-frame feature fusion at
+different spatial and temporal positions, which can avoid error-prone optical flow
+estimation. Then we propose a memory-augmented refinement (MAR) module
+9
+
+𝐼𝑇−1
+𝐼𝑇
+𝐼𝑇+1
+𝐟𝑇−1
+𝐟𝑇
+𝐟𝑇+1
+Spatial-Temporal
+Fusion Module
+Framework
+Memory-Augmented
+Refinement Module
+Backbone
+1、相邻多帧特征经过STRM实现特征融合
+2、融合特征经过MARM实现进一步优化
+መ𝐟𝑇
+Feature 
+Memory
+𝑆𝑇
+𝑆𝑇−1
+…
+…
+Sliding Window
+…
+…
+Classifier
+𝐟𝑇
+′
+Video Feature Enhancement
+መ𝐟𝑇−1
+Figure 2: The framework of our proposed approach. First, the feature is extracted by
+an image segmentation model for each frame. Then the features of consecutive frames are fed
+into our proposed STF module to perform feature fusion. After that, the fused feature f
+′
+T
+is further refined by our proposed MAR module, resulting in �fT . Finally, the segmentation
+result is obtained by applying the classifier on �fT . Best viewed in color.
+to further refine the boundary features during inference, which is essential to
+utilize the stored experience from training samples. In the following, we first
+introduce the framework of our proposed approach, and then elaborate on two
+key modules, namely, STF and MAR.
+3.1. Framework
+Our proposed video semantic segmentation framework is illustrated in Fig-
+ure. 2. Formally, given a sequence of n video frames denoted by {I1, I2, · · · ,
+In}, our purpose is to get the accurate semantic segmentation maps for every
+video frame, denoted by {S1, S2, · · · , Sn}. Specifically, we first extract features
+from each frame image using an off-the-shelf segmentation model. Then we con-
+duct video feature enhancement for the current timestamp T with a sequence
+of three-frame features {fT −1, fT , fT +1}, resulting in �fT for final prediction.
+Finally, we apply the classifier on �fT to produce the segmentation result ST .
+Since such a procedure can be performed in a sliding-window manner, we can
+obtain the corresponding segmentation sequence.
+In this work, we dedicate to enhance video features to improve the segmen-
+tation performance. To be specific, we first feed the sequence of frame features
+10
+
+𝐟𝑇−1
+𝐟𝑇
+𝐟𝑇+1
+Concat
+Interlaced
+Cross-Self
+Attention
+Add & Norm
+FFN
+Add & Norm
+Encoder
+Interlaced
+Cross-Self
+Attention
+Add & Norm
+FFN
+Add & Norm
+Decoder
+𝐟𝑇
+Interlaced
+Cross-Self
+Attention
+Add & Norm
+𝐟𝑇
+′
+𝐟𝐸𝑛𝑐
+′
+𝐟𝐸𝑛𝑐
+Figure 3: Illustration of transformer based spatial-temporal fusion module. STF
+consists of an encoder for modeling spatial-temporal relationships and feature encoding, and
+a decoder for retrieving the feature of current frame from the encoded feature f
+′
+Enc. Best
+viewed in color.
+into our proposed STF module to capture spatial-temporal dependencies and
+complete pixel-wise feature fusion, resulting in the fused feature f
+′
+T . After that,
+our proposed MAR module further refines f
+′
+T into �fT by exploiting the stored
+feature memory to enhance the discriminativeness of the boundary features. Ev-
+idently, STF and MAR are the key components of our method that determine
+the performance of video semantic segmentation.
+3.2. Spatial-Temporal Fusion
+In this work, we propose a spatial-temporal fusion module to effectively
+integrate the features of consecutive frames. Here it is expected that the spatial-
+temporal relationship among consecutive frames is well modeled and the optical
+flow estimation is avoided. In particular, we use the transformer [10] to perform
+inter-frame fusion, which recently achieves the amazing performance in both
+NLP and CV areas. Thus our STF consists of an encoder and a decoder, as
+shown in Figure. 3.
+11
+
+Encoder. In STF, the encoder is used to capture the spatial-temporal relation-
+ships of pixel-level features. To this end, we concatenate the 2D features of
+multiple frames {fT −1, fT , fT +1} to obtain a 3D feature fEnc ∈ Rd×3×H×W ,
+where d is the dimension of pixel-level features, H and W represent the spatial
+size of frame features. That is, there are 3HW features in total for processing in
+the encoder. We first pass fEnc into our proposed interlaced cross-self attention
+(ICSA) module to model dense spatial-temporal relationships, and the features
+are adjusted by weighting on all features. Then we feed the new features into
+feed-forward network (FFN) to perform feature transformation. Similar to [10],
+we employ the residual connections for the attention module and FFN followed
+by layer normalization. Finally, we obtain the encoded features f
+′
+Enc. Com-
+pared with the previous optical flow based methods [4, 5], our proposed STF
+uniformly aggregates all features at different spatial and temporal positions, and
+no explicit feature alignment is required. Essentially, a single feature in STF
+is implicitly aligned with multiple similar features by attention other than the
+temporally-aligned ones. This is reasonable since the purpose of feature fusion
+is to mutually enhance the features belonging to the same semantic class.
+Decoder. In STF, the decoder is used to get the prediction features of the current
+frame. To this end, we use the original feature of current frame to retrieve from
+the encoded features f
+′
+Enc. To be specific, we first feed the feature of current
+frame into an ICSA module to enhance the features similar in the encoder. Then
+we pass the enhanced features together with f
+′
+Enc into another ICSA module
+for cross attention and produce the features f
+′
+T with FFN. Different from the
+previous one, here the enhanced fT serves as the query and f
+′
+Enc serves as the
+key and value. Intuitively, we retrieve the encoded features from f
+′
+Enc for each
+pixel-level feature in fT , and consequently the f
+′
+T would contain rich information
+from other spatial and temporal positions.
+Interlaced Cross-Self Attention. In the original transformer, the attention op-
+eration would involve O(N 2) complexity given an input of size N (e.g., here
+N = 3HW in our case), which is impractical to the video semantic segmen-
+12
+
+query
+value
+key
+permute
+permute
+permute
+query
+value
+key
+Positional
+Encoding
+Positional
+Encoding
+BWA
+permute
+output
+output
+query
+value
+key
+BWA
+Interlaced Cross-Self Attention (ICSA)
+Interlaced Sparse Attention (ISA)
+Positional
+Encoding
+Positional
+Encoding
+Long-range Cross-Attention
+Short-range Self-Attention
+permute
+BWA
+permute
+BWA
+Long-range Attention
+Short-range Attention
+Figure 4:
+Illustration of differences between our interlaced cross-self attention
+(ICSA) and with interlaced sparse attention (ISA) [11]. ICSA takes query, key and
+value separately for long-rang cross-attention first and then conduct short-range self-attention
+on the previous enhanced feature, which can be seamlessly integrated in the transformer
+structure, especially for cross-attention module in the decoder. Besides, ICSA implements
+necessary positional encoding and can deal with features from multiple frames directly, which
+can uniformly model spatial-temporal relationships. Best viewed in color.
+tation task since computation on pixel-level features would consume too much
+memory. To tackle this issue, a recent work ISA [11] provides a successful so-
+lution. It decomposes the whole attention calculation as the combination of
+long-range and short-range sparse attention calculations, as shown in the upper
+subplot in Figure. 4. In this way, it can retain the ability of modeling global
+relationship while effectively reduce the memory consumption. However, ISA is
+designed for self-attention mechanism like non-local [38], which is not well com-
+patible with the transformer structure. Specifically, ISA takes a single feature
+as input and performs enhancement by modeling inner relationship. Thus it
+can not be directly integrated into cross attention in the transformer decoder.
+Besides, how to insert necessary positional encoding and deal with features of
+multiple frames are not considered by ISA.
+In this work, we extend the original ISA into a more general form and propose
+13
+
+Method
+query
+key
+value
+Divide
+Group
+q
+k
+v
+Block-wise Attention Module
+MHA: Multi-Head Attention
+MHA
+MHA
+MHA
+MHA
+Figure 5: Illustration of block-wise attention (BWA). The input 3D features, i.e.query,
+key and value, are spatially divided into patches with the same shape. Then we apply multi-
+head attention (MHA) [10] operation on corresponding query, key and value patches indepen-
+dently, and combine their results back to the entire one. Best viewed in color.
+interlaced cross-self attention (ICSA), which can be seamlessly integrated into
+transformer structure, as illustrated in the Figure. 4. Generally, we reorganize
+ISA with long-range cross-attention and short-range self-attention operations.
+First, we take query, key and value separately as inputs for cross-attention. Par-
+ticularly, the query, key, and value are the same feature fEnc for the STF module
+encoder, while the key and value are f
+′
+Enc and the query is the enhanced fT for
+the STF module decoder. Here we directly takes 3D features as input to uni-
+formly model spatial-temporal relationships. For query and key, we supplement
+the features with positional encoding. Particularly, we choose the learnable po-
+sitional encoding by following [10]. In this work, we extend positional encoding
+to the 3D version and they have the same shape as the corresponding input.
+Following ISA, we divide features into k blocks with the same shape (e.g.,
+k = 4 in Figure. 4 and Figure. 5). To model long-range cross-attention, we
+harvest features with same spatial positions from different blocks in query, key
+and value via permutation operation, respectively. Then we conduct block-wise
+attention (BWA) operation for relationship modeling. As shown in Figure. 5, we
+first divide input query, key and value features into pre-defined blocks. Then,
+we apply multi-head attention (MHA) [10] on corresponding query, key and
+14
+
+Relationship Computation
+Feature Refinement
+Boundary Feature of class 0
+Prototype of class 0
+Boundary Feature of class 1
+Prototype of class 1
+Figure 6: Illustration of feature refinement. We first compute the relationships between
+the stored boundary features and the test feature to estimate the class likelihoods. Then we
+refine the test feature using the class prototypes, which essentially makes the feature move
+closer to the most likely class. Best viewed in color.
+value patches independently, and combine their results back to the entire one.
+For short-range self-attention, we first permute the feature back to the original
+positions and then regard it as query, key and value for the next attention cal-
+culation. After adding positional encoding, we conduct BWA operation again
+and obtain the final enhanced feature. With ICSA, STF can conveniently har-
+vest global spatial-temporal information for feature enhancement while keeps
+an efficient attention computation. Besides, if we take a single feature from one
+frame as query, key and value, and remove positional encoding, ICSA would
+degenerate into ISA. Evidently, ISA is a special case of ICSA.
+3.3. Memory-Augmented Refinement
+In this work, we propose a novel memory-augmented refinement module to
+further refine the fused features. Different from previous works that explore
+the relationship among the inference features [8, 39, 9], we focus on refining
+the hard features (e.g., boundary features) using the memory from the training
+samples.
+The idea is illustrated in Figure. 6, and it is actually inspired by
+an intuitive mechanism of humans to process semantically ambiguous contents.
+Specifically, given a test feature during inference, it usually lies in the boundary
+area of different classes in the feature space if it is hard to distinguish (e.g., with
+15
+
+Method
+SDA: Scaled Dot-product Attention
+FFN: Feed Forward Network
+𝐟
+Key-Value Memory
+𝐟𝑅
+FFN
+SDA
+𝑆𝑖 = 𝜃(𝑄𝑝) ∅(𝐾𝑖)𝑇, 𝑖 ∈ 1, 𝐶𝐾 , p = (x, y),d is channel num
+𝑆 = 𝑆𝑜𝑓𝑡𝑚𝑎𝑥(𝑆)
+෢
+𝑄𝑝 = ෍
+𝑖=1
+𝐶𝐾
+𝑆𝑖𝑉𝑗 ,
+𝑗 is the class index of 𝐾𝑖, 𝑗 ∈ [1, 𝐶]
+SDA的计算步骤：
+Add &
+Norm
+Add &
+Norm
+Figure 7: Illustration of memory-augmented refinement module. The input feature
+f is refined into fR using the key-value memory extracted from the training samples. Here
+f serves as the query, the key is the stored boundary features, and the value is the class
+prototypes.
+Here ’SDA’ represents scaled dot-product attention and ’FFN’ represents feed
+forward network.
+low confidence score). To enhance its discriminativeness, we first estimates its
+likelihoods to different classes by computing the similarities between the feature
+and stored boundary features of each class. Then we use the class prototypes
+to refine the feature according to the estimated likelihoods, where the class
+prototype refers to the mean feature representing a category. Through this way,
+the test feature would move closer to the most likely category.
+Our proposed MAR module is used to implement such an idea and is illus-
+trated in Figure. 7. Specifically, we build the key-value memory for each class
+that stores two kinds of data from the training samples, namely, the bound-
+ary features and class prototypes.
+The boundary features serve as the keys
+K ∈ Rd×CKL and the class prototypes serve as the values V ∈ Rd×C, where C
+denotes the number of classes and KL is a hyper-parameter to control the size of
+memory. In the MAR module, the input feature F is refined into FR using the
+key-value memory. Inspired by the transformer, we use the scaled dot-product
+attention (SDA) and FFN to construct the MAR block. To be specific, we take
+the test feature as query Q ∈ Rd, and use the key-value in memory to refine it,
+resulting in Q
+′. Formally,
+si = θ(Q)T φ(Ki),
+(1)
+si =
+esi
+�CKL
+i=1 esi ,
+(2)
+Q
+′ =
+CKL
+�
+i=1
+siVj,
+(3)
+16
+
+Training
+Set
+Memory Organization
+Sky
+Features with
+Lowest Scores
+Car 
+Sky
+Features with
+Highest Scores
+Car 
+𝐾𝐻 = 4, 𝐾𝐿 = 4, 𝐶 = 2 for Visualization
+𝐾𝐻𝐶 Features
+Prototype Generation
+𝐾𝐿𝐶 Features
+Score-Based Selection
+Backbone
+Sky
+Key
+Car 
+Sky
+Value
+Car 
+𝐶 Features
+𝐾𝐿𝐶 Features
+Key-Value Groups
+Figure 8: Illustration of the key-value memory.
+From the extracted features on the
+training set, we select KH ”good” features with the highest scores and KL ”hard” features
+with the lowest scores per class.
+Then we generate the class prototypes by averaging the
+”good” features, and organize them with ”hard” features to form the key-value memory. Here
+KH = 4, KL = 4, and C = 2 are used for visualization.
+where i ∈ [1, CKL] denotes the sample in memory and j is the class index cor-
+responding to the i-th sample. Here θ(Q) = WθQ and φ(Ki) = WφKi, and Wθ
+and Wφ are two learnable matrices. Notably, in Eq. (3), we index V by j rather
+than i, which is different from the original self-attention calculation. We employ
+the residual connections for SDA and FFN followed by layer normalization, like
+in the original transformer [10].
+Next we explain how to generate the key-value memory from the training
+samples, which is shown in Figure. 8. We first train the segmentation network
+without the MAR module. Using this model, we extract the features for all
+training samples. Note that a feature would be discarded if it is misclassified by
+the classifier. According to the ground truth, for each class, we select KL ”hard”
+features with the lowest confidence scores and KH ”good” features with the
+highest confidence scores. The former are considered to suffer from semantically
+ambiguity while the latter are to accurately represent the semantic category.
+After that, we compute the mean feature of the ”good” features for each class,
+resulting in the class prototype. Finally, we store the ”hard” features as keys
+and the corresponding class prototype as values in the memory, which essentially
+represent the task-specific experience.
+17
+
+3.4. Training Strategy
+Our proposed network consists of four main components, i.e., backbone, clas-
+sifier, STF, and MAR. Here, we adopt a multi-stage training schedule, which is a
+common strategy in advanced works, e.g., Faster RCNN and knowledge distilla-
+tion. First, the backbone and classifier together are pretrained on ImageNet and
+finetuned on a particular segmentation dataset (e.g., Cityscapes and CamVid).
+The backbone would keep fixed and the classifier would be re-initialized in the
+following training procedures. Then, we train STF together with the backbone
+and classifier, and use this model to generate the key-value memory. Finally,
+we train the MAR and classifier by fixing STF. In the test phase, we perform
+the end-to-end inference with STF and MAR.
+4. Experiment
+In this section, we experimentally evaluate our proposed method on two
+challenging datasets by following the previous works, namely, Cityscapes [2] and
+CamVid [3]. Here some state-of-the-art methods are adopted for comparison
+and the results from the literatures are listed. We follow the standard protocols
+of video semantic segmentation and report the mean Intersection over Union
+(mIoU) as the performance metric.
+4.1. Dataset
+Cityscapes [2] is a popular dataset in semantic segmentation and autonomous
+driving domain. It focuses on semantic understanding of urban street scenes.
+The training and validation subsets contain 2, 975 and 500 video clips, respec-
+tively, and each video clip contains 30 frames. The 20th frame in each clip is
+annotated by the pixel-level semantic labels with 19 categories.
+CamVid [3] also focuses on the semantic understanding of urban street
+scenes, but it contains less data than Cityscapes. It only has 701 color images
+with annotations of 11 semantic classes. CamVid is divided into the trainval
+set with 468 samples and test set with 233 samples. All samples are extracted
+18
+
+Method
+Backbone
+mIoU (%)
+PSPNet [13]
+ResNet18
+69.79
++ Liu et al. [25]
+ResNet18
+73.06 (+3.27)
++ Ours
+ResNet18
+74.58 (+4.79)
+PSPNet [13]
+ResNet50
+76.24
++ Accel [22]
+ResNet50
+70.20 (-6.04)
++ TDNet [24]
+ResNet50
+76.40 (+0.27)
++ EFC [40]
+ResNet50
+78.44 (+2.31)
++ Ours
+ResNet50
+79.22 (+2.98)
+PSPNet [13]
+ResNet101
+79.70
++ TDNet [24]
+ResNet101
+79.90 (+0.20)
++ NetWarp [4]
+ResNet101
+80.60 (+0.90)
++ GRFP [5]
+ResNet101
+80.20 (+0.50)
++ Ours
+ResNet101
+80.96 (+1.26)
+Swin-B [30]
+Swin Transformer
+81.34
++ Ours
+Swin Transformer
+81.67 (+0.33)
+Table 1: Performance comparison on Cityscapes val subset. PSPNet and Swin Transformer
+are chosen as the image segmentation models.
+from the driving videos captured at daytime and dusk, and have pixel-level
+semantic annotations. Each CamVid video contains 3, 600 to 11, 000 frames at
+a resolution of 720 × 960.
+4.2. Performance Comparison
+Here we compare our proposed method with the state-of-the-art methods on
+Cityscapes and CamVid. In particular, the image segmentation model is used
+as the baseline. The PSPNet [13] with the backbone ResNet18/50/101 has been
+widely used on Cityscapes, and Dilation8 [41] is mainly adopted on CamVid.
+Table 1 and Table 2 show the results, and we have the following observations.
+First, our proposed method achieves the state-of-the-art performance on both
+datasets and various baseline model, which demonstrate the effectiveness and
+generalization of our method. Second, our proposed method can get more gains
+19
+
+Method
+Backbone
+mIoU (%)
+Dilation8 [41]
+VGG16
+65.3
++ STFCN [27]
+VGG16
+65.9 (+0.4)
++ GRFP [5]
+VGG16
+66.1 (+0.8)
++ FSO [42]
+VGG16
+66.1 (+0.8)
++ VPN [43]
+VGG16
+66.7 (+1.4)
++ NetWarp [4]
+VGG16
+67.1 (+1.8)
++ EFC [40]
+VGG16
+67.4 (+2.1)
++ Ours
+VGG16
+67.9 (+2.6)
+PSPNet [13]
+ResNet101
+76.2
++ Accel [22]
+ResNet101
+71.5 (-4.7)
++ TDNet [24]
+ResNet101
+76.0 (-0.2)
++ Ours
+ResNet101
+76.6 (+0.4)
+Swin-B [30]
+Swin Transformer
+77.6
++ Ours
+Swin Transformer
+77.9 (+0.3)
+Table 2:
+Performance comparison on CamVid test subset.
+Dilation8, PSPNet and Swin
+Transformer are chosen as the image segmentation model.
+on light-weight baseline model. This is reasonable since improving more com-
+plicated model is generally more difficult. Third, TDNet [24], Accel [22] and
+Liu et al. [25] have nearly no improvement and even degradation on accuracy
+comparing to the baseline, since they mainly focus on improving inference speed.
+Fourth, even on the strong baseline, e.g., Swin Transformer [30], our method
+can also bring improvement.
+4.3. Ablation Study
+Effectiveness of our method. In this work, we propose two key modules, namely
+STF and MAR. To investigate their effects, we also give the results of applying
+one of them, as shown in Table 3.
+We can have the following observations.
+First, our proposed STF and MAR can bring significant performance improve-
+ment separately compared with the baseline, and the version equipped with
+both of them performs best. Second, STF can brings more gains than MAR,
+20
+
+Method
+Dataset
+Backbone
+mIoU (%)
+PSPNet [13]
+Cityscapes
+ResNet50
+76.24
++ STF
+Cityscapes
+ResNet50
+78.75 (+2.62)
++ MAR
+Cityscapes
+ResNet50
+78.37 (+2.24)
++ Both
+Cityscapes
+ResNet50
+79.22 (+2.98)
+Dilation8 [41]
+CamVid
+VGG16
+65.3
++ STF
+CamVid
+VGG16
+67.5 (+2.2)
++ MAR
+CamVid
+VGG16
+67.3 (+2.0)
++ Both
+CamVid
+VGG16
+67.9 (+2.6)
+Table 3: Ablation study on key modules of our proposed method. Performance comparison
+on Cityscapes val subset and CamVid test subset. PSPNet and Dilation8 are chosen as the
+image segmentation model, respectively.
+Method
+mIoU (%)
+DeepLabv3 [44]
+79.5
++ DenseCRF [8]
+79.7 (+0.2)
++ GUM [39]
+79.8 (+0.3)
++ SegFix [9]
+80.5 (+1.0)
++ Our MAR
+81.0 (+1.5)
+Table 4:
+Comparison of different feature refinement methods on Cityscapes val subset.
+DeepLabv3 is chosen as the baseline model.
+since STF integrates the multi-frame information while MAR only optimizes the
+features within the current frame. Third, our proposed STF outperforms other
+multi-frame fusion methods (e.g., TDNet [24] in Table 1 and GRFP [5] and
+NetWarp [4] in Table 2), which indicates the effectiveness of modeling spatial-
+temporal relationship.
+Analysis of MAR. In this paper, we propose MAR to refine the video features.
+Actually, this technique can also be used in other tasks. Here we particularly
+investigate its effect on image segmentation, and show its superiority by com-
+paring with other representative refinement methods, including DenseCRF [8],
+21
+
+Current Frame
+Baseline
+w/ STF
+Ours
+Ground Truth
+Figure 9: Visualization of some sample segmentation results from Cityscapes. It
+can be seen that STF can significantly improve the baseline results, and MAR can further
+bring gains. Here the red rectangles highlight the important regions. Best viewed in color.
+GUM [39], and SegFix [9]. DenseCRF [8] establishes pairwise potentials on all
+pairs of pixels and poses segmentation refinement problem as maximum a pos-
+teriori (MAP) inference, which is a classic post-processing method. GUM [39]
+proposes to enrich bilinear upsampling operators by introducing a learnable
+transformation for semantic maps, which can steer the sampling towards the
+correct semantic class.
+SegFix [9] proposes to replace the unreliable predic-
+tions of boundary pixels with the predictions of interior pixels, which currently
+achieves the state-of-the-art performance. Table 4 provides the comparison re-
+sults, where the DeepLabv3 is adopted as the baseline by following previous
+works. We can see that our MAR outperforms the previous methods, which
+indicates the effectiveness of refining feature by memory.
+To intuitively show the effect of MAR on feature refinement, we particularly
+choose two easily ambiguous categories, i.e., wall and building, to visualize the
+features before and after applying MAR. To be specific, we randomly sample
+100 hard features (with confidence scores lower than 0.8) per category, and then
+visualize their distribution using t-SNE. The results are shown in Figure. 10.
+Before using MAR, two kinds of features are confused together. MAR can move
+features closer to their corresponding class prototypes and make them easier to
+be separated.
+22
+
+w/o MAR
+w/ MAR
+Wall
+Building
+Wall
+Building
+Figure 10: Visualization on the change of feature distribution. It can be seen that
+features become more separable after using MAR module. Best viewed in color.
+Method
+road
+side.
+build.
+wall
+fence
+pole
+light
+sign
+vege.
+terr.
+PSPNet-50
+97.82
+83.23
+91.70
+35.86
+58.07
+63.87
+70.76
+78.93
+91.95
+62.85
++ MAR
+98.13
+85.02
+92.39
+51.34
+60.81
+63.46
+71.62
+80.49
+92.55
+65.47
+Method
+sky
+pers.
+rider
+car
+truck
+bus
+train
+motor
+bike
+mean
+PSPNet-50
+94.16
+81.86
+60.96
+94.82
+76.34
+85.83
+77.67
+64.43
+77.61
+76.24
++ MAR
+94.52
+82.42
+60.88
+95.34
+80.72
+88.72
+78.73
+68.28
+78.21
+78.37
+Table 5: Category-wise performance on Cityscapes val subset. PSPNet-50 is chosen as the
+baseline model.
+Hyper-parameter KL and KH. In our MAR, KL and KH are used to control the
+number of boundary features for memory and good features for prototype per
+class. Here we explore their influence on the segmentation accuracy. Considering
+the memory size, we particularly evaluate the KL from {10, 50, 100, 300} and
+the KH from {1, 5, 10, 50} on Cityscapes val subset with PSPNet-ResNet50 as
+the base model. We found that there is almost no performance fluctuation for
+different settings. Finally, KL = 10 and KH = 10 are adopted throughout the
+experiments.
+Analysis of segmentation results. Our proposed MAR mainly handles the am-
+biguous cases, especially for the hard classes. Table 5 lists the segmentation
+accuracy of different semantic classes on Cityscapes, where PSPNet with the
+23
+
+wall
+buildingwall
+buildingModule
+MACs (G)
+PSPNet-50 (3 Frames)
+4285.9
+PSPNet-101 (3 Frames)
+6152.9
+STF
+563.5
+MAR
+31.5
+Classifier
+0.5
+Table 6: Computational cost of different modules (GMACs). The resolution of input image
+is 1024 × 2048.
+ResNet50 backbone is particularly adopted as the baseline. We can see that
+our method can consistently boost the accuracy over all classes and the gain
+is especially significant for the hard classes, e.g., wall, terrain, and truck. In
+addition, to intuitively show the effectiveness of our proposed STF and MAR,
+we visualize three sample segmentation results from Cityscapes in Figure. 9. It
+can be seen that the original segmentation results can be progressively improved
+by STF and MAR.
+Cost of STF and MAR. Here we analyze the computational cost of different
+components in our proposed method, and the statistics are provided in Table 6.
+It can be seen that our STF and MAR involve little computational cost com-
+pared with the base model. In particular, our proposed MAR is more efficient
+to achieve good segmentation performance than devising more complicated net-
+work structures.
+5. Conclusion
+In this paper, we design a novel video semantic segmentation framework
+with inter-frame feature fusion and inner-frame feature refinement, and pro-
+pose two novel techniques to boost the accuracy. Specifically, we first propose
+a spatial-temporal fusion module based on the transformer, which can effec-
+tively aggregate multi-frame features at different spatial and temporal positions,
+and meanwhile avoid error-prone optical flow estimation. Then we propose a
+24
+
+memory-augmented refinement module that exploits the stored features from
+the training samples to augment the hard features during inference. Our ex-
+perimental results on Cityscapes and CamVid show that the proposed method
+outperforms the state-of-the-art methods.
+Acknowledgements
+This work is supported by the National Natural Science Foundation of China
+under Grant No.62176246 and No.61836008. We acknowledge the support of
+GPU cluster built by MCC Lab of Information Science and Technology Institu-
+tion, USTC.
+References
+[1] J. Long, E. Shelhamer, T. Darrell, Fully convolutional networks for seman-
+tic segmentation, in: CVPR, 2015 (2015).
+[2] M. Cordts, M. Omran, S. Ramos, T. Rehfeld, M. Enzweiler, R. Benenson,
+U. Franke, S. Roth, B. Schiele, The cityscapes dataset for semantic urban
+scene understanding, in: CVPR, 2016 (2016).
+[3] G. J. Brostow, J. Fauqueur, R. Cipolla, Semantic object classes in video: A
+high-definition ground truth database, Pattern Recognition Letters (2009).
+[4] R. Gadde, V. Jampani, P. V. Gehler, Semantic video cnns through repre-
+sentation warping, in: ICCV, 2017 (2017).
+[5] D. Nilsson, C. Sminchisescu, Semantic video segmentation by gated recur-
+rent flow propagation, in: CVPR, 2018 (2018).
+[6] P. Liu, M. Lyu, I. King, J. Xu, Selflow: Self-supervised learning of optical
+flow, in: CVPR, 2019 (2019).
+[7] J. Zhuang,
+Z. Wang,
+B. Wang,
+Video semantic segmentation with
+distortion-aware feature correction, TCSVT (2020).
+25
+
+[8] P. Kr¨ahenb¨uhl, V. Koltun, Efficient inference in fully connected crfs with
+gaussian edge potentials, NeurIPS (2011).
+[9] Y. Yuan, J. Xie, X. Chen, J. Wang, Segfix: Model-agnostic boundary re-
+finement for segmentation, in: ECCV, 2020 (2020).
+[10] A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez,
+L. Kaiser, I. Polosukhin, Attention is all you need, in: NeurIPS, 2017
+(2017).
+[11] L. Huang, Y. Yuan, J. Guo, C. Zhang, X. Chen, J. Wang, Interlaced sparse
+self-attention for semantic segmentation, arXiv preprint arXiv:1907.12273
+(2019).
+[12] L.-C. Chen, G. Papandreou, I. Kokkinos, K. Murphy, A. L. Yuille, Deeplab:
+Semantic image segmentation with deep convolutional nets, atrous convo-
+lution, and fully connected crfs, TPAMI (2017).
+[13] H. Zhao, J. Shi, X. Qi, X. Wang, J. Jia, Pyramid scene parsing network,
+in: CVPR, 2017 (2017).
+[14] C. Peng, J. Ma, Semantic segmentation using stride spatial pyramid pooling
+and dual attention decoder, Pattern Recognition (2020).
+[15] X. Lian, Y. Pang, J. Han, J. Pan, Cascaded hierarchical atrous spatial
+pyramid pooling module for semantic segmentation, Pattern Recognition
+(2021).
+[16] Q. Zhou, X. Wu, S. Zhang, B. Kang, Z. Ge, L. Jan Latecki, Contextual
+ensemble network for semantic segmentation, Pattern Recognition (2022).
+[17] Y. Zhang, X. Sun, J. Dong, C. Chen, Q. Lv, Gpnet: Gated pyramid network
+for semantic segmentation, Pattern Recognition (2021).
+[18] M. Orˇsi´c, S. ˇSegvi´c, Efficient semantic segmentation with pyramidal fusion,
+Pattern Recognition (2021).
+26
+
+[19] Z. Wang, R. Song, P. Duan, X. Li, Efnet: Enhancement-fusion network for
+semantic segmentation, Pattern Recognition (2021).
+[20] X. Zhu, Y. Xiong, J. Dai, L. Yuan, Y. Wei, Deep feature flow for video
+recognition, in: CVPR, 2017 (2017).
+[21] E. Ilg, N. Mayer, T. Saikia, M. Keuper, A. Dosovitskiy, T. Brox, Flownet
+2.0: Evolution of optical flow estimation with deep networks, in: CVPR,
+2017 (2017).
+[22] S. Jain, X. Wang, J. E. Gonzalez, Accel: A corrective fusion network for
+efficient semantic segmentation on video, in: CVPR, 2019 (2019).
+[23] J. Wu, Z. Wen, S. Zhao, K. Huang, Video semantic segmentation via feature
+propagation with holistic attentio, Pattern Recognition (2020).
+[24] P. Hu, F. Caba, O. Wang, Z. Lin, S. Sclaroff, F. Perazzi, Temporally dis-
+tributed networks for fast video semantic segmentation, in: CVPR, 2020
+(2020).
+[25] Y. Liu, C. Shen, C. Yu, J. Wang, Efficient semantic video segmentation
+with per-frame inference, in: ECCV, 2020 (2020).
+[26] D. Tran, L. Bourdev, R. Fergus, L. Torresani, M. Paluri, Deep end2end
+voxel2voxel prediction, in: CVPRW, 2016 (2016).
+[27] M. Fayyaz, M. H. Saffar, M. Sabokrou, M. Fathy, R. Klette, F. Huang,
+Stfcn: spatio-temporal fcn for semantic video segmentation, arXiv preprint
+arXiv:1608.05971 (2016).
+[28] Y. Wang, J. Liu, Y. Li, J. Fu, M. Xu, H. Lu, Hierarchically supervised
+deconvolutional network for semantic video segmentation, Pattern Recog-
+nition (2017).
+[29] N. Carion, F. Massa, G. Synnaeve, N. Usunier, A. Kirillov, S. Zagoruyko,
+End-to-end object detection with transformers, in: ECCV, 2020 (2020).
+27
+
+[30] Z. Liu, Y. Lin, Y. Cao, H. Hu, Y. Wei, Z. Zhang, S. Lin, B. Guo, Swin trans-
+former: Hierarchical vision transformer using shifted windows, in: ICCV,
+2021 (2021).
+[31] R. Girdhar, J. Carreira, C. Doersch, A. Zisserman, Video action trans-
+former network, in: CVPR, 2019 (2019).
+[32] K. Gavrilyuk, R. Sanford, M. Javan, C. G. Snoek, Actor-transformers for
+group activity recognition, in: CVPR, 2020 (2020).
+[33] C. de Masson d'Autume, S. Ruder, L. Kong, D. Yogatama, Episodic mem-
+ory in lifelong language learning, in: NeurIPS, 2020 (2020).
+[34] L. Zhang, X. Chang, J. Liu, M. Luo, M. Prakash, A. G. Hauptmann,
+Few-shot activity recognition with cross-modal memory network, Pattern
+Recognition (2020).
+[35] Q. Cai, Y. Pan, T. Yao, C. Yan, T. Mei, Memory matching networks for
+one-shot image recognition, in: CVPR, 2018 (2018).
+[36] H. Deng, Y. Hua, T. Song, Z. Zhang, Z. Xue, R. Ma, N. Robertson,
+H. Guan, Object guided external memory network for video object de-
+tection, in: ICCV, 2019 (2019).
+[37] C.-Y. Wu, C. Feichtenhofer, H. Fan, K. He, P. Krahenbuhl, R. Girshick,
+Long-term feature banks for detailed video understanding, in: CVPR, 2019
+(2019).
+[38] X. Wang, R. Girshick, A. Gupta, K. He, Non-local neural networks, in:
+CVPR, 2017 (2017).
+[39] D. Mazzini, Guided upsampling network for real-time semantic segmenta-
+tion, in: BMVC, 2018 (2018).
+[40] M. Ding, Z. Wang, B. Zhou, J. Shi, Z. Lu, P. Luo, Every frame counts: joint
+learning of video segmentation and optical flow, in: AAAI, 2020 (2020).
+28
+
+[41] F. Yu, V. Koltun, Multi-scale context aggregation by dilated convolutions,
+arXiv preprint arXiv:1511.07122 (2015).
+[42] A. Kundu, V. Vineet, V. Koltun, Feature space optimization for semantic
+video segmentation, in: CVPR, 2016 (2016).
+[43] V. Jampani, R. Gadde, P. V. Gehler, Video propagation networks, in:
+CVPR, 2017, pp. 451–461 (2017).
+[44] L.-C. Chen, G. Papandreou, F. Schroff, H. Adam, Rethinking atrous con-
+volution for semantic image segmentation, arXiv preprint arXiv:1706.05587
+(2017).
+29
+
diff --git a/RtE2T4oBgHgl3EQfWQe7/content/tmp_files/load_file.txt b/RtE2T4oBgHgl3EQfWQe7/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..473b6acbd193739b9d4b12b2c928c6148f93d7ba
--- /dev/null
+++ b/RtE2T4oBgHgl3EQfWQe7/content/tmp_files/load_file.txt
@@ -0,0 +1,852 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf,len=851
+page_content='Video Semantic Segmentation with Inter-Frame Feature  Fusion and Inner-Frame Feature Refinement  Jiafan Zhuang, Zilei Wang∗, Junjie Li  National Engineering Laboratory for Brain-inspired Intelligence Technology and  Application, University of Science and Technology of China, Hefei 230027, China  Abstract  Video semantic segmentation aims to generate accurate semantic maps for each  video frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To this end, many works dedicate to integrate diverse information  from consecutive frames to enhance the features for prediction, where a feature  alignment procedure via estimated optical flow is usually required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' However, the  optical flow would inevitably suffer from inaccuracy, and then introduce noises  in feature fusion and further result in unsatisfactory segmentation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In  this paper, to tackle the misalignment issue, we propose a spatial-temporal fu-  sion (STF) module to model dense pairwise relationships among multi-frame  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Different from previous methods, STF uniformly and adaptively fuses  features at different spatial and temporal positions, and avoids error-prone opti-  cal flow estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Besides, we further exploit feature refinement within a sin-  gle frame and propose a novel memory-augmented refinement (MAR) module to  tackle difficult predictions among semantic boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Specifically, MAR can  store the boundary features and prototypes extracted from the training samples,  which together form the task-specific memory, and then use them to refine the  features during inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Essentially, MAR can move the hard features closer to  the most likely category and thus make them more discriminative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We conduct  extensive experiments on Cityscapes and CamVid, and the results show that  our proposed methods significantly outperform previous methods and achieves  ∗Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Email addresses: jfzhuang@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='ustc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='cn (Jiafan Zhuang), zlwang@ustc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='cn  (Zilei Wang), hnljj@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='ustc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='cn (Junjie Li)  Preprint submitted to Pattern Recognition  January 11, 2023  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='03832v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='CV]  10 Jan 2023  the state-of-the-art performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Code and pretrained models are available at  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='com/jfzhuang/ST Memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Keywords:  Video semantic segmentation, Spatial-temporal feature fusion,  Memory mechanism, Feature refinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Introduction  Semantic segmentation targets to assign each pixel in scene images a se-  mantic class, which is one of the fundamental tasks in computer vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  In  recent years, image semantic segmentation has achieved unprecedented per-  formance benefited from the great progress of deep convolutional neural net-  work (DCNN) [1] and construction of various datasets (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Cityscapes [2] and  CamVid [3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' However, many real-world applications have strong demands for  accurate video semantic segmentation, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', robotics, autonomous driving, and  video surveillance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Actually, video data offer richer information than static im-  ages, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', diverse presentations from multiple frames and temporal consistency  prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Thus video can provide good potential to achieve more accurate seman-  tic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The key is how to produce more discriminative features by  exploiting the characteristics of videos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  A natural way to enhance video features is to integrate the diverse informa-  tion of consecutive frames [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Specifically, the feature alignment is commonly  performed via the optical flow based feature warping, which ensures that pixel-  level features at the same spatial position represent the identical object, and  then the temporal feature fusion is conducted for each pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Evidently, the  accurate optical flow is critical for feature fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' However, the optical flow  estimation inevitably suffers from inaccuracy in the boundary areas due to ob-  ject occlusion and plain texture [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' If the features are not well-aligned, the  noises would be introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Consequently, the quality of fused features would  be reduced and the segmentation performance would be deteriorated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Besides, after aggregating information from consecutive frames, can we fur-  ther refine the fused feature?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Different from inter-frame feature fusion in video  2  (b)  f  f  f𝑡−1  f𝑡  f𝑡  f𝑡+1  (a)  f𝑡−1  f𝑡  f𝑡  f𝑡+1  f𝑡  (c)  Backbone  Classifier  Feature  Fusion  Feature  Refinement  Inter-Frame  Feature  Fusion  Inner-Frame  Feature  Refinement  Figure 1: Architecture illustrations for different methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' (a) Feature fusion in video  segmentation methods (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', NetWarp [4] and GRFP [5]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' (b) Feature refinement in image  segmentation methods (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', DenseCRF [8] and SegFix [9]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' (c) Our proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Best  viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  segmentation methods, some image-based methods adopt the post-processing  techniques to optimize the features for prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' For example, DenseCRF [8]  uses a graph structure to model pairwise potentials on all pixels and iteratively  adjusts the feature by optimizing an energy function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Essentially, it uses simi-  lar features to mutually enhance themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' SegFix [9] proposes to replace the  difficult boundary features with some better ones, whose locations are predicted  by a network and often lie around the boundary areas in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Actually, feature fusion is proposed to aggregate useful information from  different frames while feature refinement is designed for correcting error-prone  features, which are potentially complementary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Based on this motivation, in  this paper, we aim to improve the accuracy of video semantic segmentation by  simultaneously considering inter-frame feature fusion and inner-frame feature  refinement, as shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' For the inter-frame fusion, we need to tackle  the feature misalignment issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  To this end, we propose a spatial-temporal  fusion (STF) module that uniformly fuses the features at different spatial and  temporal positions and does not require explicit feature alignment via error-  prone optical flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here the transformer [10] is particularly adopted due to  the power to model long-range dependencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  To be specific, the encoder is  fed with the features extracted from consecutive frames, and the decoder is  used to generate the prediction features by retrieving the current frame from  3  the encoded features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In particular, we utilize the self-attention mechanism in  transformer to guide the feature fusion in latent space, in which more similar  features are supposed to be more likely to represent the same object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' For an  image pixel, hence, STF would integrate multiple similar features at different  temporal and spatial positions, rather than only the temporal-aligned features  in the previous works [4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  In addition, an image with the resolution of (1024, 2048) would typically  produce the features with the resolution of (128, 256).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The transformer taking  three frames needs to process 3 × 128 × 256 = 98304 pixel-level features, which  results in unacceptable computation and memory cost with O(N 2) complexity  when computing affinity matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Inspired by a recent work [11], we propose an  interlaced cross-self attention (ICSA) attention mechanism to divide the dense  affinity matrix computation in transformer as the product of a long-range cross-  attention and a short-range self-attention, which can greatly reduce the memory  consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  On the other hand, we propose inner-frame feature refinement to further ad-  just the fused features for better prediction without devising more complicated  network structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In this work, we focus on refining the hard features that are  error-prone and always lie in the boundary areas of different classes [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To this  end, we propose a novel memory-augmented refinement (MAR) module that  uses the stored features in memory to augment the hard features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Actually, this  is motivated by an intuitive observation that humans would retrieve memory to  enhance the judgement when facing semantically ambiguous contents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here the  memory represents the experience from the training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' For each semantic  category, we particularly store the hard features and their corresponding class  prototypes (refer to the mean feature representing a single category), which to-  gether form a key-value memory bank.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' During inference, a hard feature would  be refined by the class prototypes, where the weights of different classes are  computed by comparing it with the stored hard features in the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In this  way, the discriminativeness of boundary features would be enhanced since MAR  would make them move closer to the most likely category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Evidently, MAR has  4  good interpretability and can be conveniently inserted into different models as  an independent module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  We experimentally evaluate the proposed method on the Cityscapes and  CamVid datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The results validate the effectiveness of our STF and MAR  to improve the quality of features, and their combination can achieve the state-  of-the-art segmentation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  The contributions of this work are summarized as  We design a novel video semantic segmentation framework by simultane-  ously considering inter-frame feature fusion and inner-frame feature re-  finement, which can take advantages from both two feature enhancement  techniques and effectively improve segmentation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  We propose an effective spatial-temporal fusion module based on the trans-  former, which can uniformly aggregate the features at different spatial and  temporal positions and avoid error-prone temporal feature alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  We propose a novel memory-augmented refinement module to particularly  refine hard features using the experience from training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In par-  ticular, the key-value memory is stored to refine the hard features closer  to the most likely category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  We experimentally evaluate the effectiveness of our proposed methods,  and the results on Cityscapes and CamVid demonstrate the superiority of  our methods to previous state-of-the-art methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  The rest of this paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We review the related works on  image and video semantic segmentation, transformer and memory mechanism  in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Section 3 provides the details of our approach, and Section 4  experimentally evaluates the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Finally, we conclude the work  in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Related Work  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Image Semantic Segmentation  With the development of DCNN, more semantic segmentation networks  spring up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Specifically, the fully convolutional networks (FCNs) [1] firstly uses  the convolutional layers to replace fully-connected layers and can achieve better  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Inspired by FCN, many extensions have been proposed to ad-  vance image semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The dilated layers [12] are used to replace  the pooling layers, which can better balance the computational cost and size  of receptive fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To further improve segmentation accuracy, spatial pyramid  pooling and atrous spatial pyramid pooling (ASPP) are used in PSPNet [13]  and DeepLab [12] to capture multi-scale contextual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Mitivated  by ASPP, Peng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' [14] proposes a stride spatial pyramid pooling (SSPP)  to capture multiscale semantic information from the high-level feature map,  while Lian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' [15] proposes a cascaded hierarchical atrous pyramid pooling  module to simultaneously extract rich local detail characteristics and impor-  tant global contextual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' CENet [16] aggregates contextual cues via  densely usampling the convolutional features of deep layer to the shallow decon-  volutional layers, which can fully explore multiple scale contextual information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  GPNet [17] densely captures and filters the multi-scale information in a gated  and pair-wise manner with a gated pyramid module and a cross-layer attention  module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Marin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' [18] propose a novel architecture based on shared pyrami-  dal representation and fusion of heterogeneous features along the upsampling  path, which is effective for dense inference in images with large scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Different  from enhancing features, EFNet [19] propose to produce multiple enhanced im-  ages and fuses them to yield one new image, which can encourage the model to  exploit complementary information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Differently, our proposed methods focus on exploiting both spatial and tem-  poral contexts to further improve the performance and can build upon any  existing image segmentation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Video Semantic Segmentation  Different from static images, videos embody rich temporal information that  can be exploited to improve the semantic segmentation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Existing  video semantic segmentation methods mainly fall into two categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The first  category aims to accelerate inference speed by reusing the features in previous  frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' DFF [20] estimates the optical flow fields [21] from the key frame to  other frames and then propagates the high-level features using the predicted  optical flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Accel [22] proposes a reference branch to extract high-quality  segmentation from the key frames and an update branch to efficiently extract  low-quality segmentation from the current frames, and the fuses them to improve  the segmentation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' DAVSS [7] designs a feature correction mechanism  to tackle distorted features after propagation due to inaccurate optical flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  LERNet [23] proposes to propagate multi-level features from the key frame via a  temporal holistic attention module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' TDNet [24] distributes several sub-networks  over sequential frames and then recomposes the extracted features for segmen-  tation via an attention propagation module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Differently, Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' [25] designs  a new temporal knowledge distillation methods to narrow the performance gap  between compact models and large models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Another category focus on improving segmentation accuracy by modeling  cross-frame relations to integrate information from consecutive frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' V2V [26]  utilizes a 3D CNN to perform a voxel-level prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' STFCN [27] utilizes a  spatial-temporal LSTM over per-frame CNN features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' However, these methods  cannot achieve high performance due to rough processing of different frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  HDCNN [28] proposes a transition layer structure to make the pixel-wise label  prediction consist with adjacent pixels across space and time domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Recently,  some works [4, 5] propose to fuse features from multiple frames to produce the  better features for prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' They usually adopt the optical flow to model  cross-frame relationships and perform temporal alignment by warping features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  In particular, NetWarp [4] uses a set of learnable weights to fuse multiple fea-  tures, and GRFP [5] proposes the gated recurrent units STGRU to estimate the  uncertainty of warped features and then conducts feature fusion on the areas  7  with high reliability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Obviously, the optical flow is critical for feature align-  ment and would affect the final accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' However, the optical flow estimation  inevitably suffers from inaccuracy, especially for the occlusion areas and small  objects (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', pedestrian, pole) [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In this work, we follow the route of sec-  ond category and focus on improving segmentation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Different from  previous works, we propose to simultaneously model the spatial-temporal re-  lationship without feature alignment, which can avoid error-prone optical-flow  estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Furthermore, we propose to use memory to refine the prediction  features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Transformer  Transformer is originally proposed for the sequence-to-sequence machine  translation [10], and currently has dominated various NLP tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' As the core  component of transformer, the self-attention is particularly suitable for mod-  eling long-range dependencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Due to the success of transformer in the NLP  field, some works attempt to explore the benefits of transformer in computer  vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' DETR [29] first builds an object detection system based on transformer,  which can reason about relationships between objects and global context and  directly output the final set of predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Swin Transformer [30] designs a  novel shifted windowing scheme, which can limit attention computation to local  windows while also allow for cross-window connection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' It achieves an impressive  performance on a broad range of vision tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In this paper, we propose STF by  using transformer to model the spatial-temporal relationship among pixel-wise  features extracted from consecutive frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To our best knowledge, this is the  first attempt to exploit the transformer in video semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Recently, Action Transformer [31] and Actor Transformer [32] also adopt  transformer to model spatial-temporal relationship in action detection and group  action recognition tasks, which are closely related to our proposed STF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' They  naturally adopt transformer for modeling proposal-context and proposal-proposal  relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' But our proposed STF is different from these two works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' STF is  designed for modeling pixel-wise relationship, which would involve huge memory  8  and computation overhead issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In this work, we propose interlaced cross-self  attention (ICSA) mechanism to tackle these issues and achieve efficient global  relationship modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' External Memory  In DCNN, external memory is generally used to enhance feature represen-  tations by storing history data, which is especially useful for the tasks without  enough samples, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', life-long learning [33] and few-shot learning [34, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' For  example, MM-Net [35] proposes to store the representative features in the sup-  port set for one-shot learning, and then use them to predict the parameters of  feature extraction network on query images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Actually, this can make the query  features more relevant to the support features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In recent years, the memory  mechanism is also exploited to store long-range temporal contexts for video  tasks during inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In video object detection, [36] proposes to store pixel-  level and instance-level features extracted from previous frames and then use  them to enhance the current frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  LFB [37] proposes a long-term feature  bank for action localization to store supportive information extracted over the  entire span of a video, and then uses them to enhance the short-term features  extracted from short video clips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Different from the previous works that store  temporal [36, 37] or sample [35] contexts, in this paper we propose to store  the hard features and class prototypes from the training samples to form a  task-specific memory, and then use them to refine the boundary features during  inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Our Approach  In this work, we aim to boost the accuracy of video semantic segmenta-  tion by enhancing the features for prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To this end, we first propose a  spatial-temporal fusion (STF) module to perform inter-frame feature fusion at  different spatial and temporal positions, which can avoid error-prone optical flow  estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then we propose a memory-augmented refinement (MAR) module  9  𝐼𝑇−1  𝐼𝑇  𝐼𝑇+1  𝐟𝑇−1  𝐟𝑇  𝐟𝑇+1  Spatial-Temporal  Fusion Module  Framework  Memory-Augmented  Refinement Module  Backbone  1、相邻多帧特征经过STRM实现特征融合  2、融合特征经过MARM实现进一步优化  መ𝐟𝑇  Feature  Memory  𝑆𝑇  𝑆𝑇−1  …  …  Sliding Window  …  …  Classifier  𝐟𝑇  ′  Video Feature Enhancement  መ𝐟𝑇−1  Figure 2: The framework of our proposed approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' First, the feature is extracted by  an image segmentation model for each frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then the features of consecutive frames are fed  into our proposed STF module to perform feature fusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' After that, the fused feature f  ′  T  is further refined by our proposed MAR module, resulting in �fT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Finally, the segmentation  result is obtained by applying the classifier on �fT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Best viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  to further refine the boundary features during inference, which is essential to  utilize the stored experience from training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In the following, we first  introduce the framework of our proposed approach, and then elaborate on two  key modules, namely, STF and MAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Framework  Our proposed video semantic segmentation framework is illustrated in Fig-  ure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Formally, given a sequence of n video frames denoted by {I1, I2, · · · ,  In}, our purpose is to get the accurate semantic segmentation maps for every  video frame, denoted by {S1, S2, · · · , Sn}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Specifically, we first extract features  from each frame image using an off-the-shelf segmentation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then we con-  duct video feature enhancement for the current timestamp T with a sequence  of three-frame features {fT −1, fT , fT +1}, resulting in �fT for final prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Finally, we apply the classifier on �fT to produce the segmentation result ST .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Since such a procedure can be performed in a sliding-window manner, we can  obtain the corresponding segmentation sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  In this work, we dedicate to enhance video features to improve the segmen-  tation performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To be specific, we first feed the sequence of frame features  10  𝐟𝑇−1  𝐟𝑇  𝐟𝑇+1  Concat  Interlaced  Cross-Self  Attention  Add & Norm  FFN  Add & Norm  Encoder  Interlaced  Cross-Self  Attention  Add & Norm  FFN  Add & Norm  Decoder  𝐟𝑇  Interlaced  Cross-Self  Attention  Add & Norm  𝐟𝑇  ′  𝐟𝐸𝑛𝑐  ′  𝐟𝐸𝑛𝑐  Figure 3: Illustration of transformer based spatial-temporal fusion module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' STF  consists of an encoder for modeling spatial-temporal relationships and feature encoding, and  a decoder for retrieving the feature of current frame from the encoded feature f  ′  Enc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Best  viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  into our proposed STF module to capture spatial-temporal dependencies and  complete pixel-wise feature fusion, resulting in the fused feature f  ′  T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' After that,  our proposed MAR module further refines f  ′  T into �fT by exploiting the stored  feature memory to enhance the discriminativeness of the boundary features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Ev-  idently, STF and MAR are the key components of our method that determine  the performance of video semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Spatial-Temporal Fusion  In this work, we propose a spatial-temporal fusion module to effectively  integrate the features of consecutive frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here it is expected that the spatial-  temporal relationship among consecutive frames is well modeled and the optical  flow estimation is avoided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In particular, we use the transformer [10] to perform  inter-frame fusion, which recently achieves the amazing performance in both  NLP and CV areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Thus our STF consists of an encoder and a decoder, as  shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  11  Encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In STF, the encoder is used to capture the spatial-temporal relation-  ships of pixel-level features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To this end, we concatenate the 2D features of  multiple frames {fT −1, fT , fT +1} to obtain a 3D feature fEnc ∈ Rd×3×H×W ,  where d is the dimension of pixel-level features, H and W represent the spatial  size of frame features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' That is, there are 3HW features in total for processing in  the encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We first pass fEnc into our proposed interlaced cross-self attention  (ICSA) module to model dense spatial-temporal relationships, and the features  are adjusted by weighting on all features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then we feed the new features into  feed-forward network (FFN) to perform feature transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Similar to [10],  we employ the residual connections for the attention module and FFN followed  by layer normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Finally, we obtain the encoded features f  ′  Enc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Com-  pared with the previous optical flow based methods [4, 5], our proposed STF  uniformly aggregates all features at different spatial and temporal positions, and  no explicit feature alignment is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Essentially, a single feature in STF  is implicitly aligned with multiple similar features by attention other than the  temporally-aligned ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' This is reasonable since the purpose of feature fusion  is to mutually enhance the features belonging to the same semantic class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In STF, the decoder is used to get the prediction features of the current  frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To this end, we use the original feature of current frame to retrieve from  the encoded features f  ′  Enc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To be specific, we first feed the feature of current  frame into an ICSA module to enhance the features similar in the encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then  we pass the enhanced features together with f  ′  Enc into another ICSA module  for cross attention and produce the features f  ′  T with FFN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Different from the  previous one, here the enhanced fT serves as the query and f  ′  Enc serves as the  key and value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Intuitively, we retrieve the encoded features from f  ′  Enc for each  pixel-level feature in fT , and consequently the f  ′  T would contain rich information  from other spatial and temporal positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Interlaced Cross-Self Attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In the original transformer, the attention op-  eration would involve O(N 2) complexity given an input of size N (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' here  N = 3HW in our case),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' which is impractical to the video semantic segmen-  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='query  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='value  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='key  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='permute  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='permute  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='permute  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='query  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='value  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='key  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Positional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Encoding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Positional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Encoding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='BWA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='permute  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='output  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='output  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='query  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='value  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='key  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='BWA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Interlaced Cross-Self Attention (ICSA)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Interlaced Sparse Attention (ISA)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Positional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Encoding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Positional  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Encoding  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Long-range Cross-Attention  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Short-range Self-Attention  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='permute  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='BWA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='permute  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='BWA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Long-range Attention  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Short-range Attention  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Figure 4:  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='Illustration of differences between our interlaced cross-self attention  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='(ICSA) and with interlaced sparse attention (ISA) [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' ICSA takes query, key and  value separately for long-rang cross-attention first and then conduct short-range self-attention  on the previous enhanced feature, which can be seamlessly integrated in the transformer  structure, especially for cross-attention module in the decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Besides, ICSA implements  necessary positional encoding and can deal with features from multiple frames directly, which  can uniformly model spatial-temporal relationships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Best viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  tation task since computation on pixel-level features would consume too much  memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To tackle this issue, a recent work ISA [11] provides a successful so-  lution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' It decomposes the whole attention calculation as the combination of  long-range and short-range sparse attention calculations, as shown in the upper  subplot in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In this way, it can retain the ability of modeling global  relationship while effectively reduce the memory consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' However, ISA is  designed for self-attention mechanism like non-local [38], which is not well com-  patible with the transformer structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Specifically, ISA takes a single feature  as input and performs enhancement by modeling inner relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Thus it  can not be directly integrated into cross attention in the transformer decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Besides, how to insert necessary positional encoding and deal with features of  multiple frames are not considered by ISA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  In this work, we extend the original ISA into a more general form and propose  13  Method  query  key  value  Divide  Group  q  k  v  Block-wise Attention Module  MHA: Multi-Head Attention  MHA  MHA  MHA  MHA  Figure 5: Illustration of block-wise attention (BWA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The input 3D features, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='query,  key and value, are spatially divided into patches with the same shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then we apply multi-  head attention (MHA) [10] operation on corresponding query, key and value patches indepen-  dently, and combine their results back to the entire one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Best viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  interlaced cross-self attention (ICSA), which can be seamlessly integrated into  transformer structure, as illustrated in the Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Generally, we reorganize  ISA with long-range cross-attention and short-range self-attention operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  First, we take query, key and value separately as inputs for cross-attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Par-  ticularly, the query, key, and value are the same feature fEnc for the STF module  encoder, while the key and value are f  ′  Enc and the query is the enhanced fT for  the STF module decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here we directly takes 3D features as input to uni-  formly model spatial-temporal relationships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' For query and key, we supplement  the features with positional encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Particularly, we choose the learnable po-  sitional encoding by following [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In this work, we extend positional encoding  to the 3D version and they have the same shape as the corresponding input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Following ISA, we divide features into k blocks with the same shape (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=',  k = 4 in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 4 and Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To model long-range cross-attention, we  harvest features with same spatial positions from different blocks in query, key  and value via permutation operation, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then we conduct block-wise  attention (BWA) operation for relationship modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' As shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 5, we  first divide input query, key and value features into pre-defined blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then,  we apply multi-head attention (MHA) [10] on corresponding query, key and  14  Relationship Computation  Feature Refinement  Boundary Feature of class 0  Prototype of class 0  Boundary Feature of class 1  Prototype of class 1  Figure 6: Illustration of feature refinement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We first compute the relationships between  the stored boundary features and the test feature to estimate the class likelihoods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then we  refine the test feature using the class prototypes, which essentially makes the feature move  closer to the most likely class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Best viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  value patches independently, and combine their results back to the entire one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  For short-range self-attention, we first permute the feature back to the original  positions and then regard it as query, key and value for the next attention cal-  culation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' After adding positional encoding, we conduct BWA operation again  and obtain the final enhanced feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' With ICSA, STF can conveniently har-  vest global spatial-temporal information for feature enhancement while keeps  an efficient attention computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Besides, if we take a single feature from one  frame as query, key and value, and remove positional encoding, ICSA would  degenerate into ISA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Evidently, ISA is a special case of ICSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Memory-Augmented Refinement  In this work, we propose a novel memory-augmented refinement module to  further refine the fused features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Different from previous works that explore  the relationship among the inference features [8, 39, 9], we focus on refining  the hard features (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', boundary features) using the memory from the training  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  The idea is illustrated in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 6, and it is actually inspired by  an intuitive mechanism of humans to process semantically ambiguous contents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Specifically, given a test feature during inference, it usually lies in the boundary  area of different classes in the feature space if it is hard to distinguish (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', with  15  Method  SDA: Scaled Dot-product Attention  FFN: Feed Forward Network  𝐟  Key-Value Memory  𝐟𝑅  FFN  SDA  𝑆𝑖 = 𝜃(𝑄𝑝) ∅(𝐾𝑖)𝑇, 𝑖 ∈ 1, 𝐶𝐾 , p = (x, y),d is channel num  𝑆 = 𝑆𝑜𝑓𝑡𝑚𝑎𝑥(𝑆)  \u0de2  𝑄𝑝 = \u0dcd  𝑖=1  𝐶𝐾  𝑆𝑖𝑉𝑗 ,  𝑗 is the class index of 𝐾𝑖, 𝑗 ∈ [1, 𝐶]  SDA的计算步骤：  Add &  Norm  Add &  Norm  Figure 7: Illustration of memory-augmented refinement module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The input feature  f is refined into fR using the key-value memory extracted from the training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here  f serves as the query, the key is the stored boundary features, and the value is the class  prototypes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Here ’SDA’ represents scaled dot-product attention and ’FFN’ represents feed  forward network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  low confidence score).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To enhance its discriminativeness, we first estimates its  likelihoods to different classes by computing the similarities between the feature  and stored boundary features of each class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then we use the class prototypes  to refine the feature according to the estimated likelihoods, where the class  prototype refers to the mean feature representing a category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Through this way,  the test feature would move closer to the most likely category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Our proposed MAR module is used to implement such an idea and is illus-  trated in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Specifically, we build the key-value memory for each class  that stores two kinds of data from the training samples, namely, the bound-  ary features and class prototypes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  The boundary features serve as the keys  K ∈ Rd×CKL and the class prototypes serve as the values V ∈ Rd×C, where C  denotes the number of classes and KL is a hyper-parameter to control the size of  memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In the MAR module, the input feature F is refined into FR using the  key-value memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Inspired by the transformer, we use the scaled dot-product  attention (SDA) and FFN to construct the MAR block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To be specific, we take  the test feature as query Q ∈ Rd, and use the key-value in memory to refine it,  resulting in Q  ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Formally,  si = θ(Q)T φ(Ki),  (1)  si =  esi  �CKL  i=1 esi ,  (2)  Q  ′ =  CKL  �  i=1  siVj,  (3)  16  Training  Set  Memory Organization  Sky  Features with  Lowest Scores  Car  Sky  Features with  Highest Scores  Car  𝐾𝐻 = 4, 𝐾𝐿 = 4, 𝐶 = 2 for Visualization  𝐾𝐻𝐶 Features  Prototype Generation  𝐾𝐿𝐶 Features  Score-Based Selection  Backbone  Sky  Key  Car  Sky  Value  Car  𝐶 Features  𝐾𝐿𝐶 Features  Key-Value Groups  Figure 8: Illustration of the key-value memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  From the extracted features on the  training set, we select KH ”good” features with the highest scores and KL ”hard” features  with the lowest scores per class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Then we generate the class prototypes by averaging the  ”good” features, and organize them with ”hard” features to form the key-value memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here  KH = 4, KL = 4, and C = 2 are used for visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  where i ∈ [1, CKL] denotes the sample in memory and j is the class index cor-  responding to the i-th sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here θ(Q) = WθQ and φ(Ki) = WφKi, and Wθ  and Wφ are two learnable matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Notably, in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' (3), we index V by j rather  than i, which is different from the original self-attention calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We employ  the residual connections for SDA and FFN followed by layer normalization, like  in the original transformer [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Next we explain how to generate the key-value memory from the training  samples, which is shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We first train the segmentation network  without the MAR module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Using this model, we extract the features for all  training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Note that a feature would be discarded if it is misclassified by  the classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' According to the ground truth, for each class, we select KL ”hard”  features with the lowest confidence scores and KH ”good” features with the  highest confidence scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The former are considered to suffer from semantically  ambiguity while the latter are to accurately represent the semantic category.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  After that, we compute the mean feature of the ”good” features for each class,  resulting in the class prototype.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Finally, we store the ”hard” features as keys  and the corresponding class prototype as values in the memory, which essentially  represent the task-specific experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  17  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Training Strategy  Our proposed network consists of four main components, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', backbone, clas-  sifier, STF, and MAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here, we adopt a multi-stage training schedule, which is a  common strategy in advanced works, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', Faster RCNN and knowledge distilla-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' First, the backbone and classifier together are pretrained on ImageNet and  finetuned on a particular segmentation dataset (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', Cityscapes and CamVid).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  The backbone would keep fixed and the classifier would be re-initialized in the  following training procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then, we train STF together with the backbone  and classifier, and use this model to generate the key-value memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Finally,  we train the MAR and classifier by fixing STF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In the test phase, we perform  the end-to-end inference with STF and MAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Experiment  In this section, we experimentally evaluate our proposed method on two  challenging datasets by following the previous works, namely, Cityscapes [2] and  CamVid [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here some state-of-the-art methods are adopted for comparison  and the results from the literatures are listed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We follow the standard protocols  of video semantic segmentation and report the mean Intersection over Union  (mIoU) as the performance metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Dataset  Cityscapes [2] is a popular dataset in semantic segmentation and autonomous  driving domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' It focuses on semantic understanding of urban street scenes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  The training and validation subsets contain 2, 975 and 500 video clips, respec-  tively, and each video clip contains 30 frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The 20th frame in each clip is  annotated by the pixel-level semantic labels with 19 categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  CamVid [3] also focuses on the semantic understanding of urban street  scenes, but it contains less data than Cityscapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' It only has 701 color images  with annotations of 11 semantic classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' CamVid is divided into the trainval  set with 468 samples and test set with 233 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' All samples are extracted  18  Method  Backbone  mIoU (%)  PSPNet [13]  ResNet18  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='79  + Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' [25]  ResNet18  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='06 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='27)  + Ours  ResNet18  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='58 (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='79)  PSPNet [13]  ResNet50  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='24  + Accel [22]  ResNet50  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='20 (-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='04)  + TDNet [24]  ResNet50  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='40 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='27)  + EFC [40]  ResNet50  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='44 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='31)  + Ours  ResNet50  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='22 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='98)  PSPNet [13]  ResNet101  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='70  + TDNet [24]  ResNet101  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='90 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='20)  + NetWarp [4]  ResNet101  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='60 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='90)  + GRFP [5]  ResNet101  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='20 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='50)  + Ours  ResNet101  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='96 (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='26)  Swin-B [30]  Swin Transformer  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='34  + Ours  Swin Transformer  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='67 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='33)  Table 1: Performance comparison on Cityscapes val subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' PSPNet and Swin Transformer  are chosen as the image segmentation models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  from the driving videos captured at daytime and dusk, and have pixel-level  semantic annotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Each CamVid video contains 3, 600 to 11, 000 frames at  a resolution of 720 × 960.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Performance Comparison  Here we compare our proposed method with the state-of-the-art methods on  Cityscapes and CamVid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In particular, the image segmentation model is used  as the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The PSPNet [13] with the backbone ResNet18/50/101 has been  widely used on Cityscapes, and Dilation8 [41] is mainly adopted on CamVid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Table 1 and Table 2 show the results, and we have the following observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  First, our proposed method achieves the state-of-the-art performance on both  datasets and various baseline model, which demonstrate the effectiveness and  generalization of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Second, our proposed method can get more gains  19  Method  Backbone  mIoU (%)  Dilation8 [41]  VGG16  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='3  + STFCN [27]  VGG16  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='9 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='4)  + GRFP [5]  VGG16  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='1 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='8)  + FSO [42]  VGG16  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='1 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='8)  + VPN [43]  VGG16  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='7 (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='4)  + NetWarp [4]  VGG16  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='1 (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='8)  + EFC [40]  VGG16  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='4 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='1)  + Ours  VGG16  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='9 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='6)  PSPNet [13]  ResNet101  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='2  + Accel [22]  ResNet101  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='5 (-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='7)  + TDNet [24]  ResNet101  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='0 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='2)  + Ours  ResNet101  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='6 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='4)  Swin-B [30]  Swin Transformer  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='6  + Ours  Swin Transformer  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='9 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='3)  Table 2:  Performance comparison on CamVid test subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Dilation8, PSPNet and Swin  Transformer are chosen as the image segmentation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  on light-weight baseline model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' This is reasonable since improving more com-  plicated model is generally more difficult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Third, TDNet [24], Accel [22] and  Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' [25] have nearly no improvement and even degradation on accuracy  comparing to the baseline, since they mainly focus on improving inference speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Fourth, even on the strong baseline, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', Swin Transformer [30], our method  can also bring improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Ablation Study  Effectiveness of our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In this work, we propose two key modules, namely  STF and MAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To investigate their effects, we also give the results of applying  one of them, as shown in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  We can have the following observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  First, our proposed STF and MAR can bring significant performance improve-  ment separately compared with the baseline, and the version equipped with  both of them performs best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Second, STF can brings more gains than MAR,  20  Method  Dataset  Backbone  mIoU (%)  PSPNet [13]  Cityscapes  ResNet50  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='24  + STF  Cityscapes  ResNet50  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='75 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='62)  + MAR  Cityscapes  ResNet50  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='37 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='24)  + Both  Cityscapes  ResNet50  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='22 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='98)  Dilation8 [41]  CamVid  VGG16  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='3  + STF  CamVid  VGG16  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='5 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='2)  + MAR  CamVid  VGG16  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='3 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='0)  + Both  CamVid  VGG16  67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='9 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='6)  Table 3: Ablation study on key modules of our proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Performance comparison  on Cityscapes val subset and CamVid test subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' PSPNet and Dilation8 are chosen as the  image segmentation model, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Method  mIoU (%)  DeepLabv3 [44]  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='5  + DenseCRF [8]  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='7 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='2)  + GUM [39]  79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='8 (+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='3)  + SegFix [9]  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='5 (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='0)  + Our MAR  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='0 (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='5)  Table 4:  Comparison of different feature refinement methods on Cityscapes val subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  DeepLabv3 is chosen as the baseline model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  since STF integrates the multi-frame information while MAR only optimizes the  features within the current frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Third, our proposed STF outperforms other  multi-frame fusion methods (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', TDNet [24] in Table 1 and GRFP [5] and  NetWarp [4] in Table 2), which indicates the effectiveness of modeling spatial-  temporal relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Analysis of MAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In this paper, we propose MAR to refine the video features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Actually, this technique can also be used in other tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here we particularly  investigate its effect on image segmentation, and show its superiority by com-  paring with other representative refinement methods, including DenseCRF [8],  21  Current Frame  Baseline  w/ STF  Ours  Ground Truth  Figure 9: Visualization of some sample segmentation results from Cityscapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' It  can be seen that STF can significantly improve the baseline results, and MAR can further  bring gains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here the red rectangles highlight the important regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Best viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  GUM [39], and SegFix [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' DenseCRF [8] establishes pairwise potentials on all  pairs of pixels and poses segmentation refinement problem as maximum a pos-  teriori (MAP) inference, which is a classic post-processing method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' GUM [39]  proposes to enrich bilinear upsampling operators by introducing a learnable  transformation for semantic maps, which can steer the sampling towards the  correct semantic class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  SegFix [9] proposes to replace the unreliable predic-  tions of boundary pixels with the predictions of interior pixels, which currently  achieves the state-of-the-art performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Table 4 provides the comparison re-  sults, where the DeepLabv3 is adopted as the baseline by following previous  works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We can see that our MAR outperforms the previous methods, which  indicates the effectiveness of refining feature by memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  To intuitively show the effect of MAR on feature refinement, we particularly  choose two easily ambiguous categories, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', wall and building, to visualize the  features before and after applying MAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' To be specific, we randomly sample  100 hard features (with confidence scores lower than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='8) per category, and then  visualize their distribution using t-SNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The results are shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Before using MAR, two kinds of features are confused together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' MAR can move  features closer to their corresponding class prototypes and make them easier to  be separated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  22  w/o MAR  w/ MAR  Wall  Building  Wall  Building  Figure 10: Visualization on the change of feature distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' It can be seen that  features become more separable after using MAR module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Best viewed in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Method  road  side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  build.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  wall  fence  pole  light  sign  vege.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  terr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  PSPNet-50  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='82  83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='23  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='70  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='86  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='07  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='87  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='76  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='93  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='95  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='85  + MAR  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='13  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='02  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='39  51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='34  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='81  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='46  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='62  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='49  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='55  65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='47  Method  sky  pers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  rider  car  truck  bus  train  motor  bike  mean  PSPNet-50  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='16  81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='86  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='96  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='82  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='34  85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='83  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='67  64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='43  77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='61  76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='24  + MAR  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='52  82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='42  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='88  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='34  80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='72  88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='72  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='73  68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='28  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='21  78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='37  Table 5: Category-wise performance on Cityscapes val subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' PSPNet-50 is chosen as the  baseline model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Hyper-parameter KL and KH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In our MAR, KL and KH are used to control the  number of boundary features for memory and good features for prototype per  class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here we explore their influence on the segmentation accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Considering  the memory size, we particularly evaluate the KL from {10, 50, 100, 300} and  the KH from {1, 5, 10, 50} on Cityscapes val subset with PSPNet-ResNet50 as  the base model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We found that there is almost no performance fluctuation for  different settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Finally, KL = 10 and KH = 10 are adopted throughout the  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Analysis of segmentation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Our proposed MAR mainly handles the am-  biguous cases, especially for the hard classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Table 5 lists the segmentation  accuracy of different semantic classes on Cityscapes, where PSPNet with the  23  wall  buildingwall  buildingModule  MACs (G)  PSPNet-50 (3 Frames)  4285.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='9  PSPNet-101 (3 Frames)  6152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='9  STF  563.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='5  MAR  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='5  Classifier  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='5  Table 6: Computational cost of different modules (GMACs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' The resolution of input image  is 1024 × 2048.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  ResNet50 backbone is particularly adopted as the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We can see that  our method can consistently boost the accuracy over all classes and the gain  is especially significant for the hard classes, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=', wall, terrain, and truck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In  addition, to intuitively show the effectiveness of our proposed STF and MAR,  we visualize three sample segmentation results from Cityscapes in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' It  can be seen that the original segmentation results can be progressively improved  by STF and MAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Cost of STF and MAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Here we analyze the computational cost of different  components in our proposed method, and the statistics are provided in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  It can be seen that our STF and MAR involve little computational cost com-  pared with the base model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' In particular, our proposed MAR is more efficient  to achieve good segmentation performance than devising more complicated net-  work structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Conclusion  In this paper, we design a novel video semantic segmentation framework  with inter-frame feature fusion and inner-frame feature refinement, and pro-  pose two novel techniques to boost the accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Specifically, we first propose  a spatial-temporal fusion module based on the transformer, which can effec-  tively aggregate multi-frame features at different spatial and temporal positions,  and meanwhile avoid error-prone optical flow estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Then we propose a  24  memory-augmented refinement module that exploits the stored features from  the training samples to augment the hard features during inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Our ex-  perimental results on Cityscapes and CamVid show that the proposed method  outperforms the state-of-the-art methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  Acknowledgements  This work is supported by the National Natural Science Foundation of China  under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='62176246 and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='61836008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' We acknowledge the support of  GPU cluster built by MCC Lab of Information Science and Technology Institu-  tion, USTC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  References  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Long, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Shelhamer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Darrell, Fully convolutional networks for seman-  tic segmentation, in: CVPR, 2015 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Cordts, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Omran, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Ramos, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Rehfeld, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Enzweiler, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Benenson,  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Franke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Roth, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Schiele, The cityscapes dataset for semantic urban  scene understanding, in: CVPR, 2016 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Brostow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Fauqueur, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Cipolla, Semantic object classes in video: A  high-definition ground truth database, Pattern Recognition Letters (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Gadde, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Jampani, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Gehler, Semantic video cnns through repre-  sentation warping, in: ICCV, 2017 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [5] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Nilsson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Sminchisescu, Semantic video segmentation by gated recur-  rent flow propagation, in: CVPR, 2018 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [6] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Lyu, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' King, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Xu, Selflow: Self-supervised learning of optical  flow, in: CVPR, 2019 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhuang,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang,  Video semantic segmentation with  distortion-aware feature correction, TCSVT (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  25  [8] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Kr¨ahenb¨uhl, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Koltun, Efficient inference in fully connected crfs with  gaussian edge potentials, NeurIPS (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [9] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Yuan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Xie, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, Segfix: Model-agnostic boundary re-  finement for segmentation, in: ECCV, 2020 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Vaswani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Shazeer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Parmar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Uszkoreit, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Jones, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Gomez,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Kaiser, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Polosukhin, Attention is all you need, in: NeurIPS, 2017  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [11] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Yuan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Guo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, Interlaced sparse  self-attention for semantic segmentation, arXiv preprint arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='12273  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [12] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Papandreou, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Kokkinos, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Murphy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Yuille, Deeplab:  Semantic image segmentation with deep convolutional nets, atrous convo-  lution, and fully connected crfs, TPAMI (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [13] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Shi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Qi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Jia, Pyramid scene parsing network,  in: CVPR, 2017 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [14] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Peng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Ma, Semantic segmentation using stride spatial pyramid pooling  and dual attention decoder, Pattern Recognition (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [15] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Lian, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Pang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Han, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Pan, Cascaded hierarchical atrous spatial  pyramid pooling module for semantic segmentation, Pattern Recognition  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [16] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Kang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Ge, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Jan Latecki, Contextual  ensemble network for semantic segmentation, Pattern Recognition (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [17] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Sun, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Dong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Chen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Lv, Gpnet: Gated pyramid network  for semantic segmentation, Pattern Recognition (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Orˇsi´c, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' ˇSegvi´c, Efficient semantic segmentation with pyramidal fusion,  Pattern Recognition (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  26  [19] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Song, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Duan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Li, Efnet: Enhancement-fusion network for  semantic segmentation, Pattern Recognition (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [20] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Xiong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Dai, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Yuan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wei, Deep feature flow for video  recognition, in: CVPR, 2017 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [21] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Ilg, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Mayer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Saikia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Keuper, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Dosovitskiy, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Brox, Flownet  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='0: Evolution of optical flow estimation with deep networks, in: CVPR,  2017 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [22] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Jain, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Gonzalez, Accel: A corrective fusion network for  efficient semantic segmentation on video, in: CVPR, 2019 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Huang, Video semantic segmentation via feature  propagation with holistic attentio, Pattern Recognition (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [24] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Hu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Caba, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Sclaroff, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Perazzi, Temporally dis-  tributed networks for fast video semantic segmentation, in: CVPR, 2020  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [25] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Liu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Shen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Yu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, Efficient semantic video segmentation  with per-frame inference, in: ECCV, 2020 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [26] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Tran, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Bourdev, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Fergus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Torresani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Paluri, Deep end2end  voxel2voxel prediction, in: CVPRW, 2016 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Fayyaz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Saffar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Sabokrou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Fathy, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Klette, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Huang,  Stfcn: spatio-temporal fcn for semantic video segmentation, arXiv preprint  arXiv:1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='05971 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [28] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Fu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Lu, Hierarchically supervised  deconvolutional network for semantic video segmentation, Pattern Recog-  nition (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [29] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Carion, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Massa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Synnaeve, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Usunier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Kirillov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zagoruyko,  End-to-end object detection with transformers, in: ECCV, 2020 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  27  [30] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Cao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wei, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Lin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Guo, Swin trans-  former: Hierarchical vision transformer using shifted windows, in: ICCV,  2021 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [31] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Girdhar, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Carreira, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Doersch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zisserman, Video action trans-  former network, in: CVPR, 2019 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [32] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Gavrilyuk, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Sanford, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Javan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Snoek, Actor-transformers for  group activity recognition, in: CVPR, 2020 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [33] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=" de Masson d'Autume, S." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Ruder, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Kong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Yogatama, Episodic mem-  ory in lifelong language learning, in: NeurIPS, 2020 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [34] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Chang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Luo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Prakash, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Hauptmann,  Few-shot activity recognition with cross-modal memory network, Pattern  Recognition (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [35] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Cai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Pan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Yao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Yan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Mei, Memory matching networks for  one-shot image recognition, in: CVPR, 2018 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [36] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Deng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Hua, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Song, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Xue, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Ma, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Robertson,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Guan, Object guided external memory network for video object de-  tection, in: ICCV, 2019 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [37] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Feichtenhofer, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Fan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' He, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Krahenbuhl, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Girshick,  Long-term feature banks for detailed video understanding, in: CVPR, 2019  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [38] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Girshick, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Gupta, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' He, Non-local neural networks, in:  CVPR, 2017 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [39] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Mazzini, Guided upsampling network for real-time semantic segmenta-  tion, in: BMVC, 2018 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Ding, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Shi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Lu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Luo, Every frame counts: joint  learning of video segmentation and optical flow, in: AAAI, 2020 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  28  [41] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Yu, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Koltun, Multi-scale context aggregation by dilated convolutions,  arXiv preprint arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='07122 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Kundu, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Vineet, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Koltun, Feature space optimization for semantic  video segmentation, in: CVPR, 2016 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [43] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Jampani, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Gadde, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Gehler, Video propagation networks, in:  CVPR, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' 451–461 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  [44] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Papandreou, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Schroff, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content=' Adam, Rethinking atrous con-  volution for semantic image segmentation, arXiv preprint arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='05587  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
+page_content='  29' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RtE2T4oBgHgl3EQfWQe7/content/2301.03832v1.pdf'}
diff --git a/W9FQT4oBgHgl3EQfcjYS/content/2301.13327v1.pdf b/W9FQT4oBgHgl3EQfcjYS/content/2301.13327v1.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..7ee6d0185e8ece0cabc635c749a747c691635046
--- /dev/null
+++ b/W9FQT4oBgHgl3EQfcjYS/content/2301.13327v1.pdf
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:54dcc44fd49da779d89253fa2f2b00d2bf60d2370c920750c4163e96938c8a05
+size 916847
diff --git a/_dFAT4oBgHgl3EQfqx1t/content/tmp_files/2301.08649v1.pdf.txt b/_dFAT4oBgHgl3EQfqx1t/content/tmp_files/2301.08649v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..31ee4422e495334cb982888c3392619212e114b4
--- /dev/null
+++ b/_dFAT4oBgHgl3EQfqx1t/content/tmp_files/2301.08649v1.pdf.txt
@@ -0,0 +1,1101 @@
+Offline Policy Evaluation with Out-of-Sample Guarantees
+Sofia Ek
+sofia.ek@it.uu.se
+Department of Information Technology
+Uppsala University
+Dave Zachariah
+dave.zachariah@it.uu.se
+Department of Information Technology
+Uppsala University
+Abstract
+We consider the problem of evaluating the performance of a decision policy using past
+observational data. The outcome of a policy is measured in terms of a loss or disutility (or
+negative reward) and the problem is to draw valid inferences about the out-of-sample loss
+of the specified policy when the past data is observed under a, possibly unknown, policy.
+Using a sample-splitting method, we show that it is possible to draw such inferences with
+finite-sample coverage guarantees that evaluate the entire loss distribution. Importantly, the
+method takes into account model misspecifications of the past policy – including unmeasured
+confounding. The evaluation method can be used to certify the performance of a policy using
+observational data under an explicitly specified range of credible model assumptions.
+1
+Introduction
+In this work, we are interested in evaluating the performance of a decision policy, denoted π, which chooses
+an action A from a discrete action set. Each action A is taken in a context with observable covariates X and
+incurs a real-valued loss L (aka. disutility or negative reward). Such policies are considered in contextual
+bandit problems and precision medicine (Langford & Zhang, 2007; Qian & Murphy, 2011; Lattimore &
+Szepesvári, 2020; Tsiatis et al., 2019). For instance, A may be one of several treatment options for a patient
+with observable characteristics X and L measures the severity of the outcome.
+A target policy π can be evaluated using experimental data obtained from trials. Such experiments are,
+however, often costly and may lead to rather restrictive sample sizes. Moreover, in safety-critical applications
+it is often unethical to test new policies without severe restrictions. A more fundamental inferential problem,
+however, is the lack of ‘external’ validity, i.e., the limited ability to extrapolate from the trial population
+to the intended target population leads to invalid inferences (Westreich, 2019; Manski, 2019). The main
+alternative is off-policy evaluation, i.e., using observational data from a past decision process to infer the
+performance of the target policy. This requires that the past process is modelled without systematic errors
+– by assuming well-specified models and no unmeasured confounding. The credibility of these assumptions
+therefore determine the ‘internal’ validity of inferences about π from observational data (Manski, 2003).
+Inferences that lack validity are particularly serious when evaluating π in decision processes that are costly
+or safety-critical. In such cases even inferences that are asymptotically valid with increasing sample size
+may not be adequate. Moreover, when the resulting distribution of losses is skewed or is widely dispersed,
+its tails are important to evaluate. Then inferring the expected loss Eπ[L], as is commonly done, provides
+a very limited evaluation of π. For instance, the average loss in a population maybe low but the tail losses
+are unacceptable (Wang et al., 2018). In such applications, we are more concerned with providing valid
+certifications of the overall performance (see Figure 1a), rather than precise but invalid inferences of a single
+distributional parameter.
+In this paper we propose a method for evaluating a specified target policy using observational data that
+1
+arXiv:2301.08649v1  [stat.ML]  20 Jan 2023
+
+• provides finite-sample coverage guarantees for the out-of-sample loss,
+• evaluates the entire loss distribution instead of the expected value,
+• and takes model misspecification, including unmeasured confounding, into account.
+0.0
+0.5
+1.0
+1.5
+ℓα
+0%
+20%
+40%
+60%
+80%
+100%
+1 − α
+π
+π1
+π0
+(a) Evaluation of out-of-sample loss L.
+0%
+20%
+40%
+60%
+80%
+100%
+Target coverage
+0%
+20%
+40%
+60%
+80%
+100%
+Actual coverage
+π
+π1
+π0
+(b) Evaluation of coverage of limit curves.
+Figure 1: Evaluating out-of-sample losses under target policy with binary decisions A ∈ {0, 1}. Policies π0
+and π1 correspond to ‘treat none’ (A ≡ 0) and ‘treat all’ (A ≡ 1), respectively, while π denotes a policy that
+adapts to context X, see Section 5.1 for more details. (a) Each curve certifies that a new loss L falls below
+the limit ℓα with a probability of least 1 − α. The certified performance of the adaptive policy π dominates
+those of the alternative policies. (b) Evaluation of actual coverage, that is, the probability of L ≤ ℓα, across
+target coverage 1 − α.
+2
+Problem formulation
+We consider a target policy π for deciding actions A in different contexts, which are described by observed
+and unobserved covariates X and U, respectively. The policy can be either deterministic or random, and
+corresponds to a distribution pπ(A|X), which can be conditional on observed covariates X. Our aim is to
+evaluate the losses L that result from applying any given π. Each instance of contextual covariates, action
+and loss, i.e., (X, U, A, L), is drawn independently from a target distribution pπ(X, U, A, L). At our disposal
+is an observational data set
+D =
+�
+(Xi, Ai, Li)
+�n
+i=1,
+(1)
+and our goal is to use it to characterize the out-of-sample loss Ln+1. Specifically, for any miscoverage level
+α ∈ (0, 1), we seek an informative limit ℓα(D) on the loss such that
+Pπ
+�
+Ln+1 ≤ ℓα(D)
+�
+≥ 1 − α,
+(2)
+In other words, ℓα(D) evaluated across α yields a finite-sample performance certification of π as is illustrated
+in Figure 1a. Unlike a single point estimate, the limit curve characterizes the distribution of losses under π.
+The causal structure of the decision process is illustrated in Figure 2a and the target distribution admits a
+causal factorization
+pπ(X, U, A, L) = p(X, U) pπ(A|X) p(L|A, X, U),
+(3)
+where p(X, U) and p(L|A, X, U) are unknown. The central challenge in off-policy evaluation of π is that (1)
+is not sampled from (3) but from a shifted training distribution which admits a causal factorization
+p(X, U, A, L) = p(X, U) p(A|X, U) p(L|A, X, U),
+(4)
+2
+
+where p(A|X, U) characterizes a different, past policy (aka.
+behavioral policy).
+The causal structure is
+illustrated in Figure 2b. If the past policy were known, it is possible to adjust for the distribution shift from
+training to target distribution using the ratio
+pπ(X, U, A, L)
+p(X, U, A, L) ≡ pπ(A|X)
+p(A|X, U) ≥ 0.
+(5)
+This is feasible in certain problems with fully automated decision-making, such as online recommendation
+systems, where the past policy is designed using observable covariates only, i.e., p(A|X, U) ≡ p(A|X). In more
+general problems, however, we have only a nominal model of the past policy �p(A|X) (aka. propensity model),
+typically estimated from prior observable data. The nominal model may therefore diverge from p(A|X, U)
+due to various modelling errors that persist even in the large-sample scenario: model misspecification and
+unmeasured confounding via U (Peters et al., 2017; Westreich, 2019). Here we follow the marginal sensitivity
+methodology of (Tan, 2006) and characterize the model divergence with respect to the odds of taking action
+A. That is, the nominal odds diverge from the unknown odds by some bounded factor Γ ≥ 1 as follows:
+1
+Γ ≤
+p(A|X, U)
+1 − p(A|X, U)
+�
+��
+�
+unknown odds
+�
+�p(A|X)
+1 − �p(A|X)
+�
+��
+�
+nominal odds
+≤ Γ.
+(6)
+When the bound equals Γ = 1, the nominal model is perfectly specified and there is no unmeasured con-
+founding. In general, we consider all cases where the nominal odds diverge by at most a factor Γ.
+In summary, the problem we consider is to construct a limit ℓα(D) for target policy π using training data
+D and a nominal model �p(A|X). The resulting limit should satisfy the finite-sample guarantee (2) across
+all miscoverage levels α, and thereby certify the target policy performance for any specified bound Γ in
+(6). This enables a robust off-policy evaluation of target policies using observational data, since it can be
+performed across a range of credible odds bounds Γ as we will illustrate in the numerical experiments below.
+By increasing the odds bound Γ, the credibility of our assumptions on �p(A|X) increases, but the strength of
+our conclusions about Ln+1 decrease, cf. (Manski, 2003). The trade-off between credibility of assumptions
+and informativeness of inferences will be quantified as well.
+X
+A
+L
+U
+(a) Causal structure that yields target distribution (3).
+X
+A
+L
+U
+(b) Causal structure that yields training distribution (4).
+Figure 2: Directed acyclic diagrams (DAGs) representing the causal structure of decision process under (a)
+target policy and (b) past policy. In (b), both contextual covariates (X, U) may affect actions A as well as
+the outcome loss L and thus U gives rise to unmeasured confounding.
+3
+Background
+We situate the problem considered in this paper and our proposed method within the context of off-policy
+evaluation.
+Expected loss: In most off-policy evaluation literature, the target quantity is the unknown expected loss
+Eπ[L] of policy π. A standard estimator of the mean, that dates back to Horvitz & Thompson (1952), is
+based on inverse propensity weighting:
+VIPW(D) = 1
+n
+n
+�
+i=1
+�w(Xi, Ai) Li,
+(7)
+3
+
+where �w(X, A) = pπ(A|X)
+�p(A|X) is a model of (5), see for instance (Rosenbaum & Rubin, 1983; Beygelzimer et al.,
+2009; Qian & Murphy, 2011; Zhang et al., 2012; Zhao et al., 2012; Kallus, 2018). We note that the estimator
+is unbiased when Γ = 1. An alternative standard estimator is based on regression modeling:
+VRM(D) = 1
+n
+n
+�
+i=1
+�
+a∈A
+pπ(a|Xi) �ℓ(a, Xi),
+(8)
+where �ℓ(A, X) is a model of E[L|A, X].
+The approaches in (7) and (8) have complementary strenghts and weaknesses based on the challenges of
+modelling the past policy or the conditional mean of losses, respectively.
+Even when models are well-
+specified, the accuracy of the estimators depend highly on the overlap of covariates X across decisions A
+in the training data Oberst et al. (2020); D’Amour et al. (2021). When the overlap is weak, the variance
+of VIPW(D) can become excessively large, even when it is unbiased. This can be mitigated by clipping the
+weights (Rubin, 2001; Kang & Schafer, 2007; Schafer & Kang, 2008; Strehl et al., 2010).
+When the models �w(X, A) or �ℓ(A, X) are systematically in error, however, their corresponding estimators
+are biased and may invalidate the evaluation of π. The ‘doubly robust’ estimator
+VDR(D) = 1
+n
+n
+�
+i=1
+�w(Xi, Ai)
+�
+Li − �ℓ(Ai, Xi)
+�
++
+�
+a∈A
+pπ(a|Xi) �ℓ(a, Xi),
+is one way to protect against one of the models being misspecified and reduces the estimator variance provided
+�ℓ(A, X) is sufficiently accurate (Bang & Robins, 2005; Dudík et al., 2011; Rotnitzky et al., 2012).
+Distribution of losses: When loss distribution is highly skewed and/or the tails are wide, the expected loss
+can be inadequate to evaluate policies, especially in high-stakes problems. There are alternative parameters
+of the loss distribution, decribed by the cumulative distribution function F(ℓ) = Pπ{Ln+1 ≤ ℓ} (cdf), that
+one can consider in such problems, such as the Conditional Value at Risk or a quantile (Wang et al., 2018;
+Chandak et al., 2021; Huang et al., 2021).
+Off-policy evaluation of π with respect to some alternative parameter can be achieved using cdf-estimators
+that are analogous to the mean estimators above, see (Huang et al., 2021). In analogy to (7), the inverse
+propensity weighted cdf-estimator
+�FIPW(ℓ; D) = 1
+n
+n
+�
+i=1
+�w(Xi, Ai) 1(Li ≤ ℓ),
+(9)
+is point-wise unbiased when Γ = 1. Similar to (8), the estimator
+�FRM(ℓ; D) = 1
+n
+n
+�
+i=1
+�
+a∈A
+pπ(a|Xi) �c(ℓ; a, Xi),
+requires a model �c(ℓ; a, x) of the conditional distribution P{L ≤ ℓ|A, X}. To mitigate against model mis-
+specification that threaten the validity of the evaluation of π, one can use the ‘doubly robust’ estimator
+�FDR(ℓ; D) = 1
+n
+n
+�
+i=1
+�w(Xi, Ai)
+�
+1(Li ≤ ℓ) − �c(ℓ; Ai, Xi)
+�
++
+�
+a∈A
+pπ(a|Xi) �c(ℓ; a, Xi),
+which protects against one of the models being in misspecified. While this estimator is consistent, it is not
+guaranteed yield a valid cdf.
+In this paper, we are interested in limiting the out-of-sample loss Ln+1 and the quantile is the smallest ℓα
+such that Pπ{Ln+1 ≤ ℓα} ≥ 1 − α. It can be estimated as
+ℓα(D) = inf
+�
+ℓ : �F(ℓ; D) ≥ 1 − α
+�
+,
+4
+
+using a cdf-estimator above.
+Distribution-free inference: Derivations of finite-sample valid, nonparametric limits on random variables
+date back to the works of Wilks (1941); Wald (1943); Scheffe & Tukey (1945). More recently, the related
+methodology of conformal prediction has focused on developing covariate-specific prediction regions (Vovk
+et al., 2005; Shafer & Vovk, 2008; Vovk, 2012). See Lei & Wasserman (2014); Lei et al. (2018); Romano
+et al. (2019) for further developments. Tibshirani et al. (2019) adapt the methodology to be valid also under
+known covariate shifts. This result was subsequently used to provide context-specific prediction intervals for
+any given policy π that are statistically valid under the assumption that the past policy p(A|X, U) is known
+Osama et al. (2020); Taufiq et al. (2022).
+The marginal sensitivity methodology developed in Tan (2006) enables us to specify a more credible range
+of assumptions using (6). This methodology was used for robust policy learning in Kallus & Zhou (2021)
+and sensitivity analysis of treatment effects in Jin et al. (2021) under unobserved confounding. This paper
+considers the overall performance of π, similar to Huang et al. (2021).
+However, we focus on ensuring
+inferences on the out-of-sample losses that are valid even with finite training data and under systematic
+modelling errors – including unobserved confounding – using a sample-splitting technique that leverages
+results derived in Jin et al. (2021).
+4
+Method
+We show that one can limit the out-of-sample losses under π using a sample-splitting technique and by
+bounding the unknown ratio in (5).
+For any specified odds bound Γ ≥ 1 in (6), we have that the ratio in (5) is bounded as:
+W ≤ pπ(X, U, A, L)
+p(X, U, A, L) ≤ W,
+(10)
+where the bounds equal
+W = pπ(A|X) ·
+�
+1 + Γ−1�
+�p(A|X
+�−1 − 1)
+�
+and
+W = pπ(A|X) ·
+�
+1 + Γ
+�
+�p(A|X)−1 − 1
+��
+.
+(11)
+That is, the bounds are functions of X and A drawn from the training distribution (4).
+We randomly split the training data (1) into two separate sets,
+D = D0 ∪ D1,
+with samples sizes n0 and n − n0, respectively. The first set D0 is used to construct a set of upper bounds
+�
+W i
+�n0
+i=1 via (11). The remaining set D1 is used to form the function
+�F(ℓ; D1, w) =
+�n
+i=n0+1 W i1(Li ≤ ℓ)
+�n
+i=n0+1 W i1(Li ≤ ℓ) + �n
+i=n0+1 W i1(Li > ℓ) + w,
+(12)
+as a proxy for the unknown cdf of the out-of-sample loss Ln+1. As the following result shows, (12) enables
+the construction of a valid limit ℓα.
+Theorem 4.1. Define the quantile function of (12) as
+�F −1(·; D1, w) = inf
+�
+ℓ : �F(ℓ; D1, w) ≥ ·
+�
+.
+For any miscoverage probability α ∈ (0, 1), construct the limit
+ℓα(D) =
+min
+β:0<β<α
+�F −1
+�1 − α
+1 − β ; D1, wβ(D0)
+�
+,
+(13)
+5
+
+where
+wβ(D0) =
+�
+W [⌈(n0+1)(1−β)⌉],
+⌈(n0 + 1)(1 − β)⌉ ≤ n0,
+∞,
+otherwise,
+(14)
+and W [k] denotes the kth order statistic of (W i)n0
+i=1.
+Then ℓα(D) limits the out-of-sample loss Ln+1 with a probability of at least 1 − α as specified in (2).
+4.1
+Implementation
+We note that (12) is piecewise constant and can readily be represented using a vector with n − n0 elements.
+The limit curve can be evaluated across a discrete grid of miscoverage levels α and the computation is
+summarized in Algorithm 1. Also, note that wβ as a function of β changes in discrete steps in (14), therefore
+the relevant values of β form a discrete set.
+Algorithm 1 Limit curve of policy π
+Input: Training data D, model �p(A|X), bound Γ ≥ 1 and sample split size n0.
+1: Randomly split D into D0 and D1.
+2: for α ∈ {0, . . . , 1} do
+3:
+for β ∈ {0, . . . , α} do
+4:
+Compute wβ using (14).
+5:
+Compute ℓα,β = inf
+�
+ℓ : �F(ℓ; D1, wβ) ≥ 1−α
+1−β
+�
+using (12).
+6:
+end for
+7:
+Set ℓα to the smallest ℓα,β above.
+8:
+Store (α, ℓα).
+9: end for
+Output: {(α, ℓα)}
+4.2
+Derivation of result
+Proof. The first part of the proof builds on techniques used to derive weighted conformal prediction intervals
+in Tibshirani et al. (2019).
+Let us consider a sequence of n − n0 samples drawn from (4) followed by a new sample drawn from (3), i.e.,
+D+ =
+�
+(Xn0+1, Un0+1, An0+1, Ln0+1), . . . , (Xn, Un, An, Ln), (Xn+1, Un+1, An+1, Ln+1)
+�
+.
+The joint distribution of this sequence can be expressed using:
+n
+�
+i=n+
+p(xi, ui, ai, ℓi) · p(xn+1, un+1, an+1, ℓn+1)wn+1 = p(D+)wn+1 = p(S+)wn+1,
+where n+ = n0 + 1 for notational simplicity, S+ is an unordered set of elements from D+, and the weight
+wi = pπ(xi, ui, ai, ℓi)
+p(xi, ui, ai, ℓi) ,
+is the (unobservable) ratio (5) that quantifies the distribution shift from training to target distribution. We
+shall use the expression for the joint distribution to derive the distribution function for the new loss Ln+1.
+Suppose we are given unordered set S+ alone, then the particular sequence D+ is unknown. Let Ei denote
+the event that the sample (Xn+1, Un+1, An+1, Ln+1) equals the ith sample (xi, ui, ai, ℓi) in the unknown
+sequence D+. We consider all possible sequences D+ obtained by permutations σ of elements in the set S+.
+The joint probability the event Ei and S+ is then
+P{Ei, S+} =
+�
+σ:σ(n+1)=n+i
+p(S+)wi = p(S+)win!.
+6
+
+The conditional probability of event Ei can now be expressed as
+pi = P{Ei|S+} =
+P{Ei, S+}
+�n+1
+j=n+ P{Ej, S+}
+=
+wi
+�n+1
+j=n+ wj
+,
+where the first equality follows from the law of total probability. The probability that the loss Ln+1 of the
+new sample equals ℓi, when conditioning on the unordered set S+, is equal to
+P{Ln+1 = ℓi|S+} = P{Ei|S+} = pi.
+Thus conditional on S+, the new loss Ln+1 follows the cdf:
+P{Ln+1 ≤ ℓ|S+} =
+n+1
+�
+i=n+
+pi1(ℓi ≤ ℓ) =
+�n+1
+i=n+ wi1(Li ≤ ℓ)
+�n+1
+i=n+ wi
+.
+(15)
+Before marginalizing out S+ from (15), we consider a limit ℓ that is a function of the observable elements in
+S+. For this part, we will build on the proof technique in (Jin et al., 2021, thm. 2.2).
+Specifically, using (12) we define the following limit:
+ℓα(D1, W n+1) = inf
+�
+ℓ : �F(ℓ; D1, W n+1) ≥ 1 − α
+1 − β
+�
+,
+(16)
+for any 0 < β < α, where W n+1 ≥ Wn+1 is given in (11). Now insert the limit ℓα(D1, W n+1) into (15) and
+use the law of total expectation to marginalize out S+:
+P{Ln+1 ≤ ℓα(D1, W n+1)} = E
+�
+Pπ{Ln+1 ≤ ℓα(D1, W n+1)|S+}
+�
+= E
+��n+1
+i=n+ Wi1(Li ≤ ℓα(D1, W n+1))
+�n+1
+i=n+ Wi
+�
+.
+We now proceed to lower bound this probability. Note that by construction:
+E
+�
+�F(ℓα; D1, W n+1)
+�
+= E
+�
+�
+i∈D1 W i1(Li ≤ ℓα)
+�
+i∈D1 W i1(Li ≤ ℓα) + �
+i∈D1 W i1(Li > ℓα) + W n+1
+�
+≥ (1 − α)
+(1 − β).
+Using this expression, we have that
+P{Ln+1 ≤ ℓα(D1, W n+1)} − (1 − α)
+(1 − β)
+≥ E
+��n+1
+i=n+ Wi1(Li ≤ ℓα)
+�n+1
+i=n+ Wi
+�
+− E
+�
+�n
+i=n+ W i1(Li ≤ ℓα)
+�n
+i=n+ W i1(Li ≤ ℓα) + �n
+i=n+ W i1(Li > ℓα) + W n+1
+�
+= E
+�
+�
+(∗)
+��n+1
+i=n+ Wi
+� ��n
+i=n+ W i1(Li ≤ ℓα) + �n
+i=n+ W i1(Li > ℓα) + W n+1
+�
+�
+� ,
+7
+
+where
+(∗) =
+� n+1
+�
+i=n+
+Wi1(Li ≤ ℓα)
+��
+n
+�
+i=n+
+W i1(Li ≤ ℓα) +
+n
+�
+i=n+
+W i1(Li > ℓα) + W n+1
+�
+−
+�
+n
+�
+i=n+
+W i1(Li ≤ ℓα)
+�� n+1
+�
+i=n+
+Wi
+�
+≥
+�
+n
+�
+i=n+
+Wi1(Li ≤ ℓα)
+��
+n
+�
+i=n+
+W i1(Li ≤ ℓα) +
+n
+�
+i=n+
+W i1(Li > ℓα) + W n+1
+�
+−
+�
+n
+�
+i=n+
+W i1(Li ≤ ℓα)
+�� n+1
+�
+i=n+
+Wi
+�
+≥
+�
+n
+�
+i=n+
+Wi1(Li ≤ ℓα)
+��
+n
+�
+i=n+
+W i1(Li > ℓα) + W n+1
+�
+−
+�
+n
+�
+i=n+
+W i1(Li ≤ ℓα)
+��
+n
+�
+i=n+
+Wi1(Li > ℓα) + Wn+1
+�
+≥
+�
+n
+�
+i=n+
+Wi1(Li ≤ ℓα)
+��
+n
+�
+i=n+
+Wi1(Li > ℓα) + Wn+1
+�
+−
+�
+n
+�
+i=n+
+Wi1(Li ≤ ℓα)
+��
+n
+�
+i=n+
+Wi1(Li > ℓα) + Wn+1
+�
+= 0,
+using the bounds (10) on the fourth line. Therefore we obtain a valid limit:
+P{Ln+1 ≤ ℓα(D1, W n+1)} ≥ (1 − α)
+(1 − β).
+(17)
+However, W n+1 depends on a new sample drawn from the training distribution and thus the limit is unusable.
+In lieu of W n+1, we use wβ(D0) in (14) to define the modified limit
+ℓα(D) = inf
+�
+ℓ : �F(ℓ; D1, wβ(D0)) ≥ 1 − α
+1 − β
+�
+.
+(18)
+Comparing it with (16), we see that
+ℓα(D) ≥ ℓα(D1, W n+1),
+(19)
+whenever W n+1 ≤ wβ(D0). By the construction in (14), the probability of this event is lower bounded by
+P{W n+1 ≤ wβ(D0)} ≥ 1 − β,
+(20)
+see (Vovk et al., 2005; Lei et al., 2018).
+We use this property to lower bound the probability of Ln+1 ≤ ℓα(D). First note that
+P{Ln+1 ≤ ℓα(D)} = P{Ln+1 ≤ ℓα(D) | W n+1 ≤ wβ(D0)} P{W n+1 ≤ wβ(D0)}
++ P{Ln+1 ≤ ℓα(D) | W n+1 > wβ(D0)} P{ W n+1 > wβ(D0)}
+≥ P{Ln+1 ≤ ℓα(D) | W n+1 ≤ wβ(D0)} P{W n+1 ≤ wβ(D0)} + 0.
+The first factor can be lower bounded using (19), so that
+P{Ln+1 ≤ ℓα(D)} ≥ P{Ln+1 ≤ ℓα(D1, W n+1) | W n+1 ≤ wβ(D0)} P{W n+1 ≤ wβ(D0)}
+= P{Ln+1 ≤ ℓα(D1, W n+1)} P{W n+1 ≤ wβ(D0)}
+≥ (1 − α)
+(1 − β) P{W n+1 ≤ wβ(D0)}
+≥ 1 − α.
+(21)
+The second line follows from using sample splitting, which ensures that Ln+1 ≤ ℓα(D1, W n+1) and W n+1 ≤
+wβ(D0) are independent events. The third and fourth lines follow from (17) and (20), respectively. Since
+(21) holds for any 0 < β < α, we choose β in (18) that yields the tightest limit, cf. (13).
+8
+
+5
+Numerical experiments
+In the experiments below, we evaluate policies using the limit curves (α, ℓα). Note that the extremum loss
+ℓmax in a given problem provides a valid but uninformative limit across all α. We therefore quantify the
+informativeness of a valid limit curve as follows:
+Informativeness = 1 − α∗, where α∗ = sup{α : ℓα < ℓmax}.
+That is, the lowest coverage probability at which we can informatively certify the performance of π. We can
+therefore quantify increasing the credibility of our model assumption by Γ affects the informativeness of the
+limit curve. We also consider the coverage probability of the curves:
+Miscoverage gap = Pπ{Ln+1 > ℓα(D)} − α.
+(22)
+When this gap is positive, the limit is conservative and when the gap is negative the limit is invalid,
+respectively, at level α.
+A natural benchmark for the proposed limit (13) in this problem setting is the estimated quantile
+ℓα(D) = inf
+�
+ℓ : �FIPW(ℓ; D) ≥ 1 − α
+�
+,
+(23)
+using the inverse propensity weighted cdf-estimator (9).
+In all examples below, the limit (13) is computed using sample splits of equal size, i.e., n0 = n/2.
+5.1
+Synthetic data
+In the first example, we consider synthetic data in order to evaluate the coverage of the derived limit curves.
+We use a simulation setting similar to Jin et al. (2021). The miscoverage gap (22) is estimated by Monte
+Carlo simulation using n′ = 1000 independent samples over N = 1000 independent runs, i.e., in total 106
+samples.
+We consider a population of individuals with two-dimensional covariates distributed uniformly as
+X =
+�X1
+X2
+�
+∼ U(0, 1)2.
+The actions are binary A ∈ {0, 1} corresponding to ‘not treat’ and ‘treat’, respectively. We want to evaluate
+a deterministic target policy, described by
+pπ(A = 0|X) = 1(X1X2 ≥ τ),
+(24)
+for different τ ∈ [0, 1]. That is, all individuals whose covariate product X1X2 falls below τ are treated. Note
+that τ = 0 corresponds a ‘treat none’ policy (A ≡ 0 for all X) and τ = 1 corresponds to a ‘treat all’ policy
+(A ≡ 1 for all X). What can we say about the resulting losses under this policy using observational data
+with sample sizes n ∈ {250, 500, 1000}.
+Case: Known past policy (Γ = 1) In the first scenario, we assume that the past policy is known exactly
+and there is therefore no unmeasured confounding.
+For the training data, the past policy determined actions as a Bernoulli process, where
+p(A = 0|X) ≡ �p(A = 0|X) = f
+�
+c(X1X2 + 1)
+�
+,
+c ∈
+�1
+2, 2
+�
+,
+(25)
+and f(·) is the sigmoid function. The conditional loss distribution is given by
+L|A = 0, X ∼ N(1 − X1X2, 0.1)
+and
+L|A = 1, X ∼ N(X1X2, 0.1).
+9
+
+We consider three configurations c of past policies (25), which yield inverse propensity weights in three
+ranges:
+1
+p1(A|X) < 3.72 (c = 1/2),
+1
+p2(A|X) < 8.39 (c = 1), and
+1
+p3(A|X) < 55.6 (c = 2). Thus we anticipate
+p3(A|X) to be the most challenging case.
+Here we evaluate three target policies τ = {0, 0.5, 1} in (24) and present their resulting limit curves using
+data from different past policies (25) in Figure 3. The differing dashed lines shows the corresponding past
+policy.
+The limit curves for a given target policy are very similar across training distributions and are
+informative above the 90% level. The main difference is in the inferred tail losses and is notable for when
+τ = 1 under the more challenging past policy p3(A|X).
+We now turn to evaluating miscoverage gap (22). Figure 4 presents gaps for target policy τ = 0.5 in (24).
+The solid lines illustrate the proposed method and the dashed lines show the benchmark (23). We see that
+the proposed method is slightly conservative, but remains valid for all α. By contrast, the benchmark is not
+valid in the tail of the distribution, but is less conservative for higher α in this well-specified case.
+−0.5
+0.0
+0.5
+1.0
+1.5
+0%
+20%
+40%
+60%
+80%
+100%
+1 − α
+p1(A|X)
+−0.5
+0.0
+0.5
+1.0
+1.5
+ℓα
+0%
+20%
+40%
+60%
+80%
+100%
+p2(A|X)
+−0.5
+0.0
+0.5
+1.0
+1.5
+0%
+20%
+40%
+60%
+80%
+100%
+p3(A|X)
+pπ(A|X)
+τ = 0.0
+τ = 0.5
+τ = 1.0
+pπ = p
+Figure 3: Limit curves (ℓα, 1 − α) when the past policy is known (Γ = 1) for three different potential target
+policies (i.e. τ = {0.0, 0.5, 1.0} in (24)). Dashed curve denotes the past policy. n = 1000.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+−0.025
+0.000
+0.025
+0.050
+0.075
+0.100
+0.125
+0.150
+Miscoverage gap
+n = 250
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Target α
+−0.025
+0.000
+0.025
+0.050
+0.075
+0.100
+0.125
+0.150
+n = 500
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+−0.025
+0.000
+0.025
+0.050
+0.075
+0.100
+0.125
+0.150
+n = 1000
+Past policy
+p1(A|X)
+p2(A|X)
+p3(A|X)
+Type
+Proposed
+Benchmark
+Figure 4: Miscoverage gaps (22) across α, when the past policy is known (Γ = 1). Dashed curve denotes the
+benchmark (23).
+Case: Estimated past policy (Γ > 1) In the second scenario, we assume that we only have access to an
+estimate �p(A|X) and that there is unmeasured confounding in the training distribution. To render visually
+distinct curves from the previous case, we consider here a rather extreme case of confounding following Jin
+et al. (2021).
+In this case we have an unobserved variable drawn as
+U|X ∼ N(0, 0.1(X1 + X2)),
+and the loss L|A, X, U is generated as
+L =
+�
+1 − X1X2 + U,
+A = 0,
+X1X2 + U,
+A = 1.
+10
+
+We define the past policy in a manner that enables us to control the divergence from the nominal model
+�p(A|X) in (25):
+p(A = 0|X, U) = 1(U ≤ t(X))
+�
+1 + Γ−1
+0
+�
+�p(A = 0|X
+�−1 − 1)
+�
++ 1(U > t(X))
+�
+1 + Γ0
+�
+�p(A = 0|X)−1 − 1
+��
+,
+(26)
+where the threshold function t(X) is designed empirically to ensure that the resulting median loss of the
+past policy for A = 1 is maximized. Our design of the past policy can be seen as a worst case among all
+unknown past policies that diverge by a factor Γ0 in (6). We fix Γ0 = 2 here, but treat it as unknown.
+For clarity, we consider a ‘treat all’ target policy (τ = 1). Its limit curves, under different assumed odds
+bounds Γ = {1, 2, 3}, are presented in Figure 5. Note that under unmeasured confounding, the resulting
+curves differ notably across the training distributions unlike in Figure 3. We see that under the first and
+second distributions, the informativeness of all curves stays around the 90% level. However, in the most
+extreme third case, the informativeness drops to barely above the 60% level when we increase the credibility
+of our model assumption to an odds bound of Γ = 3. This example illustrates an inherent trade-off between
+credibility and informativeness.
+Figure 6 validates our guarantees using data drawn from p1(A|X). When Γ ≥ Γ0 = 2, the limit curves are
+valid and as Γ increases to 3, the limits become quite conservative. Note that the conservativeness persists
+even as the sample size n is increased fourfold. For Γ = 1, there is no guarantee of coverage and in this worst
+case scenario the limit curve is invalid. The benchmark does not take unmeasured confounding into account
+and is consequently invalid throughout.
+−0.5
+0.0
+0.5
+1.0
+0%
+20%
+40%
+60%
+80%
+100%
+1 − α
+p1(A|X)
+−0.5
+0.0
+0.5
+1.0
+ℓα
+0%
+20%
+40%
+60%
+80%
+100%
+p2(A|X)
+−0.5
+0.0
+0.5
+1.0
+0%
+20%
+40%
+60%
+80%
+100%
+p3(A|X)
+Gamma Γ
+1
+2
+3
+Figure 5: Limit curves (ℓα, 1 − α) for ‘treat all’ target policy using odds bounds Γ = {1, 2, 3}, when the past
+policy is unknown and subject to unmeasured confounding (Γ0 = 2 in (26)). n = 1000.
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+−0.2
+−0.1
+0.0
+0.1
+0.2
+Miscoverage gap
+n = 250
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Target α
+−0.2
+−0.1
+0.0
+0.1
+0.2
+n = 500
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+−0.2
+−0.1
+0.0
+0.1
+0.2
+n = 1000
+Gamma Γ
+1
+2
+3
+Type
+Proposed
+Benchmark
+Figure 6: Miscoverage gaps (22) across α, when the past policy is unknown and subject to unmeasured
+confounding. Dashed curve denotes the benchmark (23) which does not take confounding into account.
+11
+
+6
+Conclusion
+We have considered the problem of off-policy evaluation, i.e., drawing valid inferences of a target policy
+using past observational data obtained under a different decision process with a, possibly unknown, policy.
+Using the marginal sensitivity model, we derive a sample-splitting method that provides limit curves with
+finite-sample coverage guarantees and, importantly, takes into account model misspecifications and unmea-
+sured confounding. The validity, informativeness, and conservativeness of the resulting limit curves were
+demonstrated in the numerical experiments.
+Using this method in any specific problem, we can specify range of credible model assumptions and assess the
+corresponding degrees of informativeness of the limits, which are guaranteed to be valid up to any specified
+odds ratio bound.
+References
+Heejung Bang and James M Robins. Doubly robust estimation in missing data and causal inference models.
+Biometrics, 61(4):962–973, 2005.
+Alina Beygelzimer, Sanjoy Dasgupta, and John Langford. Importance weighted active learning. In Proceed-
+ings of the 26th annual international conference on machine learning, pp. 49–56, 2009.
+Yash Chandak, Scott Niekum, Bruno da Silva, Erik Learned-Miller, Emma Brunskill, and Philip S Thomas.
+Universal off-policy evaluation.
+Advances in Neural Information Processing Systems, 34:27475–27490,
+2021.
+Miroslav Dudík, John Langford, and Lihong Li. Doubly robust policy evaluation and learning. In Proceedings
+of the 28th International Conference on International Conference on Machine Learning, pp. 1097–1104,
+2011.
+Alexander D’Amour, Peng Ding, Avi Feller, Lihua Lei, and Jasjeet Sekhon. Overlap in observational studies
+with high-dimensional covariates. Journal of Econometrics, 221(2):644–654, 2021.
+Daniel G Horvitz and Donovan J Thompson. A generalization of sampling without replacement from a finite
+universe. Journal of the American statistical Association, 47(260):663–685, 1952.
+Audrey Huang, Liu Leqi, Zachary Lipton, and Kamyar Azizzadenesheli. Off-policy risk assessment in con-
+textual bandits. Advances in Neural Information Processing Systems, 34:23714–23726, 2021.
+Ying Jin, Zhimei Ren, and Emmanuel J Candès. Sensitivity analysis of individual treatment effects: A
+robust conformal inference approach. arXiv preprint arXiv:2111.12161, 2021.
+Nathan Kallus. Balanced policy evaluation and learning. Advances in neural information processing systems,
+31, 2018.
+Nathan Kallus and Angela Zhou. Minimax-optimal policy learning under unobserved confounding. Manage-
+ment Science, 67(5):2870–2890, 2021.
+Joseph DY Kang and Joseph L Schafer.
+Demystifying double robustness: A comparison of alternative
+strategies for estimating a population mean from incomplete data.
+Statistical science, 22(4):523–539,
+2007.
+John Langford and Tong Zhang. The epoch-greedy algorithm for contextual multi-armed bandits. Advances
+in neural information processing systems, 20(1):96–1, 2007.
+Tor Lattimore and Csaba Szepesvári. Bandit algorithms. Cambridge University Press, 2020.
+Jing Lei and Larry Wasserman. Distribution-free prediction bands for non-parametric regression. Journal
+of the Royal Statistical Society: Series B (Statistical Methodology), 76(1):71–96, 2014.
+12
+
+Jing Lei, Max G’Sell, Alessandro Rinaldo, Ryan J Tibshirani, and Larry Wasserman.
+Distribution-free
+predictive inference for regression. Journal of the American Statistical Association, 113(523):1094–1111,
+2018.
+Charles F Manski. Identification problems in the social sciences and everyday life. Southern Economic
+Journal, 70(1):11–21, 2003.
+Charles F Manski. Patient Care Under Uncertainty. Princeton University Press, 2019.
+Michael Oberst, Fredrik Johansson, Dennis Wei, Tian Gao, Gabriel Brat, David Sontag, and Kush Varshney.
+Characterization of overlap in observational studies. In International Conference on Artificial Intelligence
+and Statistics, pp. 788–798. PMLR, 2020.
+Muhammad Osama, Dave Zachariah, and Peter Stoica. Learning robust decision policies from observational
+data. Advances in Neural Information Processing Systems, 33:18205–18214, 2020.
+Jonas Peters, Dominik Janzing, and Bernhard Schölkopf. Elements of causal inference: foundations and
+learning algorithms. The MIT Press, 2017.
+Min Qian and Susan A Murphy.
+Performance guarantees for individualized treatment rules. Annals of
+statistics, 39(2):1180, 2011.
+Yaniv Romano, Evan Patterson, and Emmanuel Candes. Conformalized quantile regression. In Advances in
+Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019.
+Paul R Rosenbaum and Donald B Rubin. The central role of the propensity score in observational studies
+for causal effects. Biometrika, 70(1):41–55, 1983.
+Andrea Rotnitzky, Quanhong Lei, Mariela Sued, and James M Robins. Improved double-robust estimation
+in missing data and causal inference models. Biometrika, 99(2):439–456, 2012.
+Donald B Rubin. Using propensity scores to help design observational studies: application to the tobacco
+litigation. Health Services and Outcomes Research Methodology, 2(3):169–188, 2001.
+Joseph L Schafer and Joseph Kang. Average causal effects from nonrandomized studies: a practical guide
+and simulated example. Psychological methods, 13(4):279, 2008.
+Henry Scheffe and John W Tukey. Non-parametric estimation. i. validation of order statistics. The Annals
+of Mathematical Statistics, 16(2):187–192, 1945.
+Glenn Shafer and Vladimir Vovk. A tutorial on conformal prediction. Journal of Machine Learning Research,
+9(3), 2008.
+Alex Strehl, John Langford, Lihong Li, and Sham M Kakade. Learning from logged implicit exploration
+data. Advances in neural information processing systems, 23, 2010.
+Zhiqiang Tan. A distributional approach for causal inference using propensity scores. Journal of the American
+Statistical Association, 101(476):1619–1637, 2006.
+Muhammad Faaiz Taufiq, Jean-Francois Ton, Rob Cornish, Yee Whye Teh, and Arnaud Doucet.
+Con-
+formal off-policy prediction in contextual bandits.
+In Alice H. Oh, Alekh Agarwal, Danielle Bel-
+grave, and Kyunghyun Cho (eds.), Advances in Neural Information Processing Systems, 2022.
+URL
+https://openreview.net/forum?id=IfgOWI5v2f.
+Ryan J Tibshirani, Rina Foygel Barber, Emmanuel Candes, and Aaditya Ramdas. Conformal prediction un-
+der covariate shift. In Advances in Neural Information Processing Systems, volume 32. Curran Associates,
+Inc., 2019.
+Anastasios A Tsiatis, Marie Davidian, Shannon T Holloway, and Eric B Laber. Dynamic treatment regimes:
+Statistical methods for precision medicine. Chapman and Hall/CRC, 2019.
+13
+
+Vladimir Vovk. Conditional validity of inductive conformal predictors. In Asian conference on machine
+learning, pp. 475–490. PMLR, 2012.
+Vladimir Vovk, Alexander Gammerman, and Glenn Shafer. Algorithmic learning in a random world. Springer
+Science & Business Media, 2005.
+Abraham Wald. An extension of wilks’ method for setting tolerance limits. The Annals of Mathematical
+Statistics, 14(1):45–55, 1943.
+Lan Wang, Yu Zhou, Rui Song, and Ben Sherwood. Quantile-optimal treatment regimes. Journal of the
+American Statistical Association, 113(523):1243–1254, 2018.
+D. Westreich. Epidemiology by Design: A Causal Approach to the Health Sciences. Oxford University Press,
+Incorporated, 2019. ISBN 9780190665760. URL https://books.google.se/books?id=5R2yDwAAQBAJ.
+Samuel S Wilks. Determination of sample sizes for setting tolerance limits. The Annals of Mathematical
+Statistics, 12(1):91–96, 1941.
+Baqun Zhang, Anastasios A Tsiatis, Marie Davidian, Min Zhang, and Eric Laber.
+Estimating optimal
+treatment regimes from a classification perspective. Stat, 1(1):103–114, 2012.
+Yingqi Zhao, Donglin Zeng, A John Rush, and Michael R Kosorok. Estimating individualized treatment rules
+using outcome weighted learning. Journal of the American Statistical Association, 107(499):1106–1118,
+2012.
+14
+
diff --git a/_dFAT4oBgHgl3EQfqx1t/content/tmp_files/load_file.txt b/_dFAT4oBgHgl3EQfqx1t/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ef7a97a3ed55a27ee8123910e2ce0959f8099166
--- /dev/null
+++ b/_dFAT4oBgHgl3EQfqx1t/content/tmp_files/load_file.txt
@@ -0,0 +1,695 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf,len=694
+page_content='Offline Policy Evaluation with Out-of-Sample Guarantees  Sofia Ek  sofia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='ek@it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='uu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='se  Department of Information Technology  Uppsala University  Dave Zachariah  dave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='zachariah@it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='uu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='se  Department of Information Technology  Uppsala University  Abstract  We consider the problem of evaluating the performance of a decision policy using past  observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The outcome of a policy is measured in terms of a loss or disutility (or  negative reward) and the problem is to draw valid inferences about the out-of-sample loss  of the specified policy when the past data is observed under a, possibly unknown, policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Using a sample-splitting method, we show that it is possible to draw such inferences with  finite-sample coverage guarantees that evaluate the entire loss distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Importantly, the  method takes into account model misspecifications of the past policy – including unmeasured  confounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The evaluation method can be used to certify the performance of a policy using  observational data under an explicitly specified range of credible model assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  1  Introduction  In this work, we are interested in evaluating the performance of a decision policy, denoted π, which chooses  an action A from a discrete action set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Each action A is taken in a context with observable covariates X and  incurs a real-valued loss L (aka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' disutility or negative reward).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Such policies are considered in contextual  bandit problems and precision medicine (Langford & Zhang, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Qian & Murphy, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Lattimore &  Szepesvári, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Tsiatis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' For instance, A may be one of several treatment options for a patient  with observable characteristics X and L measures the severity of the outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  A target policy π can be evaluated using experimental data obtained from trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Such experiments are,  however, often costly and may lead to rather restrictive sample sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Moreover, in safety-critical applications  it is often unethical to test new policies without severe restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' A more fundamental inferential problem,  however, is the lack of ‘external’ validity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', the limited ability to extrapolate from the trial population  to the intended target population leads to invalid inferences (Westreich, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Manski, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The main  alternative is off-policy evaluation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', using observational data from a past decision process to infer the  performance of the target policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' This requires that the past process is modelled without systematic errors  – by assuming well-specified models and no unmeasured confounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The credibility of these assumptions  therefore determine the ‘internal’ validity of inferences about π from observational data (Manski, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Inferences that lack validity are particularly serious when evaluating π in decision processes that are costly  or safety-critical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In such cases even inferences that are asymptotically valid with increasing sample size  may not be adequate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Moreover, when the resulting distribution of losses is skewed or is widely dispersed,  its tails are important to evaluate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Then inferring the expected loss Eπ[L], as is commonly done, provides  a very limited evaluation of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' For instance, the average loss in a population maybe low but the tail losses  are unacceptable (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In such applications, we are more concerned with providing valid  certifications of the overall performance (see Figure 1a), rather than precise but invalid inferences of a single  distributional parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  In this paper we propose a method for evaluating a specified target policy using observational data that  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='08649v1  [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='ML]  20 Jan 2023  provides finite-sample coverage guarantees for the out-of-sample loss,  evaluates the entire loss distribution instead of the expected value,  and takes model misspecification, including unmeasured confounding, into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  ℓα  0%  20%  40%  60%  80%  100%  1 − α  π  π1  π0  (a) Evaluation of out-of-sample loss L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  0%  20%  40%  60%  80%  100%  Target coverage  0%  20%  40%  60%  80%  100%  Actual coverage  π  π1  π0  (b) Evaluation of coverage of limit curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Figure 1: Evaluating out-of-sample losses under target policy with binary decisions A ∈ {0, 1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Policies π0  and π1 correspond to ‘treat none’ (A ≡ 0) and ‘treat all’ (A ≡ 1), respectively, while π denotes a policy that  adapts to context X, see Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (a) Each curve certifies that a new loss L falls below  the limit ℓα with a probability of least 1 − α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The certified performance of the adaptive policy π dominates  those of the alternative policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (b) Evaluation of actual coverage, that is, the probability of L ≤ ℓα, across  target coverage 1 − α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  2  Problem formulation  We consider a target policy π for deciding actions A in different contexts, which are described by observed  and unobserved covariates X and U, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The policy can be either deterministic or random, and  corresponds to a distribution pπ(A|X), which can be conditional on observed covariates X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Our aim is to  evaluate the losses L that result from applying any given π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Each instance of contextual covariates, action  and loss, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', (X, U, A, L), is drawn independently from a target distribution pπ(X, U, A, L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' At our disposal  is an observational data set  D =  �  (Xi, Ai, Li)  �n  i=1,  (1)  and our goal is to use it to characterize the out-of-sample loss Ln+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Specifically, for any miscoverage level  α ∈ (0, 1), we seek an informative limit ℓα(D) on the loss such that  Pπ  �  Ln+1 ≤ ℓα(D)  �  ≥ 1 − α,  (2)  In other words, ℓα(D) evaluated across α yields a finite-sample performance certification of π as is illustrated  in Figure 1a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Unlike a single point estimate, the limit curve characterizes the distribution of losses under π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The causal structure of the decision process is illustrated in Figure 2a and the target distribution admits a  causal factorization  pπ(X, U, A, L) = p(X, U) pπ(A|X) p(L|A, X, U),  (3)  where p(X, U) and p(L|A, X, U) are unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The central challenge in off-policy evaluation of π is that (1)  is not sampled from (3) but from a shifted training distribution which admits a causal factorization  p(X, U, A, L) = p(X, U) p(A|X, U) p(L|A, X, U),  (4)  2  where p(A|X, U) characterizes a different, past policy (aka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  behavioral policy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The causal structure is  illustrated in Figure 2b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' If the past policy were known, it is possible to adjust for the distribution shift from  training to target distribution using the ratio  pπ(X, U, A, L)  p(X, U, A, L) ≡ pπ(A|X)  p(A|X, U) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  (5)  This is feasible in certain problems with fully automated decision-making, such as online recommendation  systems, where the past policy is designed using observable covariates only, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', p(A|X, U) ≡ p(A|X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In more  general problems, however, we have only a nominal model of the past policy �p(A|X) (aka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' propensity model),  typically estimated from prior observable data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The nominal model may therefore diverge from p(A|X, U)  due to various modelling errors that persist even in the large-sample scenario: model misspecification and  unmeasured confounding via U (Peters et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Westreich, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Here we follow the marginal sensitivity  methodology of (Tan, 2006) and characterize the model divergence with respect to the odds of taking action  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' That is, the nominal odds diverge from the unknown odds by some bounded factor Γ ≥ 1 as follows:  1  Γ ≤  p(A|X, U)  1 − p(A|X, U)  �  ��  �  unknown odds  �  �p(A|X)  1 − �p(A|X)  �  ��  �  nominal odds  ≤ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  (6)  When the bound equals Γ = 1, the nominal model is perfectly specified and there is no unmeasured con-  founding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In general, we consider all cases where the nominal odds diverge by at most a factor Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  In summary, the problem we consider is to construct a limit ℓα(D) for target policy π using training data  D and a nominal model �p(A|X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The resulting limit should satisfy the finite-sample guarantee (2) across  all miscoverage levels α, and thereby certify the target policy performance for any specified bound Γ in  (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' This enables a robust off-policy evaluation of target policies using observational data, since it can be  performed across a range of credible odds bounds Γ as we will illustrate in the numerical experiments below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  By increasing the odds bound Γ, the credibility of our assumptions on �p(A|X) increases, but the strength of  our conclusions about Ln+1 decrease, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (Manski, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The trade-off between credibility of assumptions  and informativeness of inferences will be quantified as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  X  A  L  U  (a) Causal structure that yields target distribution (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  X  A  L  U  (b) Causal structure that yields training distribution (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Figure 2: Directed acyclic diagrams (DAGs) representing the causal structure of decision process under (a)  target policy and (b) past policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In (b), both contextual covariates (X, U) may affect actions A as well as  the outcome loss L and thus U gives rise to unmeasured confounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  3  Background  We situate the problem considered in this paper and our proposed method within the context of off-policy  evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Expected loss: In most off-policy evaluation literature, the target quantity is the unknown expected loss  Eπ[L] of policy π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' A standard estimator of the mean, that dates back to Horvitz & Thompson (1952), is  based on inverse propensity weighting:  VIPW(D) = 1  n  n  �  i=1  �w(Xi, Ai) Li,  (7)  3  where �w(X, A) = pπ(A|X)  �p(A|X) is a model of (5), see for instance (Rosenbaum & Rubin, 1983;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Beygelzimer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=',  2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Qian & Murphy, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Kallus, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We note that the estimator  is unbiased when Γ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' An alternative standard estimator is based on regression modeling:  VRM(D) = 1  n  n  �  i=1  �  a∈A  pπ(a|Xi) �ℓ(a, Xi),  (8)  where �ℓ(A, X) is a model of E[L|A, X].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The approaches in (7) and (8) have complementary strenghts and weaknesses based on the challenges of  modelling the past policy or the conditional mean of losses, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Even when models are well-  specified, the accuracy of the estimators depend highly on the overlap of covariates X across decisions A  in the training data Oberst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D’Amour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' When the overlap is weak, the variance  of VIPW(D) can become excessively large, even when it is unbiased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' This can be mitigated by clipping the  weights (Rubin, 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Kang & Schafer, 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Schafer & Kang, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Strehl et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  When the models �w(X, A) or �ℓ(A, X) are systematically in error, however, their corresponding estimators  are biased and may invalidate the evaluation of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The ‘doubly robust’ estimator  VDR(D) = 1  n  n  �  i=1  �w(Xi, Ai)  �  Li − �ℓ(Ai, Xi)  �  +  �  a∈A  pπ(a|Xi) �ℓ(a, Xi),  is one way to protect against one of the models being misspecified and reduces the estimator variance provided  �ℓ(A, X) is sufficiently accurate (Bang & Robins, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Dudík et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Rotnitzky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Distribution of losses: When loss distribution is highly skewed and/or the tails are wide, the expected loss  can be inadequate to evaluate policies, especially in high-stakes problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' There are alternative parameters  of the loss distribution, decribed by the cumulative distribution function F(ℓ) = Pπ{Ln+1 ≤ ℓ} (cdf), that  one can consider in such problems, such as the Conditional Value at Risk or a quantile (Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Chandak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Off-policy evaluation of π with respect to some alternative parameter can be achieved using cdf-estimators  that are analogous to the mean estimators above, see (Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In analogy to (7), the inverse  propensity weighted cdf-estimator  �FIPW(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D) = 1  n  n  �  i=1  �w(Xi, Ai) 1(Li ≤ ℓ),  (9)  is point-wise unbiased when Γ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Similar to (8), the estimator  �FRM(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D) = 1  n  n  �  i=1  �  a∈A  pπ(a|Xi) �c(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' a, Xi),  requires a model �c(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' a, x) of the conditional distribution P{L ≤ ℓ|A, X}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' To mitigate against model mis-  specification that threaten the validity of the evaluation of π, one can use the ‘doubly robust’ estimator  �FDR(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D) = 1  n  n  �  i=1  �w(Xi, Ai)  �  1(Li ≤ ℓ) − �c(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Ai, Xi)  �  +  �  a∈A  pπ(a|Xi) �c(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' a, Xi),  which protects against one of the models being in misspecified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' While this estimator is consistent, it is not  guaranteed yield a valid cdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  In this paper, we are interested in limiting the out-of-sample loss Ln+1 and the quantile is the smallest ℓα  such that Pπ{Ln+1 ≤ ℓα} ≥ 1 − α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' It can be estimated as  ℓα(D) = inf  �  ℓ : �F(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D) ≥ 1 − α  �  ,  4  using a cdf-estimator above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Distribution-free inference: Derivations of finite-sample valid, nonparametric limits on random variables  date back to the works of Wilks (1941);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Wald (1943);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Scheffe & Tukey (1945).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' More recently, the related  methodology of conformal prediction has focused on developing covariate-specific prediction regions (Vovk  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Shafer & Vovk, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Vovk, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' See Lei & Wasserman (2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Romano  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2019) for further developments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Tibshirani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2019) adapt the methodology to be valid also under  known covariate shifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' This result was subsequently used to provide context-specific prediction intervals for  any given policy π that are statistically valid under the assumption that the past policy p(A|X, U) is known  Osama et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Taufiq et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The marginal sensitivity methodology developed in Tan (2006) enables us to specify a more credible range  of assumptions using (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' This methodology was used for robust policy learning in Kallus & Zhou (2021)  and sensitivity analysis of treatment effects in Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2021) under unobserved confounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' This paper  considers the overall performance of π, similar to Huang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  However, we focus on ensuring  inferences on the out-of-sample losses that are valid even with finite training data and under systematic  modelling errors – including unobserved confounding – using a sample-splitting technique that leverages  results derived in Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  4  Method  We show that one can limit the out-of-sample losses under π using a sample-splitting technique and by  bounding the unknown ratio in (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  For any specified odds bound Γ ≥ 1 in (6), we have that the ratio in (5) is bounded as:  W ≤ pπ(X, U, A, L)  p(X, U, A, L) ≤ W,  (10)  where the bounds equal  W = pπ(A|X) ·  �  1 + Γ−1�  �p(A|X  �−1 − 1)  �  and  W = pπ(A|X) ·  �  1 + Γ  �  �p(A|X)−1 − 1  ��  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  (11)  That is, the bounds are functions of X and A drawn from the training distribution (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  We randomly split the training data (1) into two separate sets,  D = D0 ∪ D1,  with samples sizes n0 and n − n0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The first set D0 is used to construct a set of upper bounds  �  W i  �n0  i=1 via (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The remaining set D1 is used to form the function  �F(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D1, w) =  �n  i=n0+1 W i1(Li ≤ ℓ)  �n  i=n0+1 W i1(Li ≤ ℓ) + �n  i=n0+1 W i1(Li > ℓ) + w,  (12)  as a proxy for the unknown cdf of the out-of-sample loss Ln+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' As the following result shows, (12) enables  the construction of a valid limit ℓα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Define the quantile function of (12) as  �F −1(·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D1, w) = inf  �  ℓ : �F(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D1, w) ≥ ·  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  For any miscoverage probability α ∈ (0, 1), construct the limit  ℓα(D) =  min  β:0<β<α  �F −1  �1 − α  1 − β ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D1, wβ(D0)  �  ,  (13)  5  where  wβ(D0) =  �  W [⌈(n0+1)(1−β)⌉],  ⌈(n0 + 1)(1 − β)⌉ ≤ n0,  ∞,  otherwise,  (14)  and W [k] denotes the kth order statistic of (W i)n0  i=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Then ℓα(D) limits the out-of-sample loss Ln+1 with a probability of at least 1 − α as specified in (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1  Implementation  We note that (12) is piecewise constant and can readily be represented using a vector with n − n0 elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The limit curve can be evaluated across a discrete grid of miscoverage levels α and the computation is  summarized in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Also, note that wβ as a function of β changes in discrete steps in (14), therefore  the relevant values of β form a discrete set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Algorithm 1 Limit curve of policy π  Input: Training data D, model �p(A|X), bound Γ ≥ 1 and sample split size n0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  1: Randomly split D into D0 and D1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  2: for α ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' , 1} do  3:  for β ∈ {0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' , α} do  4:  Compute wβ using (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  5:  Compute ℓα,β = inf  �  ℓ : �F(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D1, wβ) ≥ 1−α  1−β  �  using (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  6:  end for  7:  Set ℓα to the smallest ℓα,β above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  8:  Store (α, ℓα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  9: end for  Output: {(α, ℓα)}  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  Derivation of result  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The first part of the proof builds on techniques used to derive weighted conformal prediction intervals  in Tibshirani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Let us consider a sequence of n − n0 samples drawn from (4) followed by a new sample drawn from (3), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=',  D+ =  �  (Xn0+1, Un0+1, An0+1, Ln0+1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' , (Xn, Un, An, Ln), (Xn+1, Un+1, An+1, Ln+1)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The joint distribution of this sequence can be expressed using:  n  �  i=n+  p(xi, ui, ai, ℓi) · p(xn+1, un+1, an+1, ℓn+1)wn+1 = p(D+)wn+1 = p(S+)wn+1,  where n+ = n0 + 1 for notational simplicity, S+ is an unordered set of elements from D+, and the weight  wi = pπ(xi, ui, ai, ℓi)  p(xi, ui, ai, ℓi) ,  is the (unobservable) ratio (5) that quantifies the distribution shift from training to target distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We  shall use the expression for the joint distribution to derive the distribution function for the new loss Ln+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Suppose we are given unordered set S+ alone, then the particular sequence D+ is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Let Ei denote  the event that the sample (Xn+1, Un+1, An+1, Ln+1) equals the ith sample (xi, ui, ai, ℓi) in the unknown  sequence D+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We consider all possible sequences D+ obtained by permutations σ of elements in the set S+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The joint probability the event Ei and S+ is then  P{Ei, S+} =  �  σ:σ(n+1)=n+i  p(S+)wi = p(S+)win!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='.  6  The conditional probability of event Ei can now be expressed as  pi = P{Ei|S+} =  P{Ei, S+}  �n+1  j=n+ P{Ej, S+}  =  wi  �n+1  j=n+ wj  ,  where the first equality follows from the law of total probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The probability that the loss Ln+1 of the  new sample equals ℓi, when conditioning on the unordered set S+, is equal to  P{Ln+1 = ℓi|S+} = P{Ei|S+} = pi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Thus conditional on S+, the new loss Ln+1 follows the cdf:  P{Ln+1 ≤ ℓ|S+} =  n+1  �  i=n+  pi1(ℓi ≤ ℓ) =  �n+1  i=n+ wi1(Li ≤ ℓ)  �n+1  i=n+ wi  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  (15)  Before marginalizing out S+ from (15), we consider a limit ℓ that is a function of the observable elements in  S+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' For this part, we will build on the proof technique in (Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2021, thm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Specifically, using (12) we define the following limit:  ℓα(D1, W n+1) = inf  �  ℓ : �F(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D1, W n+1) ≥ 1 − α  1 − β  �  ,  (16)  for any 0 < β < α, where W n+1 ≥ Wn+1 is given in (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Now insert the limit ℓα(D1, W n+1) into (15) and  use the law of total expectation to marginalize out S+:  P{Ln+1 ≤ ℓα(D1, W n+1)} = E  �  Pπ{Ln+1 ≤ ℓα(D1, W n+1)|S+}  �  = E  ��n+1  i=n+ Wi1(Li ≤ ℓα(D1, W n+1))  �n+1  i=n+ Wi  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  We now proceed to lower bound this probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Note that by construction:  E  �  �F(ℓα;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D1, W n+1)  �  = E  �  �  i∈D1 W i1(Li ≤ ℓα)  �  i∈D1 W i1(Li ≤ ℓα) + �  i∈D1 W i1(Li > ℓα) + W n+1  �  ≥ (1 − α)  (1 − β).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Using this expression,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' we have that  P{Ln+1 ≤ ℓα(D1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' W n+1)} − (1 − α)  (1 − β)  ≥ E  ��n+1  i=n+ Wi1(Li ≤ ℓα)  �n+1  i=n+ Wi  �  − E  �  �n  i=n+ W i1(Li ≤ ℓα)  �n  i=n+ W i1(Li ≤ ℓα) + �n  i=n+ W i1(Li > ℓα) + W n+1  �  = E  �  �  (∗)  ��n+1  i=n+ Wi  � ��n  i=n+ W i1(Li ≤ ℓα) + �n  i=n+ W i1(Li > ℓα) + W n+1  �  �  � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='where  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='(∗) =  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='� n+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi1(Li ≤ ℓα)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='W i1(Li ≤ ℓα) +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='W i1(Li > ℓα) + W n+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='W i1(Li ≤ ℓα)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�� n+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='≥  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi1(Li ≤ ℓα)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='W i1(Li ≤ ℓα) +  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='W i1(Li > ℓα) + W n+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='W i1(Li ≤ ℓα)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�� n+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='≥  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi1(Li ≤ ℓα)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='W i1(Li > ℓα) + W n+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='W i1(Li ≤ ℓα)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi1(Li > ℓα) + Wn+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='≥  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi1(Li ≤ ℓα)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi1(Li > ℓα) + Wn+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='−  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi1(Li ≤ ℓα)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='��  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='n  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='i=n+  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='Wi1(Li > ℓα) + Wn+1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='= 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  using the bounds (10) on the fourth line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Therefore we obtain a valid limit:  P{Ln+1 ≤ ℓα(D1, W n+1)} ≥ (1 − α)  (1 − β).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  (17)  However, W n+1 depends on a new sample drawn from the training distribution and thus the limit is unusable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  In lieu of W n+1, we use wβ(D0) in (14) to define the modified limit  ℓα(D) = inf  �  ℓ : �F(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D1, wβ(D0)) ≥ 1 − α  1 − β  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  (18)  Comparing it with (16), we see that  ℓα(D) ≥ ℓα(D1, W n+1),  (19)  whenever W n+1 ≤ wβ(D0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' By the construction in (14), the probability of this event is lower bounded by  P{W n+1 ≤ wβ(D0)} ≥ 1 − β,  (20)  see (Vovk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  We use this property to lower bound the probability of Ln+1 ≤ ℓα(D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' First note that  P{Ln+1 ≤ ℓα(D)} = P{Ln+1 ≤ ℓα(D) | W n+1 ≤ wβ(D0)} P{W n+1 ≤ wβ(D0)}  + P{Ln+1 ≤ ℓα(D) | W n+1 > wβ(D0)} P{ W n+1 > wβ(D0)}  ≥ P{Ln+1 ≤ ℓα(D) | W n+1 ≤ wβ(D0)} P{W n+1 ≤ wβ(D0)} + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The first factor can be lower bounded using (19), so that  P{Ln+1 ≤ ℓα(D)} ≥ P{Ln+1 ≤ ℓα(D1, W n+1) | W n+1 ≤ wβ(D0)} P{W n+1 ≤ wβ(D0)}  = P{Ln+1 ≤ ℓα(D1, W n+1)} P{W n+1 ≤ wβ(D0)}  ≥ (1 − α)  (1 − β) P{W n+1 ≤ wβ(D0)}  ≥ 1 − α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  (21)  The second line follows from using sample splitting, which ensures that Ln+1 ≤ ℓα(D1, W n+1) and W n+1 ≤  wβ(D0) are independent events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The third and fourth lines follow from (17) and (20), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Since  (21) holds for any 0 < β < α, we choose β in (18) that yields the tightest limit, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  8  5  Numerical experiments  In the experiments below, we evaluate policies using the limit curves (α, ℓα).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Note that the extremum loss  ℓmax in a given problem provides a valid but uninformative limit across all α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We therefore quantify the  informativeness of a valid limit curve as follows:  Informativeness = 1 − α∗, where α∗ = sup{α : ℓα < ℓmax}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  That is, the lowest coverage probability at which we can informatively certify the performance of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We can  therefore quantify increasing the credibility of our model assumption by Γ affects the informativeness of the  limit curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We also consider the coverage probability of the curves:  Miscoverage gap = Pπ{Ln+1 > ℓα(D)} − α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  (22)  When this gap is positive, the limit is conservative and when the gap is negative the limit is invalid,  respectively, at level α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  A natural benchmark for the proposed limit (13) in this problem setting is the estimated quantile  ℓα(D) = inf  �  ℓ : �FIPW(ℓ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' D) ≥ 1 − α  �  ,  (23)  using the inverse propensity weighted cdf-estimator (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  In all examples below, the limit (13) is computed using sample splits of equal size, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', n0 = n/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1  Synthetic data  In the first example, we consider synthetic data in order to evaluate the coverage of the derived limit curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  We use a simulation setting similar to Jin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The miscoverage gap (22) is estimated by Monte  Carlo simulation using n′ = 1000 independent samples over N = 1000 independent runs, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', in total 106  samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  We consider a population of individuals with two-dimensional covariates distributed uniformly as  X =  �X1  X2  �  ∼ U(0, 1)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The actions are binary A ∈ {0, 1} corresponding to ‘not treat’ and ‘treat’, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We want to evaluate  a deterministic target policy, described by  pπ(A = 0|X) = 1(X1X2 ≥ τ),  (24)  for different τ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' That is, all individuals whose covariate product X1X2 falls below τ are treated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Note  that τ = 0 corresponds a ‘treat none’ policy (A ≡ 0 for all X) and τ = 1 corresponds to a ‘treat all’ policy  (A ≡ 1 for all X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' What can we say about the resulting losses under this policy using observational data  with sample sizes n ∈ {250, 500, 1000}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Case: Known past policy (Γ = 1) In the first scenario, we assume that the past policy is known exactly  and there is therefore no unmeasured confounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  For the training data, the past policy determined actions as a Bernoulli process, where  p(A = 0|X) ≡ �p(A = 0|X) = f  �  c(X1X2 + 1)  �  ,  c ∈  �1  2, 2  �  ,  (25)  and f(·) is the sigmoid function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The conditional loss distribution is given by  L|A = 0, X ∼ N(1 − X1X2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1)  and  L|A = 1, X ∼ N(X1X2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  9  We consider three configurations c of past policies (25), which yield inverse propensity weights in three  ranges:  1  p1(A|X) < 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='72 (c = 1/2),  1  p2(A|X) < 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='39 (c = 1), and  1  p3(A|X) < 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='6 (c = 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Thus we anticipate  p3(A|X) to be the most challenging case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Here we evaluate three target policies τ = {0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5, 1} in (24) and present their resulting limit curves using  data from different past policies (25) in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The differing dashed lines shows the corresponding past  policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The limit curves for a given target policy are very similar across training distributions and are  informative above the 90% level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The main difference is in the inferred tail losses and is notable for when  τ = 1 under the more challenging past policy p3(A|X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  We now turn to evaluating miscoverage gap (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Figure 4 presents gaps for target policy τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5 in (24).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  The solid lines illustrate the proposed method and the dashed lines show the benchmark (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We see that  the proposed method is slightly conservative, but remains valid for all α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' By contrast, the benchmark is not  valid in the tail of the distribution, but is less conservative for higher α in this well-specified case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  0%  20%  40%  60%  80%  100%  1 − α  p1(A|X)  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  ℓα  0%  20%  40%  60%  80%  100%  p2(A|X)  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  0%  20%  40%  60%  80%  100%  p3(A|X)  pπ(A|X)  τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  τ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  τ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  pπ = p  Figure 3: Limit curves (ℓα, 1 − α) when the past policy is known (Γ = 1) for three different potential target  policies (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' τ = {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0} in (24)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Dashed curve denotes the past policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' n = 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='150  Miscoverage gap  n = 250  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  Target α  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='150  n = 500  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='025  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='050  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='075  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='125  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='150  n = 1000  Past policy  p1(A|X)  p2(A|X)  p3(A|X)  Type  Proposed  Benchmark  Figure 4: Miscoverage gaps (22) across α, when the past policy is known (Γ = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Dashed curve denotes the  benchmark (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Case: Estimated past policy (Γ > 1) In the second scenario, we assume that we only have access to an  estimate �p(A|X) and that there is unmeasured confounding in the training distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' To render visually  distinct curves from the previous case, we consider here a rather extreme case of confounding following Jin  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  In this case we have an unobserved variable drawn as  U|X ∼ N(0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1(X1 + X2)),  and the loss L|A, X, U is generated as  L =  �  1 − X1X2 + U,  A = 0,  X1X2 + U,  A = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  10  We define the past policy in a manner that enables us to control the divergence from the nominal model  �p(A|X) in (25):  p(A = 0|X, U) = 1(U ≤ t(X))  �  1 + Γ−1  0  �  �p(A = 0|X  �−1 − 1)  �  + 1(U > t(X))  �  1 + Γ0  �  �p(A = 0|X)−1 − 1  ��  ,  (26)  where the threshold function t(X) is designed empirically to ensure that the resulting median loss of the  past policy for A = 1 is maximized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Our design of the past policy can be seen as a worst case among all  unknown past policies that diverge by a factor Γ0 in (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We fix Γ0 = 2 here, but treat it as unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  For clarity, we consider a ‘treat all’ target policy (τ = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Its limit curves, under different assumed odds  bounds Γ = {1, 2, 3}, are presented in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Note that under unmeasured confounding, the resulting  curves differ notably across the training distributions unlike in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' We see that under the first and  second distributions, the informativeness of all curves stays around the 90% level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' However, in the most  extreme third case, the informativeness drops to barely above the 60% level when we increase the credibility  of our model assumption to an odds bound of Γ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' This example illustrates an inherent trade-off between  credibility and informativeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Figure 6 validates our guarantees using data drawn from p1(A|X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' When Γ ≥ Γ0 = 2, the limit curves are  valid and as Γ increases to 3, the limits become quite conservative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Note that the conservativeness persists  even as the sample size n is increased fourfold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' For Γ = 1, there is no guarantee of coverage and in this worst  case scenario the limit curve is invalid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The benchmark does not take unmeasured confounding into account  and is consequently invalid throughout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0%  20%  40%  60%  80%  100%  1 − α  p1(A|X)  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  ℓα  0%  20%  40%  60%  80%  100%  p2(A|X)  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0%  20%  40%  60%  80%  100%  p3(A|X)  Gamma Γ  1  2  3  Figure 5: Limit curves (ℓα, 1 − α) for ‘treat all’ target policy using odds bounds Γ = {1, 2, 3}, when the past  policy is unknown and subject to unmeasured confounding (Γ0 = 2 in (26)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' n = 1000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  Miscoverage gap  n = 250  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  Target α  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  n = 500  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='2  n = 1000  Gamma Γ  1  2  3  Type  Proposed  Benchmark  Figure 6: Miscoverage gaps (22) across α, when the past policy is unknown and subject to unmeasured  confounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Dashed curve denotes the benchmark (23) which does not take confounding into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  11  6  Conclusion  We have considered the problem of off-policy evaluation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', drawing valid inferences of a target policy  using past observational data obtained under a different decision process with a, possibly unknown, policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Using the marginal sensitivity model, we derive a sample-splitting method that provides limit curves with  finite-sample coverage guarantees and, importantly, takes into account model misspecifications and unmea-  sured confounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The validity, informativeness, and conservativeness of the resulting limit curves were  demonstrated in the numerical experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Using this method in any specific problem, we can specify range of credible model assumptions and assess the  corresponding degrees of informativeness of the limits, which are guaranteed to be valid up to any specified  odds ratio bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  References  Heejung Bang and James M Robins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Doubly robust estimation in missing data and causal inference models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Biometrics, 61(4):962–973, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Alina Beygelzimer, Sanjoy Dasgupta, and John Langford.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Importance weighted active learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In Proceed-  ings of the 26th annual international conference on machine learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' 49–56, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Yash Chandak, Scott Niekum, Bruno da Silva, Erik Learned-Miller, Emma Brunskill, and Philip S Thomas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Universal off-policy evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Advances in Neural Information Processing Systems, 34:27475–27490,  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Miroslav Dudík, John Langford, and Lihong Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Doubly robust policy evaluation and learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In Proceedings  of the 28th International Conference on International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' 1097–1104,  2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Alexander D’Amour, Peng Ding, Avi Feller, Lihua Lei, and Jasjeet Sekhon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Overlap in observational studies  with high-dimensional covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Journal of Econometrics, 221(2):644–654, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Daniel G Horvitz and Donovan J Thompson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' A generalization of sampling without replacement from a finite  universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Journal of the American statistical Association, 47(260):663–685, 1952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Audrey Huang, Liu Leqi, Zachary Lipton, and Kamyar Azizzadenesheli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Off-policy risk assessment in con-  textual bandits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 34:23714–23726, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Ying Jin, Zhimei Ren, and Emmanuel J Candès.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Sensitivity analysis of individual treatment effects: A  robust conformal inference approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' arXiv preprint arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='12161, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Nathan Kallus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Balanced policy evaluation and learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Advances in neural information processing systems,  31, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Nathan Kallus and Angela Zhou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Minimax-optimal policy learning under unobserved confounding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Manage-  ment Science, 67(5):2870–2890, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Joseph DY Kang and Joseph L Schafer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Demystifying double robustness: A comparison of alternative  strategies for estimating a population mean from incomplete data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Statistical science, 22(4):523–539,  2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  John Langford and Tong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The epoch-greedy algorithm for contextual multi-armed bandits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Advances  in neural information processing systems, 20(1):96–1, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Tor Lattimore and Csaba Szepesvári.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Bandit algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Cambridge University Press, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Jing Lei and Larry Wasserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Distribution-free prediction bands for non-parametric regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Journal  of the Royal Statistical Society: Series B (Statistical Methodology), 76(1):71–96, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  12  Jing Lei, Max G’Sell, Alessandro Rinaldo, Ryan J Tibshirani, and Larry Wasserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Distribution-free  predictive inference for regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Journal of the American Statistical Association, 113(523):1094–1111,  2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Charles F Manski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Identification problems in the social sciences and everyday life.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Southern Economic  Journal, 70(1):11–21, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Charles F Manski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Patient Care Under Uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Princeton University Press, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Michael Oberst, Fredrik Johansson, Dennis Wei, Tian Gao, Gabriel Brat, David Sontag, and Kush Varshney.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Characterization of overlap in observational studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In International Conference on Artificial Intelligence  and Statistics, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' 788–798.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' PMLR, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Muhammad Osama, Dave Zachariah, and Peter Stoica.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Learning robust decision policies from observational  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Advances in Neural Information Processing Systems, 33:18205–18214, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Jonas Peters, Dominik Janzing, and Bernhard Schölkopf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Elements of causal inference: foundations and  learning algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The MIT Press, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Min Qian and Susan A Murphy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Performance guarantees for individualized treatment rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Annals of  statistics, 39(2):1180, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Yaniv Romano, Evan Patterson, and Emmanuel Candes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Conformalized quantile regression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In Advances in  Neural Information Processing Systems, volume 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Paul R Rosenbaum and Donald B Rubin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The central role of the propensity score in observational studies  for causal effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Biometrika, 70(1):41–55, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Andrea Rotnitzky, Quanhong Lei, Mariela Sued, and James M Robins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Improved double-robust estimation  in missing data and causal inference models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Biometrika, 99(2):439–456, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Donald B Rubin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Using propensity scores to help design observational studies: application to the tobacco  litigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Health Services and Outcomes Research Methodology, 2(3):169–188, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Joseph L Schafer and Joseph Kang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Average causal effects from nonrandomized studies: a practical guide  and simulated example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Psychological methods, 13(4):279, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Henry Scheffe and John W Tukey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Non-parametric estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' validation of order statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The Annals  of Mathematical Statistics, 16(2):187–192, 1945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Glenn Shafer and Vladimir Vovk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' A tutorial on conformal prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Journal of Machine Learning Research,  9(3), 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Alex Strehl, John Langford, Lihong Li, and Sham M Kakade.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Learning from logged implicit exploration  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Advances in neural information processing systems, 23, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Zhiqiang Tan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' A distributional approach for causal inference using propensity scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Journal of the American  Statistical Association, 101(476):1619–1637, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Muhammad Faaiz Taufiq, Jean-Francois Ton, Rob Cornish, Yee Whye Teh, and Arnaud Doucet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Con-  formal off-policy prediction in contextual bandits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  In Alice H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Oh, Alekh Agarwal, Danielle Bel-  grave, and Kyunghyun Cho (eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' ), Advances in Neural Information Processing Systems, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  URL  https://openreview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='net/forum?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='id=IfgOWI5v2f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Ryan J Tibshirani, Rina Foygel Barber, Emmanuel Candes, and Aaditya Ramdas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Conformal prediction un-  der covariate shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In Advances in Neural Information Processing Systems, volume 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Curran Associates,  Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Anastasios A Tsiatis, Marie Davidian, Shannon T Holloway, and Eric B Laber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Dynamic treatment regimes:  Statistical methods for precision medicine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Chapman and Hall/CRC, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  13  Vladimir Vovk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Conditional validity of inductive conformal predictors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' In Asian conference on machine  learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' 475–490.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' PMLR, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Vladimir Vovk, Alexander Gammerman, and Glenn Shafer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Algorithmic learning in a random world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Springer  Science & Business Media, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Abraham Wald.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' An extension of wilks’ method for setting tolerance limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The Annals of Mathematical  Statistics, 14(1):45–55, 1943.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Lan Wang, Yu Zhou, Rui Song, and Ben Sherwood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Quantile-optimal treatment regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Journal of the  American Statistical Association, 113(523):1243–1254, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Westreich.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Epidemiology by Design: A Causal Approach to the Health Sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Oxford University Press,  Incorporated, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' ISBN 9780190665760.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' URL https://books.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='se/books?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='id=5R2yDwAAQBAJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Samuel S Wilks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Determination of sample sizes for setting tolerance limits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' The Annals of Mathematical  Statistics, 12(1):91–96, 1941.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Baqun Zhang, Anastasios A Tsiatis, Marie Davidian, Min Zhang, and Eric Laber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Estimating optimal  treatment regimes from a classification perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Stat, 1(1):103–114, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  Yingqi Zhao, Donglin Zeng, A John Rush, and Michael R Kosorok.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Estimating individualized treatment rules  using outcome weighted learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content=' Journal of the American Statistical Association, 107(499):1106–1118,  2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
+page_content='  14' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/_dFAT4oBgHgl3EQfqx1t/content/2301.08649v1.pdf'}
diff --git a/bNAzT4oBgHgl3EQfLPu9/content/tmp_files/2301.01112v1.pdf.txt b/bNAzT4oBgHgl3EQfLPu9/content/tmp_files/2301.01112v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cea43d2bf1e5ba08a234d5157c7155f73d4f0830
--- /dev/null
+++ b/bNAzT4oBgHgl3EQfLPu9/content/tmp_files/2301.01112v1.pdf.txt
@@ -0,0 +1,1206 @@
+arXiv:2301.01112v1  [quant-ph]  3 Jan 2023
+Time-Optimal Transport of a Harmonic Oscillator: Analytic Solution
+Gerhard C. Hegerfeldt1
+1Institut f¨ur Theoretische Physik, Universit¨at G¨ottingen,
+Friedrich-Hund-Platz 1, D-37077 G¨ottingen, Germany
+Motivated by the experimental transport of a trap with a quantum mechanical system modeled
+as a harmonic oscillator (h.o.) the corresponding classical problem is investigated. Protocols for
+the fastest possible transport of a classical h.o. in a wagon over a distance d are derived where
+both initially and finally the wagon is at rest and the h.o. is in its equilibrium position and also at
+rest. The acceleration of the wagon is assumed to be bounded. For fixed oscillator frequency Ω it is
+shown that there are in general three switches in the acceleration and for special values of Ω only
+one switch. In the latter case the optimal transport time is Tabs, that of a wagon without oscillator.
+The optimal transport time and the switch times are determined. It is shown that in some cases it
+is advantageous to go backwards for a while. In addition a time-dependent Ω(t), bounded by Ω±,
+is allowed. In this case the behavior depends sensitively on Ω± and is spelled out in detail. In
+particular, depending on Ω±, Tabs may be obtained in continuously many ways.
+PACS numbers:
+I.
+INTRODUCTION
+Adiabatic processes may serve to transform an initial
+state of a system to a proscribed final state. Such pro-
+cesses, however, are very slow and, in principle, infinitely
+slow. Protocols for speeding up the time development
+have been introduced in the past, with numerous appli-
+cations in quantum optics [1–22] and to classical systems,
+e.g.
+cranes [23].
+These methods include ‘shortcuts to
+adiabadicity’ (STA) [1–10], ‘counterdiabatic’ approaches
+[11–13] and the ‘fast-forward’ approach [15–18]. In gen-
+eral the above mentioned protocols yield a speed-up, but
+not necessarily the fastest possible time development.
+Other methods are combinations with control theory [24–
+26], cf. e.g. [19, 27, 28]. While a time development as
+fast as possible is often desired, other considerations like
+robustness and further conditions may prolong the re-
+sulting time duration.
+A particular example is the efficient transport of ul-
+tra cold atoms and ions by moving the confining trap.
+An atom or ion in a harmonic trap can be treated to
+good approximation as a quantum harmonic oscillator.
+For harmonic traps efficient protocols have been inves-
+tigated with STA and the invariant-based inverse engi-
+neering method to obtain transitionless evolutions under
+imposed constraints, faster than by an adiabatic process
+[6, 28]. It is therefore natural to ask how fast the trans-
+port of a quantum harmonic oscillator can be made. This
+depends of course on the particular question one is inter-
+ested in, for example a time-optimal transport a a har-
+monic oscillator under additional conditions.
+Insight for the quantum case may be obtained by ask-
+ing the same question for a classical harmonic oscillator.
+Therefore in this paper the time-optimal transport of a
+classical harmonic oscillator will be investigated.
+Consider a classical one-dimensional harmonic oscilla-
+tor (h.o.) without friction in the center of a long wagon,
+such as depicted in Fig. 1 where a small mass m is at-
+tached to a spring on the wagon. When the wagon is
+accelerated the h.o. will start to perform oscillations. In
+this case the frequency Ω of the h.o.
+depends on the
+spring constant and on m.
+The problem to be investigated is the following:
+(i) Initially the wagon is at rest and the h.o. is in its
+equilibrium position, also at rest.
+(ii) Then the wagon undergoes an acceleration a(t),
+where a(t) can vary between ±amax, until it has traveled
+a prescribed distance d.
+(iii) Upon arrival at the end point the system should
+again be in its initial state, i.e.
+the wagon should be
+at rest, and the h.o. should again be in its equilibrium
+position and at rest.
+The questions to be answered here are: Is this achiev-
+able, and if so what is the shortest time possible? Can
+this time be further lowered by allowing the h.o.
+fre-
+quency Ω to be time dependent, i.e. Ω(t)? Both ques-
+tions will be answered in the affirmative.
+a(t)
+everything
+at rest
+everything
+at rest
+a(t)
+FIG. 1: Oscillating mass m attached to a spring in an
+accelerated wagon
+The plan of the paper is as follows. First, in Section II,
+a fixed oscillator frequency will be considered, examples
+will be given and a complete solution of the problem and
+an explicit protocol for fixed Ω will be formulated. In
+Section III detailed proofs are provided. In Section IV the
+case of a time-dependent oscillator frequency is treated
+where Ω(t) satisfies Ω− ≤ Ω(t) ≤ Ω+, with arbitrary Ω±.
+The results and protocols will be seen to depend critically
+on the particular choice of Ω±. Finally, in Section V the
+results are summarized and discussed.
+
+2
+II.
+OPTIMAL PROTOCOL FOR FIXED
+OSCILLATOR FREQUENCY
+We consider a classical one-dimensional harmonic os-
+cillator on a long wagon. The position of the h.o. (i.e.
+mass point) relative to the wagon center will be denoted
+by xh and the position of the wagon center in the external
+rest frame by xw. When the wagon is accelerated with
+acceleration a(t), the mass point additionally experiences
+the corresponding inertial force −ma in the rest frame of
+the wagon so that one has
+¨xh = −Ω2xh − a
+(1)
+¨xw = a .
+It is assumed that a(t) can vary between ±amax.
+Example 1. With no h.o. present, to move a wagon a
+distance d in shortest time, with initial and final veloc-
+ity equal to zero, it is optimal to accelerate with amax
+for half the distance and then decelerate with −amax [25]
+(cf. solid line in Fig.2). The corresponding time Tabs(d),
+T 2
+abs = 4 d/amax, can at most be achieved, but not un-
+dercut, if a h.o. in the wagon is to be initially and finally
+at rest in its equilibrium position.
+Example 2. For special ’resonant values’ of Ω this time
+can indeed be achieved, e.g. for
+Ω = n Ωres(d) ,
+n = 1, 2, · · ·
+Ωres(d) =
+�
+4π2amax/d = 4π/Tabs .
+(2)
+To see this consider n = 1. Initially, the wagon and h.o.
+are at rest. Upon accelerating the wagon by amax the h.o.
+experiences, in the wagon frame, the additional inertial
+force −ma and starts to move to the left. During the
+time Tabs/2 it has just performed a single oscillation, has
+returned to its initial position in the wagon and is at rest
+relative to the wagon. In this instant, the acceleration
+of the wagon is reversed, the h.o. starts moving to the
+right and at a further time duration of Tabs/2 is back
+at rest at the initial position, with the wagon at rest
+and having traveled the distance d. For n > 1 one has
+correspondingly more oscillations.
+For fixed Ω a protocol to obtain the unique optimal
+transport time is constructed as follows.
+(i) For given d determine the unique optimal time tf by
+the equation
+d = 1
+4amax t2
+f [1 −
+8
+(Ω tf)2
+�
+arccos(cos2(Ω tf/4))
+�2] . (3)
+(ii) With wagon and oscillator at rest at t = 0, accelerate
+with amax until time 1
+2tf − t1 where t1, 0 ≤ Ωt1 ≤ π/2, is
+given by
+t1 = 1
+Ω arccos(cos2(Ω tf/4)) .
+(4)
+(iii) Decelerate with −amax until time 1
+2tf.
+(iv) Accelerate with amax until time 1
+2tf + t1.
+FIG. 2: Typical wagon velocities for the acceleration
+alternating between±1. Solid curve: No oscillator
+present and Example 2 with resonant Ω. Dashed and
+dotted curves: General Ω. For the dotted curve the
+wagon velocity becomes partially negative, i.e. the
+wagon moves backwards for some time.
+(v) Finally decelerate with −amax until time tf.
+Typical wagon velocities are depicted in Fig. 2. At the
+end the wagon is obviously at rest. The oscillator may
+perform several oscillations. That finally it is also again
+at rest and in its equilibrium position will be shown at
+the end of this section.
+In the next section it will be
+shown that tf is indeed the unique optimal time. The
+above protocol has a certain symmetry; there may, or
+may not, be other, nonsymmetric, protocols which lead
+to the same unique optimal time.
+Note that t1 = 0 if Ω tf = 4nπ, n = 1, 2, · · · , which
+recovers Example 2 with tf = Tabs. If t1 > 1
+4tf the wagon
+velocity temporarily becomes negative (dotted curve in
+Fig. 2), i.e. then it is advantageous to go backwards for
+a while. From Eqs. (3, 4) this is seen to happen if
+Ω2 < 1
+4 Ωres(d)2,
+(5)
+i.e. for small oscillator frequency. However, it can easily
+be shown that the backward motion will not go back as
+far as the original starting position of the wagon.
+If one plots d as a function of tf in Eq.(3) then tf
+as a function of d is given by reflecting it at the diag-
+onal. In dimensionless scaled variables, the solid curve
+in Fig.
+3 displays Ω tf as a function of d/dΩ where
+dΩ = 4π2amax Ω−2 is the distance for which Ω is reso-
+nant, i.e. Ωres(dΩ) = Ω. The dashed curve is the corre-
+sponding Tabs(d). Note that at d/dΩ = n2, n = 1, 2, · · ·
+the two transport times coincide, which is again Example
+2.
+For fixed d, one can also obtain tf as a function of Ω
+from Eq. (3). In dimensionless scaled variables the result
+is plotted in Fig. 4. It is seen that tf diverges for Ω → 0.
+This can be made more explicit by expanding Eq. (3) in
+terms of Ω tf. A short calculation gives, in dimensionless
+
+3
+1
+2
+3
+4
+5
+10
+15
+20
+25
+FIG. 3: Solid curve: Optimal transport time tf as a
+function of distance d in units of dΩ = 4π2amax Ω−2, for
+fixed Ω. Dashed curve: Tabs(d) (without oscillator). For
+d/dΩ = 1, 22, · · · the times coincide.
+scaled variables,
+tf/Tabs(d) ≈ {6/π2}1/4 (Ω/Ωabs(d))−1/2.
+(6)
+Replacing 6 by 5.3 in Eq.(6) one obtains an excel-
+lent approximation for tf/Tabs(d) in the range 0.05 ≤
+Ω/Ωabs(d) ≤ 0.7.
+0.5
+1.0
+1.5
+2.0
+2.5
+1.02
+1.04
+1.06
+1.08
+1.10
+1.12
+FIG. 4: Fixed d: Optimal transport time tf in units of
+Tabs(d) as a function of Ω in units of Ωabs(d).
+Protocol
+evaluation.
+For
+the
+oscillator
+time-
+development Eq.
+(1) has to be evaluated with a =
+±amax. This is conveniently done in the complex plane.
+With
+z = xh + i Ω−1 ˙xh ± amax/Ω2
+(7)
+one finds ˙z = −iΩ z and thus z(t) = exp[−iΩ(t−t0) z(t0).
+Hence
+xh(t) + i Ω−1 ˙xh(t) = exp[−iΩ(t − t0)]
+(8)
+· (xh(t0) + i Ω−1 ˙xh(t0) ± amax/Ω2) ∓ amax/Ω2.
+In the complex plane the right-hand side corresponds to
+a clock-wise rotation of xh(t0) + i Ω−1 ˙xh(t0) by the an-
+gle Ω(t − t0) around the point −amax/Ω2 and amax/Ω2,
+respectively.
+In the protocol one starts with xh(0)
+=
+0 and
+˙xh(0) = 0 and rotates clock-wise around −amax/Ω2, then
+around amax/Ω2, then again around −amax/Ω2 and fi-
+nally around amax/Ω2.
+Analytically this gives for the
+-1
+1
+FIG. 5: Time-development of xh in complex
+phase-space for Ω = 1, amax = 1, d = 2.82 π2,
+tf = 3.41 π, and t1 = .205 π. Starting at the origin, i.e.
+equilibrium position and at rest, there is first a rotation
+around -1, then around 1, then around -1 and finally
+again around 1, back to the origin.
+first two rotations
+ζ1 ≡ xh(tf/2 − t1) + i Ω−1 ˙xh(tf/2 − t1)
+= exp[−iΩ(tf/2 − t1)] amax/Ω2 − amax/Ω2
+ζ2 ≡ xh(tf/2) + i Ω−1 ˙xh(tf/2)
+= exp[−iΩt1](ζ1 − amax/Ω2) + amax/Ω2.
+(9)
+xh(tf/2) is the real part of ζ2 and one finds
+xh(tf/2) = 2 a max/Ω2 (cos2(Ω tf/4)) − cos(Ω t1))
+= 0
+(10)
+by Eq. (4), i.e. ζ2 lies on the imaginary axis. The cor-
+responding trajectories in the complex plane correspond
+
+LALTL3L24
+to the two curves in the left half-plane in Fig. 5. By
+the symmetry of the protocol the next two steps give the
+two curves in the right half-plane where the last one ends
+again at the origin. This follows of course also analyti-
+cally. Hence after the final step the oscillator is again at
+rest in its equilibrium position. Thus the protocol satis-
+fies the initial and final conditions.
+III.
+PROOF OF OPTIMALITY FOR FIXED Ω
+First the equivalent converse problem will be consid-
+ered: Finding the longest distance d for a given time
+duration tf under the conditions (i) - (iii) in Section I
+and a corresponding protocol.
+Symmetry. Consider some given tf and d. In the fol-
+lowing it is convenient to let time run from − 1
+2tf to 1
+2tf.
+Let xh and xw satisfy Eqs. (1) for some a(t) and the
+boundary conditions at ± 1
+2tf. Then 1
+2(xh(t) − xh(−t))
+and
+1
+2(xw(t) − xw(−t) + d) satisfy Eqs.
+(1) with a(t)
+replaced by 1
+2(a(t) − a(−t)) and the same boundary con-
+ditions. Hence without loss of generality one can assume
+that xh and a are anti-symmetric while ˙xh and ˙xw are
+symmetric under time reversal.
+Scaled variables. We go over to dimensionless scaled
+variables. We choose some fixed length unit d0 and put
+Ω2
+0
+= amax/d0
+ω
+= Ω/Ω0
+τ
+= Ω0t
+u(τ)
+= a(t)/amax
+ξ1(τ)
+= xh(t)/d0
+ξ2(τ)
+= d
+dτ ξ1(τ)
+ξ3(τ) = xw(t)/d0
+ξ4(τ) = d
+dτ ξ3(τ)
+(11)
+so that u(τ) can vary between −1 and 1.
+Then one
+obtains
+¨ξ1 ≡ d2
+dτ 2 ξ1 = −ω2ξ1 − u(τ)
+(12)
+¨ξ3 = u(τ) .
+For fixed Ω and a suitable d0 one can assume Ω0 = Ω
+and then ω = 1.
+Pontryagin Maximum (or Minimum) Principle (PMP)
+[24–26]. This is a far-reaching generalization of the cal-
+culus of variations and regarded as a milestone in control
+theory. A simple example is a car moving in shortest time
+from standstill at A to standstill at B, under the only
+condition that the time-dependent acceleration resp. de-
+celeration (the ’control’) is bounded, but not necessarily
+continuous.
+The PMP serves to determine necessary conditions for
+an optimal control function u∗(t) (or possibly several con-
+trol functions) which minimizes a given cost function J
+of the form J =
+� T
+0 L(u(τ), ...)dτ, where L is a func-
+tion of the control u(τ) and some state functions ξi and
+their derivatives. For the present distance-optimal con-
+trol problem, one can take L = ξ4 since J =
+� T
+0
+˙ξ3dτ is
+the (scaled) distance. To minimize it, the PMP considers
+a control Hamiltonian Hc,
+Hc = −L+p1 ˙ξ1 + p2 ˙ξ2 + p3 ˙ξ3 + p4 ˙ξ4,
+(13)
+where one inserts ˙ξi from Eqs. (11-12) and where the
+adjoint states pi are Lagrange multipliers which can not
+all be identically zero.
+Then, for an extremal control
+u(τ) = u ∗ (t), Hamilton’s equations
+˙pi = −∂Hc/∂ξi,
+˙ξi = ∂Hc/∂pi
+(14)
+hold.
+For almost all −τf/2 ≤ τ ≤ τf/2, the function
+Hc(pi(t), ξi(t), u(t)) attains its maximum at u(t) = u∗(t),
+and Hc = const. For simplicity we omit the asterisk on
+u∗. Inserting for ˙ξi, Hc becomes
+Hc = −ξ4 + p1ξ2 + p2(−ω2ξ1 − u) + p3ξ4 + p4u .
+(15)
+From the term (p4−p2) u it follows that for a maximum
+one has to choose u(τ) = 1 if p4 − p2 > 0 and -1 if
+p4 − p2 < 0. When p4 − p2 = 0, or more precisely, when
+p4 − p2 changes sign, there is a switch from ±1 to ∓1 in
+u. Hamilton’s equations become
+˙p1 = ω2p2,
+˙p2 = −p1
+˙p3 = 0,
+˙p4 = −p3 + 1
+(16)
+The solutions are
+p2(τ) = A cos τ + B sin ωτ,
+p1 = − ˙p2
+p3 = c3,
+p4 = (−c3 + 1) τ + c4
+(17)
+where A, B, c3, and c4 are constants. If p4 − p2 ≡ 0
+in some extended interval, then p4 = p2 ≡ 0, by linear
+independence. Therefore it is not possible to have u ≡ 0
+and ξ4 ≡ const in some extended interval so that there
+are only isolated switches. Hence, by anti-symmetry of
+u, there is a switch at τ = 0, i.e. −p2(0) + p4(0) = 0,
+and thus A = c4. By the boundary conditions on ξi at
+±τf/2 only the terms containing u remain in Hc which
+by antisemitic of u lead to two equations and to
+A (cos(ωτf/2) − 1) = 0 .
+(18)
+Thus either A = 0 or ωτf = 4πn. In the latter case the
+situation is analogous to Example 2, i.e. the h.o. can per-
+form 2n complete oscillations and the optimal distance
+is the same as without oscillator. We can therefore as-
+sume A = c4 = 0.
+For ωτf ̸= 4πn there are at least
+two switches of u and therefore B ̸= 0 since otherwise
+−c3 + 1 = 0, c3 = 1, and ξ4 ≡ const. The explicit values
+of B and c3 are not needed, they can in principle be cal-
+culated at the end; it suffices to discuss the cases B < 0
+and B > 0.
+Note: From the remark after Eq. (15) it follows that
+u(τ) = 1 when the line p4(τ) lies above the sine curve
+p2(τ) and u(τ) = −1 when it lies below.
+
+5
+Case B < 0. (i) Single switch for τ < 0, at −τ1, say.
+Then the line p4(τ), denoted by L1 in Fig. 6, intersects
+with the -sine curve p2(τ) once.
+The analog of Eqs.
+(9) for ξ + iω−1 ˙ξ in the scaled
+variables, now with initial time -τf/2 and final time 0
+yields
+ξ1(0) = cos(ωτf/2) − 2 cos(ωτ1) + 1.
+(19)
+From the anti-symmetry of ξ1 one has ξ1(0) = 0, and
+from this one obtains
+cos ωτ1 = cos2(ωτf/4)
+(20)
+with −π/2ω < −τ1 < 0. Thus line L1 in Fig. 6 is typical
+in this case, while line L2 is not possible.
+-3 π
+-2 π
+-π
+FIG. 6: Case B < 0. With ω = 1. L1 and L2 denote
+possible lines for p4(τ). Their intersections with p2(τ)
+(-sine curve) are possible switching points. In regions
+where p4(τ) is above p2(τ) one has acceleration,
+otherwise deceleration. Only L1 with a single switch is
+optimal.
+(ii) If there are two or more switches for τ < 0, e.g. if
+p4(τ) is given by line L2 in Fig. 6, then the last decelera-
+tion period before τ = 0 is longer than π/2ω. Hence the
+total acceleration time is less than in (i) and the distance
+traveled by the wagon during τf is less than that in (i).
+Hence for B < 0 there is only a single switch for τ < 0.
+Case B > 0. From Fig. 7 this is case B < 0 reflected at
+the τ axis, with u = ±1 interchanged and thus positive
+wagon distances for B < 0 now become negative. But
+there might also be negative distances for B < 0, corre-
+sponding to positive distances for B > 0, and therefore a
+more detailed discussion is required. Here we use ω = 1.
+(i) Single switch for τ < 0: As for B < 0 there is only a
+single solution for fixed τf, and this is the corresponding
+optimal backward motion, with p4(τ) typically given by
+L3 in Fig. 7.
+(ii) Exactly two switches for τ < 0. Typical for this
+would be lines L4 and L5 in Fig.
+7, with switches at
+−τ2 < −τ1 < 0, say.
+a) Case τ2 − τ1 > π/2.
+From Fig. 7 one easily finds ˙ξ3(0) = τf/2 − 2(τ2 − τ1) <
+τf/2 − π while, from case B < 0, ˙ξ3opt ≥ τf/2 − π since
+here the switching point lies to the right of −π/2. Hence
+in case B < 0 the distance is larger.
+b) Case τ2 − τ1 < π/2.
+This will be shown to be incompatible with the bound-
+ary conditions on the h.o.. One has ξ1(0) = 0, by anti-
+symmetry, while ˙ξ1(0) ≡ λ is unknown. Reversing the
+time development from τ = 0 to τ = −τ2 one obtains
+ξ1(−τ1) + i ˙ξ1(−τ1) = exp[−iτ1]{iλ + 1} − 1
+ξ1(−τ2) + i−1 ˙ξ1(−τ2) =
+exp[i(−τ1 + τ2)]{ξ1(−τ1) + i ˙ξ1(−τ1) − 1} + 1
+= exp[i(−τ1 + τ2){exp[iτ1](iλ + 1) − 2} + 1
+(21)
+Since this must lie on the circle around −1 passing
+through 0, upon adding 1 the rhs becomes a number of
+modulus 1:
+1 = | exp[i(−τ1 + τ2)]{exp[iτ1](iλ + 1) − 2} + 2|
+= |iλ + 1 − 2 exp[−iτ1] + 2 exp[−iτ2]|
+(22)
+Hence the modulus of the real part,
+|1 − 2 cos τ1 + 2 cosτ2|,
+(23)
+must be less than, or equal to, 1. However, from Fig.
+7, one has −3π/2 < −τ1 < −π and so cos τ1 < 0.
+For −2π < −τ2 < −3π/2 one has cos τ2 > 0 while for
+−3π/2 < −τ2 < −π one has −2 cosτ1 + 2 cosτ2 > 0.
+Hence the bracket in Eq.
+(23) is larger than 1, a
+contradiction. Thus this case can not occur.
+(iii) Three or more switches for τ < 0: A typical line is
+L5 in Fig. 7. From Fig.7 it is evident that the area under
+the curve (i.e. distance) decreases.
+FIG. 7: Case B > 0. With ω = 1. L3, L4 and L5 denote
+possible lines for p4(τ). Their intersections with p2(τ)
+(sine curve) are possible switching points. Dashed: ˙ξ3
+with 2 intersection points −τ1 and −τ2. Dotdashed:
+˙ξ3opt from case B < 0. For τ2 − τ1 > π/2 one has
+˙ξopt > ˙ξ. L3 is typical for the optimal backwards
+motion.
+
+L5.L3L4L2L16
+As a consequence, case B > 0 is not possible and case
+B < 0 (i) gives the unique optimal distance for given τf
+and fixed ω in scaled variables. This distance is easily
+calculated to be τ 2
+f /4 − 2τ 2
+1, with τ1, 0 ≤ τ1 ≤ π/2, given
+by Eq. (20). In the original variables one has
+d = 1
+4amaxt2
+f − 2amaxt2
+1.
+(24)
+Going back to the original problem one obtains the
+protocol of Section II.
+IV.
+PROTOCOLS FOR TIME-DEPENDENT
+OSCILLATOR FREQUENCY
+In this case one allows in addition to a(t) also Ω(t) to
+be time-dependent and seeks a minimal transport time
+tf for a distance d under the condition that the wagon
+is initially and finally at rest and the oscillator is at rest
+in its equilibrium position. This situation is more com-
+plicated. If there are no bounds on Ω then for Ω → ∞
+one obtains the absolute minimal time as without oscilla-
+tor. Therefore, in addition to |a(t)| ≤ amax one imposes
+bounds
+0 ≤ Ω− ≤ Ω(t) ≤ Ω+ < ∞.
+(25)
+If a ’resonant value’ from Eq.
+(2) lies in this interval
+then, from Example 2, one chooses this value for Ω and
+then obtains the absolute minimal time.
+Distance optimization.
+Again we first consider the
+equivalent problem of finding a protocol that maximizes
+the distance d for given time tf and let time run from
+− 1
+2tf to 1
+2tf. We will seek solutions that satisfy the same
+symmetry properties as in Section III, i.e.
+we assume
+that Ω(t) is symmetric.
+The same scaled variables as in Eq.
+(11) are used.
+Introducing
+u1(τ) ≡ ω2(τ)
+(26)
+as a second control variable, Eq. (12) reads
+¨ξ1 ≡ d2
+dτ 2 ξ1 = −u1(τ)ξ1 − u(τ)
+(27)
+¨ξ3 = u(τ) .
+The condition on Ω(t) becomes ω2
+− ≤ u1(τ) ≤ ω2
++. The
+control Hamiltonian for the PMP now reads
+Hc = −ξ4 + p1ξ2 + p2(−u1ξ1 − u) + p3ξ4 + p4u .
+(28)
+As before it follows that for a maximum one has to choose
+u(τ) = 1 if p4 > p2 and -1 if p4 < p2. When p4 − p2 = 0,
+or more precisely, when p4 − p2 changes sign, there is
+a switch from ±1 to ∓1 in u.
+Similarly, u1 = ω2
++ if
+p2ξ1 < 0, and u1 = ω2
+− if p2ξ1 > 0. A switch occurs
+when p2ξ1 changes sign.
+Depending on whether u1 = ω2
++ or u1 = ω2
+−, Hamil-
+ton’s equations in the respective τ intervals become
+˙p1 = ω2
+± p2,
+˙p2 = −p1
+˙p3 = 0,
+˙p4 = −p3 + 1.
+(29)
+Between switches of u1 the solutions are of the form
+p2(τ) = A± cos ω±τ + B± sin ω±τ = C± sin(ω±τ − ϕ±)
+(30)
+p1 = − ˙p2,
+p3 = c3,
+p4 = (−c3 + 1) τ + c4
+where c3, c4, C± are constants, and A±, B±, ϕ± are con-
+stants which may dependent on the respective interval.
+If p2(τ) ≡ 0 in some interval then it is zero everywhere
+because it cannot be joined continuously to the a nonzero
+p2 from Eq. (30).
+Since ω(τ) is symmetric there must be intervals of
+equal length with ω(τ) = ω+ directly to the left and right
+of τ = 0 (or ω− intervals, but this will not be optimal as
+shown later). Hence one must have ϕ+ = 0 in this inter-
+val since then there are switches in ω(τ) at τ = ±π/ω+
+because p2ξ1 vanishes there. It also vanishes at τ = 0
+but does not change sign because of anti-symmetry of ξ1
+and p2 so that ω has no switch at τ = 0 although u does.
+Thus p2 is of the form
+p2(τ) = B+ sin(ω+τ)
+(31)
+in the interval −π/ω+ ≤ τ ≤ π/ω+.
+To the left of τ = −π/ω+ there is an interval with ω−,
+then again an ω+ interval and so on, and similarly to the
+right of τ = π/ω+. Since p2(τ) is differentiable different
+parts of p2 have to be joined accordingly. This yields an
+anti-symmetric p2 as typically displayed in Fig. 8.
+FIG. 8: Solid: p2(τ) with symmetric ω± sequence.
+Dashed: p4(τ).
+The procedure for the determination of τ1 uses the
+time-development of ξ1 and depends on the interval in
+which 1
+2τf lies. This will be exemplified for 1
+2τf ≤ π/ω++
+π/ω−.When 1
+2τf ≤ π/ω+ the situation is the same as in
+Section III and τ1 is given by Eq. (20), with ω replaced
+by ω+.
+
+7
+When π/ω+ <
+1
+2τf ≤ π/ω+ + π/ω− we calculate
+ξ1(τf/2) and ˙ξ1(τf/2) from ξ1(0) and ˙ξ10).
+By anti-
+symmetry one has ξ1(0) = 0 and we put ˙ξ1(0) = λ, the
+exact value of which will not be needed. Using Eq. (8)
+one obtains
+η1 ≡ ξ1(τ1) +
+i
+ω+
+˙ξ1(τ1)
+= exp[−iω+(τ1 − 0)]( i
+ω+
+λ + 1
+ω2
++
+) − 1
+ω2
++
+η2 ≡ ξ1(π/ω+) +
+i
+ω+
+˙ξ1(π/ω+)
+= exp[−iω+( π
+ω+
+− τ1)]{ℜη1 +
+i
+ω+ω+ℑη1 − 1
+ω2
++
+} + 1
+ω2
++
+˜η3 ≡ ξ1(τf/2) +
+i
+ω−
+˙ξ1(τf/2)
+= exp[−iω−(τf/2 − π
+ω+
+)]{ℜη2 +
+i
+ω−
+ω+ℑη2 − 1
+ω2
+−
+} + 1
+ω2
+−
+(32)
+By the boundary conditions at 1
+2τf one has ˜η3 = 0, and
+thus
+0 = ℜη2 +
+i
+ω−
+ω+ℑη2 − 1
+ω2
+−
++ exp[iω−(τf/2 − π
+ω+
+)] 1
+ω2
+−
+.
+(33)
+Taking the real part of this one obtains after a short
+calculation
+cos[ω+τ1] = ω2
++
+2ω2
+−
+{1 + cos(ω−τf/2 + ω+ − ω−
+ω+
+π)}. (34)
+The l.h.s. cannot exceed 1, while the r.h.s. becomes 1
+for τf = τopt where
+τopt/2 = π
+ω+
++ π
+ω−
+− 2
+ω−
+arccos[ω−
+ω+
+],
+(35)
+which lies between π/ω+ and π/ω++π/ω−. Then τ1 = 0
+and the distance becomes the absolute optimum for this
+particular τf = τopt.
+Example 3. Let ω− = ω+/2. Then Eq. (35) yields
+τopt/2 = 5
+3π/ω+ and the distance d/d0 becomes 1
+4τ 2
+opt.
+If one considered only ω+ and the corresponding τopt,
+one would have ω+τ1 = arccos[3/4] ̸= 0 and the distance
+would be less.
+How to proceed when the r.h.s. of Eq. (34) is larger
+than 1? To answer this question we recall that p2 has
+also the trivial solution p2(τ) ≡ 0. Then there are no
+restrictions on the choice of ω(τ). If one decreases ω+
+on the r.h.s of Eq. (34) to ω− the r.h.s. becomes less
+or equal to 1. Hence there must be an intermediate ω,
+denoted by ˜ω+, such that the r.h.s becomes 1. Hence if
+one uses [ω−, ˜ω+] instead of [ω−, ω+] one gets a solution
+for τ1, namely τ1 = 0, so that the sequence ω− and ˜ω+
+gives the largest distance for the given τf. This means
+going over to a sub-interval [ω−, ˜ω+] of [ω, ω+] optimizes
+the distance in this case. There are many sub-intervals
+with the same property, as seen further below.
+In the case π/ω+ + π/ω− < τf/2 ≤ π/ω+ + π/ω− +
+π/ω+, i.e. if one starts with ω+, switches to ω−, and to
+ω+ before τ = 0, i.e. a sequence +−+|+−+ in Fig. 8, then
+η1 and η2 in Eq. (32) remain unchanged while in η3 one
+replaces τf/2 by π/ω+ + π/ω− and there is an additional
+η4,
+η3 = −ℜη2 + 2/ω2
+− −
+i
+ω−
+ω−ℑη2
+η4 ≡ ξ1(τf/2) +
+i
+ω+
+˙ξ1(τf/2)
+= exp[−iω+(τf/2 − π/ω+ − π/ω−)]
+{ℜη3 +
+i
+ω+
+ω−ℑη3 + 1
+ω2
++
+} − 1
+ω2
++
+.
+(36)
+The condition η4 = 0 now gives
+cos ω+τ1 = ω2
++
+ω2
+−
+− 1 + 1
+2{1 + cos(ω+τf/2 − ω+ − ω−
+ω−
+π)}.
+(37)
+For complete ω± intervals the exponentials in Eqs. (32)
+and (36) equal -1 and using this the results are easily
+generalized. In particular, for the ω± sequence − + − + | +
+− + − one obtains
+cos(ω+τ1) = ω2
++
+ω2
+−
+− 1 + ω2
++
+2ω2
+−
+{1 + cos(ω−τf/2 − 2π ω−
+ω+
+)}.
+(38)
+Time optimization. These results will now be applied
+to the original problem in which a distance, now denoted
+by d0, is fixed and the shortest transport time for given
+Ω± is sought. If this d0 is taken for the definition of the
+scaled variables, d0 becomes ξ3(τf/2) = 1. The absolutely
+shortest possible time, τabs, and corresponding ωres is
+then, by Example 2, given by
+τabs = 2
+ωres = 2π.
+(39)
+From Fig. 2 the distance traveled in time τf is 1
+4τ 2
+f − 2τ 2
+1
+and if τf is to be optimal it must satisfy
+1 = 1
+4τ 2
+f − 2τ 2
+1
+(40)
+where τf = τf(ω−, ω+). For given ω± one obtains τ1 from
+Eqs. (20, 34, 37) and generalizations thereof, depending
+on in which interval the as yet unknown τf/2 lies.
+If
+ωres or an integer multiple n thereof lies in [ω−, ω+] one
+chooses ω(τ) ≡ nωres and obtains the absolute optimal
+τabs. Different case of increasing complexity will now be
+discussed.
+Case: ω− = 0, 0 < ω+ < 2π and the distance 1. If
+the spring constant is 0 then in the lab frame the mass
+point m travels free of force and in the the wagon frame
+under the inertial force. It can happen that it is optimal
+
+8
+to start with ω−.
+Then m initially remains at rest in
+the lab frame until a switch to ω+ occurs. If the time
+development starts with ω+ there can be no switch to
+ω− because the associated time interval π/ω− is infinite.
+Hence in this case the results of Section II and III apply.
+From Fig. 4 it is seen that τf decreases with increasing
+ω+ < 2π. Since τf/2 ≤ π/ω+ one has, for optimality,
+τf = 2π/ω+ and τ1 = 0, by Eqs. (3,4). From Eq. (40)
+one then obtains τ 2
+f = 4 so that in this case one must
+have ω+ = π/
+√
+2 ≡ ˜ω+. Thus if ω+ > ˜ω+ one starts
+with ω− = 0 and then there is a switch to ω+ at some
+later time.
+In this case Eq.
+(34) holds for τ1 and it
+becomes 0 for τf = τopt given by Eq. (35). Taking the
+limit ω− → 0 one finds τopt = (2π + 4)/ω+. This must
+equal τabs = 2 which gives ω+ = π + 2 ≡ ωabs. From this
+value of ω+ on one obtains the absolute time minimum.
+The optimal time as a function of ω+ is displayed in Fig.
+9.
+Protocol. This depends on ω+ and is as in Section II
+when ω+ ≤ ˜ω+. When ˜ω+ < ω+ ≤ ωabs one determines
+τf and τ1 from Eqs. (37) and (40), starts with ω− = 0 for
+the time duration −π/˜ω+ + τf/2 and with u = 1, then
+switches to ω+ and continues for the time −τ1 + π/˜ω+,
+then switches to u = −1 for the time τ1 and continues by
+symmetry, resp. anti-symmetry. When ωabs = 2 + π <
+ω+ ≤ ωres one chooses the protocol for ω+ = ωabs.
+0.4
+0.6
+0.8
+1.0
+1.0
+1.1
+1.2
+1.3
+1.4
+1.5
+1.6
+FIG. 9: Shortest transport time tf for fixed distance d0,
+Ω− = 0 and 0 ≤ Ω+/Ωres(d0) ≤ 1. Dotted: tf for fixed
+Ω+ without switch in Ω. Solid: Ω+/Ωres(d0) >
+√
+2/4;
+initially Ω(t) ≡ 0 and then a switch to Ω+. For
+1/2 + 1/π ≤ Ω+/Ωres(d0) ≤ 1 one has Tabs(d). The
+switch in Ω can thus lead to a shorter transport time
+than for Ω+ alone.
+Case: 0 < ω− < ω+ < ωres = 2π.
+As in the pre-
+ceding case, only ω+ is relevant if ω+ ≤ ˜ω+ = π/
+√
+2.
+Then τf(ω−, ω+)/2 ≤ π/ω+ and is independent of ω−.
+This is the upper close meshed region in Fig. 10. For
+ω+ > ˜ω+ there are on the l.h.s. of Fig. 8 two or more
+alternating ω±’s for the time development. If there are
+two, one starts with ω−, and the initial time −τf/2 sat-
+isfies π/ω+ ≤ τf/2 ≤ π/ω+ + π/ω−. In this case Eqs.
+(40) and (34) apply. If the l.h.s. of Eq. (34) is less or
+equal to 1 then one can determine τ1 and τf(ω−, ω+), dis-
+played by the coarse meshed region in Fig. 10. Putting
+cos[ω+τ1] = 1 one obtains with τf = τabs = 2π from
+Eq. (34) the boundary curve at the bottom of the coarse
+meshed surface which borders the region denoted by Tabs.
+In this region there is no solution for τ1. As before, here
+the solution p2(τ) ≡ 0 can be used and then there are
+no restrictions on ω(τ).
+If one starts from the point
+{ω−, ω+} and first decreases ω+ until one hits the bound-
+ary curve and then similarly increases ω− one obtains the
+end points of an arc on the boundary curve. Every point
+{ˆω−, ˆω+} on this arc satisfies {ω− ≤ ˆω− ≤ ˆω+ ≤ ω+} and
+yields τabs. Thus there is again an improvement over the
+single ω+ case.
+If there were a third, preceding, interval, i.e.
+with
+ω+, then τf(ω−, ω+)/2 > π/ω+ + π/ω− and τf would
+thus be larger than that with only two periods. Hence
+a third period does not occur. By a similar calculation,
+interchanging ω+ and ω− leads to a larger transport time.
+Protocol: When ω+ ≤ ˜ω+ = π/
+√
+2 one proceeds with
+ω+ as in Section II. When ω+ > ˜ω+ one determines
+τf(ω−, ω+) and τ1 from Eqs.
+(34) and (40), provided
+a solution for τ1 exists. Then one has an ω± sequence
+of the form − + | + − and thus one starts with u = 1 and
+ω− from time −τf/2 to time −π/ω+ where one switches
+to ω+. Then one continues until time −τ1, where one
+switches to u = −1 and continues to τ = 0 where there
+is a switch back to u = 1. For τ > 0 one continues by
+symmetry, resp. anti-symmetry. When there is no solu-
+tion for τ1, i.e when the point {ω−, ω+} lies in the region
+denoted by Tabs in Fig. 10, then one can choose a proto-
+col for any point on the above arc. This will yield τabs
+and in this case the protocol is not unique.
+Case: ωres = 2π ≤ ω− < ω+ < 2 ωres. Arguing as
+before, one has + − +| + −+ and − + − + | + − + − as possible
+ω± sequences.
+To the first sequence Eq.
+(37) applies
+and to the second Eq. (38). One now solves Eq. (40)
+together with Eq. (37) for τf under the condition thatτf/2
+lies in the last ω+ interval. In Fig. 11 this gives the left
+surface outside of which there is no solution for τ1. In a
+similar way one obtains the right surface for the second
+sequence.
+On the boundary curve at the bottom one
+has τabs and the curve is obtained from cos(ω+τ1) = 1.
+The two ω± sequences are separated by the dashed curve
+under the surface.
+This curve is obtained by putting
+τf/2 = 2π/ω+ + π/ω− in Eqs. (37, 40). Its end point on
+the boundary curve is given by { 1
+2 + 1
+2
+√
+2, 1 + 1
+2
+√
+2} ωres
+and on the diagonal by 1
+4
+√
+34 ωres.
+In the region denoted by Tabs there is no solution for
+τ1.
+Again one can choose any point {ˆω−, ˆω+} on the
+arc constructed as before to obtain τabs. Reversing the
+sequence to − + −| − +− leads to larger transport times.
+Protocol: If for a given {ω−, ω+} one has ω− ≤ ( 1
+2 +
+
+9
+FIG. 10: Shortest transport time tf for fixed distance d0
+and 0 ≤ Ω−/Ωres(d0) ≤ Ω+/Ωres(d0) ≤ 1. For
+Ω+/Ωres(d0) ≤ π/
+√
+2 there is only Ω+ and no switch
+(close meshed region). For {Ω−, Ω+} in the region
+denoted by Tabs at the r.h.s. one has the shortest time
+Tabs. The intersection of the surface with the front
+plane is the curve of Fig. 9 and that with the diagonal
+plane is the left part of the curve of Fig. 4 until 1.
+1
+2
+√
+2) ωres or if a solution for τ1 in Eq. (37) exists, one has
+a sequence +−+|+−+, from Fig. 11. If a solution exists the
+protocol is analogous to the previous case above. If not,
+one picks a point {ˆω−, ˆω+} on the arc on the boundary
+curve, as before, and uses the protocol for this point with
+τf = τabs. Otherwise, one has a sequence
+− + − + | + − + −
+and the procedure is analogous.
+V.
+SUMMARY AND DISCUSSION
+Protocols for the fastest possible transport of a classi-
+cal harmonic oscillator (h.o.) over a distance d have been
+derived where both initially and finally everything is at
+rest, i.e. the position of the h.o. is at rest and the h.o.
+is in its equilibrium position and also at rest. The accel-
+eration a(t) is assumed to satisfy −amax ≤ a(t) ≤ amax.
+First, with fixed h.o.
+frequency Ω, for the shortest
+transport time the optimal acceleration alternates be-
+tween ±amax. It was shown that one starts with amax
+and that there are three switches or, for special values
+Ω = nΩres(d) = 2πn
+�
+amax/d, n = 1, 2, · · ·, only one
+switch. The switch times were determined.
+The dependence of the shortest transport time, de-
+noted by tf, on d, Ω and amax was found, cf. Figs. 3 and 4.
+The optimal time tf is proportional to 1/√amax, diverges
+FIG. 11: Shortest transport time tf for fixed distance d0
+and 1 ≤ Ω−/Ωres(d0) ≤ Ω+/Ωres(d0) ≤ 2. The left side
+of the surface belongs to an Ω± sequence + − +| + −+,
+the right side to − + − + | + − + −, separated by the
+dashed line in the bottom plane. For {Ω−, Ω+} in the
+region denoted by Tabs one obtains the shortest time
+Tabs by going over to a point on the boundary
+corresponding to a sub-interval of [Ω−, Ω+].
+for Ω → 0 and, not surprisingly, for Ω → ∞ converges
+to Tabs(d) = 2
+�
+d/amax, the optimal time for a wagon
+without h.o.. The function tf(d) approaches Tabs(d) for
+large d. Surprisingly, sometimes it is advantageous to go
+backwards for a while, but not as far back as the initial
+position.
+Second, in addition to a(t) a time-dependent Ω(t) sat-
+isfying Ω− ≤ Ω(t) ≤ Ω+ was considered. In this case
+the behavior of tf depends sensitively on Ω±. If n Ωres(d)
+lies in the interval [Ω−, Ω+] for some n then choosing
+n Ωres(d) will give the minimal time Tabs(d).
+If Ω+ ≤
+1
+2
+√
+2Ωres then Ω(t) ≡ Ω+, there is no switch
+in Ω, and Ω− does not enter. Otherwise there are two
+alternatives if Ω+ < Ωres:
+(i) One starts with Ω−, switches to Ω+ and then back to
+Ω−.
+(ii) Or there are ˜Ω±, depending on Ω±, with Ω− ≤ ˜Ω− ≤
+˜Ω+ ≤ Ω+ and one starts with ˜Ω−, switches to ˜Ω+ and
+then back to ˜Ω−. In this case one obtains the minimal
+time Tabs(d).
+In the Ω− − Ω+ plane this happens for
+{Ω−, Ω+} in a region, cf. Fig. 10.
+If n Ωres < Ω− ≤ Ω+ < (n + 1)Ωres the situation is
+similarly involved and depicted for n = 1 in Fig. 11 .
+The Pontryagin Maximum Principle was employed,
+first for constant Ω with a(t) as a control variable, and
+then with a(t) and Ω(t) as control variables. Symmetry
+
+2.0
+2- /Sres(do)
+1.5
+1.0
+1.03
+1.02
+t /Tabs(do)
+1.01
+1.00
+1.0
+1.5
+(op)s/+
+2.01.0
+2- /Sres(do)
+0.5
+0.0
+1.4
+t /Tabs(do)
+1.2
+1.0
+0.0
+a.n
+0.5
+(p)sa/+
+1.010
+properties played an important role which were proved
+for constant Ω and assumed in an analogous form for
+time-dependent Ω.
+One may also want to impose restrictions on the veloc-
+ities ˙xw and ˙xh or on the relative displacement xh of the
+h.o.. Within the PMP this may be formulated by means
+of Lagrangian multipliers. In [28] the relative displace-
+ment was assumed to be bounded and taken as the only
+control. However, in this case there are δ(t)-like forces at
+the time of a switch acting on the h.o., and no oscillations
+occur.
+The above results for constant Ω have immediate appli-
+cations to cranes for small-angle oscillations of the pay-
+load where the the rope length l is constant. For time
+dependent l(t) modifications are needed since l(t) is not
+related to the frequency Ω(t) in the same way as the
+spring constant.
+The harmonic oscillator considered here is an idealized
+system. However, it may serve as a benchmark for more
+realistic models, e.g. if the switches are short but smooth
+rather than instantaneous.
+[1] D. Gu´ery-Odelin, A. Ruschhaupt, A. Kiely, E. Tor-
+rontegui, S. Mart´ınez-Garaot and J.G. Muga, Shortcuts
+to adiabaticity:
+Concepts, methods, and applications,
+Rev. Mod. Phys. 91, 045001 (2019).
+[2] E. Torrontegui, S. Iba˜nez, S. Mart´ınez-Garaot, M. Mod-
+ugno, A. del Campo, D. Gu´ery-Odelin, A. Ruschhaupt,
+X. Chen, and J. G. Muga, Shortcuts to adiabaticity, Adv.
+At. Mol. Opt. Phys. 62, 117 (2013).
+[3] Yue Ban, Xi Chen, E. Torrontegui, E. Solano, and J.
+Casanova, Speeding up quantum perceptron via short-
+cuts to adiabaticity Scientific Reports volume 11, Article
+number: 5783, (2021).
+[4] N.N. Hegade, K. Paul, Yongcheng Ding, M. Sanz, F. Al-
+barr´an-Arriagada, E. Solano, and Xi Chen, Shortcuts to
+Adiabaticity in Digitized Adiabatic Quantum Comput-
+ing, Phys. Rev. Applied 15, 024038 (2021)
+[5] J. G. Muga, X. Chen, A. Ruschhaupt, and D. Gu´ery-
+Odelin, Frictionless dynamics of Bose-Einstein conden-
+sates under fast trap variations, J. Phys. B 42, 241001
+(2009).
+[6] X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D.
+Gu´ery-Odelin, and J. G. Muga, Fast Optimal Frictionless
+Atom Cooling in Harmonic Traps, Phys. Rev. Lett. 104,
+063002 (2010).
+[7] D. Gu´ery-Odelin, J. G. Muga, M. J. Ruiz-Montero, and
+E. Trizac, Exact Nonequilibrium Solutions of the Boltz-
+mann Equation under a Time-Dependent External Force,
+Phys. Rev. Lett. 112, 180602 (2014).
+[8] D. Gu´ery-Odelin and J. G. Muga, Transport in a har-
+monic trap: Shortcuts to adiabaticity and robust proto-
+cols, Phys. Rev. A 90, 063425 (2014).
+[9] A. Ruschhaupt, X. Chen, D. Alonso, and J. G. Muga, Op-
+timally robust shortcuts to population inversion in two-
+level quantum systems, New J. Phys. 14, 093040 (2012).
+[10] S. Mart´ınez-Garaot, E. Torrontegui, X. Chen, M. Mod-
+ugno, D. Gu´ery-Odelin, Shuo-Yen Tseng, and J. G.
+Muga,
+Vibrational
+Mode
+Multiplexing of
+Ultracold
+Atoms, Phys. Rev. Lett. 111, 213001 (2013).
+[11] M. Demirplak and S. A. Rice, On the consistency, ex-
+tremal, and global properties of counterdiabatic fields, J.
+Chem. Phys. 129, 154111 (2008).
+[12] M. V. Berry, Transitionless quantum driving, J. Phys. A
+42, 365303 (2009).
+[13] X. Chen, I. Lizuain, A. Ruschhaupt, D. Gu´ery-Odelin,
+and J. G. Muga, Shortcut to Adiabatic Passage in Two-
+and Three-Level Atoms, Phys. Rev. Lett. 105, 123003
+(2010).
+[14] E. Carolan, A. Kiely, and S. Campbell, Counterdiabatic
+control in the impulse regime Phys. Rev. A 105, 012605
+(2022)
+[15] S. Masuda and K. Nakamura, Fast-forward of adiabatic
+dynamics in quantum mechanics, Proc. R. Soc. A 466,
+1135 (2010).
+[16] S. Masuda and K. Nakamura, Acceleration of adiabatic
+quantum dynamics in electromagnetic fields, Phys. Rev.
+A 84, 043434 (2011).
+[17] Katsuhiro Nakamura, Jasur Matrasulov, and Yuki Izu-
+mida, Fast-forward approach to stochastic heat engine,
+Phys. Rev. E 102, 012129 (2020).
+[18] E. Torrontegui, S. Mart´ınez-Garaot, A. Ruschhaupt, and
+J. G. Muga, Shortcuts to adiabaticity: Fast-forward ap-
+proach, Phys. Rev. A 86, 013601 (2012).
+[19] G.C. Hegerfeldt, Driving at the Quantum Speed Limit:
+Optimal Control of a Two-Level System, Phys. Rev. Lett.
+111, 260501 (2013)
+[20] E. Dionis and D. Sugny, Time-optimal control of two-
+level quantum systems by piecewise constant pulses,
+arXiv.2211.09167
+[21] G.C. Hegerfeldt, High-speed driving of a two-level sys-
+tem, Phys. Rev. A 90, 032110 (2014).
+[22] Xi Chen, Yue Ban, and G.C. Hegerfeldt, Time-optimal
+quantum control of nonlinear two-level systems, Phys.
+Rev. A 94, 023624 (2016)
+[23] S. Gonz´alez-Resines, D. Gu´ery-Odelin, A. Tobalina, I.
+Lizuain, E. Torrontegui, and J.G. Muga, Invariant-Based
+Inverse Engineering of Crane Control Parameters, Phys.
+Rev. Applied 8, 054008 (2017).
+[24] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze,
+and E. F. Mishchenko, The Mathematical Theory of Op-
+timal Processes, Interscience (1962).
+[25] L.M. Hocking, Optimal control: an introduction to the
+theory with applications, Clarendon Press (Oxford 1991)
+[26] U. Boscain, M. Sigalotti, and D. Sugny, Introduction to
+the Pontryagin Maximum Principle for Quantum Opti-
+mal Control, PRX Quantum 2, 030203 (2021)
+[27] E. Torrontegui, I. Lizuain, S. Gonz´alez-Resines, A. To-
+balina, A. Ruschhaupt, R. Kosloff, and J. G. Muga, En-
+ergy consumption for shortcuts to adiabaticity, Phys.
+Rev. A 96, 022133 (2017)
+[28] Xi Chen, E. Torrontegui, D. Stefanatos, Jr-Shin Li, and
+J. G. Muga, Optimal trajectories for efficient atomic
+transport without final excitation, Phys. Rev. A 84,
+043415 (2011).
+
diff --git a/bNAzT4oBgHgl3EQfLPu9/content/tmp_files/load_file.txt b/bNAzT4oBgHgl3EQfLPu9/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f43f31373a37f0652edd1f88aa833600070f9921
--- /dev/null
+++ b/bNAzT4oBgHgl3EQfLPu9/content/tmp_files/load_file.txt
@@ -0,0 +1,822 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf,len=821
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='01112v1  [quant-ph]  3 Jan 2023  Time-Optimal Transport of a Harmonic Oscillator: Analytic Solution  Gerhard C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hegerfeldt1  1Institut f¨ur Theoretische Physik, Universit¨at G¨ottingen,  Friedrich-Hund-Platz 1, D-37077 G¨ottingen, Germany  Motivated by the experimental transport of a trap with a quantum mechanical system modeled  as a harmonic oscillator (h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=') the corresponding classical problem is investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Protocols for  the fastest possible transport of a classical h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' in a wagon over a distance d are derived where  both initially and finally the wagon is at rest and the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' is in its equilibrium position and also at  rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The acceleration of the wagon is assumed to be bounded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For fixed oscillator frequency Ω it is  shown that there are in general three switches in the acceleration and for special values of Ω only  one switch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In the latter case the optimal transport time is Tabs, that of a wagon without oscillator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The optimal transport time and the switch times are determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' It is shown that in some cases it  is advantageous to go backwards for a while.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In addition a time-dependent Ω(t), bounded by Ω±,  is allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In this case the behavior depends sensitively on Ω± and is spelled out in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In  particular, depending on Ω±, Tabs may be obtained in continuously many ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  PACS numbers:  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  INTRODUCTION  Adiabatic processes may serve to transform an initial  state of a system to a proscribed final state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Such pro-  cesses, however, are very slow and, in principle, infinitely  slow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Protocols for speeding up the time development  have been introduced in the past, with numerous appli-  cations in quantum optics [1–22] and to classical systems,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  cranes [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  These methods include ‘shortcuts to  adiabadicity’ (STA) [1–10], ‘counterdiabatic’ approaches  [11–13] and the ‘fast-forward’ approach [15–18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In gen-  eral the above mentioned protocols yield a speed-up, but  not necessarily the fastest possible time development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Other methods are combinations with control theory [24–  26], cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' [19, 27, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' While a time development as  fast as possible is often desired, other considerations like  robustness and further conditions may prolong the re-  sulting time duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  A particular example is the efficient transport of ul-  tra cold atoms and ions by moving the confining trap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  An atom or ion in a harmonic trap can be treated to  good approximation as a quantum harmonic oscillator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  For harmonic traps efficient protocols have been inves-  tigated with STA and the invariant-based inverse engi-  neering method to obtain transitionless evolutions under  imposed constraints, faster than by an adiabatic process  [6, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' It is therefore natural to ask how fast the trans-  port of a quantum harmonic oscillator can be made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This  depends of course on the particular question one is inter-  ested in, for example a time-optimal transport a a har-  monic oscillator under additional conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Insight for the quantum case may be obtained by ask-  ing the same question for a classical harmonic oscillator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Therefore in this paper the time-optimal transport of a  classical harmonic oscillator will be investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Consider a classical one-dimensional harmonic oscilla-  tor (h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=') without friction in the center of a long wagon,  such as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 1 where a small mass m is at-  tached to a spring on the wagon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' When the wagon is  accelerated the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' will start to perform oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In  this case the frequency Ω of the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  depends on the  spring constant and on m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The problem to be investigated is the following:  (i) Initially the wagon is at rest and the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' is in its  equilibrium position, also at rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (ii) Then the wagon undergoes an acceleration a(t),  where a(t) can vary between ±amax, until it has traveled  a prescribed distance d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (iii) Upon arrival at the end point the system should  again be in its initial state, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  the wagon should be  at rest, and the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' should again be in its equilibrium  position and at rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The questions to be answered here are: Is this achiev-  able, and if so what is the shortest time possible?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Can  this time be further lowered by allowing the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  fre-  quency Ω to be time dependent, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ω(t)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Both ques-  tions will be answered in the affirmative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  a(t)  everything  at rest  everything  at rest  a(t)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 1: Oscillating mass m attached to a spring in an  accelerated wagon  The plan of the paper is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' First, in Section II,  a fixed oscillator frequency will be considered, examples  will be given and a complete solution of the problem and  an explicit protocol for fixed Ω will be formulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In  Section III detailed proofs are provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In Section IV the  case of a time-dependent oscillator frequency is treated  where Ω(t) satisfies Ω− ≤ Ω(t) ≤ Ω+, with arbitrary Ω±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The results and protocols will be seen to depend critically  on the particular choice of Ω±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Finally, in Section V the  results are summarized and discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  2  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  OPTIMAL PROTOCOL FOR FIXED  OSCILLATOR FREQUENCY  We consider a classical one-dimensional harmonic os-  cillator on a long wagon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The position of the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  mass point) relative to the wagon center will be denoted  by xh and the position of the wagon center in the external  rest frame by xw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' When the wagon is accelerated with  acceleration a(t), the mass point additionally experiences  the corresponding inertial force −ma in the rest frame of  the wagon so that one has  ¨xh = −Ω2xh − a  (1)  ¨xw = a .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  It is assumed that a(t) can vary between ±amax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Example 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' With no h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' present, to move a wagon a  distance d in shortest time, with initial and final veloc-  ity equal to zero, it is optimal to accelerate with amax  for half the distance and then decelerate with −amax [25]  (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' solid line in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The corresponding time Tabs(d),  T 2  abs = 4 d/amax, can at most be achieved, but not un-  dercut, if a h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' in the wagon is to be initially and finally  at rest in its equilibrium position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For special ’resonant values’ of Ω this time  can indeed be achieved, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' for  Ω = n Ωres(d) ,  n = 1, 2, · · ·  Ωres(d) =  �  4π2amax/d = 4π/Tabs .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (2)  To see this consider n = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Initially, the wagon and h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  are at rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Upon accelerating the wagon by amax the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  experiences, in the wagon frame, the additional inertial  force −ma and starts to move to the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' During the  time Tabs/2 it has just performed a single oscillation, has  returned to its initial position in the wagon and is at rest  relative to the wagon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In this instant, the acceleration  of the wagon is reversed, the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' starts moving to the  right and at a further time duration of Tabs/2 is back  at rest at the initial position, with the wagon at rest  and having traveled the distance d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For n > 1 one has  correspondingly more oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  For fixed Ω a protocol to obtain the unique optimal  transport time is constructed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (i) For given d determine the unique optimal time tf by  the equation  d = 1  4amax t2  f [1 −  8  (Ω tf)2  �  arccos(cos2(Ω tf/4))  �2] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (3)  (ii) With wagon and oscillator at rest at t = 0, accelerate  with amax until time 1  2tf − t1 where t1, 0 ≤ Ωt1 ≤ π/2, is  given by  t1 = 1  Ω arccos(cos2(Ω tf/4)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (4)  (iii) Decelerate with −amax until time 1  2tf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (iv) Accelerate with amax until time 1  2tf + t1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 2: Typical wagon velocities for the acceleration  alternating between±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Solid curve: No oscillator  present and Example 2 with resonant Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Dashed and  dotted curves: General Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For the dotted curve the  wagon velocity becomes partially negative, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' the  wagon moves backwards for some time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (v) Finally decelerate with −amax until time tf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Typical wagon velocities are depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' At the  end the wagon is obviously at rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The oscillator may  perform several oscillations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' That finally it is also again  at rest and in its equilibrium position will be shown at  the end of this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  In the next section it will be  shown that tf is indeed the unique optimal time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The  above protocol has a certain symmetry;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' there may, or  may not, be other, nonsymmetric, protocols which lead  to the same unique optimal time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Note that t1 = 0 if Ω tf = 4nπ, n = 1, 2, · · · , which  recovers Example 2 with tf = Tabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If t1 > 1  4tf the wagon  velocity temporarily becomes negative (dotted curve in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 2), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' then it is advantageous to go backwards for  a while.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' From Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (3, 4) this is seen to happen if  Ω2 < 1  4 Ωres(d)2,  (5)  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' for small oscillator frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' However, it can easily  be shown that the backward motion will not go back as  far as the original starting position of the wagon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  If one plots d as a function of tf in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (3) then tf  as a function of d is given by reflecting it at the diag-  onal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In dimensionless scaled variables, the solid curve  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  3 displays Ω tf as a function of d/dΩ where  dΩ = 4π2amax Ω−2 is the distance for which Ω is reso-  nant, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ωres(dΩ) = Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The dashed curve is the corre-  sponding Tabs(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Note that at d/dΩ = n2, n = 1, 2, · · ·  the two transport times coincide, which is again Example  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  For fixed d, one can also obtain tf as a function of Ω  from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In dimensionless scaled variables the result  is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' It is seen that tf diverges for Ω → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  This can be made more explicit by expanding Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (3) in  terms of Ω tf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A short calculation gives, in dimensionless  3  1  2  3  4  5  10  15  20  25  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 3: Solid curve: Optimal transport time tf as a  function of distance d in units of dΩ = 4π2amax Ω−2, for  fixed Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Dashed curve: Tabs(d) (without oscillator).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For  d/dΩ = 1, 22, · · · the times coincide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  scaled variables,  tf/Tabs(d) ≈ {6/π2}1/4 (Ω/Ωabs(d))−1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (6)  Replacing 6 by 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='3 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (6) one obtains an excel-  lent approximation for tf/Tabs(d) in the range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='05 ≤  Ω/Ωabs(d) ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='02  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='04  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='06  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='12  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 4: Fixed d: Optimal transport time tf in units of  Tabs(d) as a function of Ω in units of Ωabs(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Protocol  evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  For  the  oscillator  time-  development Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (1) has to be evaluated with a =  ±amax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This is conveniently done in the complex plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  With  z = xh + i Ω−1 ˙xh ± amax/Ω2  (7)  one finds ˙z = −iΩ z and thus z(t) = exp[−iΩ(t−t0) z(t0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Hence  xh(t) + i Ω−1 ˙xh(t) = exp[−iΩ(t − t0)]  (8)  (xh(t0) + i Ω−1 ˙xh(t0) ± amax/Ω2) ∓ amax/Ω2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  In the complex plane the right-hand side corresponds to  a clock-wise rotation of xh(t0) + i Ω−1 ˙xh(t0) by the an-  gle Ω(t − t0) around the point −amax/Ω2 and amax/Ω2,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  In the protocol one starts with xh(0)  =  0 and  ˙xh(0) = 0 and rotates clock-wise around −amax/Ω2, then  around amax/Ω2, then again around −amax/Ω2 and fi-  nally around amax/Ω2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Analytically this gives for the  1  1  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 5: Time-development of xh in complex  phase-space for Ω = 1, amax = 1, d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='82 π2,  tf = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='41 π, and t1 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='205 π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Starting at the origin, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  equilibrium position and at rest, there is first a rotation  around -1, then around 1, then around -1 and finally  again around 1, back to the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  first two rotations  ζ1 ≡ xh(tf/2 − t1) + i Ω−1 ˙xh(tf/2 − t1)  = exp[−iΩ(tf/2 − t1)] amax/Ω2 − amax/Ω2  ζ2 ≡ xh(tf/2) + i Ω−1 ˙xh(tf/2)  = exp[−iΩt1](ζ1 − amax/Ω2) + amax/Ω2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (9)  xh(tf/2) is the real part of ζ2 and one finds  xh(tf/2) = 2 a max/Ω2 (cos2(Ω tf/4)) − cos(Ω t1))  = 0  (10)  by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (4), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' ζ2 lies on the imaginary axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The cor-  responding trajectories in the complex plane correspond  LALTL3L24  to the two curves in the left half-plane in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' By  the symmetry of the protocol the next two steps give the  two curves in the right half-plane where the last one ends  again at the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This follows of course also analyti-  cally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hence after the final step the oscillator is again at  rest in its equilibrium position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Thus the protocol satis-  fies the initial and final conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  PROOF OF OPTIMALITY FOR FIXED Ω  First the equivalent converse problem will be consid-  ered: Finding the longest distance d for a given time  duration tf under the conditions (i) - (iii) in Section I  and a corresponding protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Consider some given tf and d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In the fol-  lowing it is convenient to let time run from − 1  2tf to 1  2tf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Let xh and xw satisfy Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (1) for some a(t) and the  boundary conditions at ± 1  2tf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Then 1  2(xh(t) − xh(−t))  and  1  2(xw(t) − xw(−t) + d) satisfy Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (1) with a(t)  replaced by 1  2(a(t) − a(−t)) and the same boundary con-  ditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hence without loss of generality one can assume  that xh and a are anti-symmetric while ˙xh and ˙xw are  symmetric under time reversal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Scaled variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' We go over to dimensionless scaled  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' We choose some fixed length unit d0 and put  Ω2  0  = amax/d0  ω  = Ω/Ω0  τ  = Ω0t  u(τ)  = a(t)/amax  ξ1(τ)  = xh(t)/d0  ξ2(τ)  = d  dτ ξ1(τ)  ξ3(τ) = xw(t)/d0  ξ4(τ) = d  dτ ξ3(τ)  (11)  so that u(τ) can vary between −1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Then one  obtains  ¨ξ1 ≡ d2  dτ 2 ξ1 = −ω2ξ1 − u(τ)  (12)  ¨ξ3 = u(τ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  For fixed Ω and a suitable d0 one can assume Ω0 = Ω  and then ω = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Pontryagin Maximum (or Minimum) Principle (PMP)  [24–26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This is a far-reaching generalization of the cal-  culus of variations and regarded as a milestone in control  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A simple example is a car moving in shortest time  from standstill at A to standstill at B, under the only  condition that the time-dependent acceleration resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' de-  celeration (the ’control’) is bounded, but not necessarily  continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The PMP serves to determine necessary conditions for  an optimal control function u∗(t) (or possibly several con-  trol functions) which minimizes a given cost function J  of the form J =  � T  0 L(u(τ), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=')dτ, where L is a func-  tion of the control u(τ) and some state functions ξi and  their derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For the present distance-optimal con-  trol problem, one can take L = ξ4 since J =  � T  0  ˙ξ3dτ is  the (scaled) distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' To minimize it, the PMP considers  a control Hamiltonian Hc,  Hc = −L+p1 ˙ξ1 + p2 ˙ξ2 + p3 ˙ξ3 + p4 ˙ξ4,  (13)  where one inserts ˙ξi from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (11-12) and where the  adjoint states pi are Lagrange multipliers which can not  all be identically zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Then, for an extremal control  u(τ) = u ∗ (t), Hamilton’s equations  ˙pi = −∂Hc/∂ξi,  ˙ξi = ∂Hc/∂pi  (14)  hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  For almost all −τf/2 ≤ τ ≤ τf/2, the function  Hc(pi(t), ξi(t), u(t)) attains its maximum at u(t) = u∗(t),  and Hc = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For simplicity we omit the asterisk on  u∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Inserting for ˙ξi, Hc becomes  Hc = −ξ4 + p1ξ2 + p2(−ω2ξ1 − u) + p3ξ4 + p4u .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (15)  From the term (p4−p2) u it follows that for a maximum  one has to choose u(τ) = 1 if p4 − p2 > 0 and -1 if  p4 − p2 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' When p4 − p2 = 0, or more precisely, when  p4 − p2 changes sign, there is a switch from ±1 to ∓1 in  u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hamilton’s equations become  ˙p1 = ω2p2,  ˙p2 = −p1  ˙p3 = 0,  ˙p4 = −p3 + 1  (16)  The solutions are  p2(τ) = A cos τ + B sin ωτ,  p1 = − ˙p2  p3 = c3,  p4 = (−c3 + 1) τ + c4  (17)  where A, B, c3, and c4 are constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If p4 − p2 ≡ 0  in some extended interval, then p4 = p2 ≡ 0, by linear  independence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Therefore it is not possible to have u ≡ 0  and ξ4 ≡ const in some extended interval so that there  are only isolated switches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hence, by anti-symmetry of  u, there is a switch at τ = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' −p2(0) + p4(0) = 0,  and thus A = c4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' By the boundary conditions on ξi at  ±τf/2 only the terms containing u remain in Hc which  by antisemitic of u lead to two equations and to  A (cos(ωτf/2) − 1) = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (18)  Thus either A = 0 or ωτf = 4πn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In the latter case the  situation is analogous to Example 2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' can per-  form 2n complete oscillations and the optimal distance  is the same as without oscillator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' We can therefore as-  sume A = c4 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  For ωτf ̸= 4πn there are at least  two switches of u and therefore B ̸= 0 since otherwise  −c3 + 1 = 0, c3 = 1, and ξ4 ≡ const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The explicit values  of B and c3 are not needed, they can in principle be cal-  culated at the end;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' it suffices to discuss the cases B < 0  and B > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Note: From the remark after Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (15) it follows that  u(τ) = 1 when the line p4(τ) lies above the sine curve  p2(τ) and u(τ) = −1 when it lies below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  5  Case B < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (i) Single switch for τ < 0, at −τ1, say.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Then the line p4(τ), denoted by L1 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 6, intersects  with the -sine curve p2(τ) once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The analog of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (9) for ξ + iω−1 ˙ξ in the scaled  variables, now with initial time -τf/2 and final time 0  yields  ξ1(0) = cos(ωτf/2) − 2 cos(ωτ1) + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (19)  From the anti-symmetry of ξ1 one has ξ1(0) = 0, and  from this one obtains  cos ωτ1 = cos2(ωτf/4)  (20)  with −π/2ω < −τ1 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Thus line L1 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 6 is typical  in this case, while line L2 is not possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  3 π  2 π  π  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 6: Case B < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' With ω = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' L1 and L2 denote  possible lines for p4(τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Their intersections with p2(τ)  (-sine curve) are possible switching points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In regions  where p4(τ) is above p2(τ) one has acceleration,  otherwise deceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Only L1 with a single switch is  optimal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (ii) If there are two or more switches for τ < 0, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' if  p4(τ) is given by line L2 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 6, then the last decelera-  tion period before τ = 0 is longer than π/2ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hence the  total acceleration time is less than in (i) and the distance  traveled by the wagon during τf is less than that in (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Hence for B < 0 there is only a single switch for τ < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Case B > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 7 this is case B < 0 reflected at  the τ axis, with u = ±1 interchanged and thus positive  wagon distances for B < 0 now become negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' But  there might also be negative distances for B < 0, corre-  sponding to positive distances for B > 0, and therefore a  more detailed discussion is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Here we use ω = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (i) Single switch for τ < 0: As for B < 0 there is only a  single solution for fixed τf, and this is the corresponding  optimal backward motion, with p4(τ) typically given by  L3 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (ii) Exactly two switches for τ < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Typical for this  would be lines L4 and L5 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  7, with switches at  −τ2 < −τ1 < 0, say.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  a) Case τ2 − τ1 > π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 7 one easily finds ˙ξ3(0) = τf/2 − 2(τ2 − τ1) <  τf/2 − π while, from case B < 0, ˙ξ3opt ≥ τf/2 − π since  here the switching point lies to the right of −π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hence  in case B < 0 the distance is larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  b) Case τ2 − τ1 < π/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  This will be shown to be incompatible with the bound-  ary conditions on the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='. One has ξ1(0) = 0, by anti-  symmetry, while ˙ξ1(0) ≡ λ is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Reversing the  time development from τ = 0 to τ = −τ2 one obtains  ξ1(−τ1) + i ˙ξ1(−τ1) = exp[−iτ1]{iλ + 1} − 1  ξ1(−τ2) + i−1 ˙ξ1(−τ2) =  exp[i(−τ1 + τ2)]{ξ1(−τ1) + i ˙ξ1(−τ1) − 1} + 1  = exp[i(−τ1 + τ2){exp[iτ1](iλ + 1) − 2} + 1  (21)  Since this must lie on the circle around −1 passing  through 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' upon adding 1 the rhs becomes a number of  modulus 1:  1 = | exp[i(−τ1 + τ2)]{exp[iτ1](iλ + 1) − 2} + 2|  = |iλ + 1 − 2 exp[−iτ1] + 2 exp[−iτ2]|  (22)  Hence the modulus of the real part,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  |1 − 2 cos τ1 + 2 cosτ2|,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (23)  must be less than,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' or equal to,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' However, from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  7, one has −3π/2 < −τ1 < −π and so cos τ1 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  For −2π < −τ2 < −3π/2 one has cos τ2 > 0 while for  −3π/2 < −τ2 < −π one has −2 cosτ1 + 2 cosτ2 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Hence the bracket in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (23) is larger than 1, a  contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Thus this case can not occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (iii) Three or more switches for τ < 0: A typical line is  L5 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='7 it is evident that the area under  the curve (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' distance) decreases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 7: Case B > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' With ω = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' L3, L4 and L5 denote  possible lines for p4(τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Their intersections with p2(τ)  (sine curve) are possible switching points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Dashed: ˙ξ3  with 2 intersection points −τ1 and −τ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Dotdashed:  ˙ξ3opt from case B < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For τ2 − τ1 > π/2 one has  ˙ξopt > ˙ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' L3 is typical for the optimal backwards  motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  L5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='L3L4L2L16  As a consequence, case B > 0 is not possible and case  B < 0 (i) gives the unique optimal distance for given τf  and fixed ω in scaled variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This distance is easily  calculated to be τ 2  f /4 − 2τ 2  1, with τ1, 0 ≤ τ1 ≤ π/2, given  by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In the original variables one has  d = 1  4amaxt2  f − 2amaxt2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (24)  Going back to the original problem one obtains the  protocol of Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  PROTOCOLS FOR TIME-DEPENDENT  OSCILLATOR FREQUENCY  In this case one allows in addition to a(t) also Ω(t) to  be time-dependent and seeks a minimal transport time  tf for a distance d under the condition that the wagon  is initially and finally at rest and the oscillator is at rest  in its equilibrium position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This situation is more com-  plicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If there are no bounds on Ω then for Ω → ∞  one obtains the absolute minimal time as without oscilla-  tor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Therefore, in addition to |a(t)| ≤ amax one imposes  bounds  0 ≤ Ω− ≤ Ω(t) ≤ Ω+ < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (25)  If a ’resonant value’ from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (2) lies in this interval  then, from Example 2, one chooses this value for Ω and  then obtains the absolute minimal time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Distance optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Again we first consider the  equivalent problem of finding a protocol that maximizes  the distance d for given time tf and let time run from  − 1  2tf to 1  2tf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' We will seek solutions that satisfy the same  symmetry properties as in Section III, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  we assume  that Ω(t) is symmetric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The same scaled variables as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (11) are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Introducing  u1(τ) ≡ ω2(τ)  (26)  as a second control variable, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (12) reads  ¨ξ1 ≡ d2  dτ 2 ξ1 = −u1(τ)ξ1 − u(τ)  (27)  ¨ξ3 = u(τ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The condition on Ω(t) becomes ω2  − ≤ u1(τ) ≤ ω2  +.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The  control Hamiltonian for the PMP now reads  Hc = −ξ4 + p1ξ2 + p2(−u1ξ1 − u) + p3ξ4 + p4u .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (28)  As before it follows that for a maximum one has to choose  u(τ) = 1 if p4 > p2 and -1 if p4 < p2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' When p4 − p2 = 0,  or more precisely, when p4 − p2 changes sign, there is  a switch from ±1 to ∓1 in u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Similarly, u1 = ω2  + if  p2ξ1 < 0, and u1 = ω2  − if p2ξ1 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A switch occurs  when p2ξ1 changes sign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Depending on whether u1 = ω2  + or u1 = ω2  −, Hamil-  ton’s equations in the respective τ intervals become  ˙p1 = ω2  ± p2,  ˙p2 = −p1  ˙p3 = 0,  ˙p4 = −p3 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (29)  Between switches of u1 the solutions are of the form  p2(τ) = A± cos ω±τ + B± sin ω±τ = C± sin(ω±τ − ϕ±)  (30)  p1 = − ˙p2,  p3 = c3,  p4 = (−c3 + 1) τ + c4  where c3, c4, C± are constants, and A±, B±, ϕ± are con-  stants which may dependent on the respective interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  If p2(τ) ≡ 0 in some interval then it is zero everywhere  because it cannot be joined continuously to the a nonzero  p2 from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Since ω(τ) is symmetric there must be intervals of  equal length with ω(τ) = ω+ directly to the left and right  of τ = 0 (or ω− intervals, but this will not be optimal as  shown later).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hence one must have ϕ+ = 0 in this inter-  val since then there are switches in ω(τ) at τ = ±π/ω+  because p2ξ1 vanishes there.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' It also vanishes at τ = 0  but does not change sign because of anti-symmetry of ξ1  and p2 so that ω has no switch at τ = 0 although u does.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Thus p2 is of the form  p2(τ) = B+ sin(ω+τ)  (31)  in the interval −π/ω+ ≤ τ ≤ π/ω+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  To the left of τ = −π/ω+ there is an interval with ω−,  then again an ω+ interval and so on, and similarly to the  right of τ = π/ω+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Since p2(τ) is differentiable different  parts of p2 have to be joined accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This yields an  anti-symmetric p2 as typically displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 8: Solid: p2(τ) with symmetric ω± sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Dashed: p4(τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The procedure for the determination of τ1 uses the  time-development of ξ1 and depends on the interval in  which 1  2τf lies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This will be exemplified for 1  2τf ≤ π/ω++  π/ω−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='When 1  2τf ≤ π/ω+ the situation is the same as in  Section III and τ1 is given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (20), with ω replaced  by ω+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  7  When π/ω+ <  1  2τf ≤ π/ω+ + π/ω− we calculate  ξ1(τf/2) and ˙ξ1(τf/2) from ξ1(0) and ˙ξ10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  By anti-  symmetry one has ξ1(0) = 0 and we put ˙ξ1(0) = λ, the  exact value of which will not be needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (8)  one obtains  η1 ≡ ξ1(τ1) +  i  ω+  ˙ξ1(τ1)  = exp[−iω+(τ1 − 0)]( i  ω+  λ + 1  ω2  +  ) − 1  ω2  +  η2 ≡ ξ1(π/ω+) +  i  ω+  ˙ξ1(π/ω+)  = exp[−iω+( π  ω+  − τ1)]{ℜη1 +  i  ω+ω+ℑη1 − 1  ω2  +  } + 1  ω2  +  ˜η3 ≡ ξ1(τf/2) +  i  ω−  ˙ξ1(τf/2)  = exp[−iω−(τf/2 − π  ω+  )]{ℜη2 +  i  ω−  ω+ℑη2 − 1  ω2  −  } + 1  ω2  −  (32)  By the boundary conditions at 1  2τf one has ˜η3 = 0, and  thus  0 = ℜη2 +  i  ω−  ω+ℑη2 − 1  ω2  −  + exp[iω−(τf/2 − π  ω+  )] 1  ω2  −  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (33)  Taking the real part of this one obtains after a short  calculation  cos[ω+τ1] = ω2  +  2ω2  −  {1 + cos(ω−τf/2 + ω+ − ω−  ω+  π)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (34)  The l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' cannot exceed 1, while the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' becomes 1  for τf = τopt where  τopt/2 = π  ω+  + π  ω−  − 2  ω−  arccos[ω−  ω+  ],  (35)  which lies between π/ω+ and π/ω++π/ω−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Then τ1 = 0  and the distance becomes the absolute optimum for this  particular τf = τopt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Let ω− = ω+/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Then Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (35) yields  τopt/2 = 5  3π/ω+ and the distance d/d0 becomes 1  4τ 2  opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  If one considered only ω+ and the corresponding τopt,  one would have ω+τ1 = arccos[3/4] ̸= 0 and the distance  would be less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  How to proceed when the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (34) is larger  than 1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' To answer this question we recall that p2 has  also the trivial solution p2(τ) ≡ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Then there are no  restrictions on the choice of ω(τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If one decreases ω+  on the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='s of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (34) to ω− the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' becomes less  or equal to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hence there must be an intermediate ω,  denoted by ˜ω+, such that the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='s becomes 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hence if  one uses [ω−, ˜ω+] instead of [ω−, ω+] one gets a solution  for τ1, namely τ1 = 0, so that the sequence ω− and ˜ω+  gives the largest distance for the given τf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This means  going over to a sub-interval [ω−, ˜ω+] of [ω, ω+] optimizes  the distance in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' There are many sub-intervals  with the same property, as seen further below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  In the case π/ω+ + π/ω− < τf/2 ≤ π/ω+ + π/ω− +  π/ω+, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' if one starts with ω+, switches to ω−, and to  ω+ before τ = 0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' a sequence +−+|+−+ in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 8, then  η1 and η2 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (32) remain unchanged while in η3 one  replaces τf/2 by π/ω+ + π/ω− and there is an additional  η4,  η3 = −ℜη2 + 2/ω2  − −  i  ω−  ω−ℑη2  η4 ≡ ξ1(τf/2) +  i  ω+  ˙ξ1(τf/2)  = exp[−iω+(τf/2 − π/ω+ − π/ω−)]  {ℜη3 +  i  ω+  ω−ℑη3 + 1  ω2  +  } − 1  ω2  +  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (36)  The condition η4 = 0 now gives  cos ω+τ1 = ω2  +  ω2  −  − 1 + 1  2{1 + cos(ω+τf/2 − ω+ − ω−  ω−  π)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (37)  For complete ω± intervals the exponentials in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (32)  and (36) equal -1 and using this the results are easily  generalized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In particular, for the ω± sequence − + − + | +  − + − one obtains  cos(ω+τ1) = ω2  +  ω2  −  − 1 + ω2  +  2ω2  −  {1 + cos(ω−τf/2 − 2π ω−  ω+  )}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (38)  Time optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' These results will now be applied  to the original problem in which a distance, now denoted  by d0, is fixed and the shortest transport time for given  Ω± is sought.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If this d0 is taken for the definition of the  scaled variables, d0 becomes ξ3(τf/2) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The absolutely  shortest possible time, τabs, and corresponding ωres is  then, by Example 2, given by  τabs = 2  ωres = 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (39)  From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 2 the distance traveled in time τf is 1  4τ 2  f − 2τ 2  1  and if τf is to be optimal it must satisfy  1 = 1  4τ 2  f − 2τ 2  1  (40)  where τf = τf(ω−, ω+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For given ω± one obtains τ1 from  Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (20, 34, 37) and generalizations thereof, depending  on in which interval the as yet unknown τf/2 lies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  If  ωres or an integer multiple n thereof lies in [ω−, ω+] one  chooses ω(τ) ≡ nωres and obtains the absolute optimal  τabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Different case of increasing complexity will now be  discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Case: ω− = 0, 0 < ω+ < 2π and the distance 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If  the spring constant is 0 then in the lab frame the mass  point m travels free of force and in the the wagon frame  under the inertial force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' It can happen that it is optimal  8  to start with ω−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Then m initially remains at rest in  the lab frame until a switch to ω+ occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If the time  development starts with ω+ there can be no switch to  ω− because the associated time interval π/ω− is infinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Hence in this case the results of Section II and III apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 4 it is seen that τf decreases with increasing  ω+ < 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Since τf/2 ≤ π/ω+ one has, for optimality,  τf = 2π/ω+ and τ1 = 0, by Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (3,4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (40)  one then obtains τ 2  f = 4 so that in this case one must  have ω+ = π/  √  2 ≡ ˜ω+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Thus if ω+ > ˜ω+ one starts  with ω− = 0 and then there is a switch to ω+ at some  later time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  In this case Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (34) holds for τ1 and it  becomes 0 for τf = τopt given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Taking the  limit ω− → 0 one finds τopt = (2π + 4)/ω+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This must  equal τabs = 2 which gives ω+ = π + 2 ≡ ωabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' From this  value of ω+ on one obtains the absolute time minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The optimal time as a function of ω+ is displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This depends on ω+ and is as in Section II  when ω+ ≤ ˜ω+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' When ˜ω+ < ω+ ≤ ωabs one determines  τf and τ1 from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (37) and (40), starts with ω− = 0 for  the time duration −π/˜ω+ + τf/2 and with u = 1, then  switches to ω+ and continues for the time −τ1 + π/˜ω+,  then switches to u = −1 for the time τ1 and continues by  symmetry, resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' anti-symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' When ωabs = 2 + π <  ω+ ≤ ωres one chooses the protocol for ω+ = ωabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='6  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 9: Shortest transport time tf for fixed distance d0,  Ω− = 0 and 0 ≤ Ω+/Ωres(d0) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Dotted: tf for fixed  Ω+ without switch in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Solid: Ω+/Ωres(d0) >  √  2/4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  initially Ω(t) ≡ 0 and then a switch to Ω+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For  1/2 + 1/π ≤ Ω+/Ωres(d0) ≤ 1 one has Tabs(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The  switch in Ω can thus lead to a shorter transport time  than for Ω+ alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Case: 0 < ω− < ω+ < ωres = 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  As in the pre-  ceding case, only ω+ is relevant if ω+ ≤ ˜ω+ = π/  √  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Then τf(ω−, ω+)/2 ≤ π/ω+ and is independent of ω−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  This is the upper close meshed region in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For  ω+ > ˜ω+ there are on the l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 8 two or more  alternating ω±’s for the time development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If there are  two, one starts with ω−, and the initial time −τf/2 sat-  isfies π/ω+ ≤ τf/2 ≤ π/ω+ + π/ω−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In this case Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (40) and (34) apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If the l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (34) is less or  equal to 1 then one can determine τ1 and τf(ω−, ω+), dis-  played by the coarse meshed region in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Putting  cos[ω+τ1] = 1 one obtains with τf = τabs = 2π from  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (34) the boundary curve at the bottom of the coarse  meshed surface which borders the region denoted by Tabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  In this region there is no solution for τ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' As before, here  the solution p2(τ) ≡ 0 can be used and then there are  no restrictions on ω(τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  If one starts from the point  {ω−, ω+} and first decreases ω+ until one hits the bound-  ary curve and then similarly increases ω− one obtains the  end points of an arc on the boundary curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Every point  {ˆω−, ˆω+} on this arc satisfies {ω− ≤ ˆω− ≤ ˆω+ ≤ ω+} and  yields τabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Thus there is again an improvement over the  single ω+ case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  If there were a third, preceding, interval, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  with  ω+, then τf(ω−, ω+)/2 > π/ω+ + π/ω− and τf would  thus be larger than that with only two periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hence  a third period does not occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' By a similar calculation,  interchanging ω+ and ω− leads to a larger transport time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Protocol: When ω+ ≤ ˜ω+ = π/  √  2 one proceeds with  ω+ as in Section II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' When ω+ > ˜ω+ one determines  τf(ω−, ω+) and τ1 from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (34) and (40), provided  a solution for τ1 exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Then one has an ω± sequence  of the form − + | + − and thus one starts with u = 1 and  ω− from time −τf/2 to time −π/ω+ where one switches  to ω+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Then one continues until time −τ1, where one  switches to u = −1 and continues to τ = 0 where there  is a switch back to u = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For τ > 0 one continues by  symmetry, resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' anti-symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' When there is no solu-  tion for τ1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e when the point {ω−, ω+} lies in the region  denoted by Tabs in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 10, then one can choose a proto-  col for any point on the above arc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' This will yield τabs  and in this case the protocol is not unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Case: ωres = 2π ≤ ω− < ω+ < 2 ωres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Arguing as  before, one has + − +| + −+ and − + − + | + − + − as possible  ω± sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  To the first sequence Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (37) applies  and to the second Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (38).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' One now solves Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (40)  together with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (37) for τf under the condition thatτf/2  lies in the last ω+ interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 11 this gives the left  surface outside of which there is no solution for τ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In a  similar way one obtains the right surface for the second  sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  On the boundary curve at the bottom one  has τabs and the curve is obtained from cos(ω+τ1) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The two ω± sequences are separated by the dashed curve  under the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  This curve is obtained by putting  τf/2 = 2π/ω+ + π/ω− in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (37, 40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Its end point on  the boundary curve is given by { 1  2 + 1  2  √  2, 1 + 1  2  √  2} ωres  and on the diagonal by 1  4  √  34 ωres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  In the region denoted by Tabs there is no solution for  τ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Again one can choose any point {ˆω−, ˆω+} on the  arc constructed as before to obtain τabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Reversing the  sequence to − + −| − +− leads to larger transport times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Protocol: If for a given {ω−, ω+} one has ω− ≤ ( 1  2 +  9  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 10: Shortest transport time tf for fixed distance d0  and 0 ≤ Ω−/Ωres(d0) ≤ Ω+/Ωres(d0) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For  Ω+/Ωres(d0) ≤ π/  √  2 there is only Ω+ and no switch  (close meshed region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For {Ω−, Ω+} in the region  denoted by Tabs at the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' one has the shortest time  Tabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The intersection of the surface with the front  plane is the curve of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 9 and that with the diagonal  plane is the left part of the curve of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 4 until 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  1  2  √  2) ωres or if a solution for τ1 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' (37) exists, one has  a sequence +−+|+−+, from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If a solution exists the  protocol is analogous to the previous case above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If not,  one picks a point {ˆω−, ˆω+} on the arc on the boundary  curve, as before, and uses the protocol for this point with  τf = τabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Otherwise, one has a sequence  − + − + | + − + −  and the procedure is analogous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  SUMMARY AND DISCUSSION  Protocols for the fastest possible transport of a classi-  cal harmonic oscillator (h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=') over a distance d have been  derived where both initially and finally everything is at  rest, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' the position of the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' is at rest and the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  is in its equilibrium position and also at rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The accel-  eration a(t) is assumed to satisfy −amax ≤ a(t) ≤ amax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  First, with fixed h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  frequency Ω, for the shortest  transport time the optimal acceleration alternates be-  tween ±amax.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' It was shown that one starts with amax  and that there are three switches or, for special values  Ω = nΩres(d) = 2πn  �  amax/d, n = 1, 2, · · ·, only one  switch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The switch times were determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The dependence of the shortest transport time, de-  noted by tf, on d, Ω and amax was found, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The optimal time tf is proportional to 1/√amax, diverges  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 11: Shortest transport time tf for fixed distance d0  and 1 ≤ Ω−/Ωres(d0) ≤ Ω+/Ωres(d0) ≤ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' The left side  of the surface belongs to an Ω± sequence + − +| + −+,  the right side to − + − + | + − + −, separated by the  dashed line in the bottom plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For {Ω−, Ω+} in the  region denoted by Tabs one obtains the shortest time  Tabs by going over to a point on the boundary  corresponding to a sub-interval of [Ω−, Ω+].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  for Ω → 0 and, not surprisingly, for Ω → ∞ converges  to Tabs(d) = 2  �  d/amax, the optimal time for a wagon  without h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='. The function tf(d) approaches Tabs(d) for  large d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Surprisingly, sometimes it is advantageous to go  backwards for a while, but not as far back as the initial  position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Second, in addition to a(t) a time-dependent Ω(t) sat-  isfying Ω− ≤ Ω(t) ≤ Ω+ was considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In this case  the behavior of tf depends sensitively on Ω±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' If n Ωres(d)  lies in the interval [Ω−, Ω+] for some n then choosing  n Ωres(d) will give the minimal time Tabs(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  If Ω+ ≤  1  2  √  2Ωres then Ω(t) ≡ Ω+, there is no switch  in Ω, and Ω− does not enter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Otherwise there are two  alternatives if Ω+ < Ωres:  (i) One starts with Ω−, switches to Ω+ and then back to  Ω−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  (ii) Or there are ˜Ω±, depending on Ω±, with Ω− ≤ ˜Ω− ≤  ˜Ω+ ≤ Ω+ and one starts with ˜Ω−, switches to ˜Ω+ and  then back to ˜Ω−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In this case one obtains the minimal  time Tabs(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  In the Ω− − Ω+ plane this happens for  {Ω−, Ω+} in a region, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  If n Ωres < Ω− ≤ Ω+ < (n + 1)Ωres the situation is  similarly involved and depicted for n = 1 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 11 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The Pontryagin Maximum Principle was employed,  first for constant Ω with a(t) as a control variable, and  then with a(t) and Ω(t) as control variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Symmetry  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  2- /Sres(do)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='03  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='02  t /Tabs(do)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='01  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='5  (op)s/+  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  2- /Sres(do)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='4  t /Tabs(do)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='0  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='n  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='5  (p)sa/+  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='010  properties played an important role which were proved  for constant Ω and assumed in an analogous form for  time-dependent Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  One may also want to impose restrictions on the veloc-  ities ˙xw and ˙xh or on the relative displacement xh of the  h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='. Within the PMP this may be formulated by means  of Lagrangian multipliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' In [28] the relative displace-  ment was assumed to be bounded and taken as the only  control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' However, in this case there are δ(t)-like forces at  the time of a switch acting on the h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=', and no oscillations  occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The above results for constant Ω have immediate appli-  cations to cranes for small-angle oscillations of the pay-  load where the the rope length l is constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' For time  dependent l(t) modifications are needed since l(t) is not  related to the frequency Ω(t) in the same way as the  spring constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  The harmonic oscillator considered here is an idealized  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' However, it may serve as a benchmark for more  realistic models, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' if the switches are short but smooth  rather than instantaneous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [1] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gu´ery-Odelin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ruschhaupt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Kiely, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Tor-  rontegui, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Mart´ınez-Garaot and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, Shortcuts  to adiabaticity:  Concepts, methods, and applications,  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 91, 045001 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [2] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Torrontegui, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Iba˜nez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Mart´ınez-Garaot, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Mod-  ugno, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' del Campo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gu´ery-Odelin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ruschhaupt,  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Chen, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, Shortcuts to adiabaticity, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  At.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 62, 117 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [3] Yue Ban, Xi Chen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Torrontegui, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Solano, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Casanova, Speeding up quantum perceptron via short-  cuts to adiabaticity Scientific Reports volume 11, Article  number: 5783, (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [4] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hegade, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Paul, Yongcheng Ding, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Sanz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Al-  barr´an-Arriagada, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Solano, and Xi Chen, Shortcuts to  Adiabaticity in Digitized Adiabatic Quantum Comput-  ing, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Applied 15, 024038 (2021)  [5] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ruschhaupt, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gu´ery-  Odelin, Frictionless dynamics of Bose-Einstein conden-  sates under fast trap variations, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' B 42, 241001  (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [6] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ruschhaupt, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Schmidt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' del Campo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Gu´ery-Odelin, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, Fast Optimal Frictionless  Atom Cooling in Harmonic Traps, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 104,  063002 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [7] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gu´ery-Odelin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ruiz-Montero, and  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Trizac, Exact Nonequilibrium Solutions of the Boltz-  mann Equation under a Time-Dependent External Force,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 112, 180602 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [8] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gu´ery-Odelin and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, Transport in a har-  monic trap: Shortcuts to adiabaticity and robust proto-  cols, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A 90, 063425 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ruschhaupt, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Alonso, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, Op-  timally robust shortcuts to population inversion in two-  level quantum systems, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 14, 093040 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Mart´ınez-Garaot, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Torrontegui, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Mod-  ugno, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gu´ery-Odelin, Shuo-Yen Tseng, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Muga,  Vibrational  Mode  Multiplexing of  Ultracold  Atoms, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 111, 213001 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Demirplak and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rice, On the consistency, ex-  tremal, and global properties of counterdiabatic fields, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 129, 154111 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Berry, Transitionless quantum driving, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A  42, 365303 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [13] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Chen, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Lizuain, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ruschhaupt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gu´ery-Odelin,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, Shortcut to Adiabatic Passage in Two-  and Three-Level Atoms, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' 105, 123003  (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [14] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Carolan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Kiely, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Campbell, Counterdiabatic  control in the impulse regime Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A 105, 012605  (2022)  [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Masuda and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Nakamura, Fast-forward of adiabatic  dynamics in quantum mechanics, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A 466,  1135 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Masuda and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Nakamura, Acceleration of adiabatic  quantum dynamics in electromagnetic fields, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  A 84, 043434 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [17] Katsuhiro Nakamura, Jasur Matrasulov, and Yuki Izu-  mida, Fast-forward approach to stochastic heat engine,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' E 102, 012129 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [18] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Torrontegui, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Mart´ınez-Garaot, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ruschhaupt, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, Shortcuts to adiabaticity: Fast-forward ap-  proach, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A 86, 013601 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [19] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hegerfeldt, Driving at the Quantum Speed Limit:  Optimal Control of a Two-Level System, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  111, 260501 (2013)  [20] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Dionis and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Sugny, Time-optimal control of two-  level quantum systems by piecewise constant pulses,  arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='09167  [21] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hegerfeldt, High-speed driving of a two-level sys-  tem, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A 90, 032110 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [22] Xi Chen, Yue Ban, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hegerfeldt, Time-optimal  quantum control of nonlinear two-level systems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A 94, 023624 (2016)  [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gonz´alez-Resines, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gu´ery-Odelin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Tobalina, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Lizuain, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Torrontegui, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, Invariant-Based  Inverse Engineering of Crane Control Parameters, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Applied 8, 054008 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [24] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Pontryagin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Boltyanskii, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gamkrelidze,  and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Mishchenko, The Mathematical Theory of Op-  timal Processes, Interscience (1962).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  [25] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Hocking, Optimal control: an introduction to the  theory with applications, Clarendon Press (Oxford 1991)  [26] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Boscain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Sigalotti, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Sugny, Introduction to  the Pontryagin Maximum Principle for Quantum Opti-  mal Control, PRX Quantum 2, 030203 (2021)  [27] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Torrontegui, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Lizuain, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Gonz´alez-Resines, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' To-  balina, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Ruschhaupt, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Kosloff, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, En-  ergy consumption for shortcuts to adiabaticity, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A 96, 022133 (2017)  [28] Xi Chen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Torrontegui, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Stefanatos, Jr-Shin Li, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Muga, Optimal trajectories for efficient atomic  transport without final excitation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
+page_content=' A 84,  043415 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bNAzT4oBgHgl3EQfLPu9/content/2301.01112v1.pdf'}
diff --git a/bdAyT4oBgHgl3EQf-PoQ/content/tmp_files/2301.00887v1.pdf.txt b/bdAyT4oBgHgl3EQf-PoQ/content/tmp_files/2301.00887v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..845315c5c6930ca2c7b872c97ecf7fe288c1dc07
--- /dev/null
+++ b/bdAyT4oBgHgl3EQf-PoQ/content/tmp_files/2301.00887v1.pdf.txt
@@ -0,0 +1,303 @@
+Towards Computer-Vision Based Vineyard
+Navigation for Quadruped Robots
+Lee Milburn
+Dynamic Legged Systems Lab
+Istituto Italiano di Tecnologia
+Genova, Italy
+lee.milburn@iit.it
+Juan Gamba
+Dynamic Legged Systems Lab
+Istituto Italiano di Tecnologia
+Genova, Italy
+juan.gamba@iit.it
+Claudio Semini
+Dynamic Legged Systems Lab
+Istituto Italiano di Tecnologia
+Genova, Italy
+claudio.semini@iit.it
+Abstract—There is a dramatic shortage of skilled labor for
+modern vineyards. The Vinum project is developing a mobile
+robotic solution to autonomously navigate through vineyards for
+winter grapevine pruning. This necessitates an autonomous navi-
+gation stack for the robot pruning a vineyard. The Vinum project
+is using the quadruped robot HyQReal. This paper introduces
+an architecture for a quadruped robot to autonomously move
+through a vineyard by identifying and approaching grapevines
+for pruning. The higher level control is a state machine switch-
+ing between searching for destination positions, autonomously
+navigating towards those locations, and stopping for the robot
+to complete a task. The destination points are determined by
+identifying grapevine trunks using instance segmentation from
+a Mask Region-Based Convolutional Neural Network (Mask-
+RCNN). These detections are sent through a filter to avoid
+redundancy and remove noisy detections. The combination of
+these features is the basis for the proposed architecture.
+Index Terms—Agricultural Robotics, Computer-Vision, Vine-
+yard Navigation, Quadruped Control
+I. INTRODUCTION
+Fig. 1: HyQReal in Vineyard.
+There is a major shortage of labor in vineyards across the
+world. Vineyards rely on seasonal labor, which in a lot of cases
+includes international workforces. Seasonal labor shortages
+began with the COVID-19 pandemic and have continued
+since1. Vineyards have looked towards robotic automation of
+seasonal work to account for the labor shortage.
+The Vinum project is built on the HyQReal quadruped
+robot that is being developed to autonomously do the winter
+pruning of grapevines, see Fig. 1 [8]. To accomplish this,
+1https://www.winemag.com/2021/12/07/wine-industry-labor-supply/
+the Vinum robot has to autonomously navigate vineyards,
+arriving at each grapevine that needs winter pruning. This
+extended abstract introduces a navigation architecture based
+on computer vision for quadruped robots. Previous vineyard
+navigation has described moving down each row, using a
+laser sensor, until there are no more grapevines in a row
+[7]. Other navigation stacks have been developed which also
+move down rows but they use laser scanners for perception
+[2]. Our proposed navigation stack initializes itself with a
+search of a vineyard row and will choose whether to start
+from right or left. It uses computer vision to detect the
+grapevines and a filter to average the detections and eliminate
+noise. In other papers, grapevine trunks were identified using
+instance segmentation [5]. We implemented a similar sensor
+navigation control using a RGB-D for grapevine trunk image
+segmentation. So, detections of the grapevine trunks are made
+using a Mask-RCNN trained off a created dataset with 100
+images. The combination of the higher level control with the
+grapevine detections makes the basis for the Vinum navigation
+stack.
+The contribution of this extended abstract is a navigation
+for precise placement of quadruped robots moving through
+vineyard rows. It will allow for precise robot placement within
+the vineyard that is ideal for a robotic workspace. This allows
+the robot to perform selective, plant-by-plant task automation
+within the vineyard. A series of experiments were preformed
+with the Aliengo robot and our approach achieved a mean of
+3.36cm and standard deviation of 2.19cm of distance from the
+desired position, which is sufficient for an automated task.
+II. STATE OF THE ART
+As of today, different robots and vehicles have been de-
+veloped that can move autonomously throughout vineyards.
+These robots either move continuously throughout the row
+and/or are not quadrupeds. The EU Project BACCHUS robot
+is a wheeled vehicle that is under development to harvest
+grapes and take care of vineyards. The BACCHUS robot uses
+semantic segmentation of vineyard trunks for its localization
+[5]. Our proposed navigation architecture takes the same
+segmentation approach but it is used to identify positions for
+the robot to walk to instead. The EU Project CANOPIES is
+aimed at developing a human-robot collaborative paradigm for
+arXiv:2301.00887v1  [cs.RO]  2 Jan 2023
+
+harvesting and pruning in vineyards1. It is a wheeled robot
+that works over the vineyard row. A similar autonomous over
+the vineyard row robot is the ViTiBOT Bakus which is used
+to improve vineyard help by removing herbicides and using
+precision spraying. This solution does not include stopping at
+each grapevine. YANMAR’s autonomous over-the-row robot,
+YV01, does a similar task that autonomously sprays vineyard
+rows, without stopping at a specific grapevine2. A proposed
+wheeled robot for precision agriculture is the Agri.q02 which
+is meant to work in unstructured environments in collaboration
+with a UAV [6]. A navigation stack was created for the
+wheeled Ackerman Vehicles in percision farming, path plan-
+ning from pose to pose [3]. There was autonomous navigation
+outlined in the Echord++ GRAPE experiment which maps a
+vineyard that uses a wheeled robot and moves to locations on
+the map to perform tasks [1]. These autonomous robots are
+all wheeled and most do not have to stop at precise locations
+in the vineyard. The proposed navigation architecture of this
+paper is quadruped navigation based on previous techniques
+used for localization to find precise positions for automated
+tasks to take place such as winter pruning and harvesting
+grapes.
+III. NAVIGATION ARCHITECTURE
+The navigation architecture is a combination of higher-level
+control and object detection. The higher level control will
+make decisions on its movement path through a vineyard row
+based on the grapevine trunks detected. The object detection
+was done by training a Mask-RCNN from Detectron2 [9].
+A. Higher Level Control
+Fig. 2: Navigation Flow.
+The higher level control is a state machine for the robot
+to move throughout a vineyard row, as illustrated in Fig. 2.
+It begins with an initial search to find the starting lines for
+both sides of the row. The user can set initially if they want
+the robot to move to the left or right of the row. The initial
+detections get sent through a filter which will find the rolling
+averages of each detection. From the filtered detection points,
+the control will find the lines on which the vineyard rows
+begin.
+The robot has to approach parallel to the grapevines for it to
+be able to prune properly. To find the correct destination point,
+initially, the robot determines the orientation of the approach
+by calculating the vector of the vineyards in a row. This is
+1www.canopies-project.eu
+2https://www.yanmar.com/eu/campaign/2021/10/vineyard/
+derived from a list of points found in the initial search. It
+updates the vector for possible deviances of grapevines as the
+robot moves along the row. The robot then approaches the
+grapevines in parallel at a desired distance that depends on
+the robot size and the workspace of the arm.
+After the robot has reached the determined location in the
+vineyard, it removes that grapevine from the list of vines to
+approach. Next, the control will choose the closest grapevine
+to the robot as its next target. It will continue this method until
+there are no more grapevines to identify in a row.
+B. Grapevine Identification
+Instance segmentation using a Mask-RCNN is used to detect
+the grapevine trunks in a vineyard. The training of the neural
+network was done in Detectron2 using 100 hand annotated
+images of potted grapevines. The corresponding depth of the
+detections is found by using the aligned depth image and
+from there the grapevine locations are found in relation to
+the quadruped.
+Fig. 3: Result of the image segmentation to detect grapevine
+trunks. (4 examples).
+IV. EXPERIMENTS
+A. Higher Level Control
+1) Goals: The goals of these experiments are to determine
+the precision of moving the robot’s center of mass to desired
+positions. They are aimed to align the geometric center of
+the robot with the grapevine trunk, this way an arm mounted
+on the front of the robot is in the center of the grapevine’s
+main cordon, and thus optimizes the workspace of the arm for
+single-plant operations, such as pruning.
+Fig. 4: Experiment setup.
+2) Setup: The higher level control was tested in a lab using
+Unitree’s Aliengo robot. Aliengo was used for simplification
+
+RowEnd
+No
+Yes
+Segment
+Filter segmented
+If next
+Derive pose to
+Move to next
+Grapevine Trunks
+detections
+Grapevineexists
+approach
+Grapevine
+Update detected grapevine trunkslit
+lit
+ISTITUTO ITALIANO
+ISTITUTO ITALIANO
+DI TECNOLOGIA
+DI TECNOLOGIA
+STIC
+DLS
+DYNAMIC LEGGED SYSTEMS
+DYNAMIC LEGGED SYSTEMSFig. 5: Measurement of Aliengo’s arrival at a position.
+of experiments since it is 21kg and 61cm in length. Aliengo
+is equipped with Intel’s Realsense D435 RGB-D camera. Red
+balls for segmenting were used to test in lab instead of the
+grapevine trunks. The red balls are spaced out at about 80cm
+from each other, the approximate distance that grapevines are
+from each other. The setup of the experiment can be seen in
+Fig. 4. How the precision of the robot approaching a position
+was measured is shown in Fig. 5.
+3) Tests: The robot does an initial search of the area using
+its RGB-D camera to segment the red balls. After it finds the
+row of red balls, it approaches the first position in the row.
+After the robot’s arrival at the initial position, it pauses for
+an automated task and update its detections. It repeats this
+process until the row is finished and then stops.
+Ten trials were conducted with five balls. To measure the
+error between the destination point and the red ball, a laser
+pointer was used to show the point that Aliengo’s center of
+mass reached.
+4) Results: The error of reaching the destination point is
+a mean of 3.36cm and standard deviation of 2.19cm. The
+accompanying video shows complete trials.
+B. Grapevine Identification
+1) Goals: The goal of this is to test how well the Mask-
+RCNN was trained for working in vineyards.
+2) Setup: The training of the neural network was done in
+Detectron2 using the framework set up in the paper [4].
+3) Tests: The results were tested on a previously recorded
+video of a potted vineyard at University Cattolica of Piacenza
+during winter.
+4) Results: Outputs from the model are shown in Fig. 3.
+Currently the model needs to be trained on more data for
+robustness and for functionality in other vineyards as well.
+V. CONCLUSION
+This paper presented a method of computer-vision based
+navigation in vineyards for quadruped robots. This method
+will allow for precise placement to preform selective task
+automation.
+The control architecture works accurately with the exper-
+iments in the lab, and the trunk detections from the image
+segmentation can accurately identify grapevine trunks. The
+quadruped can reach a desired destination position with a mean
+error of 3.36cm error.
+The next steps for this architecture is combining the
+grapevine trunk semantic segmentation with the higher level
+control to test in the field. The dataset created for this project
+has to be expanded to train a more robust Mask-RCNN as
+well.
+VI. ACKNOWLEDGMENTS
+Thanks to the contributions of Miguel Fernandes for helping
+train the dataset and Lorenzo Amatucci for the configuration
+of the robot’s controllers for experiments.
+REFERENCES
+[1]
+P. Astolfi, A. Gabrielli, L. Bascetta, and M. Matteucci.
+“Vineyard Autonomous Navigation in the Echord++ GRAPE
+Experiment (FP7-601116). http://echord.eu/grape/”. In: IFAC-
+PapersOnLine 51.11 (2018). 16th IFAC Symposium on In-
+formation Control Problems in Manufacturing INCOM 2018,
+pp. 704–709. ISSN: 2405-8963. DOI: https://doi.org/10.1016/
+j.ifacol.2018.08.401. URL: https://www.sciencedirect.com/
+science/article/pii/S2405896318315271.
+[2]
+M. Bergerman, S. M. Maeta, J. Zhang, G. M. Freitas, B. Ham-
+ner, S. Singh, and G. Kantor. “Robot Farmers: Autonomous Or-
+chard Vehicles Help Tree Fruit Production”. In: IEEE Robotics
+& Automation Magazine 22.1 (2015), pp. 54–63. DOI: 10.1109/
+MRA.2014.2369292.
+[3]
+R. F. Carpio, C. Potena, J. Maiolini, G. Ulivi, N. B. Rossell´o,
+E. Garone, and A. Gasparri. “A Navigation Architecture for
+Ackermann Vehicles in Precision Farming”. In: IEEE Robotics
+and Automation Letters 5.2 (2020), pp. 1103–1110. DOI: 10.
+1109/LRA.2020.2967306.
+[4]
+M. Fernandes, A. Scaldaferri, P. Guadagna, G. Fiameni, T. Teng,
+M. Gatti, S. Poni, C. Semini, D. G. Caldwell, and F. Chen.
+“Towards Precise Pruning Points Detection using Semantic-
+Instance-Aware Plant Models for Grapevine Winter Pruning
+Automation”. In: CoRR abs/2109.07247 (2021). arXiv: 2109.
+07247. URL: https://arxiv.org/abs/2109.07247.
+[5]
+A. Papadimitriou, I. Kleitsiotis, I. Kostavelis, I. Mariolis, D.
+Giakoumis, S. Likothanassis, and D. Tzovaras. “Loop Closure
+Detection and SLAM in Vineyards with Deep Semantic Cues”.
+In: 2022 International Conference on Robotics and Automation
+(ICRA). 2022, pp. 2251–2258. DOI: 10.1109/ICRA46639.2022.
+9812419.
+[6]
+G. Quaglia, C. Visconte, L. S. Scimmi, M. Melchiorre, P.
+Cavallone, and S. Pastorelli. “Design of a UGV Powered
+by Solar Energy for Precision Agriculture”. In: Robotics 9.1
+(2020). ISSN: 2218-6581. DOI: 10.3390/robotics9010013. URL:
+https://www.mdpi.com/2218-6581/9/1/13.
+[7]
+G. Riggio, C. Fantuzzi, and C. Secchi. “A Low-Cost Navigation
+Strategy for Yield Estimation in Vineyards”. In: May 2018,
+pp. 2200–2205. DOI: 10.1109/ICRA.2018.8462839.
+[8]
+C. Semini, V. Barasuol, M. Focchi, C. Boelens, M. Emara,
+S. Casella, O. Villarreal, R. Orsolino, G. Fink, S. Fahmi,
+et al. “Brief introduction to the quadruped robot HyQReal”.
+In: Istituto di Robotica e Macchine Intelligenti (I-RIM) (2019).
+[9]
+Y. Wu, A. Kirillov, F. Massa, W.-Y. Lo, and R. Girshick.
+“Detectron2”. In: (2019).
+
+w.burster.it
+7
+61
+81
+14
\ No newline at end of file
diff --git a/bdAyT4oBgHgl3EQf-PoQ/content/tmp_files/load_file.txt b/bdAyT4oBgHgl3EQf-PoQ/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b0aea2d26112dc18bff0b2437107bd487e6164e6
--- /dev/null
+++ b/bdAyT4oBgHgl3EQf-PoQ/content/tmp_files/load_file.txt
@@ -0,0 +1,286 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf,len=285
+page_content='Towards Computer-Vision Based Vineyard  Navigation for Quadruped Robots  Lee Milburn  Dynamic Legged Systems Lab  Istituto Italiano di Tecnologia  Genova, Italy  lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='milburn@iit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='it  Juan Gamba  Dynamic Legged Systems Lab  Istituto Italiano di Tecnologia  Genova, Italy  juan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='gamba@iit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='it  Claudio Semini  Dynamic Legged Systems Lab  Istituto Italiano di Tecnologia  Genova, Italy  claudio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='semini@iit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='it  Abstract—There is a dramatic shortage of skilled labor for  modern vineyards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The Vinum project is developing a mobile  robotic solution to autonomously navigate through vineyards for  winter grapevine pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' This necessitates an autonomous navi-  gation stack for the robot pruning a vineyard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The Vinum project  is using the quadruped robot HyQReal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' This paper introduces  an architecture for a quadruped robot to autonomously move  through a vineyard by identifying and approaching grapevines  for pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The higher level control is a state machine switch-  ing between searching for destination positions, autonomously  navigating towards those locations, and stopping for the robot  to complete a task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The destination points are determined by  identifying grapevine trunks using instance segmentation from  a Mask Region-Based Convolutional Neural Network (Mask-  RCNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' These detections are sent through a filter to avoid  redundancy and remove noisy detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The combination of  these features is the basis for the proposed architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  Index Terms—Agricultural Robotics, Computer-Vision, Vine-  yard Navigation, Quadruped Control  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' INTRODUCTION  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 1: HyQReal in Vineyard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  There is a major shortage of labor in vineyards across the  world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Vineyards rely on seasonal labor, which in a lot of cases  includes international workforces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Seasonal labor shortages  began with the COVID-19 pandemic and have continued  since1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Vineyards have looked towards robotic automation of  seasonal work to account for the labor shortage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  The Vinum project is built on the HyQReal quadruped  robot that is being developed to autonomously do the winter  pruning of grapevines, see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 1 [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' To accomplish this,  1https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='winemag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='com/2021/12/07/wine-industry-labor-supply/  the Vinum robot has to autonomously navigate vineyards,  arriving at each grapevine that needs winter pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' This  extended abstract introduces a navigation architecture based  on computer vision for quadruped robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Previous vineyard  navigation has described moving down each row, using a  laser sensor, until there are no more grapevines in a row  [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Other navigation stacks have been developed which also  move down rows but they use laser scanners for perception  [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Our proposed navigation stack initializes itself with a  search of a vineyard row and will choose whether to start  from right or left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' It uses computer vision to detect the  grapevines and a filter to average the detections and eliminate  noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' In other papers, grapevine trunks were identified using  instance segmentation [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' We implemented a similar sensor  navigation control using a RGB-D for grapevine trunk image  segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' So, detections of the grapevine trunks are made  using a Mask-RCNN trained off a created dataset with 100  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The combination of the higher level control with the  grapevine detections makes the basis for the Vinum navigation  stack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  The contribution of this extended abstract is a navigation  for precise placement of quadruped robots moving through  vineyard rows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' It will allow for precise robot placement within  the vineyard that is ideal for a robotic workspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' This allows  the robot to perform selective, plant-by-plant task automation  within the vineyard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' A series of experiments were preformed  with the Aliengo robot and our approach achieved a mean of  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='36cm and standard deviation of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='19cm of distance from the  desired position, which is sufficient for an automated task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' STATE OF THE ART  As of today, different robots and vehicles have been de-  veloped that can move autonomously throughout vineyards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  These robots either move continuously throughout the row  and/or are not quadrupeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The EU Project BACCHUS robot  is a wheeled vehicle that is under development to harvest  grapes and take care of vineyards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The BACCHUS robot uses  semantic segmentation of vineyard trunks for its localization  [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Our proposed navigation architecture takes the same  segmentation approach but it is used to identify positions for  the robot to walk to instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The EU Project CANOPIES is  aimed at developing a human-robot collaborative paradigm for  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='00887v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='RO]  2 Jan 2023  harvesting and pruning in vineyards1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' It is a wheeled robot  that works over the vineyard row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' A similar autonomous over  the vineyard row robot is the ViTiBOT Bakus which is used  to improve vineyard help by removing herbicides and using  precision spraying.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' This solution does not include stopping at  each grapevine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' YANMAR’s autonomous over-the-row robot,  YV01, does a similar task that autonomously sprays vineyard  rows, without stopping at a specific grapevine2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' A proposed  wheeled robot for precision agriculture is the Agri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='q02 which  is meant to work in unstructured environments in collaboration  with a UAV [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' A navigation stack was created for the  wheeled Ackerman Vehicles in percision farming, path plan-  ning from pose to pose [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' There was autonomous navigation  outlined in the Echord++ GRAPE experiment which maps a  vineyard that uses a wheeled robot and moves to locations on  the map to perform tasks [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' These autonomous robots are  all wheeled and most do not have to stop at precise locations  in the vineyard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The proposed navigation architecture of this  paper is quadruped navigation based on previous techniques  used for localization to find precise positions for automated  tasks to take place such as winter pruning and harvesting  grapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' NAVIGATION ARCHITECTURE  The navigation architecture is a combination of higher-level  control and object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The higher level control will  make decisions on its movement path through a vineyard row  based on the grapevine trunks detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The object detection  was done by training a Mask-RCNN from Detectron2 [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Higher Level Control  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 2: Navigation Flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  The higher level control is a state machine for the robot  to move throughout a vineyard row, as illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  It begins with an initial search to find the starting lines for  both sides of the row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The user can set initially if they want  the robot to move to the left or right of the row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The initial  detections get sent through a filter which will find the rolling  averages of each detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' From the filtered detection points,  the control will find the lines on which the vineyard rows  begin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  The robot has to approach parallel to the grapevines for it to  be able to prune properly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' To find the correct destination point,  initially, the robot determines the orientation of the approach  by calculating the vector of the vineyards in a row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' This is  1www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='canopies-project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='eu  2https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='yanmar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='com/eu/campaign/2021/10/vineyard/  derived from a list of points found in the initial search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' It  updates the vector for possible deviances of grapevines as the  robot moves along the row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The robot then approaches the  grapevines in parallel at a desired distance that depends on  the robot size and the workspace of the arm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  After the robot has reached the determined location in the  vineyard, it removes that grapevine from the list of vines to  approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Next, the control will choose the closest grapevine  to the robot as its next target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' It will continue this method until  there are no more grapevines to identify in a row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Grapevine Identification  Instance segmentation using a Mask-RCNN is used to detect  the grapevine trunks in a vineyard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The training of the neural  network was done in Detectron2 using 100 hand annotated  images of potted grapevines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The corresponding depth of the  detections is found by using the aligned depth image and  from there the grapevine locations are found in relation to  the quadruped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 3: Result of the image segmentation to detect grapevine  trunks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' (4 examples).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' EXPERIMENTS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Higher Level Control  1) Goals: The goals of these experiments are to determine  the precision of moving the robot’s center of mass to desired  positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' They are aimed to align the geometric center of  the robot with the grapevine trunk, this way an arm mounted  on the front of the robot is in the center of the grapevine’s  main cordon, and thus optimizes the workspace of the arm for  single-plant operations, such as pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 4: Experiment setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  2) Setup: The higher level control was tested in a lab using  Unitree’s Aliengo robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Aliengo was used for simplification  RowEnd  No  Yes  Segment  Filter segmented  If next  Derive pose to  Move to next  Grapevine Trunks  detections  Grapevineexists  approach  Grapevine  Update detected grapevine trunkslit  lit  ISTITUTO ITALIANO  ISTITUTO ITALIANO  DI TECNOLOGIA  DI TECNOLOGIA  STIC  DLS  DYNAMIC LEGGED SYSTEMS  DYNAMIC LEGGED SYSTEMSFig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 5: Measurement of Aliengo’s arrival at a position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  of experiments since it is 21kg and 61cm in length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Aliengo  is equipped with Intel’s Realsense D435 RGB-D camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Red  balls for segmenting were used to test in lab instead of the  grapevine trunks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The red balls are spaced out at about 80cm  from each other, the approximate distance that grapevines are  from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The setup of the experiment can be seen in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' How the precision of the robot approaching a position  was measured is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  3) Tests: The robot does an initial search of the area using  its RGB-D camera to segment the red balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' After it finds the  row of red balls, it approaches the first position in the row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  After the robot’s arrival at the initial position, it pauses for  an automated task and update its detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' It repeats this  process until the row is finished and then stops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  Ten trials were conducted with five balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' To measure the  error between the destination point and the red ball, a laser  pointer was used to show the point that Aliengo’s center of  mass reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  4) Results: The error of reaching the destination point is  a mean of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='36cm and standard deviation of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='19cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The  accompanying video shows complete trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Grapevine Identification  1) Goals: The goal of this is to test how well the Mask-  RCNN was trained for working in vineyards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  2) Setup: The training of the neural network was done in  Detectron2 using the framework set up in the paper [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  3) Tests: The results were tested on a previously recorded  video of a potted vineyard at University Cattolica of Piacenza  during winter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  4) Results: Outputs from the model are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  Currently the model needs to be trained on more data for  robustness and for functionality in other vineyards as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' CONCLUSION  This paper presented a method of computer-vision based  navigation in vineyards for quadruped robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' This method  will allow for precise placement to preform selective task  automation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  The control architecture works accurately with the exper-  iments in the lab, and the trunk detections from the image  segmentation can accurately identify grapevine trunks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The  quadruped can reach a desired destination position with a mean  error of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='36cm error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  The next steps for this architecture is combining the  grapevine trunk semantic segmentation with the higher level  control to test in the field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' The dataset created for this project  has to be expanded to train a more robust Mask-RCNN as  well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' ACKNOWLEDGMENTS  Thanks to the contributions of Miguel Fernandes for helping  train the dataset and Lorenzo Amatucci for the configuration  of the robot’s controllers for experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  REFERENCES  [1]  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Astolfi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Gabrielli, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Bascetta, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Matteucci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  “Vineyard Autonomous Navigation in the Echord++ GRAPE  Experiment (FP7-601116).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' http://echord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='eu/grape/”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' In: IFAC-  PapersOnLine 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='11 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 16th IFAC Symposium on In-  formation Control Problems in Manufacturing INCOM 2018,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 704–709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' ISSN: 2405-8963.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' DOI: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='1016/  j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='ifacol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' URL: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='sciencedirect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='com/  science/article/pii/S2405896318315271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  [2]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Bergerman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Maeta, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Zhang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Freitas, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Ham-  ner, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Singh, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Kantor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' “Robot Farmers: Autonomous Or-  chard Vehicles Help Tree Fruit Production”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' In: IEEE Robotics  & Automation Magazine 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='1 (2015), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 54–63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='1109/  MRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='2369292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  [3]  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Carpio, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Potena, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Maiolini, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Ulivi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Rossell´o,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Garone, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Gasparri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' “A Navigation Architecture for  Ackermann Vehicles in Precision Farming”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' In: IEEE Robotics  and Automation Letters 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='2 (2020), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 1103–1110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  1109/LRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='2967306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  [4]  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Fernandes, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Scaldaferri, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Guadagna, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Fiameni, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Teng,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Gatti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Poni, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Semini, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Caldwell, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  “Towards Precise Pruning Points Detection using Semantic-  Instance-Aware Plant Models for Grapevine Winter Pruning  Automation”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' In: CoRR abs/2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='07247 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' arXiv: 2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  07247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' URL: https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='org/abs/2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='07247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  [5]  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Papadimitriou, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Kleitsiotis, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Kostavelis, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Mariolis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  Giakoumis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Likothanassis, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Tzovaras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' “Loop Closure  Detection and SLAM in Vineyards with Deep Semantic Cues”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  In: 2022 International Conference on Robotics and Automation  (ICRA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 2251–2258.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='1109/ICRA46639.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  9812419.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  [6]  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Quaglia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Visconte, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Scimmi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Melchiorre, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  Cavallone, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Pastorelli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' “Design of a UGV Powered  by Solar Energy for Precision Agriculture”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' In: Robotics 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='1  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' ISSN: 2218-6581.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='3390/robotics9010013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' URL:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='mdpi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='com/2218-6581/9/1/13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  [7]  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Riggio, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Fantuzzi, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Secchi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' “A Low-Cost Navigation  Strategy for Yield Estimation in Vineyards”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' In: May 2018,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' 2200–2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='1109/ICRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='8462839.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  [8]  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Semini, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Barasuol, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Focchi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Boelens, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Emara,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Casella, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Villarreal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Orsolino, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Fink, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Fahmi,  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' “Brief introduction to the quadruped robot HyQReal”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  In: Istituto di Robotica e Macchine Intelligenti (I-RIM) (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  [9]  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Wu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Kirillov, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Massa, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Lo, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' Girshick.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  “Detectron2”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content=' In: (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='  w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='burster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
+page_content='it  7  61  81  14' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdAyT4oBgHgl3EQf-PoQ/content/2301.00887v1.pdf'}
diff --git a/bdFAT4oBgHgl3EQfXh2G/content/tmp_files/2301.08534v1.pdf.txt b/bdFAT4oBgHgl3EQfXh2G/content/tmp_files/2301.08534v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..90670207caf30d0c839cd1d45cd3d70350ac6870
--- /dev/null
+++ b/bdFAT4oBgHgl3EQfXh2G/content/tmp_files/2301.08534v1.pdf.txt
@@ -0,0 +1,910 @@
+Galaz, Z. et al. (2022). Prodromal Diagnosis of Lewy Body Diseases Based on the Assessment of Graphomotor 
+and Handwriting Difficulties. In: Carmona-Duarte, C., Diaz, M., Ferrer, M.A., Morales, A. (eds) Intertwining 
+Graphonomics with Human Movements. IGS 2022. Lecture Notes in Computer Science, vol 13424. Springer, 
+Cham. https://doi.org/10.1007/978-3-031-19745-1_19 
+ 
+ 
+Prodromal Diagnosis of Lewy Body 
+Diseases Based on the Assessment 
+of Graphomotor and Handwriting 
+Difficulties 
+ 
+Zoltan Galaz1, Jiri Mekyska1, Jan Mucha1, Vojtech Zvoncak1, Zdenek Smekal1, 
+Marcos Faundez-Zanuy2, Lubos Brabenec3, Ivona Moravkova3,4,5, and Irena 
+Rektorova3,4 
+1 Department of Telecommunications, Faculty of Electrical Engineering and 
+Communication, Brno University of Technology, Brno, Czech Republic 
+xgalaz00@gmail.com 
+2 Escola Superior Politecnica, Tecnocampus, Mataro, Barcelona, Spain 
+3 Applied Neuroscience Research Group, Central European Institute 
+of Technology – CEITEC, Masaryk University, Brno, Czech Republic 
+4 First Department of Neurology, Faculty of Medicine and St. Anne’s University 
+Hospital, Masaryk University, Brno, Czech Republic 
+5 Faculty of Medicine, Masaryk University, Brno, Czech Republic 
+ 
+Abstract. To this date, studies focusing on the prodromal diagnosis of 
+Lewy body diseases (LBDs) based on quantitative analysis of graphomo- 
+tor and handwriting difficulties are missing. In this work, we enrolled 18 
+subjects diagnosed with possible or probable mild cognitive impairment 
+with Lewy bodies (MCI-LB), 7 subjects having more than 50% prob- 
+ability of developing Parkinson’s disease (PD), 21 subjects with both 
+possible/probable MCI-LB and probability of PD > 50%, and 37  age- 
+and gender-matched healthy controls (HC). Each participant performed 
+three tasks: Archimedean spiral drawing (to quantify graphomotor diffi- 
+culties), sentence writing task (to quantify handwriting difficulties), and 
+pentagon copying test (to quantify cognitive decline). Next, we parame- 
+terized the acquired data by various temporal, kinematic, dynamic, spa- 
+tial, and task-specific features. And finally, we trained classification mod- 
+els for each task separately as well as a model for their combination to 
+estimate the predictive power of the features for the identification of 
+LBDs. Using this approach we were able to identify prodromal LBDs 
+with 74% accuracy and showed the promising potential of computerized 
+objective and non-invasive diagnosis of LBDs based on the assessment 
+of graphomotor and handwriting difficulties. 
+ 
+ 
+This work was supported by grant no. NU20-04-00294 (Diagnostics  of  Lewy  body 
+diseases in prodromal stage based on multimodal data analysis) of the Czech Ministry 
+of Health and by Spanish grant of the Ministerio de Ciencia e Innovacio´n no. PID2020- 
+113242RB-I00. 
+
+ 
+ 
+· 
+· 
+· 
+· 
+· 
+ 
+Keywords:   Lewy  body  diseases    Online  handwriting    Graphomotor 
+difficulties     Handwriting  difficulties    Machine  learning     Prodromal 
+diagnosis 
+ 
+1 Introduction 
+ 
+Lewy body diseases (LBDs) is a term describing a group of neurodegenerative 
+disorders characterized by a pathophysiological process of α-synuclein accumu- 
+lation in specific brain regions leading to the formation of Lewy bodies and 
+Lewy neurites resulting in cell death. LBDs consists of two major clinical enti- 
+ties: Parkinson’s disease (PD) and dementia with Lewy bodies (DLB) [29,38]. 
+Although the phenotypes and temporal evolution of motor and cognitive symp- 
+toms of these two diseases vary, they share many clinical and pathophysiolog- 
+ical features and are therefore referred to as LBDs spectrum. Together with 
+Alzheimer’s disease (AD), LBDs comprise the major part of all cases of neu- 
+rodegenerative disorders. 
+It is known that LBDs do not start suddenly. At the time the clinical symp- 
+toms occur, the neurodegenerative process has reached a severe degree in which 
+most of the targeted neurons have already been damaged. Before the clinical 
+diagnosis based on the presence of typical clinical symptoms becomes possible, 
+there is a long period of the underlying neurodegenerative process with subtle or 
+nonspecific symptoms [18,29] such as sleep disturbances, mood changes, smell 
+loss, constipation, etc. This period of LBDs is called the prodromal stage. 
+One of the early markers of PD is PD dysgraphia (micrographia and other 
+alterations in handwriting, e.g. kinematic and dynamic) [21,32,33]. Similarly, 
+some manifestations of dysgraphia have been observed in the prodromal DLB 
+as well [23]. Although modern approaches to the analysis of graphomotor and 
+handwriting difficulties (utilising digitising tablets) were proved to work well 
+during e.g. diagnosis of the clinical stage of PD [9,11,35], assessment of cogni- 
+tion in PD patients [4], or discrimination of AD and mild cognitive impairment 
+(MCI) [15], to the best of our knowledge, no studies employed this technology 
+(with high potential) in the prodromal diagnosis of LBDs in a larger scale. 
+Identification of the early stages of LBDs is crucial for the development 
+of disease-modifying treatment since the neurodegeneration may be possibly 
+stopped or treated before the pathological cascades start. Therefore, the goal 
+of this study is to explore whether the computerised assessment of graphomo- 
+tor and handwriting difficulties could support the prodromal diagnosis of LBDs, 
+more specifically, we aim to: 
+1. identify which task significantly discriminates LBD patients and age- and 
+gender-matched healthy controls (HC), 
+2. identify what conventional online handwriting features have good discrimina- 
+tion power. 
+
+ 
+ 
+± 
+± 
+± 
+ 
+2 Materials and Methods 
+ 
+2.1 
+Dataset 
+We enrolled 39 subjects (19 females, 20 males, age = 69.53 
+6.61) diagnosed 
+with possible or probable MCI (based on the scores of the MoCA – Montreal 
+Cognitive Assessment [25] and based on the CCB – Complex Cognitive Battery, 
+see the explanation below) who were simultaneously diagnosed with possible or 
+probable MCI-LB (i.e. mild cognitive impairment with Lewy bodies) based on 
+the criteria published by McKeith et al. [22]. In this group, 21 subjects also 
+had more than 50% probability of developing PD (calculated following the MDS 
+criteria published in [18]). In addition, we enrolled 7 subjects (2 females, 5 males, 
+age = 66.41    4.32) without possible/probable MCI-LB, but still with more than 
+50% probability of developing PD. Finally, we enrolled 37 HC (26 females, 11 
+males, age = 67.60 
+5.61). In the experiments, we stratified the subjects into 
+two groups, HC vs. LBD (i.e. people with a high risk of developing PD or DLB). 
+CCB was used to evaluate four cognitive domains: 1) memory (The Brief 
+Visuospatial memory test–revised [2], Philadelphia Verbal Learning Test [3]); 
+2) attention (Wechsler Adult Intelligence Scale-III: Letter-Number Sequencing, 
+Digit Symbol Substitution [37]); 3) executive functions (Semantic and phonemic 
+verbal fluency [30], Picture arrangement test [37]); and 4) visuospatial functions 
+(Judgment of Line Orientation [36]). The cognitive domain z-scores were com- 
+puted as the average z-scores of the tests included in the particular domain. 
+The participants were asked to perform a set of three tasks: 
+1. Archimedean spiral (spiral) – we consider this task as a graphomotor one, i.e. 
+it is a building block of some letter shapes; in addition, it is a golden standard 
+in PD dysgraphia diagnosis [35] 
+2. sentence  “Tramvaj   dnes  uˇz  nepojede”  (translation:   “A  tram  will  not  go 
+today.”) writing (sentence) – this handwriting task was used e.g. in the 
+PaHaW database [11] 
+3. pentagon copying test (pentagons) – it is a task frequently used for quantifi- 
+cation of cognitive decline [4] 
+All participants were right-handed and had Czech as their native language. 
+They all signed an informed consent form that was approved by the local ethics 
+committee. 
+ 
+2.2 
+Feature Extraction 
+The participants were asked to perform the tasks (using the Wacom Ink pen) 
+on an A4 paper that was laid down and fixed to a digitizing tablet Wacom 
+Intuos 4 M (sampling frequency fs = 130 Hz). Before the acquisition, they had 
+some time to get familiar with the hardware. The recorded time series (x and 
+y position; timestamp; a binary variable, being 0 for in-air movement and 1 for 
+on-surface movement, respectively; pressure exert on the tablet’s surface during 
+
+ 
+ 
+ 
+writing; pen tilt; azimuth) were consequently parameterised utilising the follow- 
+ing set of features (we selected the set based on available reviews and based on 
+our experience [9,11,35]): 
+1. temporal – duration of writing, ratio of the on-surface/in-air duration, dura- 
+tion of strokes, and ratio of the on-surface/in-air stroke duration 
+2. kinematic – velocity, and acceleration 
+3. dynamic – pressure, tilt, and azimuth 
+4. spatial – width, height, and length of the whole product, as well as its partic- 
+ular strokes, i.e. stroke width, height, and length 
+5. spiral-specific – degree of spiral drawing severity [31], mean drawing speed of 
+spiral [31], second-order smoothness of spiral [31], spiral precision index [5], 
+spiral tightness [31], variability of spiral width [31], and first-order zero- 
+crossing rate of spiral [31] 
+6. other – number of interruptions (pen elevations), number of pen stops [27], 
+tempo (number of strokes normalised by duration), number of on-surface 
+intra-stroke intersections, relative number of on-surface intra-stroke intersec- 
+tions, number of on-surface inter-stroke intersections, and relative number of 
+on-surface inter-stroke intersections, Shannon entropy [4], number of changes 
+in the velocity profile, relative number of changes in the velocity profile 
+Most of the features were extracted using the recently released Python library 
+handwriting-features (v 1.0.1) [14], the rest of them were coded in Matlab. Some 
+features (mainly spatial, temporal and kinematic) were extracted from both on- 
+surface and in-air movements. In addition, kinematic features were also analysed 
+in horizontal and vertical projection. Features represented by vectors were con- 
+sequently transformed to a scalar value using median, non-parametric coefficient 
+of variation (nCV; interquartile range of feature divided by its median), slope 
+and 95th percentile (95p). 
+ 
+2.3 
+Statistical Analysis and Machine Learning 
+To compare the distribution of features between the HC and LBD subjects, we 
+conducted Mann-Whitney U-test with the significance level of 0.05. Moreover, 
+to assess the strength of a relationship between the features and the subject’s 
+clinical status (HC/LBD), we computed Spearman’s correlation coefficient (ρ) 
+with the significance level of 0.05. Finally, during this exploratory step, we calcu- 
+lated Spearman’s correlation with the domains of CCB and the overall score of 
+MDS–Unified Parkinson’s Disease Rating Scale (MDS–UPDRS), part III (motor 
+part) [16]. 
+To identify the presence of graphomotor or handwriting difficulties, we built 
+binary classification models using an ensemble extreme gradient boosting algo- 
+rithm known as XGBoost [6] (with 100 estimators). This algorithm was chosen 
+due to its robustness to outliers, ability to find complex interactions among fea- 
+tures as well as the possibility of ranking their importance. To build models with 
+an optimal set of hyperparameters, we conducted 1000 iteration of randomized 
+
+ 
+ 
+× 
+× 
+× 
+2 
+TP + FN TN + FP  
+ 
+search strategy via stratified 5-fold cross-validation with 10 repetitions aiming 
+to optimize balanced accuracy score (BACC; described in more detail along with 
+other evaluation scores below). The following set of hyperparameters were opti- 
+mized: the learning rate [0.001, 0.01, 0.1, 0.2, 0.3], γ [0, 0.05, 0.10, 0.15, 0.20, 
+0.25, 0.5], the maximum tree depth [6, 8, 10, 12, 15], the fraction of observations 
+to be randomly sampled for each tree (subsample ratio) [0.5, 0.6, 0.7, 0.8, 0.9, 
+1.0], the subsample ratio for the columns at each level [0.4, 0.5, 0.6, 0.7, 0.8, 
+0.9, 1.0], the subsample ratio for the columns when constructing each tree [0.4, 
+0.5, 0.6, 0.7, 0.8, 0.9, 1.0], the minimum sum of the weights of all observations 
+required in a child node [0.5, 1.0, 3.0, 5.0, 7.0, 10.0], and the balance between 
+positive and negative weights [1, 2, 3, 4]. 
+The classification test performance was determined using the following clas- 
+sification metrics: Matthew’s correlation coefficient (MCC), balanced accuracy 
+(BACC), sensitivity (SEN) also known as recall (REC), specificity (SPE), pre- 
+cision (PRE) and F1 score (F1). These metrics are defined as follows: 
+TP × TN + FP × FN  
+ 
+MCC = 
+√N 
+, 
+(1) 
+BACC = 1 
+TP 
+TN 
+, 
+(2) 
+ 
+SPE = 
+TN  
+TN + FP  
+PRE = 
+TP  
+TP + FP  
+REC = 
+TP  
+, 
+(3) 
+ 
+, 
+(4) 
+ , 
+(5) 
+ 
+TP + FN  
+F1 = 2 PRE × REC 
+PRE + REC 
+ 
+(6) 
+where N  = (TP + FP )    (TP + FN )      (TN + FP )     (TN + FN ), TP (true 
+positive) and FP (false positive) represent the number of correctly identified 
+LBD subjects and the number of subjects incorrectly identified as having LBDs, 
+respectively. Similarly, TN (true negative) and FN (false negative) represent 
+the number of correctly identified HC and the number of subjects with LBDs 
+incorrectly identified as being healthy. 
+To further optimize the trained classification models, we fine-tuned the mod- 
+els’ decision thresholds via the receiver operating characteristics (ROC) curve. 
+Using the fine-tuned decision thresholds, we evaluated the classification perfor- 
+mance of the models using the leave-one-out cross-validation. The ROC curves 
+were plotted using the probabilities of the predicted labels obtained via the 
+cross-validation procedure that was employed during the final evaluation of the 
+fine-tuned models. 
+And finally, to evaluate the statistical significance of the prediction perfor- 
+mance obtained by the built classification models, a non-parametric statisti- 
+cal method named permutation test was employed [7,28]. For this purpose, we 
+applied 1 000 permutations with the significance level of 0.05. To estimate the 
+
+ 
+ 
+− 
+ 
+performance of the models on the permuted data, we used the same classification 
+setup as employed during the training phase [26]. 
+ 
+3 Results 
+ 
+The results of the exploratory data analysis are summarized in Table 1 (sorted 
+based on the p-value for the Mann-Whitney U-test). The following features were 
+found as the most distinguishing ones in terms of the differentiation between HC 
+and subjects with LBD (the top 4 features are listed; *, **, and *** denote the p- 
+values for both the Mann-Whitney U-test and Spearman’s correlation coefficient 
+being bellow the significance level of 0.05, 0.01, and 0.001, respectively; if both p- 
+values are bellow a different significance level, the weaker statistical significance 
+is selected): a) spiral – nCV of acceleration (on-surface) ρ =    0.2438∗, variability 
+of spiral width ρ = 0.2439∗, median of azimuth ρ = 0.2378∗, and spiral precision 
+index ρ = 0.2367∗; b) sentence – number of pen stops ρ = 0.3460∗∗, slope of 
+duration of stroke (in-air) ρ = 0.2823∗∗, median of vertical velocity (on-surface) 
+ρ = −0.2438∗, and median of vertical acceleration (on-surface) ρ = 0.2317∗; and 
+c) pentagons – width of writing (on-surface) ρ = −0.3045∗∗, median of length 
+of stroke (on-surface) ρ = −0.2894∗∗, nCV of length of stroke (on-surface) ρ = 
+0.2489∗, and median of duration of stroke (on-surface) ρ = −0.2327∗. 
+ 
+Table 1. Results of the exploratory analysis. 
+ 
+Feature 
+p(U) 
+ρ 
+p(ρ) 
+Spiral 
+nCV of acceleration (s) 
+Variability of spiral width 
+0.0138 
+0.0138 
+−0.2438 
+0.2439 
+0.0263 
+0.0263 
+Median of azimuth 
+0.0158 0.2378 
+0.0304 
+Spiral precision index 
+0.0162 0.2367 
+0.0312 
+nCV of duration of stroke (s) 
+0.0438 −0.1892 0.0867 
+Sentence 
+Number of pen stops 
+0.0009 0.3460 
+0.0014 
+Slope of duration of stroke (a) 
+0.0054 0.2823 
+0.0097 
+Median of vertical velocity (s) 
+Median of vertical acceleration (s) 
+0.0138 
+0.0182 
+−0.2438 
+0.2317 
+0.0263 
+0.0351 
+Rel. total number of intra-stroke intersections 0.0232 −0.2206 0.0451 
+Pentagons 
+Width of writing (s) 
+Median of length of stroke (s) 
+nCV of length of stroke (s) 
+Median of duration of stroke (s) 
+Median of horizontal acceleration (s) 
+0.0030 
+0.0045 
+0.0123 
+0.0178 
+0.0182 
+−0.3045 
+−0.2894 
+0.2489 
+−0.2327 
+0.2317 
+0.0051 
+0.0080 
+0.0233 
+0.0343 
+0.0351 
+p(U) – p-value of Mann-Whitney U-test; ρ – Spearman’s correlation coeffi- 
+cient; p(ρ)– p-value of ρ; (s) – on-surface movement; (a) – in-air movement. 
+
+ 
+ 
+∗ 
+∗∗ 
+ 
+Next, Table 2 presents the results of the correlation analysis (*, and ** denote 
+the p-values for Spearman’s correlation coefficient being below the significance 
+level of 0.05 and 0.01, respectively) between the features summarized in Table 1 
+and the following clinical information: a) MDS–UPDRS, and b) CCB domains. 
+ 
+Table 2. Results of the correlation analysis. 
+ 
+Feature 
+ρ (UPDRS) ρ (V) 
+ρ (A) 
+ρ (E) 
+Spiral 
+nCV of acceleration (s) 
+Variability of spiral width 
+Median of azimuth 
+Spiral precision index 
+nCV of duration of stroke (s) 
+−0.3411∗ 
+0.1653 
+0.0442 
+0.0606 
+−0.1089 
+−0.0013 
+−0.3973∗∗ 
+−0.3656∗ 
+−0.0942 
+−0.1344 
+0.1130 
+−0.2981∗ 
+−0.1029 
+−0.3987∗∗ 
+−0.1618 
+0.1899 
+−0.1666 
+−0.0490 
+−0.2126 
+−0.0469 
+Sentence 
+Num. of pen stops 
+Slope of duration of stroke (a) 
+Median of vertical velocity (s) 
+−0.1018 
+0.2620 
+0.0314 
+−0.1181 
+−0.1928 
+0.1106 
+0.1012 
+−0.0513 
+0.0025 
+−0.1956 
+−0.1025 
+0.1794 
+Median of vertical acceleration (s) 
+Rel. total num. of intra-stroke intersections 
+−0.2641 
+0.0477 
+−0.0301 
+0.1647 
+0.3246∗ 
+0.1143 
+0.0193 
+0.0962 
+Pentagons 
+Width of writing (s) 
+Median of length of stroke (s) 
+nCV of length of stroke (s) 
+Median of duration of stroke (s) 
+Median of horizontal acceleration (s) 
+−0.3448∗ 
+−0.1545 
+0.3065∗ 
+−0.0348 
+0.3215∗ 
+0.2947∗ 
+0.1607 
+−0.2435 
+0.0080 
+−0.0226 
+0.1351 
+0.0501 
+−0.1126 
+−0.0085 
+−0.1632 
+0.1362 
+0.1511 
+−0.1155 
+−0.0269 
+−0.2060 
+ρ – Spearman’s correlation coefficient (∗ denotes p-value < 0.05 and ∗∗ denotes p-value 
+< 0.01);  UPDRS – MDS–Unified  Parkinson’s  Disease  Rating  Scale,  part  III  (motor 
+part) [16]; V – visuospatial domain of CCB; A – attention domain of CCB; E – executive 
+functions domain of CCB; (s) – on-surface movement; (a) – in-air movement. 
+ 
+To visualize the difference in the distribution of the top 4 features summarized 
+above for HC and subjects with LBD, the box-violin plots are presented in 
+Figs. 1, 2 and 3. The Fig. 1 shows the distribution of the features for the spiral 
+drawing, the Fig. 2 shows the distribution of the features for the sentence writing, 
+and the Fig. 3 is dedicated to the distribution of the features for the pentagon 
+copying test. 
+The results of the classification analysis are summarized in Table 3. We 
+trained 4 models in total: 3 models dedicated to each task separately and 
+a model combining all of the tasks. The following results were achieved (where 
+and 
+denote p-value of the permutation test bellow < 0.05 and < 0.01, 
+respectively): a) spiral – BACC = 0.6848∗∗, SEN = 0.8696, SPE = 0.5000; b) 
+sentence – BACC = 0.7283∗∗, SEN = 0.9783, SPE = 0.4783 c) pentagons – 
+BACC = 0.6848∗∗, SEN = 0.9348, SPE = 0.4348; and d) all tasks combined – 
+
+ 
+ 
+ 
+ 
+ 
+ 
+Fig. 1. Distribution of the top 4 most discriminating features (spiral drawing). 
+ 
+ 
+Fig. 2. Distribution of the top 4 most discriminating features (sentence writing). 
+ 
+ 
+BACC = 0.7391∗∗, SEN = 0.8043, SPE = 0.6739. The ROC curves of the trained 
+models are shown in Fig. 4. 
+ 
+4 Discussion 
+As mentioned in the methodology, the Archimedean spiral is considered as a 
+gold standard, especially in the assessment of graphomotor difficulties in PD 
+patients [5,8,31], nevertheless, it has been utilised during the quantitative anal- 
+ysis of Huntington’s disease, essential tremor, or brachial dystonia as well [13]. 
+Concerning the spiral features with the highest discrimination power (as identi- 
+fied by the Mann-Whitney U-test), we observed that the LBD group was asso- 
+ciated with a lower range in on-surface acceleration, which we suppose is caused 
+
+1.0
+0.5
+0.0
+0.5
+1.0
+HC
+LBD
+3500
+meden cf amtn
+3000
+2500
+000
+1500
+1000
+500
+.0.5
+*
+0.4
+0.3
+0.2
+0.1
+0.0
+HC
+JBJD
+40
+35
+*
+30
+25
+20
+15
+10
+5
+H50
+***
+40
+30
+20
+10
+10
+-20
+HC
+T
+80
+mscliaun qf weehel welotb fo-surtsco
+40
+10
+0
+-10
+HY0.10
+**
+0.05
+0.05
+0.10
+0.15
+HO
+L13
+100
+megbisn of wgrbicu sxalrabioa
+-50
+-100
+-150
+-200
+250 
+ 
+− 
+− 
+− 
+− 
+− 
+ 
+ 
+ 
+ 
+Fig. 3. Distribution of the top 4 most discriminating features (pentagons copying test). 
+ 
+Table 3. Results of the classification analysis. 
+ 
+Task 
+MCC BACC SEN 
+SPE 
+PRE 
+F1 
+threshold p 
+Spiral 
+0.3977 0.6848 0.8696 0.5000 0.6349 0.7339 0.26 
+∗∗ 
+Sentence 
+0.5271 0.7283 0.9783 0.4783 0.6522 0.7826 0.36 
+∗∗ 
+Pentagons 
+0.4267 0.6848 0.9348 0.4348 0.6232 0.7478 0.13 
+∗∗ 
+All tasks combined 0.4824 0.7391 0.8043 0.6739 0.7115 0.7551 0.48 
+∗∗ 
+MCC – Matthew’s correlation coefficient; BACC – balanced accuracy; SEN – 
+sensitivity; SPE – specificity; PRE – precision; F1 – F1 score; p – p-values computed by 
+the permutation test (1 000 permutations, ∗ denotes p-value < 0.05 and ∗∗ denotes p-
+value < 0.01); threshold – fine-tuned decision threshold. 
+ 
+ 
+by rigidity. This assumption is supported by the fact that the measure signifi- 
+cantly correlates (ρ = 0.3, p < 0.05) with the overall score of MDS–UPDRS III. 
+Next, the LBD group was not able to keep small variability of loop-to-loop spi- 
+ral width index, which is in line with findings reported in [31]. We also observed 
+a significant correlation between this feature and the visuospatial (ρ =  0.4, 
+p < 0.01) and the attention (ρ = 0.3, p < 0.05) domain of CCB. On the other 
+hand, the LBD group had generally higher values of the spiral precision index 
+than the HC one, which is against our initial assumptions (also the correlation 
+with the attention domain of CCB is surprisingly negative; ρ = 0.4, p < 0.01). 
+Finally, the last significant correlation with the clinical status was identified in 
+the median of azimuth, which was higher in the LBD group (in addition we 
+observed a negative correlation with the visuospatial domain of CCB; ρ = 0.4, 
+p < 0.05). 
+Regarding the classification analysis, based on the spiral features, we were 
+able to discriminate the LBD and HC groups with 68% balanced accuracy (area 
+under the curve (AUC) = 71%), which is the worst result when compared to other 
+
+90
+80
+*?
+02
+80
+50
+40
+30
+20
+10
+LBD
+9.5
+mocf emortm
+3.0
+2.5
+2.0
+1.5
+1.0
+0.5
+0.0
+0.5
+-3.200
+150
+100
+50
+50
+TLSE
+12
+10
+683
+2
+HE 
+ 
+ 
+ 
+ 
+ 
+ 
+Fig. 4. Receiver operating characteristic curves for the trained models. 
+ 
+ 
+tasks and which supports our previous findings that even though the spiral is 
+considered as a gold standard the sentence copy task accents the manifestations 
+of dysgraphia much better [11]. 
+Regarding the sentence, the most discriminative feature extracted from this 
+task is the number of pen stops (i.e. a pen is in contact with the paper and 
+does not vary its position for at least 30 ms [8]), which was higher in the LBD 
+group. This parameter has been mainly employed in the diagnosis of develop- 
+mental dysgraphia in children population [27], however, in one study, Danna et 
+al. observed that this measure (but extracted from the spiral) was significantly 
+different between PD patients in the OFF state and HC [8]. Initially, we assumed 
+that the feature could be theoretically linked with cognitive deficits, but we did 
+not observe any significant correlation with the visuospatial, attention, or execu- 
+tive functions domain of CCB. The second most significant feature was the slope 
+
+0.4
+0.@Roc (pentagoms)
+1.0
++++++++++
+hreshold:0.13
+0.8
+0.6
+0.4
+AL
+...
+ROC curve (area = 0.73)
+Random guess
+0.00.4
+0.@1.0
+Roctantaskscompined
+0.a
+Threshold : 0.48
+0.6
+FD
+0.4
+ROC curve (area =0.76)
+Random guess
+0.00.6Roe spirall
+1.0
+Threshold:0.26
+0.8
+Ruai
+0.6
+tie
+0.4
+ru
+ROC curve (area = 0.71)
+Random guess
+0.00.61.0
+Roc tsenbence
+++++++++++++++++++++++++++++++++++
+Threshold:0.36
+0.8
+Ruai
+0.6
+ositive
+0.4
+ru
+ROC curve (area = 0.80)
+Random guess
+0.0 
+ 
+− 
+− 
+ 
+of the duration of in-air strokes. The positive correlation coefficient suggests that 
+the LBD subjects were associated with progressing fatigue [1,12,17]. Next, in 
+the LBD group, we observed lower on-surface vertical velocity (this is in line 
+with e.g. [21,35]), but increased on-surface vertical acceleration. This could be 
+probably explained by the slow and less smooth handwriting. In terms of pro- 
+jection, the reason why these deficits dominate in the vertical movement could 
+be explained by the fact that the finger system (which is mainly involved in the 
+vertical movement) is more affected by muscular fatigue than the wrist system 
+(which controls horizontal movement) [20]. The vertical movement requires coor- 
+dinated movement and finer flexions/extensions of more joints (interphalangeal 
+and metacarpophalangeal), thus it is more complex than ulnar abductions of the 
+wrist [10,34] and could more accent the rigidity and bradykinesia. In addition, 
+this manifestation could be associated with the progressive/consistent vertical 
+micrographia, i.e., progressive/consistent reduction in letter amplitude [33]. 
+In terms of classification, by modelling features extracted from the sentence, 
+we were able to differentiate both groups with 73% balanced accuracy (AUC 
+= 80%). In comparison with the state of the art in supportive LBD or PD 
+diagnosis [9,19,35], it is not a competitive result, but on the other hand, we 
+would like to highlight that we deal with results evaluating diagnosis of LBDs 
+in the prodromal state that has not been targeted by other research teams yet. 
+Concerning the last (cognitive) task, all the top 5 discriminative features were 
+extracted from the on-surface movement. In our recent article [4] we proved that 
+in-air entropy-based parameters could be used to identify early cognitive deficits 
+in PD without major cognitive impairment and that they correlate with the 
+level of attention. In the current study, these in-air measures were not signifi- 
+cant, but on the other hand, their on-surface variants (i.e. median of Shannon 
+entropy calculated from the global/vertical movement) had the p-values of the 
+Mann-Whitney U-test < 0.05, moreover, they significantly correlated with the 
+visuospatial domain of CCB (e.g. ρ = 
+0.3, p < 0.05). The top 5 parameters 
+consist of the width of the product, which was smaller in the LBD group. It 
+slightly correlates with the lower median of the length of strokes (ρ = 0.3) and 
+lower median of the duration of strokes (ρ = 0.2) and probably means that the 
+subjects in the LBD group made the overlapped pentagons smaller. In addition, 
+since the non-parametric coefficient of variation of the length of strokes was 
+higher, we assume that the LBD subjects were not able to keep a stable length 
+of strokes (nevertheless, based on the scoring published in [24], this is assumed 
+as a very small deviation). Regarding the width, we also observed a negative 
+correlation (ρ =   0.3, p < 0.05) with the overall score of MDS–UPDRS III. 
+The classification based on the pentagon copying test provided 68% balanced 
+accuracy (AUC = 0.73%), which is slightly better than in the case of the spiral, 
+but not as high as in the case of the sentence. 
+And finally, a machine learning model based on the whole set of features 
+(tasks) enabled us to improve the accuracy to 74% (AUC = 76%). This shows 
+that the combination of the graphomotor, handwriting and cognitive deficits can 
+be used to achieve reasonable performance in the prodromal diagnosis of LBDs. 
+
+ 
+ 
+ 
+5 Conclusion 
+ 
+This study has several limitations. Our dataset has a small sample size and the 
+HC and LBD groups are imbalanced, therefore to get better results in terms 
+of their generalisation, a bigger database must be analysed. Next, due to the 
+small sample size, we fused subjects with a high risk of developing PD or MCI- 
+LB into one LBD group. Nevertheless, subjects with MCI-LB in its prodromal 
+stage are associated mainly with cognitive (executive or visuospatial) decline, 
+while subjects with prodromal PD experience mainly motor deficits. In other 
+words, we suppose that further stratification of these participants into two groups 
+could increase the classification accuracy (we hypothesise that MCI-LB would 
+be more pronounced in the pentagon copying task and PD in the handwriting 
+one). Finally, although we tried a correction of multiple comparisons during the 
+statistical analysis, almost no significant features appeared after this adjustment. 
+To sum up, concerning the limitations mentioned above, the study should be 
+considered as a pilot one. 
+In conclusion, despite the limitations, to the best of our knowledge, it is 
+the first work exploring the impact of computerised analysis of a graphomotor, 
+cognitive, and handwriting task on the prodromal diagnosis of these neurodegen- 
+erative disorders. It bridges the knowledge gap in the field of LBDs, and provides 
+baseline results for future studies focusing on the prodromal diagnosis of LBDs 
+via a computerized and objective analysis of graphomotor and handwriting dif- 
+ficulties. 
+ 
+References 
+ 
+1. Aouraghe, I., Alae, A., Ghizlane, K., Mrabti, M., Aboulem, G., Faouzi, B.: A novel 
+approach combining temporal and spectral features of Arabic online handwriting 
+for Parkinson’s disease prediction. J. Neurosci. Methods 339, 108727 (2020) 
+2. Benedict, H.: Brief Visual Memory Test-Revised: Professional Manual. Psycholog- 
+ical Assessment Resources, Odessa (1997) 
+3. Bezdicek, O., et al.: Development, validity, and normative data study for the 12- 
+word Philadelphia Verbal Learning Test [czP (r) VLT-12] among  older  and  very 
+old Czech adults. Clin. Neuropsychol. 28(7), 1162–1181 (2014) 
+4. Brabenec, L., Klobusiakova, P., Mekyska, J., Rektorova, I.: Shannon entropy: a 
+novel parameter for quantifying pentagon copying performance in non-demented 
+Parkinson’s disease patients. Parkinsonism Relat. Disord. 94, 45–48 (2022) 
+5. Cascarano, G.D., et al.: Biometric handwriting analysis  to  support  Parkinson’s 
+disease assessment and grading. BMC Med. Inform. Decis. Mak. 19(9), 1–11 (2019). 
+https://doi.org/10.1186/s12911-019-0989-3 
+6. Chen, T., Guestrin, C.: XGBoost. In: Proceedings of the 22nd ACM SIGKDD 
+International Conference on Knowledge Discovery and Data Mining - KDD 2016. 
+ACM Press (2016). https://doi.org/10.1145/2939672.2939785 
+7. Combrisson, E., Jerbi, K.: Exceeding chance level by chance: the caveat of the- 
+oretical chance levels in brain signal classification and statistical assessment of 
+decoding accuracy. J. Neurosci. Methods 250, 126–136 (2015). https://doi.org/10. 
+1016/j.jneumeth.2015.01.010 
+
+ 
+ 
+ 
+8. Danna, J., et al.: Digitalized spiral drawing in Parkinson’s disease: a tool for eval- 
+uating beyond the written trace. Hum. Mov. Sci. 65, 80–88 (2019) 
+9. De Stefano, C., Fontanella, F., Impedovo, D., Pirlo, G., di Freca, A.S.: Handwriting 
+analysis to support neurodegenerative diseases diagnosis: a review. Pattern Recogn. 
+Lett. 121, 37–45 (2019) 
+10. Dounskaia, N., Van Gemmert, A., Stelmach, G.: Interjoint coordination during 
+handwriting-like movements. Exp. Brain Res. 135(1), 127–140 (2000). https:// 
+doi.org/10.1007/s002210000495 
+11. Drot´ar,  P.,  Mekyska,  J.,  Rektorov´a,  I.,  Masarova´,  L.,  Sm´ekal,  Z.,  Faundez-Zanuy, 
+M.: Evaluation of handwriting kinematics and pressure for differential diagnosis of 
+Parkinson’s disease. Artif. Intell. Med. 67, 39–46 (2016) 
+12. Drot´ar,  P.,  Mekyska,  J.,  Sm´ekal,  Z.,  Rektorov´a,  I.,  Masarova´,  L.,  Faundez-Zanuy, 
+M.: Prediction potential of different handwriting tasks for diagnosis of Parkinson’s. 
+In: 2013 E-Health and Bioengineering Conference (EHB), pp. 1–4. IEEE (2013) 
+13. Faundez-Zanuy, M., Mekyska, J., Impedovo, D.: Online  handwriting,  signature 
+and touch dynamics: tasks and potential applications in the field of security and 
+health. Cogn. Comput. 13(5), 1406–1421 (2021). https://doi.org/10.1007/s12559- 
+021-09938-2 
+14. Galaz, Z., Mucha, J., Zvoncak, V., Mekyska, J.: Handwriting features (2022). www. 
+github.com/BDALab/handwriting-features 
+15. Garre-Olmo, J., Faundez-Zanuy, M., L´opez-de Ipin˜a, K., Calv´o-Perxas, L., Turr´o- 
+Garriga, O.: Kinematic and pressure features of handwriting and drawing: prelim- 
+inary results between patients with mild cognitive impairment, Alzheimer disease 
+and healthy controls. Curr. Alzheimer Res. 14(9), 960–968 (2017) 
+16. Goetz, C.G., et al.: Movement disorder society-sponsored revision of the unified 
+Parkinson’s disease rating scale (MDS-UPDRS): scale presentation and clinimetric 
+testing results. Mov. Disord. Off. J. Mov. Disord. Soc. 23(15), 2129–2170 (2008) 
+17. Harralson, H.H., Teulings, H.L., Farley, B.G.: Handwriting variability in movement 
+disorder patients and effects of fatigue. In: Proceedings of the Fourteenth Biennial 
+Conference of the International Graphonomics Society, pp. 103–107 (2009) 
+18. Heinzel, S., et al.: Update of the MDS research criteria for prodromal Parkinson’s 
+disease. Mov. Disord. 34(10), 1464–1470 (2019) 
+19. Impedovo, D., Pirlo, G.: Dynamic handwriting analysis for the assessment of neu- 
+rodegenerative diseases: a pattern recognition perspective. IEEE Rev. Biomed. 
+Eng. 12, 209–220 (2018) 
+20. Kushki, A., Schwellnus, H., Ilyas, F., Chau, T.: Changes in kinetics and kinemat- 
+ics of handwriting during a prolonged writing task in children with and without 
+dysgraphia. Res. Dev. Disabil. 32(3), 1058–1064 (2011) 
+21. Letanneux, A., Danna, J., Velay, J.L., Viallet, F., Pinto, S.: From micrographia to 
+Parkinson’s disease dysgraphia. Mov. Disord. 29(12), 1467–1475 (2014) 
+22. McKeith, I.G., et al.: Research criteria  for  the  diagnosis  of  prodromal  dementia 
+with Lewy bodies. Neurology 94(17), 743–755 (2020) 
+23. Monvoisin-Joly, T., Furcieri, E., Chabran, E., Blanc, F.: Writing in prodromal and 
+mild dementia with Lewy bodies: an exploratory and preliminary study. Geriatrie 
+et Psychologie Neuropsychiatrie du Vieillissement 19(3), 341–351 (2021) 
+24. Nagaratnam, N., Nagaratnam, K., O’Mara, D.: Intersecting pentagon copying and 
+clock drawing test in mild and moderate Alzheimer’s disease. J. Clin. Gerontol. 
+Geriatr. 5(2), 47–52 (2014) 
+25. Nasreddine, Z.S., et al.: The Montreal Cognitive Assessment, MoCA: a brief screen- 
+ing tool for mild cognitive impairment. J. Am. Geriatr. Soc. 53(4), 695–699 (2005) 
+
+ 
+ 
+ 
+26. Ojala, M., Garriga, G.: Permutation tests for studying classifier performance. In: 
+ICDM 2009: Ninth IEEE International Conference on Data Mining 2009, pp. 908– 
+913, December 2009. https://doi.org/10.1109/ICDM.2009.108 
+27. Paz-Villagra´n,  V.,  Danna,  J.,  Velay,  J.L.:  Lifts  and  stops  in  proficient  and  dys- 
+graphic handwriting. Hum. Mov. Sci. 33, 381–394 (2014) 
+28. Phipson, B., Smyth, G.K.: Permutation P-values should never be zero: calculating 
+exact P-values when permutations are randomly drawn. Stat. Appl. Genet. Mol. 
+Biol. 9(1) (2010). https://doi.org/10.2202/1544-6115.1585 
+29. Postuma, R.B., et al.: MDS clinical diagnostic criteria for Parkinson’s disease. Mov. 
+Disord. 30(12), 1591–1601 (2015) 
+30. Preiss, M., et al.: Test verb´aln´ı fluence-vod´ıtka pro vˇseobecnou dospˇelou populaci. 
+Psychiatrie 6(2), 74–77 (2002) 
+31. San Luciano, M., et al.: Digitized spiral drawing: a possible biomarker for early 
+Parkinson’s disease. PLoS ONE 11(10), e0162799 (2016) 
+32. Saunders-Pullman, R., et al.: Validity of spiral analysis in early Parkinson’s disease. 
+Mov. Disord. Off. J. Mov. Disord. Soc. 23(4), 531–537 (2008) 
+33. Thomas, M., Lenka, A., Kumar Pal, P.: Handwriting analysis in Parkinson’s dis- 
+ease: current status and future directions. Mov. Disord. Clin. Pract. 4(6), 806–818 
+(2017) 
+34. Van Galen, G.P.: Handwriting: issues for a psychomotor theory. Hum. Mov. Sci. 
+10(2–3), 165–191 (1991) 
+35. Vessio, G.: Dynamic handwriting analysis for neurodegenerative disease assess- 
+ment: a literary review. Appl. Sci. 9(21), 4666 (2019) 
+36. Warrington, E.K., James, M.: The visual object and space perception battery 
+(1991) 
+37. Wechsler, D., et al.: WAIS-III WMS-III Technical Manual. Psychological Corpo- 
+ration, San Antonio (1997) 
+38. Yamada, M., et al.: Diagnostic criteria for dementia with Lewy bodies: updates 
+and future directions. J. Mov. Disord. 13(1), 1 (2020) 
+
diff --git a/bdFAT4oBgHgl3EQfXh2G/content/tmp_files/load_file.txt b/bdFAT4oBgHgl3EQfXh2G/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fc0e4221a4dba31606034801517dcd107be163de
--- /dev/null
+++ b/bdFAT4oBgHgl3EQfXh2G/content/tmp_files/load_file.txt
@@ -0,0 +1,848 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf,len=847
+page_content='Galaz, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Prodromal Diagnosis of Lewy Body Diseases Based on the Assessment of Graphomotor and Handwriting Difficulties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In: Carmona-Duarte, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Diaz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Ferrer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Morales, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' (eds) Intertwining Graphonomics with Human Movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' IGS 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Lecture Notes in Computer Science, vol 13424.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Springer, Cham.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1007/978-3-031-19745-1_19  Prodromal Diagnosis of Lewy Body Diseases Based on the Assessment of Graphomotor and Handwriting Difficulties  Zoltan Galaz1, Jiri Mekyska1, Jan Mucha1, Vojtech Zvoncak1, Zdenek Smekal1, Marcos Faundez-Zanuy2, Lubos Brabenec3, Ivona Moravkova3,4,5, and Irena Rektorova3,4 1 Department of Telecommunications, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic xgalaz00@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='com 2 Escola Superior Politecnica, Tecnocampus, Mataro, Barcelona, Spain 3 Applied Neuroscience Research Group, Central European Institute of Technology – CEITEC, Masaryk University, Brno, Czech Republic 4 First Department of Neurology, Faculty of Medicine and St.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Anne’s University Hospital, Masaryk University, Brno, Czech Republic 5 Faculty of Medicine, Masaryk University, Brno, Czech Republic  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' To this date, studies focusing on the prodromal diagnosis of Lewy body diseases (LBDs) based on quantitative analysis of graphomo- tor and handwriting difficulties are missing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In this work, we enrolled 18 subjects diagnosed with possible or probable mild cognitive impairment with Lewy bodies (MCI-LB), 7 subjects having more than 50% prob- ability of developing Parkinson’s disease (PD), 21 subjects with both possible/probable MCI-LB and probability of PD > 50%, and 37  age- and gender-matched healthy controls (HC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Each participant performed three tasks: Archimedean spiral drawing (to quantify graphomotor diffi- culties), sentence writing task (to quantify handwriting difficulties), and pentagon copying test (to quantify cognitive decline).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Next, we parame- terized the acquired data by various temporal, kinematic, dynamic, spa- tial, and task-specific features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' And finally, we trained classification mod- els for each task separately as well as a model for their combination to estimate the predictive power of the features for the identification of LBDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Using this approach we were able to identify prodromal LBDs with 74% accuracy and showed the promising potential of computerized objective and non-invasive diagnosis of LBDs based on the assessment of graphomotor and handwriting difficulties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  This work was supported by grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' NU20-04-00294 (Diagnostics  of  Lewy  body diseases in prodromal stage based on multimodal data analysis) of the Czech Ministry of Health and by Spanish grant of the Ministerio de Ciencia e Innovacio´n no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' PID2020- 113242RB-I00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Keywords:   Lewy  body  diseases    Online  handwriting    Graphomotor difficulties     Handwriting  difficulties    Machine  learning     Prodromal diagnosis  1 Introduction  Lewy body diseases (LBDs) is a term describing a group of neurodegenerative disorders characterized by a pathophysiological process of α-synuclein accumu- lation in specific brain regions leading to the formation of Lewy bodies and Lewy neurites resulting in cell death.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' LBDs consists of two major clinical enti- ties: Parkinson’s disease (PD) and dementia with Lewy bodies (DLB) [29,38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Although the phenotypes and temporal evolution of motor and cognitive symp- toms of these two diseases vary, they share many clinical and pathophysiolog- ical features and are therefore referred to as LBDs spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Together with Alzheimer’s disease (AD), LBDs comprise the major part of all cases of neu- rodegenerative disorders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' It is known that LBDs do not start suddenly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' At the time the clinical symp- toms occur, the neurodegenerative process has reached a severe degree in which most of the targeted neurons have already been damaged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Before the clinical diagnosis based on the presence of typical clinical symptoms becomes possible, there is a long period of the underlying neurodegenerative process with subtle or nonspecific symptoms [18,29] such as sleep disturbances, mood changes, smell loss, constipation, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' This period of LBDs is called the prodromal stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' One of the early markers of PD is PD dysgraphia (micrographia and other alterations in handwriting, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' kinematic and dynamic) [21,32,33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Similarly, some manifestations of dysgraphia have been observed in the prodromal DLB as well [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Although modern approaches to the analysis of graphomotor and handwriting difficulties (utilising digitising tablets) were proved to work well during e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' diagnosis of the clinical stage of PD [9,11,35], assessment of cogni- tion in PD patients [4], or discrimination of AD and mild cognitive impairment (MCI) [15], to the best of our knowledge, no studies employed this technology (with high potential) in the prodromal diagnosis of LBDs in a larger scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Identification of the early stages of LBDs is crucial for the development of disease-modifying treatment since the neurodegeneration may be possibly stopped or treated before the pathological cascades start.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Therefore, the goal of this study is to explore whether the computerised assessment of graphomo- tor and handwriting difficulties could support the prodromal diagnosis of LBDs, more specifically, we aim to: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' identify which task significantly discriminates LBD patients and age- and gender-matched healthy controls (HC), 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' identify what conventional online handwriting features have good discrimina- tion power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  ±  ±  ±  2 Materials and Methods  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1 Dataset We enrolled 39 subjects (19 females, 20 males, age = 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='53 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='61) diagnosed with possible or probable MCI (based on the scores of the MoCA – Montreal Cognitive Assessment [25] and based on the CCB – Complex Cognitive Battery, see the explanation below) who were simultaneously diagnosed with possible or probable MCI-LB (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' mild cognitive impairment with Lewy bodies) based on the criteria published by McKeith et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In this group, 21 subjects also had more than 50% probability of developing PD (calculated following the MDS criteria published in [18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In addition, we enrolled 7 subjects (2 females, 5 males, age = 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='41    4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='32) without possible/probable MCI-LB, but still with more than 50% probability of developing PD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Finally, we enrolled 37 HC (26 females, 11 males, age = 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='60 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='61).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In the experiments, we stratified the subjects into two groups, HC vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' LBD (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' people with a high risk of developing PD or DLB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' CCB was used to evaluate four cognitive domains: 1) memory (The Brief Visuospatial memory test–revised [2], Philadelphia Verbal Learning Test [3]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 2) attention (Wechsler Adult Intelligence Scale-III: Letter-Number Sequencing, Digit Symbol Substitution [37]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 3) executive functions (Semantic and phonemic verbal fluency [30], Picture arrangement test [37]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' and 4) visuospatial functions (Judgment of Line Orientation [36]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The cognitive domain z-scores were com- puted as the average z-scores of the tests included in the particular domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  The participants were asked to perform a set of three tasks: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Archimedean spiral (spiral) – we consider this task as a graphomotor one, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' it is a building block of some letter shapes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' in addition, it is a golden standard in PD dysgraphia diagnosis [35] 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' sentence  “Tramvaj   dnes  uˇz  nepojede”  (translation:   “A  tram  will  not  go today.”) writing (sentence) – this handwriting task was used e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' in the PaHaW database [11] 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' pentagon copying test (pentagons) – it is a task frequently used for quantifi- cation of cognitive decline [4] All participants were right-handed and had Czech as their native language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' They all signed an informed consent form that was approved by the local ethics committee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2 Feature Extraction The participants were asked to perform the tasks (using the Wacom Ink pen) on an A4 paper that was laid down and fixed to a digitizing tablet Wacom Intuos 4 M (sampling frequency fs = 130 Hz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Before the acquisition, they had some time to get familiar with the hardware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The recorded time series (x and y position;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' timestamp;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' a binary variable, being 0 for in-air movement and 1 for on-surface movement, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' pressure exert on the tablet’s surface during  writing;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' pen tilt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' azimuth) were consequently parameterised utilising the follow- ing set of features (we selected the set based on available reviews and based on our experience [9,11,35]): 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' temporal – duration of writing, ratio of the on-surface/in-air duration, dura- tion of strokes, and ratio of the on-surface/in-air stroke duration 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' kinematic – velocity, and acceleration 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' dynamic – pressure, tilt, and azimuth 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' spatial – width, height, and length of the whole product, as well as its partic- ular strokes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' stroke width, height, and length 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' spiral-specific – degree of spiral drawing severity [31], mean drawing speed of spiral [31], second-order smoothness of spiral [31], spiral precision index [5], spiral tightness [31], variability of spiral width [31], and first-order zero- crossing rate of spiral [31] 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' other – number of interruptions (pen elevations),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' number of pen stops [27],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' tempo (number of strokes normalised by duration),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' number of on-surface intra-stroke intersections,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' relative number of on-surface intra-stroke intersec- tions,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' number of on-surface inter-stroke intersections,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' and relative number of on-surface inter-stroke intersections,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Shannon entropy [4],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' number of changes in the velocity profile,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' relative number of changes in the velocity profile Most of the features were extracted using the recently released Python library handwriting-features (v 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1) [14], the rest of them were coded in Matlab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Some features (mainly spatial, temporal and kinematic) were extracted from both on- surface and in-air movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In addition, kinematic features were also analysed in horizontal and vertical projection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Features represented by vectors were con- sequently transformed to a scalar value using median, non-parametric coefficient of variation (nCV;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' interquartile range of feature divided by its median), slope and 95th percentile (95p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3 Statistical Analysis and Machine Learning To compare the distribution of features between the HC and LBD subjects, we conducted Mann-Whitney U-test with the significance level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Moreover, to assess the strength of a relationship between the features and the subject’s clinical status (HC/LBD), we computed Spearman’s correlation coefficient (ρ) with the significance level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Finally, during this exploratory step, we calcu- lated Spearman’s correlation with the domains of CCB and the overall score of MDS–Unified Parkinson’s Disease Rating Scale (MDS–UPDRS), part III (motor part) [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' To identify the presence of graphomotor or handwriting difficulties, we built binary classification models using an ensemble extreme gradient boosting algo- rithm known as XGBoost [6] (with 100 estimators).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' This algorithm was chosen due to its robustness to outliers, ability to find complex interactions among fea- tures as well as the possibility of ranking their importance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' To build models with an optimal set of hyperparameters, we conducted 1000 iteration of randomized  × × × 2 TP + FN TN + FP  search strategy via stratified 5-fold cross-validation with 10 repetitions aiming to optimize balanced accuracy score (BACC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' described in more detail along with other evaluation scores below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The following set of hyperparameters were opti- mized: the learning rate [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='001, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3], γ [0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='10, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='15, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='20, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='25, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5], the maximum tree depth [6, 8, 10, 12, 15], the fraction of observations to be randomly sampled for each tree (subsample ratio) [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='9, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0], the subsample ratio for the columns at each level [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='9, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0], the subsample ratio for the columns when constructing each tree [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='9, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0], the minimum sum of the weights of all observations required in a child node [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0], and the balance between positive and negative weights [1, 2, 3, 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The classification test performance was determined using the following clas- sification metrics: Matthew’s correlation coefficient (MCC), balanced accuracy (BACC), sensitivity (SEN) also known as recall (REC), specificity (SPE), pre- cision (PRE) and F1 score (F1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' These metrics are defined as follows: TP × TN + FP × FN  MCC =  √N  ,  (1)  BACC = 1  TP  TN  ,  (2)  SPE =  TN  TN + FP  PRE =  TP  TP + FP  REC =  TP  ,  (3)  ,  (4)  ,  (5)  TP + FN F1 = 2 PRE × REC PRE + REC  (6) where N  = (TP + FP )    (TP + FN )      (TN + FP )     (TN + FN ), TP (true positive) and FP (false positive) represent the number of correctly identified LBD subjects and the number of subjects incorrectly identified as having LBDs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Similarly, TN (true negative) and FN (false negative) represent the number of correctly identified HC and the number of subjects with LBDs incorrectly identified as being healthy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' To further optimize the trained classification models, we fine-tuned the mod- els’ decision thresholds via the receiver operating characteristics (ROC) curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Using the fine-tuned decision thresholds, we evaluated the classification perfor- mance of the models using the leave-one-out cross-validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The ROC curves were plotted using the probabilities of the predicted labels obtained via the cross-validation procedure that was employed during the final evaluation of the fine-tuned models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' And finally, to evaluate the statistical significance of the prediction perfor- mance obtained by the built classification models, a non-parametric statisti- cal method named permutation test was employed [7,28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' For this purpose, we applied 1 000 permutations with the significance level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' To estimate the  −  performance of the models on the permuted data, we used the same classification setup as employed during the training phase [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  3 Results  The results of the exploratory data analysis are summarized in Table 1 (sorted based on the p-value for the Mann-Whitney U-test).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The following features were found as the most distinguishing ones in terms of the differentiation between HC and subjects with LBD (the top 4 features are listed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' *, **, and *** denote the p- values for both the Mann-Whitney U-test and Spearman’s correlation coefficient being bellow the significance level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='01, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='001, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' if both p- values are bellow a different significance level, the weaker statistical significance is selected): a) spiral – nCV of acceleration (on-surface) ρ =    0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2438∗, variability of spiral width ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2439∗, median of azimuth ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2378∗, and spiral precision index ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2367∗;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' b) sentence – number of pen stops ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3460∗∗, slope of duration of stroke (in-air) ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2823∗∗, median of vertical velocity (on-surface) ρ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2438∗, and median of vertical acceleration (on-surface) ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2317∗;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' and c) pentagons – width of writing (on-surface) ρ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3045∗∗, median of length of stroke (on-surface) ρ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2894∗∗, nCV of length of stroke (on-surface) ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2489∗, and median of duration of stroke (on-surface) ρ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2327∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Results of the exploratory analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Feature p(U) ρ p(ρ) Spiral nCV of acceleration (s) Variability of spiral width 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0138 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0138 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2438 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2439 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0263 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0263 Median of azimuth 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0158 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2378 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0304 Spiral precision index 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0162 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2367 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0312 nCV of duration of stroke (s) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0438 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1892 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0867 Sentence Number of pen stops 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0009 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3460 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0014 Slope of duration of stroke (a) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0054 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2823 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0097 Median of vertical velocity (s) Median of vertical acceleration (s) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0138 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0182 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2438 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2317 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0263 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0351 Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' total number of intra-stroke intersections 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0232 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2206 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0451 Pentagons Width of writing (s) Median of length of stroke (s) nCV of length of stroke (s) Median of duration of stroke (s) Median of horizontal acceleration (s) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0030 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0045 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0123 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0178 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0182 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3045 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2894 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2489 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2327 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2317 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0051 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0080 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0233 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0343 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0351 p(U) – p-value of Mann-Whitney U-test;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' ρ – Spearman’s correlation coeffi- cient;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' p(ρ)– p-value of ρ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' (s) – on-surface movement;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' (a) – in-air movement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  ∗  ∗∗  Next, Table 2 presents the results of the correlation analysis (*, and ** denote the p-values for Spearman’s correlation coefficient being below the significance level of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='01, respectively) between the features summarized in Table 1 and the following clinical information: a) MDS–UPDRS, and b) CCB domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Results of the correlation analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Feature ρ (UPDRS) ρ (V) ρ (A) ρ (E) Spiral nCV of acceleration (s) Variability of spiral width Median of azimuth Spiral precision index nCV of duration of stroke (s) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3411∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1653 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0442 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0606 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1089 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0013 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3973∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3656∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0942 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1344 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1130 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2981∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1029 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3987∗∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1618 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1899 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1666 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0490 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2126 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0469 Sentence Num.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' of pen stops Slope of duration of stroke (a) Median of vertical velocity (s) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1018 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2620 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0314 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1181 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1928 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1012 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0513 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0025 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1956 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1794 Median of vertical acceleration (s) Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' total num.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' of intra-stroke intersections −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2641 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0477 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0301 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1647 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3246∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1143 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0193 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0962 Pentagons Width of writing (s) Median of length of stroke (s) nCV of length of stroke (s) Median of duration of stroke (s) Median of horizontal acceleration (s) −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3448∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1545 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3065∗ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0348 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3215∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2947∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1607 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2435 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0080 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0226 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1351 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0501 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1126 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0085 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1632 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1362 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1511 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1155 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0269 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2060 ρ – Spearman’s correlation coefficient (∗ denotes p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05 and ∗∗ denotes p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='01);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  UPDRS – MDS–Unified  Parkinson’s  Disease  Rating  Scale,  part  III  (motor part) [16];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' V – visuospatial domain of CCB;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' A – attention domain of CCB;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' E – executive functions domain of CCB;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' (s) – on-surface movement;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' (a) – in-air movement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  To visualize the difference in the distribution of the top 4 features summarized above for HC and subjects with LBD, the box-violin plots are presented in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 1, 2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 1 shows the distribution of the features for the spiral drawing, the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 2 shows the distribution of the features for the sentence writing, and the Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 3 is dedicated to the distribution of the features for the pentagon copying test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The results of the classification analysis are summarized in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' We trained 4 models in total: 3 models dedicated to each task separately and a model combining all of the tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The following results were achieved (where and denote p-value of the permutation test bellow < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05 and < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='01, respectively): a) spiral – BACC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6848∗∗, SEN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8696, SPE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' b) sentence – BACC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7283∗∗, SEN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='9783, SPE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4783 c) pentagons – BACC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6848∗∗, SEN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='9348, SPE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4348;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' and d) all tasks combined –  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Distribution of the top 4 most discriminating features (spiral drawing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Distribution of the top 4 most discriminating features (sentence writing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  BACC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7391∗∗, SEN = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8043, SPE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6739.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The ROC curves of the trained models are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  4 Discussion As mentioned in the methodology, the Archimedean spiral is considered as a gold standard, especially in the assessment of graphomotor difficulties in PD patients [5,8,31], nevertheless, it has been utilised during the quantitative anal- ysis of Huntington’s disease, essential tremor, or brachial dystonia as well [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Concerning the spiral features with the highest discrimination power (as identi- fied by the Mann-Whitney U-test), we observed that the LBD group was asso- ciated with a lower range in on-surface acceleration, which we suppose is caused  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0 HC LBD 3500 meden cf amtn 3000 2500 000 1500 1000 500 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5 * 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0 HC JBJD 40 35 * 30 25 20 15 10 5 H50 *** 40 30 20 10 10 -20 HC T 80 mscliaun qf weehel welotb fo-surtsco 40 10 0 -10 HY0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='10 ** 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='15 HO L13 100 megbisn of wgrbicu sxalrabioa -50 -100 -150 -200 250  −  −  −  −  −  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Distribution of the top 4 most discriminating features (pentagons copying test).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Results of the classification analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Task MCC BACC SEN SPE PRE F1 threshold p Spiral 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3977 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6848 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8696 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6349 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7339 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='26 ∗∗ Sentence 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5271 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7283 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='9783 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4783 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6522 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7826 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='36 ∗∗ Pentagons 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4267 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6848 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='9348 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4348 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6232 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7478 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='13 ∗∗ All tasks combined 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4824 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7391 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8043 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6739 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7115 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='7551 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='48 ∗∗ MCC – Matthew’s correlation coefficient;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' BACC – balanced accuracy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' SEN – sensitivity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' SPE – specificity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' PRE – precision;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' F1 – F1 score;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' p – p-values computed by the permutation test (1 000 permutations, ∗ denotes p-value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05 and ∗∗ denotes p- value < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='01);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' threshold – fine-tuned decision threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  by rigidity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' This assumption is supported by the fact that the measure signifi- cantly correlates (ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05) with the overall score of MDS–UPDRS III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Next, the LBD group was not able to keep small variability of loop-to-loop spi- ral width index, which is in line with findings reported in [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' We also observed a significant correlation between this feature and the visuospatial (ρ =  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='01) and the attention (ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05) domain of CCB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' On the other hand, the LBD group had generally higher values of the spiral precision index than the HC one, which is against our initial assumptions (also the correlation with the attention domain of CCB is surprisingly negative;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='01).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Finally, the last significant correlation with the clinical status was identified in the median of azimuth, which was higher in the LBD group (in addition we observed a negative correlation with the visuospatial domain of CCB;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Regarding the classification analysis, based on the spiral features, we were able to discriminate the LBD and HC groups with 68% balanced accuracy (area under the curve (AUC) = 71%), which is the worst result when compared to other  90  80 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  02  80  50  40  30  20  10  LBD  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5  mocf emortm  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='200  150  100  50  50  TLSE  12  10  683  2  HE  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Receiver operating characteristic curves for the trained models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  tasks and which supports our previous findings that even though the spiral is considered as a gold standard the sentence copy task accents the manifestations of dysgraphia much better [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Regarding the sentence, the most discriminative feature extracted from this task is the number of pen stops (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' a pen is in contact with the paper and does not vary its position for at least 30 ms [8]), which was higher in the LBD group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' This parameter has been mainly employed in the diagnosis of develop- mental dysgraphia in children population [27], however, in one study, Danna et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' observed that this measure (but extracted from the spiral) was significantly different between PD patients in the OFF state and HC [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Initially, we assumed that the feature could be theoretically linked with cognitive deficits, but we did not observe any significant correlation with the visuospatial, attention, or execu- tive functions domain of CCB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The second most significant feature was the slope  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' @Roc (pentagoms) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0 +++++++++ hreshold:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4 AL .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' ROC curve (area = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='73) Random guess 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' @1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0 Roctantaskscompined 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='a Threshold : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='48 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6 FD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4 ROC curve (area =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='76) Random guess 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6Roe spirall 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0 Threshold:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8 Ruai 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6 tie 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4 ru ROC curve (area = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='71) Random guess 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0 Roc tsenbence ++++++++++++++++++++++++++++++++++ Threshold:0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='8 Ruai 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='6 ositive 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='4 ru ROC curve (area = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='80) Random guess 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='0  −  −  of the duration of in-air strokes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The positive correlation coefficient suggests that the LBD subjects were associated with progressing fatigue [1,12,17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Next, in the LBD group, we observed lower on-surface vertical velocity (this is in line with e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' [21,35]), but increased on-surface vertical acceleration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' This could be probably explained by the slow and less smooth handwriting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In terms of pro- jection, the reason why these deficits dominate in the vertical movement could be explained by the fact that the finger system (which is mainly involved in the vertical movement) is more affected by muscular fatigue than the wrist system (which controls horizontal movement) [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The vertical movement requires coor- dinated movement and finer flexions/extensions of more joints (interphalangeal and metacarpophalangeal), thus it is more complex than ulnar abductions of the wrist [10,34] and could more accent the rigidity and bradykinesia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In addition, this manifestation could be associated with the progressive/consistent vertical micrographia, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', progressive/consistent reduction in letter amplitude [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In terms of classification, by modelling features extracted from the sentence, we were able to differentiate both groups with 73% balanced accuracy (AUC = 80%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  In comparison with the state of the art in supportive LBD or PD diagnosis [9,19,35], it is not a competitive result, but on the other hand, we would like to highlight that we deal with results evaluating diagnosis of LBDs in the prodromal state that has not been targeted by other research teams yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Concerning the last (cognitive) task, all the top 5 discriminative features were extracted from the on-surface movement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In our recent article [4] we proved that in-air entropy-based parameters could be used to identify early cognitive deficits in PD without major cognitive impairment and that they correlate with the level of attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In the current study, these in-air measures were not signifi- cant, but on the other hand, their on-surface variants (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' median of Shannon entropy calculated from the global/vertical movement) had the p-values of the Mann-Whitney U-test < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05, moreover, they significantly correlated with the visuospatial domain of CCB (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The top 5 parameters consist of the width of the product, which was smaller in the LBD group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' It slightly correlates with the lower median of the length of strokes (ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3) and lower median of the duration of strokes (ρ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2) and probably means that the subjects in the LBD group made the overlapped pentagons smaller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  In addition, since the non-parametric coefficient of variation of the length of strokes was higher, we assume that the LBD subjects were not able to keep a stable length of strokes (nevertheless, based on the scoring published in [24], this is assumed as a very small deviation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Regarding the width, we also observed a negative correlation (ρ =   0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='3, p < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='05) with the overall score of MDS–UPDRS III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' The classification based on the pentagon copying test provided 68% balanced accuracy (AUC = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='73%), which is slightly better than in the case of the spiral, but not as high as in the case of the sentence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' And finally, a machine learning model based on the whole set of features (tasks) enabled us to improve the accuracy to 74% (AUC = 76%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' This shows that the combination of the graphomotor, handwriting and cognitive deficits can be used to achieve reasonable performance in the prodromal diagnosis of LBDs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  5 Conclusion  This study has several limitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Our dataset has a small sample size and the HC and LBD groups are imbalanced, therefore to get better results in terms of their generalisation, a bigger database must be analysed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Next, due to the small sample size, we fused subjects with a high risk of developing PD or MCI- LB into one LBD group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Nevertheless, subjects with MCI-LB in its prodromal stage are associated mainly with cognitive (executive or visuospatial) decline, while subjects with prodromal PD experience mainly motor deficits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In other words, we suppose that further stratification of these participants into two groups could increase the classification accuracy (we hypothesise that MCI-LB would be more pronounced in the pentagon copying task and PD in the handwriting one).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Finally, although we tried a correction of multiple comparisons during the statistical analysis, almost no significant features appeared after this adjustment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' To sum up, concerning the limitations mentioned above, the study should be considered as a pilot one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In conclusion, despite the limitations, to the best of our knowledge, it is the first work exploring the impact of computerised analysis of a graphomotor, cognitive, and handwriting task on the prodromal diagnosis of these neurodegen- erative disorders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  It bridges the knowledge gap in the field of LBDs, and provides baseline results for future studies focusing on the prodromal diagnosis of LBDs via a computerized and objective analysis of graphomotor and handwriting dif- ficulties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Aouraghe, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Alae, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Ghizlane, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Mrabti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Aboulem, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Faouzi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': A novel approach combining temporal and spectral features of Arabic online handwriting for Parkinson’s disease prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Neurosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Methods 339, 108727 (2020) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Benedict, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Brief Visual Memory Test-Revised: Professional Manual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Psycholog- ical Assessment Resources, Odessa (1997) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Bezdicek, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Development, validity, and normative data study for the 12- word Philadelphia Verbal Learning Test [czP (r) VLT-12] among  older  and  very old Czech adults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Clin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Neuropsychol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 28(7), 1162–1181 (2014) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Brabenec, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Klobusiakova, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Mekyska, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Rektorova, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Shannon entropy: a novel parameter for quantifying pentagon copying performance in non-demented Parkinson’s disease patients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Parkinsonism Relat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 94, 45–48 (2022) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Cascarano, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Biometric handwriting analysis  to  support  Parkinson’s disease assessment and grading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' BMC Med.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Decis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 19(9), 1–11 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1186/s12911-019-0989-3 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Guestrin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': XGBoost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' ACM Press (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1145/2939672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2939785 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Combrisson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Jerbi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Exceeding chance level by chance: the caveat of the- oretical chance levels in brain signal classification and statistical assessment of decoding accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Neurosci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Methods 250, 126–136 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='jneumeth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='010  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Danna, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Digitalized spiral drawing in Parkinson’s disease: a tool for eval- uating beyond the written trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Hum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 65, 80–88 (2019) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' De Stefano, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Fontanella, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Impedovo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Pirlo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', di Freca, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Handwriting analysis to support neurodegenerative diseases diagnosis: a review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Pattern Recogn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 121, 37–45 (2019) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Dounskaia, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Van Gemmert, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Stelmach, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Interjoint coordination during handwriting-like movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Brain Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 135(1), 127–140 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' https:// doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1007/s002210000495 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Drot´ar,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Mekyska,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Rektorov´a,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Masarova´,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Sm´ekal,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Faundez-Zanuy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Evaluation of handwriting kinematics and pressure for differential diagnosis of Parkinson’s disease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Artif.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Med.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 67, 39–46 (2016) 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Drot´ar,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Mekyska,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Sm´ekal,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Rektorov´a,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Masarova´,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Faundez-Zanuy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Prediction potential of different handwriting tasks for diagnosis of Parkinson’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In: 2013 E-Health and Bioengineering Conference (EHB), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' IEEE (2013) 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Faundez-Zanuy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Mekyska, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Impedovo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Online  handwriting,  signature and touch dynamics: tasks and potential applications in the field of security and health.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Cogn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 13(5), 1406–1421 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1007/s12559- 021-09938-2 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Galaz, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Mucha, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Zvoncak, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Mekyska, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Handwriting features (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='com/BDALab/handwriting-features 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Garre-Olmo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Faundez-Zanuy, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', L´opez-de Ipin˜a, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Calv´o-Perxas, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Turr´o- Garriga, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Kinematic and pressure features of handwriting and drawing: prelim- inary results between patients with mild cognitive impairment, Alzheimer disease and healthy controls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Curr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Alzheimer Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 14(9), 960–968 (2017) 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Goetz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Movement disorder society-sponsored revision of the unified Parkinson’s disease rating scale (MDS-UPDRS): scale presentation and clinimetric testing results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 23(15), 2129–2170 (2008) 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Harralson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Teulings, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Farley, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Handwriting variability in movement disorder patients and effects of fatigue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In: Proceedings of the Fourteenth Biennial Conference of the International Graphonomics Society, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 103–107 (2009) 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Heinzel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Update of the MDS research criteria for prodromal Parkinson’s disease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 34(10), 1464–1470 (2019) 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Impedovo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Pirlo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Dynamic handwriting analysis for the assessment of neu- rodegenerative diseases: a pattern recognition perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' IEEE Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Biomed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 12, 209–220 (2018) 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Kushki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Schwellnus, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Ilyas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Chau, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Changes in kinetics and kinemat- ics of handwriting during a prolonged writing task in children with and without dysgraphia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Dev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disabil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 32(3), 1058–1064 (2011) 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Letanneux, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Danna, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Velay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Viallet, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Pinto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': From micrographia to Parkinson’s disease dysgraphia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  29(12), 1467–1475 (2014) 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' McKeith, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Research criteria  for  the  diagnosis  of  prodromal  dementia with Lewy bodies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Neurology 94(17), 743–755 (2020) 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Monvoisin-Joly, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Furcieri, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Chabran, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Blanc, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Writing in prodromal and mild dementia with Lewy bodies: an exploratory and preliminary study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Geriatrie et Psychologie Neuropsychiatrie du Vieillissement 19(3), 341–351 (2021) 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Nagaratnam, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Nagaratnam, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', O’Mara, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Intersecting pentagon copying and clock drawing test in mild and moderate Alzheimer’s disease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Clin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Gerontol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Geriatr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 5(2), 47–52 (2014) 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Nasreddine, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : The Montreal Cognitive Assessment, MoCA: a brief screen- ing tool for mild cognitive impairment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Am.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Geriatr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 53(4), 695–699 (2005)  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Ojala, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Garriga, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Permutation tests for studying classifier performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' In: ICDM 2009: Ninth IEEE International Conference on Data Mining 2009, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 908– 913, December 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1109/ICDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='108 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Paz-Villagra´n,  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Danna,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=',  Velay,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' :  Lifts  and  stops  in  proficient  and  dys- graphic handwriting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Hum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 33, 381–394 (2014) 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Phipson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Smyth, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Permutation P-values should never be zero: calculating exact P-values when permutations are randomly drawn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Genet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Biol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 9(1) (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='2202/1544-6115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='1585 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Postuma, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : MDS clinical diagnostic criteria for Parkinson’s disease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 30(12), 1591–1601 (2015) 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Preiss, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Test verb´aln´ı fluence-vod´ıtka pro vˇseobecnou dospˇelou populaci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Psychiatrie 6(2), 74–77 (2002) 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' San Luciano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Digitized spiral drawing: a possible biomarker for early Parkinson’s disease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' PLoS ONE 11(10), e0162799 (2016) 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Saunders-Pullman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Validity of spiral analysis in early Parkinson’s disease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Off.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 23(4), 531–537 (2008) 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Thomas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Lenka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', Kumar Pal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Handwriting analysis in Parkinson’s dis- ease: current status and future directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Clin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Pract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 4(6), 806–818 (2017) 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Van Galen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Handwriting: issues for a psychomotor theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Hum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 10(2–3), 165–191 (1991) 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='  Vessio, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': Dynamic handwriting analysis for neurodegenerative disease assess- ment: a literary review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 9(21), 4666 (2019) 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Warrington, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', James, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=': The visual object and space perception battery (1991) 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Wechsler, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : WAIS-III WMS-III Technical Manual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Psychological Corpo- ration, San Antonio (1997) 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Yamada, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' : Diagnostic criteria for dementia with Lewy bodies: updates and future directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Mov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' Disord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
+page_content=' 13(1), 1 (2020)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdFAT4oBgHgl3EQfXh2G/content/2301.08534v1.pdf'}
diff --git a/c9E3T4oBgHgl3EQfeQoX/vector_store/index.pkl b/c9E3T4oBgHgl3EQfeQoX/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..7e1475cdd0409d3a64f26532dcf5b58601978685
--- /dev/null
+++ b/c9E3T4oBgHgl3EQfeQoX/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:7056be96b7a38790f18f3de186906d69351fcde7477114e5bbab3a3448d9adee
+size 69260
diff --git a/edE3T4oBgHgl3EQfewrM/content/tmp_files/2301.04547v1.pdf.txt b/edE3T4oBgHgl3EQfewrM/content/tmp_files/2301.04547v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ec5e6c73934d556fefcb592b39e02a75326c7903
--- /dev/null
+++ b/edE3T4oBgHgl3EQfewrM/content/tmp_files/2301.04547v1.pdf.txt
@@ -0,0 +1,3093 @@
+arXiv:2301.04547v1  [gr-qc]  11 Jan 2023
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN
+PAST-LIGHTCONES IN COSMOLOGY
+MAURO CARFORA AND FRANCESCA FAMILIARI
+Abstract. We discuss a rigorous procedure for quantifying the difference between our past light-
+cone and the past lightcone of the fiducial Friedmann-Lemaitre-Robertson-Walker spacetime mod-
+eling the large scale description of cosmological data in the standard ΛCDM scenario. This result
+is made possible by exploiting the scale-dependent distance functional between past lightcones re-
+cently introduced by us in [12]. We express this harmonic map type functional in terms of the
+physical quantities that characterize the actual measurements along our past lightcone, namely the
+area distance and the lensing distortion, also addressing the very delicate problem of the presence
+of lightcone caustics. This analysis works beautifully and seems to remove several of the difficulties
+encountered in comparing the actual geometry of our past lightcone with the geometry of the fidu-
+cial FLRW lightcone of choice. We also discuss how, from the point of view of the FLRW geometry,
+this distance functional may be interpreted as a scale-dependent effective field, the pre-homogeneity
+field, that may be of relevance in selecting the FLRW model that best fits the observational data.
+1. INTRODUCTION
+It is a pleasure to dedicate this paper to Maurizio Gasperini who has always liked it best on the
+past light cone even if the routes are tough, but in such a rugged landscape that is to be expected
+The ΛCDM model and the Friedman-Lemaitre-Robertson-Walker (FLRW) spacetimes provide a
+rather accurate physical and geometrical representation of the universe in the present era1 and over
+spatial scales ranging from2 ≈ 100 h−1 Mpc to the visual horizon of our past light cone [27], [34], [50],
+where h is the dimensionless parameter describing the relative uncertainty of the true value of the
+present-epoch Hubble-Lemaitre constant. Within such observational range, and on scales signif-
+icantly smaller than the Hubble scale3, we have a testable ground for statistical isotropy in the
+distribution of the dark and visible matter components on our past light cone. Homogeneity of
+this distribution is difficult to test directly via astronomical surveys, but a number of observational
+results [41] and in particular the kinematic Sunyaev-Zeldovich effect [55], [18] imply that fluctu-
+ations around spatial homogeneity cannot be too large. Thus, without resorting to an axiomatic
+use of the Copernican principle, we have an observational ground for assuming that spatial ho-
+mogeneity holds, in a statistically averaged sense, over large scales. It must be stressed that it is
+in a statistical sense and only over large scales that this weak form of the cosmological principle
+provides observational support for best fitting the description of spacetime geometry in terms of
+a member of the FLRW family of solutions of the Einstein equations.
+In particular, to what-
+ever degree one accepts this FLRW scenario, one has to address the fact that the role of FLRW
+spacetime geometry becomes delicate to interpret when past light cone data are gathered in our
+1Characterized by the actual temperature of the cosmic microwave background TCMB = 2.725 K as measured in
+the frame centered on us but stationary with respect to the CMB.
+2The actual averaging scale marking the statistical onset of isotropy and homogeneity is still much debated. For
+the sake of the argument presented in this paper, we adopt the rather conservative estimate of the scales over which
+an average isotropic expansion is seen to emerge, namely 70 − 120 h−1Mpc, and ideally extending to a few times this
+scale [54].
+3At the Hubble scale, the problem of cosmic variance may alter the statistical significance of the data samples we
+gather.
+1
+
+2
+M. CARFORA AND F. FAMILIARI
+cosmological neighborhood.
+As we probe spatial regions in the range ≲ 100h−1 Mpc, the ac-
+tual distribution of matter (dark and visible) becomes extremely anisotropic with a high density
+contrast. In particular, gravitational clustering gives rise to a complex network of structures, char-
+acterized by the presence of a foam-like web of voids and galaxy filaments often extending well into
+the 100h−1 Mpc range. At these scales, the Einstein evolution of the FLRW geometry uncouples
+from the dynamics of the matter sources and survives more as a useful computational assumption
+(often assisted by Newtonian theory) rather than as a bona fide perturbative background gravi-
+tationally determined by the actual matter distribution. FLRW is thus a very strong assumption
+and not a correct representation of spacetime geometry at the pre-homogeneity scales, not even
+in a statistical sense. If we want or need to go beyond FLRW perturbation theory and enter into
+a fully relativistic regime, it is fair to say that we have little mathematical control over the ac-
+tual spacetime at these pre-homogeneity scales. In particular, the transition from the large-scale
+FLRW to the actual inhomogeneous and anisotropic spacetime geometry emergent at these local
+scales is poorly understood in a model-independent way, and the idea that around 100h−1 Mpc
+we have a gradual and smooth transition between these two regimes is somewhat illusive. To wit,
+we may have non-perturbative correction terms due to the coupling between gravitationally bound
+structures and the emergent spacetime geometry (e.g. structure formation-induced curvature) that
+can be significant in cosmological modeling. For instance, they can back-react, in a top-down cau-
+sation way [52], on the choice of the large-scale FLRW spacetime that best fits the observational
+data. This complex scenario gives rise to a number of delicate and to some extent controversial
+issues that are currently much debated in discussing the existence of possible tensions between
+cosmological observations and the standard ΛCDM model and in preparation to the coming era of
+high-precision cosmology [11]. Some of the very delicate reasons4 motivating this tension is that
+large-scale isotropy can hold for a much wider class of models, the so-called effective model [30], [31]
+that need not even be a solution of Einstein’s equations. As an illustrative example, one may con-
+sider inhomogeneous spatial sections that can be smoothed into a constant-curvature space, e.g.
+with Ricci flow deformation techniques [4–6, 8–10]. While spatially, such slices can be identified
+with spatial sections of a FLRW model, their Einstein time-evolution in general does not follow
+the FLRW class of solutions, a backreaction is present [4–6]. Thus, at least in principle, one may
+actually deal with an effective model with global backreaction that can be large-scale isotropic and
+homogeneous, or almost so, and it is not necessarily perturbatively away from a FLRW model.
+Thus, restricting a priori the ”best-fit” to the class of FLRW models is indeed a strong assumption.
+By its very nature, a discussion of this very complex scenario should be related, as far as possible,
+to a model–independent direct observational cosmology approach, namely to the analysis of data
+determined on our past lightcone without using any theory of gravity. Since the dark matter and
+dark energy components cannot be measured yet via direct observations, it must be stressed that
+a full model-independent cosmographic approach is not actually possible [21]. Model hypotheses
+must be imposed for the dark components, in particular on how they interact with observed matter.
+The simplest assumptions made are that the dark matter component follows the baryonic compo-
+nent, namely that: i) we know the primordial ratio of cold dark matter (CDM) density to baryonic
+density; ii) they have the same 4-velocity; iii) we know their relative concentration in matter
+clusters. To these, one typically adds the working assumption that the dark energy component is
+described in the form of a cosmological constant Λ, the value of which should be known from non–
+cosmological physics and independently from cosmological observations (for a thorough discussion
+of the implications of these assumptions in cosmography see Chap. 8 of [21]). However, although
+there are efforts to derive Λ from non-cosmological physics, it remains a fitting parameter of the
+model. The appropriate cosmographical framework was put forward in the ’80s by G.F.R. Ellis,
+4We wish to thank one of the referees for pointing this out to us.
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+3
+R. Maartens, W. Stoeger, and A. Whitman [20] (see also [21]) by characterizing the set of cosmo-
+logical observables on the past lightcone which, together with the Einstein field equations, allows
+to reconstruct the spacetime geometry in a way adapted to the process of observation [20], [15], [16].
+In this paper we address an important step in this cosmographical framework. In particular we
+discuss a rigorous procedure for quantifying the difference between our past lightcone and the
+reference past lightcone that, for consistency, we associate with the fiducial large-scale FLRW
+spacetime. This result is made possible by exploiting the scale-dependent (harmonic map type)
+distance functional between past lightcones recently introduced by us in [12], and which extended
+the light-cone theorem [14]. We express this functional in terms of the physical quantities that
+characterize measurements along our past lightcone, namely the area distance and the lensing dis-
+tortion, also briefly addressing the very delicate problem of the presence of lightcone caustics. This
+analysis works beautifully and seems to remove several of the difficulties encountered in comparing
+the actual geometry of our past lightcone with the geometry of a fiducial FLRW lightcone of choice.
+We also discuss how, from the point of view of the FLRW geometry, this distance functional may
+be interpreted as a scale-dependent effective field that may be of relevance in selecting the FLRW
+model that best fits the observative data. In this connection and in line with the introductory
+remarks above its worthwhile to stress that our choice of a reference FLRW spacetime is strictly
+related to the prevalence of this family of metrics in discussing the ΛCDM model. The results
+presented here can be easily extended to more general reference metrics. It is also important to
+make clear that in this paper we are not addressing the extremely delicate averaging problem on
+the past lightcone, a problem to which Maurizio Gasperini has significantly contributed with the
+seminal paper [24], and that has seen importat recent progress in [7]... but the past lighcone routes
+are still tough and the landscape rugged ... .
+2. The past light cone and the celestial sphere
+Throughout this paper (M, g) denotes a cosmological spacetime where g is a Lorentzian metric,
+and where M is a smooth 4-dimensional manifold which for our purposes we can assume diffeo-
+morphic to R4 (or to V 3 × R, for some smooth compact or complete 3–manifold V 3). In local
+coordinates {xi}4
+i=1, we write g = gikdxi ⊗ dxk, where the metric components gik := g(∂i, ∂k) in
+the coordinate basis {∂i := ∂/∂xi}4
+i=1 have the Lorentzian signature (+, +, +, −), and the Einstein
+summation convention is in effect5. We assume that (M, g) is associated with the evolution of
+a universe which is (statistically) isotropic and homogeneous on sufficiently large scales L > L0
+where, according to the introductory remarks, we indicatively assume L0 ∼= 100h−1 Mpc, and let
+local inhomogeneities dominate for L < L0. The matter content in (M, g) is phenomenologically
+described by a (multi-component) energy-momentum tensor T = Tik dxi ⊗ dxk, (typically in the
+form of a perfect fluid, dust, and radiation). If not otherwise stated, the explicit expression of T is
+not needed for our analysis. We assume that in (M, g) the motion of the matter components charac-
+terize a phenomenological Hubble flow that generates a family of preferred world-lines parametrized
+by proper time τ
+γs : R>0
+−→
+(M, g)
+(1)
+τ
+�−→
+γs(τ) ,
+and labeled by suitable comoving (Lagrangian) coordinates s adapted to the flow. We denote by
+˙γs :=
+dγs(τ)
+dτ
+, g(˙γs, ˙γs) = −1, the corresponding 4-velocity field. For simplicity, we assume that
+at the present era these worldlines are geodesics, i.e. ∇ ˙γs ˙γs = 0. This phenomenological Hubble
+flow is strongly affected by the peculiar motion of the astrophysical sources and by the complex
+spacetime geometry that dominates on the pre-homogeneity scales.
+In particular, it exhibits a
+5If not otherwise stated we adopt geometrical units, c = 1 = G.
+
+4
+M. CARFORA AND F. FAMILIARI
+complex pattern of fluctuations with respect to the linear FLRW Hubble flow that sets in, relatively
+to the standard of rest provided by the cosmic microwave background (CMB), when we probe the
+homogeneity scales, L ≳ 100h−1 Mpc. Again, we stress that the transitional region between the
+phenomenological Hubble flow and the statistical onset of the large-scale FLRW linear Hubble flow
+is quite uncertain and still actively debated [54]. If we adopt the weak form of the cosmological
+principle described in the introduction, (M, g, γs) can be identified with the phenomenological
+background spacetime or Phenomenological Background Solution (PBS) [39] associated with the
+actual cosmological data gathered from our past lightcone observations. In the same vein, we define
+Phenomenological Observers the collection of observers {γs} comoving with the phenomenological
+Hubble flow (1). Since in our analysis we fix our attention on a given observer, we drop the subscript
+s in (1), and describe a finite portion of the observer’s world-line with the timelike geodesic segment
+τ �−→ γ(τ), −δ < τ < δ, for some δ > 0, where p := γ(τ = 0) is the selected event corresponding
+to which the cosmological data are gathered. To organize and describe these data in the local rest
+frame of the observer p := γ(τ = 0), let
+�
+TpM, gp, {E(i)}
+�
+be the tangent space to M at p endowed
+with a g-orthonormal frame {E(i)}i=1,...,4, gp
+�
+E(i), E(k)
+�
+= ηik, where ηik is the Minkowski metric,
+and where we identify E(4) with the observer 4-velocity ˙γ(τ)|τ=0, i.e.
+E(4) := ˙γ(τ)|τ=0. Thus, if
+we denote by { ˘E (i)}i=1,...,4, the 1-forms basis dual to {E(i)}i=1,...,4, we write
+gp = ηik ˘E (i) ⊗ ˘E (k) .
+(2)
+Since we have the distinguished choice E(4) := ˙γ(τ)|τ=0 for the timelike basis vector E(4), we can
+also introduce in
+�
+TpM, {E(i)}
+�
+a reference positive definite metric g(δ)
+p
+associated with the frame
+{E(i)}i=1,...,4 by setting
+g(δ)
+p
+:= δik ˘E (i) ⊗ ˘E (k) ,
+(3)
+where δik denote the components of the standard Euclidean metric. As discussed in detail by Chen
+and LeFloch [13], this reference metric comes in handy in the characterization of the functional
+Lipschitz and Banach space norms of tensor fields defined on the past lightcone6.
+2.1. The celestial sphere. Let
+(4)
+C− �
+TpM, {E(i)}
+�
+:=
+�
+X = XiE(i) ̸= 0 ∈ TpM | gp(X, X) = 0, X4 + r = 0
+�
+,
+(5)
+C− �
+TpM, {E(i)}
+�
+:=
+�
+X = XiE(i) ̸= 0 ∈ TpM | gp(X, X) ≤ 0, X4 + r ≤ 0
+�
+,
+respectively denote the set of past-directed null vectors and the set of past-directed causal vectors
+in (TpM, {E(i)}), where
+(6)
+r := (
+3
+�
+a=1
+(Xa)2)1/2 ,
+is the radial coordinate in the hyperplane X4 = 0 ⊂ TpM parametrizing the one-parameter family
+of 2-spheres
+(7)
+S2
+r(TpM) := {X ∈ C− �
+TpM, {E(i)}
+�
+| X4 = − r,
+3
+�
+a=1
+(Xa)2 = r2, r ∈ R>0} ,
+6The indefinite character of a Lorentzian metric makes it unsuitable for defining integral norms of tensor fields,
+and for such a purpose one is forced to introduce a reference positive definite metric. In particular, by exploiting the
+Nash embedding theorem, one typically uses the Euclidean metric and the associated definitions of the functional
+space of choice, say a Sobolev space of tensor fields. Different choices of reference metrics, as long as they are of
+controlled geometry, induce equivalent Banach space norms. In our case, we can exploit the natural choice provided
+by (3) by using normal coordinates and identifying (TpM, {E(i)}, gδ
+p) with the Euclidean space (R4, gδ
+p).
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+5
+that foliates C− �
+TpM, {E(i)}
+�
+/{p}. The sphere S2
+r(TpM) can be thought of as providing a rep-
+resentation of the sky directions, at a given value of r, in the rest space
+�
+TpM, {E(i)}
+�
+of the
+(instantaneous) observer (p, ˙γ(0)). In particular, the 2-sphere S2
+r(TpM)
+��
+r=1 or, equivalently, its
+projection on the hyperplane X4 = 0 in TpM,
+(8)
+S2 (TpM) :=
+�
+X = XiE(i) ̸= 0 ∈ TpM | X4 = 0,
+3
+�
+a=1
+(Xa)2 = 1
+�
+,
+can be used to parametrize the (spatial) past directions of sight constituting the field of vision
+of the observer (p, ˙γ(0)). In the sense described by R. Penrose [46], this is a representation of
+the abstract sphere S−(p) of past null directions parameterizing the past-directed null geodesics
+through p. Explicitly, let
+n(θ, φ)
+:=
+3
+�
+a=1
+na(θ, φ) E(a)
+(9)
+=
+cos φ sin θ E(1) + sin φ sin θ E(2) + cos θ E(3) ,
+0 ≤ θ ≤ π, 0 ≤ φ < 2π ,
+denote the spatial direction in TpM associated with the point (θ, φ) ∈ S2 (TpM), (by abusing nota-
+tion, we often write n(θ, φ) ∈ S2 (TpM)). Any such spatial direction characterizes a corresponding
+past-directed null vector ℓ(θ, φ) ∈
+�
+TpM, {E(i)}
+�
+,
+(10)
+ℓ(θ, φ) = (n(θ, φ), − ˙γ(τ)|τ=0) =
+3
+�
+a=1
+na(θ, φ)E(a) − E(4) ,
+normalized according to
+(11)
+gp (ℓ(θ, φ), ˙γ(τ)|τ=0) = gp
+�
+ℓ(θ, φ), E(4)
+�
+= 1 .
+The corresponding past-directed null rays
+(12)
+R≥0 ∋ r �−→ r ℓ(n(θ, φ)) ,
+(θ, φ) ∈ S2 (TpM) ,
+generate C− �
+TpM, {E(i)}
+�
+. Note that in such a kinematical setup for the instantaneous rest space
+�
+TpM, {E(a)}
+�
+of the observer (p, ˙γ(0)), a photon reaching p from the past-directed null direction
+ℓ(θ, φ), is characterized by the (future-pointing) wave vector
+(13)
+k(θ, φ) := − ν ℓ(θ, φ) ∈ TpM ,
+where ν = − gp
+�
+k, E(4)
+�
+is the photon frequency as measured by the instantaneous observer
+γ(τ)|τ=0. The spherical surface S2 (TpM) endowed with the standard round metric
+(14)
+�h(S2) = dθ2 + sin2 θ dφ2 ,
+and the associated area form dµS2 =
+�
+det(�h(S2)) dθdφ = sin θ dθdφ, defines [46] the celestial
+sphere
+(15)
+C S(p) :=
+�
+S2 (TpM) , �h(S2)
+�
+providing, in the instantaneous rest space
+�
+TpM, {E(i)}
+�
+, the geometrical representation of the set
+of all directions towards which the observer can look at astrophysical sources from her instanta-
+neous location in (M, g). In this connection, dµS2 can be interpreted as the element of solid angle
+subtended on the celestial sphere C S(p) by the observed astrophysical sources. It is also useful
+to keep track of the radial coordinate7 r as a possible parametrization of the past-directed null
+7To avoid any misunderstanding we stress that r is not a distance parameter on the past light cone with vertex in
+p ∈ (M, g).
+
+6
+M. CARFORA AND F. FAMILIARI
+geodesics, and introduce a celestial sphere that provides also this information according to
+(16)
+C Sr(p) :=
+�
+S2
+r (TpM) , r2�h(S2)
+�
+.
+Lacking a better name, we shall refer to C Sr(p) as the celestial sphere at radius r in
+�
+TpM, {E(i)}
+�
+.
+The celestial sphere C S(p) plays a basic role in what follows since it provides the logbook where
+astrophysical data are recorded.
+Let m(α)(θ, φ) ∈ TpM, with α = 2, 3, denote two spatial gp-orthonormal vectors spanning the
+tangent space T(θ,φ)S2 (TpM) to S2 (TpM) at the point (θ, φ), i.e.,
+(17)
+gp
+�
+m(α), n
+�
+= 0 = gp
+�
+m(α), E(4)
+�
+, gp
+�
+m(α), m(β)
+�
+= δαβ .
+The tetrad
+(18)
+�
+n, m(2), m(3), ℓ(n)
+�
+provides a basis for TpM (the Sachs basis), and the pair
+�
+T(θ,φ)S2 (TpM) , m(α)(θ, φ)
+�
+defines the
+screen plane TnC S(p) associated with the direction of sight n(θ, φ) ∈ C S(p) in the celestial sphere
+C S(p), i.e.
+(19)
+TnC S(p) :=
+�
+T(θ,φ)S2 (TpM) , m(α)(θ, φ)
+�
+.
+In the instantaneous rest space of the observer, the screen T(θ,φ)C S(p) is the (spatial) 2-plane on
+which the apparent image of the astrophysical source, pointed by the direction n ∈ C S(p), is by
+convention displayed.
+2.2. Sky sections and observational coordinates on the past light cone. We transfer the
+above kinematical setup from TpM to (M, g) by using the exponential map based at p,
+expp : Wp ⊆ TpM
+−→
+M
+(20)
+X
+�−→
+expp (X) := λX(1) ,
+where λX : IW −→ (M, g), for some maximal interval IW ⊆ R≥0, is the past-directed causal
+geodesic emanating from the point p with initial tangent vector ˙λX(0) = X ∈ Wp, and where
+Wp ⊆ TpM is the maximal domain of expp. Thus, the past lightcone C −(p, g) ∈ (M, g) with the
+vertex at p, i.e. the set of all events q ∈ (M, g) that can be reached from p along the past-pointing
+null geodesics r �−→ expp(rℓ(n(θ, φ))), r ∈ IW , (θ, φ) ∈ C S(p), can be represented as
+(21)
+C −(p, g) := expp
+�
+Wp ∩ C− (TpM, gp)
+�
+,
+and the portion of C −(p, g) accessible to observations for a given value r0 ∈ IW of the affine
+parameter r is given by
+C −(p, g; r0) :=
+�
+q ∈ M | q = expp(rℓ(n(θ, φ))), 0 ≤ r < r0, (θ, φ) ∈ C S(p)
+�
+.
+The exponential map representation, on the celestial spheres C S(p) and C Sr(p), provides a natural
+setup for a description of observational data gathered from C −(p, g). It emphasizes the basic role
+of past-directed null geodesics and provides the framework for interpreting the physical data in
+the local rest frame of the observer at p. In particular, it allows us to represent on C S(p) and
+C Sr(p) the actual geometry of the observed sky at a given length scale. This role is quite effective
+in a neighborhood of p, where we can introduce normal coordinates associated with expp, but it
+is delicate to handle in regions where expp is not a diffeomorphism of Wp ∩ C− (TpM, gp) onto
+its image.
+To set notation, our strategy is to start with the standard description [20], [21] of
+observational coordinates on C −(p, g) associated with the usual assumption that the exponential
+map is a diffeomorphism8 in a sufficiently small neighborhood of p, and then we move to the more
+8From an observational point of view, this is the geometrical set-up proper of the weak lensing regime describing
+the alteration, due to the effect of gravity, of the apparent shape and brightness of astrophysical sources.
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+7
+general, low regularity, Lipschitz case. In this connection, it is worthwhile to stress that the standard
+normal coordinates description is strictly associated with the assumption that the metric of (M, g)
+is sufficiently regular, with components gij(xℓ) which are at least twice continuously differentiable,
+i.e. gij(xℓ) ∈ Ck(R4, R),
+for k ≥ 2. Under this hypothesis, there is a star-shaped neighborhood
+N0(g) of 0 in Wp ⊆ TpM and a corresponding geodesically convex neighborhood of p, Up ⊆ (M, g),
+restricted to which expp : N0 ⊆ TpM −→
+Up ⊆ M is a diffeomorphism. In such Up we can
+introduce geodesic normal coordinates (xi) according to
+xi := Xi ◦ exp−1
+p
+: M ∩ Up
+−→
+R4
+(22)
+q
+�−→
+xi(q) := Xi �
+exp−1
+p (q)
+�
+where Xi �
+exp−1
+p (q)
+�
+are the components, in the g-orthonormal frame {E(i)}, (or with respect to
+the corresponding basis (18)), of the vector exp−1
+p (q) ∈ Wp ⊆ TpM. Thus, in C −(p, g) ∩ Up we
+can write,
+expp
+: C− �
+TpM, {E(i)}
+�
+∩ N0(g)
+−→
+C −(p, g) ∩ Up
+(23)
+rℓ(n(θ, φ)) = r
+�
+na(θ, φ)E(a) − E(4)
+�
+�−→
+expp(rℓ(n)) = q
+=⇒ q
+�−→
+{xi(q) := exp−1
+p (q) = (r na(θ, φ), − r)} .
+According to (21) and to the Gauss lemma applied to expp : C− �
+TpM, {E(i)}
+�
+∩ N0(g) −→
+C −(p, g) ∩ Up, the past ligh cone region C −(p, g) ∩ Up \ {p} is foliated by the r-dependent family
+of 2–dimensional surfaces Σ(p, r), the cosmological sky sections, defined by
+(24)
+Σ(p, r) := expp [C Sr(p)] =
+�
+expp (r ℓ(n(θ, φ)))
+�� (θ, φ) ∈ C S(p)
+�
+,
+and g-orthogonal to all null geodesics originating at p, i.e.
+(25)
+g
+�
+d(r,θ,φ) expp(ℓ(r, n)), d(r,θ,φ) expp(v)
+���
+expp(ℓ(r,n)) = 0 .
+Here d(r,θ,φ) expp(...) denotes the tangent mapping associated to expp evaluated at the point (θ, φ) ∈
+S2
+r(p), and v ∈ Tθ,φ S2
+r(p) is the generic vector tangent to S2
+r(p). In C −(p, g) ∩ Up\{p}, each surface
+Σ(p, r) is topologically a 2-sphere endowed with the r-dependent two-dimensional Riemannian
+metric
+(26)
+g|Σ(p,r) := ι∗
+r g|C −(p,g)
+induced by the inclusion ιr : Σ(p, r) ֒→ C −(p, g) of Σ(p, r) into C −(p, g) ∩ Up \ {p}. We can pull
+back this metric to the celestial sphere C Sr(p) :=
+�
+S2
+r (TpM) , r2�h(S2)
+�
+by using the exponential
+map according to
+(27)
+h(r, θ, φ) :=
+�
+exp∗
+p g|Σ(p,r)
+�
+αβ dxαdxβ���
+r ,
+α, β = 2, 3,
+x2 := θ, x3 := φ .
+This metric can be profitably compared with the pre-existing round metric r2�h(S2) on C Sr(p) (see
+(14) and (16)). To this end, let r n(θ, φ) ∈ C Sr(p) be the direction of sight pointing, in the celestial
+sphere C Sr(p), to the (extended) astrophysical source located around the point q ∈ Σ(p, r). If
+rℓ(n(θ, φ)) = r
+�
+na(θ, φ)E(a) − E(4)
+�
+is the corresponding null direction in C− �
+TpM, {E(i)}
+�
+, then
+according to (23) we have expp(rℓ(n)) = q and, via the exponential map along the past-directed
+null geodesic reaching the observer located at p from the astrophysical source located at q, we can
+pull-back the area element of
+�
+Σ(p, r), g|Σ(p,r)
+�
+on the celestial sphere C Sr(p) of the observer at p.
+We have
+(28)
+dµh(r)(p, n(θ, φ), r) := exp∗
+p dµg|Σ(p,r) ◦ expp(rℓ(n)) =
+�
+det(h(r, θ, φ)) dθdφ .
+This defines the area element associated with the metric (27), and can be interpreted [21] as the
+cross-sectional area element at the source location as seen by the observer at p. Since the round
+
+8
+M. CARFORA AND F. FAMILIARI
+measure dµS2r = r2 dµS2 = r2 sin θ dθ dϕ and the actual physical measure dµh(r) are both defined
+over the celestial sphere C Sr(p) ∈ TpM, we can introduce the relative density of dµh(r) with respect
+to the Euclidean solid angle measure dµS2, viz. the function D(r, θ, φ) defined by the relation
+(29)
+dµh(r) = D2(r, θ, φ) dµS2 ,
+or equivalently,
+�
+det(h(r, θ, φ)) = D2(r, θ, φ)
+�
+det(�h(S2)). The function D(r, θ, φ) is the observer
+area distance [20], [21], [33]. By definition, it provides the ratio of an object’s cross sectional area
+to its (apparent) angular size as seen on the celestial sphere S2(p) ⊂ TpM. Roughly speaking,
+it converts the angular separations as seen in the images of an astrophysical source, gathered by
+the observer at p, into proper separations at the source. In general, D(r) := D(r, θ, φ)|θ,φ=const.
+cannot be used as an affine parameter along the past-directed null geodesic r �→ expp(k(r, n))
+since it is not a monotonic function of r, (for instance in FLRW models, monotonicity fails around
+z ∼ 1). However, if we have an accurate knowledge of the brightness and of the spectrum of
+the astrophysical source seen at the past light cone location q := expp(ℓ(r, n)) ∈ C −(p, g), then
+D(r, θ, φ) is, at least in principle, a measurable quantity (see paragraph 4.3 of [20] and 7.4.3 of
+[21] for a discussion of this point9). As stressed above, we can also compare the physical metric
+(27), h(r, θ, φ) :=
+�
+exp∗
+p g|Σ(p,r)
+�
+αβ dxαdxβ���
+r,
+with the round metric r2�h(S2) pre-existing on the
+celestial sphere C Sr(p), and introduce [20], [21] the set of functions Lαβ(r, θ, φ), α, β = 2, 3,
+implicitly defined by representing (27) in the distorted polar form
+(30)
+hαβ|S2r = D2(r, θ, φ)
+�
+�hαβ(S2) + Lαβ
+�
+.
+We normalize this representation by imposing [20] that, in the limit r ց 0, the distortion,
+Lαβ(r, θ, φ) = hαβ(r,θ,φ)
+D2(r,θ φ − �hαβ(S2), of the normalized metric h(r)/D2(r) with respect to the round
+metric �h(S2) goes to zero uniformly, i.e.,
+(31)
+lim
+rց0
+����
+x4=0
+hαβ(r, θ, φ) dxαdxβ
+D2(r, θ, φ)
+= dθ2 + sin2 θ dφ2 .
+From the relation D− 2 hαβ = �hαβ(S2) + Lαβ we also compute
+(32)
+D− 2 �hµβ hαβ = δµ
+α + Lµ
+α =⇒ det (δµ
+α + Lµ
+α) = 1 ,
+where, for rising indexes, we used the inverse round metric �hµβ(S2) to write Lµ
+α := �hµβ(S2) Lαβ,
+and where we have exploited the relation det
+�
+�hµβ hαβ
+�
+= D4, direct consequence of det(h) =
+D4 det(�h(S2)) (see (29)). Since
+(33)
+det (δµ
+α + Lµ
+α) = 1 + trS2 (Lµ
+α) + det (Lµ
+α) ,
+from relation (32) it follows that
+(34)
+trS2 (Lµ
+α) + det (Lµ
+α) = 0 ,
+which implies that Lµ
+α cannot be trace-free. Roughly speaking, Lαβ(r) can be interpreted as the
+image distortion of the sources on (Σ(p, r), h(r)) as seen by the observer at p on her celestial sphere.
+It can in principle be directly observed and it can be related to the gravitational lensing shear [20],
+(see also chap. 8 of [21]). Explicitly, let us compute the deformation tensor Θαβ defined by the rate
+9Beware that in [20], the observer area distance D2(r, θ, φ) is denoted by r, whereas our r corresponds to their y.
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+9
+of variation of the metric tensor h(r) as r varies. Dropping the angular dependence for notational
+ease, we get
+Θαβ := d
+dr hαβ(r)
+=
+d
+dr
+�
+D2(r)
+�
+�hαβ(S2) + Lαβ(r)
+��
+(35)
+=
+2hαβ(r) d
+dr ln D(r) + D2(r) d
+dr Lαβ(r) ,
+where we exploited d�hαβ(S2)/dr = 0 and rewrote D(r)dD(r)/dr as D2(r)d ln D(r)/dr. Similarly,
+from the defining relation
+�
+det(h(r, θ, φ)) = D2(r, θ, φ)
+�
+det(�h(S2)), (see (29)), we compute
+d
+dr
+�
+det(h(r))
+=
+d
+dr
+�
+D2(r)
+�
+det(�h(S2))
+�
+= 2
+�
+det(h(r)) d
+dr ln D(r)
+(36)
+⇒
+d
+dr ln
+�
+det(h(r))
+=
+2 d
+dr ln D(r) .
+Inserting this relation in (35) we obtain
+(37)
+Θαβ := hαβ(r) d
+dr ln
+�
+det(h(r)) + D2(r) d
+dr Lαβ(r) .
+The shear �σαβ is the trace-free part of this expression, �σαβ := Θαβ − 1
+2hαβ hµνΘµν. Since
+(38)
+1
+2hαβ hµνΘµν = 1
+2hαβ hµν d
+drhµν = hαβ
+d
+dr ln
+�
+det(h(r)) ,
+we eventually get
+(39)
+�σαβ = D2(r) dLαβ(r)
+dr
+,
+as might have been expected. Note that, in contrast to Lαβ, �σαβ is trace-free (but with respect to
+the physical metric hαβ). Now, let us introduce the other basic player of our narrative.
+3. The background FLRW past light cone.
+As already pointed out, the standard ΛCDM model is built on the assumption that over scales
+L > 100 h−1 Mpc, the phenomenological background spacetime (M, g, γs) follows on average the
+dynamics of a FLRW model with a (linear) Hubble expansion law. It is also assumed that below
+the scale of statistical homogeneity, deviations from this average scenario can be described by
+FLRW perturbation theory. Since there is no smooth transition between the large-scale FLRW
+Hubble flow and the phenomenological Hubble flow, this latter assumption rests on quite delicate
+ground. For instance, the field of peculiar velocities {˙γs(τ)} of the phenomenological observers
+{τ −→ γs(τ)} shows a significant statistical variance [53] with respect to the average FLRW Hubble
+flow and the standard of rest provided by the cosmic microwave background (CMB). This remark
+has an important effect on the relation between the celestial sphere C Sr(p) of the phenomenological
+observer (p, ˙γ(0)) and the corresponding celestial sphere �
+C S�r(p) of the idealized FLRW observer
+(p, �˙γ(0)). They cannot be identified and must be connected by a Lorentz boost that takes into
+account the origin of this statistical variance. The actual scenario is significantly constrained by the
+coupling of the matter inhomogeneities with a spacetime geometry that is no longer Friedmannian.
+As a consequence, the peculiar velocity field of the phenomenological observer may have a rather
+complex origin, and its variance with respect to the FLRW average expansion may become a variable
+of relevance in cosmography. This scenario naturally calls into play a delicate comparison between
+the geometry of C−(p, g) and the geometry of the associated FLRW past light cone that sets in at
+scales L > 100 h−1 Mpc. For this purpose, along with the physical metric g, we consider on the
+spacetime manifold M a reference FLRW metric ˆg and the associated family of global Friedmannian
+observers ˆτ �−→ ˆγs(ˆτ). Strictly speaking, the FLRW model (M, ˆg, ˆγs(ˆτ)) should be used only over
+
+10
+M. CARFORA AND F. FAMILIARI
+the scales L > L0 ≃ 100 h−1 Mpc. We need to consider it also over the inhomogeneity scales
+L < L0 where it plays the role of the geometrical background used to interpret the data according
+to the standard perturbative FLRW point of view recalled above. In such an extended role, the
+chosen FLRW is the Global Background Solution (GBS according to [39]) we need to check against
+the physical metric g representing the phenomenological background solution. In this section, we set
+up the kinematical aspects for such a comparison. First some standard verbiage for introducing the
+FLRW model (M, ˆg, ˆγs(ˆτ)). In terms of the radial, and angular FRLW coordinates yα :=
+�
+ˆr, ˆθ, ˆϕ
+�
+,
+and of the proper time of the comoving fundamental observers y4 := ˆτ, we set
+�g
+:=
+−dˆτ 2 + a2(ˆτ)
+�
+dˆr2 + f 2(ˆr)
+�
+dˆθ2 + sin2 ˆθ d ˆϕ2��
+,
+�˙γ
+h = δh
+4,
+(40)
+f(ˆr)
+:=
+
+
+
+
+
+sin ˆr,
+k = +1
+ˆr,
+k = 0
+sinh ˆr, k = −1 ,
+where a(ˆτ) is the time-dependent scale factor, k is the normalized dimensionless spatial curvature
+constant, and �˙γ
+h are the components of the 4-velocity �˙γ of the fundamental FLRW observers. Ac-
+cording to the above remarks, the geodesics τ �−→ γ(τ), and ˆτ �−→ ˆγ(ˆτ), −δ < τ, ˆτ < δ, associated
+with the corresponding Hubble flow in (M, g, γ) and (M, ˆg, ˆγ), are assumed to be distinct, but
+in line with the scale-dependent cosmographic approach adopted here we assume that they share
+a common observational event p ∈ M. We denote by
+�
+C −(p, ˆg) the associated FLRW past light
+cone, and normalize the proper times τ and ˆτ along γ(τ) and ˆγ(ˆτ) so that at τ = 0 = ˆτ we
+have γ(0) = p = ˆγ(0). As stressed, the two instantaneous observers (p, ˙γ(0)) and (p, �˙γ(0)) have
+different 4-velocities, ˙γ(0) ̸= �˙γ(0), and their respective celestial spheres, C S(p) and �
+C S
+2(p) are
+quite distinct. They are related by a Lorentz trasformation describing the aberration of the sky
+mapping of one instantaneous observer with respect to the other. This mapping will play a basic
+role in our analysis, and to provide an explicit description of its properties, we start by adapting
+to the FLRW instantaneous observer (p, �˙γ(0)) ∈ (M, ˆg, ˆγ) the setup characterizing the celestial
+spheres C S(p) and C Sr(p) of the instantaneous observer (p, ˙γ(0)) ∈ (M, g, γ).
+3.1. The FLRW celestial sphere and the associated sky sections. Let
+�
+�TpM, �gp, { �E(i)}
+�
+be
+the tangent space to (M, ˆg, ˆγ) at p endowed with a �g-orthonormal frame { �E(i)}i=1,...,4, �gp
+�
+�E(i), �E(k)
+�
+=
+ηik, where ηik is the Minkowski metric, and where we identify �E(4) with the FLRW-observer’s 4-
+velocity �˙γ(τ)|τ=0, i.e.
+�E(4) := �˙γ(τ)|τ=0. For ease of notation, we shall often use the shorthand
+�TpM when referring to the tangent space to (M, ˆg, ˆγ) at p. Let
+(41)
+C− �
+�TpM, { �E(i)}
+�
+:=
+�
+Y = Yi �E(i) ̸= 0 ∈ �TpM | �gp(Y, Y ) = 0, Y4 + �r = 0
+�
+,
+(42)
+C−
+�
+�TpM, { �E(i)}
+�
+:=
+�
+Y = Yi �E(i) ̸= 0 ∈ �TpM | �gp(Y, Y ) ≤ 0, Y4 + �r ≤ 0
+�
+,
+respectively denote the set of past-directed null vectors and the set of past-directed causal vectors
+in ( �TpM, { �E(i)}), where �r := (�3
+a=1(Ya)2)1/2 is the radial coordinate (see (6)) in the hyperplane
+Y4 = 0 ⊂ �TpM parametrizing the one-parameter family of 2-spheres
+(43)
+S2
+�r( �TpM) := {Y ∈ C− �
+�TpM, { �E(i)}
+�
+| Y4 = − �r,
+3
+�
+a=1
+(Ya)2 = �r2, �r ∈ R>0} ,
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+11
+that foliate C− �
+�TpM, { �E(i)}
+�
+/{p}. The 2-spheres S2
+�r( �TpM), endowed with the round metric
+(44)
+��h(S2) = ��hαβ(S2)dyαdyβ = d�θ2 + sin2 �θ d�φ2 ,
+0 ≤ �θ ≤ π, 0 ≤ �φ < 2π
+can be thought of as providing a representation of the sky, at a given value of the radial coordinate
+�r, in the instantaneous rest space
+�
+�TpM, { �E(i)}
+�
+of the FLRW observer.
+In analogy with the
+characterization (8) of the celestial sphere C S(p), we use the projection of S2
+�r( �TpM)
+���
+�r=1 on the
+hyperplane Y4 = 0 in �TpM, to define the FLRW celestial sphere
+(45)
+�
+C S(p)
+�
+S2
+�r( �TpM)
+���
+�r=1 , ��h(S2)(p)
+�
+:=
+�
+Y = YiE(i) ̸= 0 ∈ �TpM | Y4 = 0,
+3
+�
+a=1
+(Ya)2 = 1
+�
+,
+parametrizing the directions of sight
+(46)
+�n(�θ, �φ) := (cos �φ sin �θ, sin �φ sin �θ, cos �θ) ,
+0 ≤ �θ ≤ π, 0 ≤ �φ < 2π
+in the instantaneous rest space
+�
+�TpM, { �E(i)}
+�
+of the FLRW observer. In full analogy with (16),
+we define the FLRW celestial sphere at radius �r in
+�
+�TpM, { �E(i)}
+�
+according to
+(47)
+�
+C S�r(p) :=
+�
+S2
+�r
+�
+�TpM
+�
+, �r2��h(S2(p))
+�
+.
+With a straightforward adaptation to the FLRW geometry of the definitions (10), (18), and (19),
+we also introduce in �TpM the tetrad
+(48)
+�
+�n, �m(2), �m(3), �ℓ(�n)
+�
+and associate with the pair
+�
+�T(�θ,�φ)S2 �
+�TpM
+�
+, �m(α)(�θ, �φ)
+�
+the screen plane T�n �
+C S(p) associated
+with the direction of sight �n(�θ, �φ) in the FLRW celestial sphere �
+C S(p),
+(49)
+T�n �
+C S(p) :=
+�
+T(�θ,�φ)S2 �
+�TpM
+�
+, �m(α)(�θ, �φ)
+�
+.
+Together with the observational normal coordinates {Xi} in (M, g, γ), describing the local geometry
+on the past lightcone C −(p, g) ∩ Up, we introduce corresponding (normal) coordinates {Y k} on
+the past light cone �
+C −(p, ˆg) in the reference FLRW spacetime (M, ˆg, ˆγ). To begin with, let �
+expp
+denote the exponential mapping based at the event p = ˆγ(0), i.e.
+�
+expp : �
+Wp ⊆ �TpM
+−→
+(M, ˆg),
+(50)
+Y
+�−→
+expp (Y) := λY(1) ,
+where �
+Wp is the maximal domain of �
+expp. To keep on with the notation set by (21) and (22), we
+characterize the past lightcone �
+C −(p, ˆg) ∈ (M, �g), with vertex at p, according to
+(51)
+�
+C −(p, ˆg) := �
+expp
+�
+�
+Wp ∩ C− �
+�TpM, �gp
+��
+,
+and we denote by
+�
+C −(p, �g; �r0) :=
+�
+q ∈ M | q = �
+expp(�r�ℓ(�n(�θ, �φ))), 0 ≤ �r < �r0, (�θ, �φ) ∈ �
+C S(p)
+�
+,
+the portion of
+�
+C −(p, ˆg) accessible to observations for a given value �r0 of the radial parameter �r.
+That said, if ˆUp ⊂ (M, ˆg) denotes the region of injectivity of �
+expp, then normal coordinates are
+
+12
+M. CARFORA AND F. FAMILIARI
+defined by
+(52)
+yi := Yi ◦ �
+exp−1
+p
+: (M, �g) ∩ �Up −→ R ,
+where Yi are the components of the vectors Y ∈
+�TpM with respect to a ˆg-orthonormal frame
+{ ˆE(i)}i=1,...,4 with ˆE(4) := ˆ˙γ(0). We can parametrize �
+C −(p, �g) ∩ �Up in terms of the 2-dimensional
+FLRW sky sections
+(53)
+�Σ(p, ˆr) := �
+expp
+�
+�
+C S�r(p)
+�
+=
+�
+�
+expp
+�
+�r �ℓ(�n(�θ, �φ))
+� ��� (�θ, �φ) ∈ �
+C S(p)
+�
+,
+endowed with the metric induced by the inclusion of �Σ(p, ˆr) into �
+C −(p, ˆg), i. e.
+(54)
+�g|�Σ(p,ˆr) := (�g)αβ dyαdyβ���
+ˆr = a2(�τ(�r)) f 2 (�r)
+�
+d�θ2 + sin2 �θd�φ2�
+,
+where a(�τ(�r)) is the FLRW expansion factor a(�τ) (see (40)) evaluated in correspondence of the
+given value of the radial coordinate �r ∈ �TpM. We proceed as in Subsection 2.2, and exploit the
+exponential map �
+expp to pull back �g|�Σ(p,ˆr) on the celestial sphere �
+C S�r(p),
+(55)
+�h(�r, �θ, �φ) :=
+�
+�
+exp∗
+p �g|�Σ(p,�r)
+�
+αβ dyαdyβ
+����
+�r
+,
+α, β = 2, 3,
+y2 := �θ, y3 := �φ .
+This pull-back can be explicitly computed. To wit, let yi
+q = (�rq, �θq, �φq, �τq) the normal coordinates
+of the event q ∈
+�
+C −(p, ˆg) associated with the observation of a given astrophysical source. The
+equation for the radial, past-directed, null geodesic connecting q to the observation event p reduces
+in the FLRW case to [19]
+(56)
+d�r = − d�τ
+a(�τ) ,
+�τ(p) = 0 = �r(p) ,
+that integrates to the expression providing the (matter-comoving) radial coordinate distance be-
+tween p and q
+(57)
+�rq =
+� �τq
+0
+d�τ
+a(�τ) .
+Thus, the metric (55), evaluated at �
+expp
+−1(q), can be written in terms of �τq as
+(58)
+�hq := �h(�rq, �θq, �φq) = a2(�τq) f 2 (�rq)
+�
+d�θ2
+q + sin2 �θqd�φ2
+q
+�
+,
+If we introduce the dimensionless FLRW cosmological redshift corresponding to the event q,
+(59)
+zq := z (�τq) =
+a0
+a(�τq) − 1 ,
+where a0 := a(�τ = 0), then we can rewrite �h(�rq, �θq, �φq) as
+(60)
+�hq =
+a2
+0
+(1 + zq)2 f 2 (�rq)
+�
+d�θ2
+q + sin2 �θqd�φ2
+q
+�
+.
+Note that the area element associated with the metric �hq,
+(61)
+dµ�hq =
+a2
+0
+(1 + zq)2 f 2 (�rq) dµS2
+characterizes the FLRW observer area distance (see (29)) of the event q ∈
+�
+C −(p, ˆg) according to
+(62)
+�D(�rq) =
+a0
+1 + zq
+f (�rq) .
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+13
+4. Comparing the celestial spheres C S(p) and �
+C S(p)
+As stressed in the previous Section, the celestial sphere C S(p) of the phenomenological observer
+(p, ˙γ(0)), and the celestial sphere �
+C S(p) of the FLRW ideal observer (p, �˙γ(0)) cannot be directly
+identified as they stand. The velocity fields ˙γ(0) and �˙γ(0) are distinct and to compensate for the
+induced aberration, the celestial spheres C S(p) and �
+C S(p) can be identified only up to Lorentz
+boosts. In the standard FLRW view, this is the familiar global boost taking care of the kinematical
+dipole component in the CMB spectrum due to our peculiar motion with respect to the standard
+of rest provided by the CMB. However, in a cosmographic setting and presence of a complex
+pattern of local inhomogeneities coupled with a non-FLRW spacetime geometry over scales ≲
+100h−1 Mpc, the peculiar motion of the phenomenological observer has a dynamical origin, driven
+by the gravitational interaction and not just by a kinematical velocity effect. Even if we factor out
+the effect of coherent bulk flows due to the non-linear local gravitational dynamics, and average
+the rate of expansion over spherical shells at increasing distances from (p, ˙γ(0)), the variance in
+the peculiar velocity of (p, ˙γ(0)) with respect to the average rate of expansion is significant [54].
+These remarks imply that the Lorentz boosts connecting C S(p) and �
+C S(p) acquire a dynamical
+meaning that plays a basic role in what follows. As a first step, we describe the Lorentz boost in
+the idealized pure kinematical situation where we need to compensate for a well-defined velocity
+field of the celestial sphere C S(p) with respect to the celestial sphere �
+C S(p) taken as providing
+a well-defined standard of rest. As a second step, we move to the more general setting required
+in the pre-homogeneity region where we sample scales ≲ 100h−1 Mpc. In this latter case, a pure
+kinematical Lorentz boost will not suffice, the large fluctuations in the sources distribution require
+a suitable localization of the Lorentz boosts to compare the data on C S(p) with those on �
+C S(p).
+4.1. The kinematical setting. To describe a kinematical Lorentz boost acting between �
+C S(p)
+and C S(p), we find it convenient to use in this section the well-known correspondence between
+the restricted Lorentz group and the six-dimensional projective special linear group PSL(2, C)
+describing the automorphisms of the Riemann sphere S2 ≃ C ∪ {∞}. More expressively, PSL(2, C)
+can be viewed as the group of the conformal transformations of the celestial spheres that correspond
+to the restricted Lorentz transformations connecting C S(p) to �
+C S(p). In oder to set notation, let us
+recall that the elements of PSL(2, C) can be identified with the set of the M¨obius transformations
+of the Riemann sphere S2 ≃ C ∪ {∞}, i.e. the fractional linear transformations of the form
+ζ : C ∪ {∞}
+−→
+C ∪ {∞}
+(63)
+w
+�−→
+ζ(w) := aw + b
+cw + d ,
+a, b, c, d ∈ C , ad − bc ̸= 0 ,
+where, to avoid a notational conflict with the redshift parameter z, we have labeled the complex
+coordinate in C ∪ {∞} with w rather than with the standard z. Let Y = �n(�θ, �φ) denote a point on
+the celestial sphere �
+C S(p), and let �w denote its stereographic projection10 on the Riemann sphere
+C ∪ {∞}, i.e.,
+PS2 : �
+C S(p) −→ C ∪ {∞}
+(64)
+Yα �−→ PS2(Yα) = �w := Y1 + i Y2
+1 − Y3
+= cos �φ sin �θ + i sin �φ sin �θ
+1 − cos �θ
+,
+with 0 < θ ≤ π, 0 ≤ φ < 2π. It is worthwhile to stress once more that the celestial spheres �
+C S(p)
+and C S(p) play the role of a mapping frame, a celestial globe where astrophysical positions are
+registered, and where the Lorentz boost �
+C S(p) −→ C S(p) must be interpreted actively as affecting
+only the recorded astrophysical data. In other words, the Lorentz boost affects the null directions
+10From the north pole θ = 0 ∈ �
+C S(p).
+
+14
+M. CARFORA AND F. FAMILIARI
+in �
+C S(p), mapping them in the corresponding directions in C S(p). To quote a few illustrative
+examples [46] of the PSL(2, C) transformations associated to the Lorentz group action between
+the celestial spheres �
+C S(p) and C S(p), let v denote the modulus of the relative 3-velocity of the
+FLRW ideal observer (p, �˙γ(0)) with respect to the phenomenological observer (p, ˙γ(0)), (where
+E4 is identified with the observer’s 4-velocity ˙γ(0)). If the map between �
+C S(p) and C S(p) is a
+pure Lorentz boost in a common direction, say E3, then the associated PSL(2, C) transformation
+is provided by
+PSL(2, C) × �
+C S(p)
+−→
+C S(p)
+(65)
+(ζ boost, �w)
+�−→
+ζ( �w) = w =
+�
+1 + v
+1 − v �w ,
+where
+�
+1 + v
+1 − v is the relativistic Doppler factor and w is the point in the Riemann sphere corre-
+sponding, under stereographic projection, to the direction n(θ, φ) ∈ C S(p). Similarly, if �
+C S(p) and
+C S(p) differ by a pure rotation through an angle α about the E3 direction, then the associated
+PSL(2, C) transformation is given by
+PSL(2, C) × �
+C S(p)
+−→
+C S(p)
+(66)
+(ζ rot, �w)
+�−→
+ζ( �w) = w = ei α �w .
+(67)
+By composing them, e. g. by considering a rotation through an angle α about the E3 direction,
+followed by a boost with rapidity β := log
+�
+1 + v
+1 − v along the E3 axis, we get
+PSL(2, C) × �
+C S(p)
+−→
+C S(p)
+(68)
+(ζ, �w)
+�−→
+ζ( �w) = w =
+�
+1 + v
+1 − v ei α �w ,
+describing the general fractional linear transformation mapping �
+C S(p) and C S(p). From the phys-
+ical point of view, this corresponds to the composition of the adjustment of the relative orienta-
+tion of the spatial bases {E(α)} with respect to { �E(α)}, α = 1, 2, 3, followed by a Lorentz boost
+adjusting for the relative velocity of (p, ˙γ(0)) with respect to (p, �˙γ(0)). Since the spatial direc-
+tions n(θ, φ) ∈ C S(p) and �n(�θ, �φ) ∈ �
+C S(p) characterize corresponding past-directed null vectors
+ℓ(θ, φ) ∈
+�
+TpM, {E(i)}
+�
+and �ℓ(�θ, �φ) ∈
+�
+�TpM, { �E(i)}
+�
+(see (10) and (48)), we can associate with
+the spatial directions {E(α)} and { �E(α)} the respective null directions
+ℓ(α)
+=
+E(α) − E(4) = E(α) − ˙γ(0) ,
+(69)
+�ℓ(α)
+=
+�E(α) − �E(4) = �E(α) − �˙γ(0) .
+4.2. The pre-homogeneity setting. From the above remarks, it follows that the Lorentz map-
+ping from �
+C S(p) to C S(p) is fully determined if we specify the three distinct null directions on the
+FLRW celestial sphere �
+C S(p) that are the images, under the PSL(2, C)-transformation, of three
+chosen distinct sources on C S(p). The selection of these three distinct sources of choice and of the
+corresponding null directions on C S(p) will depend on the scale L we are probing in our cosmo-
+logical observations. This is a particularly delicate matter when looking at the pre-homogeneity
+scales L ≲ 100 h−1 Mpc, where astrophysical sources are characterized by a complex distribution of
+peculiar velocities with respect to the assumed Hubble flow. To keep track of this scale dependence,
+let us consider the celestial spheres C Sr(p) and �
+C S�r(p) defined by (16) and (47), respectively. For
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+15
+L > 0, let �r(L) be the value of �r such that the FLRW sky section (53)
+(70)
+�Σ(p, ˆr(L)) := �
+expp
+�
+�
+C S�r(L)(p)
+�
+=
+�
+�
+expp
+�
+�r(L) �ℓ(�n(�θ, �φ))
+� ��� (�θ, �φ) ∈ �
+C S(p)
+�
+,
+probes the length scale L. Similarly, we let r(L) denote the value of r such that the physical sky
+section (71)
+(71)
+Σ(p, r(L)) := expp
+�
+C Sr(L)(p)
+�
+=
+�
+expp (r(L) ℓ(n(θ, φ)))
+�� (θ, φ) ∈ C S(p)
+�
+,
+probes the length scale L. Since the FLRW area distance (62),
+(72)
+�D(�r) =
+a0
+1 + z f (�r) ,
+is isotropic and may be directly expressed in terms of z, we may well use the redshift parameter
+z as the reference L. Given z, we denote by L(z) the corresponding length-scale of choice. As
+long as �D(�r) is an increasing function, we can identify L(z) with the area distance �D(�r), but in
+general, we leave the selection of the most appropriate L(z) to the nature of the cosmographical
+observations one wants to perform. Given ζ ∈ PSL(2, C) and a value of the redshift z, we have a
+corresponding relation between the ”radial” variables �r(L(z)) and r(L(z)) in (70) and (71). We can
+take advantage of this relation to simplify the notation for the celestial spheres and the associated
+sky sections according to
+(73)
+�
+C Sz(p) := �
+C S�r(L(z))(p) =⇒ �Σz := �Σ(p, ˆr(L(z))) := �
+expp
+�
+�
+C Sz(p)
+�
+,
+and
+(74)
+C Sz(p) := C Sr(L(z))(p) =⇒ Σz := Σ(p, r(L(z))) := expp [C Sz(p)] ,
+a notation that, if not otherwise stated, we adopt henceforth. Since in the pre-homogeneity region
+L(z) ≲ 100 h−1 Mpc, the large variance in peculiar velocities of the astrophysical sources implies a
+great variability in the selection of the three reference null directions that fix the PSL(2, C) action,
+we localize this action according to the following construction.
+• We assume that there is a finite collection of points {y(I)} ∈ �
+C Sz(p) and a corresponding
+collection of open disks { �B(y(I), δ)} of radius δ, centered at the points {y(I)}, and defined
+by
+(75)
+�B(y(I), δ) := {y′ ∈ �
+C Sz(p) | dS2(y′, y(I)) ≤ δ} ⊂ �
+C Sz(p)
+where dS2(y′, y(I)) denotes the distance in the round unit metric on S2. We also assume that
+any such �B(y(I), δ) contains the images of three reference astrophysical sources of choice, call
+them A(I, k), k = 1, 2, 3,, with celestial coordinates in �
+C Sz(p) given by y(I, k) =: �n(I, k)(�θ, �φ).
+• We adopt a similar partition on the celestial sphere C Sz(p), to the effect that associated
+with each disk �B(y(I), δ) there is, in C Sz(p), a corresponding metric disk
+(76)
+B(x(y(I)), δ) = {x′ ∈ C Sz(p) | dS2(x′, x(y(I))) ≤ δ} ⊂ C Sz(p) .
+We require that the images A(I, k) of the three reference astrophysical sources of choice,
+that in �B(y(I), δ) have celestial coordinates y(I, k), are represented in B(x(y(I)), δ) by three
+distinct points with celestial coordinates x(I, k) =: n(I, k)(θ, φ).
+• We further assume that the past null directions �ℓ(I, k) = �n(I, k)(�θ, �φ) − �˙γ(0), associated with
+the location of the reference sources A(I, k) in the portion of the celestial sphere �B(y(I), δ) ∩
+
+16
+M. CARFORA AND F. FAMILIARI
+�
+C Sz(p), are related to the corresponding null directions ℓ(I, k) = n(I, k)(θ, φ) − ˙γ(0), locating
+the sources A(I, k) in B(x(y(I)), δ) ∩ C Sz(p), by the PSL(2, C) map
+ζ(I) : �B(y(I), δ) ∩ �
+C Sz(p)
+−→
+B(x(y(I)), δ) ∩ C Sz(p)
+(77)
+�w
+�−→
+ζI( �w) = w =
+�
+1 + v
+1 − v ei α(A(I, k)) �w ,
+where
+�
+1 + v
+1 − v ei α(A(I, k)) is the composition of the Lorentz boost (v being the relative 3-
+velocity of ˙γ(0) with respect to �˙γ(0)) and of the spatial rotation that, at the given scale
+L(z), allow us to align the portion of the celestial sphere C Sz(p) described by B(x(y(I)), δ)
+with the portion of the FLRW celestial sphere �
+C Sz(p) described by �B(y(I), δ).
+• Finally, we require that the finite collections of celestial coordinate bins { �B(y(I), δ)} and
+�
+B(x(y(I)), δ)
+�
+cover the respective celestial spheres �
+C Sz(p) and C Sz(p).
+It is worthwhile to stress that the collections of bins { �B(y(I), δ)} and
+�
+B(x(y(I)), δ)
+�
+can be chosen
+in many distinct ways, according to the cosmographic observations one wishes to carry out (we use
+disks for mathematical convenience). Whatever choice of the above type we make, we can extend the
+localized PSL(2, C) maps (77) by using a smooth partition of unity
+�
+χ(I)
+�
+subordinated to the finite
+covering { �B(y(I), δ)} of �
+C Sz(p), i.e. a collection of smooth functions χ(I) : �B(y(I), δ) −→ [0, 1]
+whose support is such that supp χ(I) ⊆ �B(y(I), δ) and such that �
+y∈ �
+C Sz(p) χ(I)(y) = 1. We define
+the localized PSL(2, C) map connecting, at scale L(z), the celestial spheres �
+C Sz(p) and C Sz(p),
+decorated with the respective coordinate bins { �B(y(I)} and {B(x(y(I)), δ)}, according to
+ζ(z) : �
+C Sz(p)
+−→
+C Sz(p)
+(78)
+�w
+�−→
+ζ(z)( �w) :=
+�
+y∈ �
+C Sz(p)
+χ(I)(y) ζ(I)(w) ,
+where ζ(I)(w) is provided by (77). Note that, when necessary, this localized PSL(2, C) map can
+be further generalized by completing it in the Sobolev space of maps which together with their
+derivatives are square-summable over �
+C Sz(p). This completion requires some care which we do not
+enter here (see [12] for details), and it is needed when discussing the distance between the FLRW
+and the cosmographic lightcones.
+It is worthwhile to stress that in the pre-homogeneity region L(z) ≲ 100 h−1 Mpc, the large
+variance in peculiar velocities of the astrophysical sources implies a great variability in the selection
+of the three reference null directions that fix the local PSL(2, C) action characterizing the map ζ(z).
+This implies that ζ(z) may vary considerably with L(z). Recall that the role of the celestial spheres
+C Sz(p) and �
+C Sz(p) is simply that of representing past null directions at the observational event
+p ∈ M, directions that respectively point to the astrophysical sources on the sky section Σz, as
+seen by (p, ˙γ(0)), and on �Σz, as seen according to (p, �˙γ(0)). These data are transferred from these
+sky sections to the respective celestial spheres through null geodesics, thus we can associate with
+the localized PSL(2, C) action the map between the sky sections �Σz and Σz given by
+ψ(z) : �Σz
+−→
+Σz
+(79)
+q
+�−→
+ψ(z)(q) := expp ◦ ζ(z) ◦ �
+exp −1
+p (q) ,
+for any point q ∈ �Σz.
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+17
+5. The comparison between the screen planes T�n�
+C Sz(p) and TnC Sz(p)
+The localized PSL(2, C) map ζ(z) induces a corresponding map between the screen plane T�n �
+C S(p)z
+associated with the direction of sight �n(�θ, �φ) in the FLRW celestial sphere �
+C Sz(p) (see (49)), and
+the screen plane TnC Sz(p) associated with the direction of sight n(θ, φ) = ζ(z)
+�
+�n(�θ, �φ)
+�
+in the
+celestial sphere C Sz(p) (see (19)). The geometry of this correspondence is quite sophisticated since
+it is strictly related to harmonic map theory and it will be described here in some detail. To begin
+with, we denote by T �
+C Sz and by TC Sz the screen bundles associated with the screen planes on
+�
+C Sz(p) and C Sz(p), respectively. These are just two copies of the usual tangent bundle TS2 of the
+2-sphere. If there is no danger of confusion, we use both notations in what follows. Under such
+notational assumptions, we can associate with the map (78),
+(80)
+ζ(z) : �
+C Sz(p) −→ C Sz(p) ,
+the pull–back bundle ζ−1
+(z) TC Sz whose sections v ≡ ζ−1
+(z)V := V ◦ζ(z), V ∈ C∞(C Sz(p), TC Sz), are
+the vector fields over C Sz(p) covering the map ζ(z). In physical terms, the vectors v are the tangent
+vector on the celestial sphere C Sz(p) that describe the (active) effect of the combination of rotation
+and Lorentz boost induced by ζ(z) on the null direction �ℓ(�n). More expressively, let us remark that
+for a given direction of sight ζ(z)(�n) = n(θ, φ) ∈ C Sz(p), the vectors V ∈ TnC Sz(p) can be used
+to describe the geometrical characteristics of the astrophysical images on the screen TnC Sz(p), for
+instance, the apparent diameters of the source. Thus, the vectors v ≡ ζ−1
+(z)V := V ◦ ζ(z), sections of
+the pull–back bundle ζ−1
+(z) TC Sz, can be interpreted as transferring the ”images” of the screens in
+TC Sz back to �
+C Sz(p) so as to be able to compare them with the reference screen-shots in T �
+C Sz.
+In terms of the local coordinates ya :=
+�
+�θ, �φ
+�
+, a = 1, 2, on �
+C Sz(p) (see (52))11, we can write the
+section v ≡ ζ−1
+(z)V := V ◦ ζ(z) as12
+(81)
+C Sz(p) ∋ ya �−→ v(ya) = vb(y)
+∂
+∂ζb
+(z)(y) ∈ ζ−1
+(z)TC Sz
+���
+y ,
+where ζb
+(z)(y), b = 1, 2, are the coordinates of the point (direction of sight) in ζ(z)(y) ∈ C Sz(p)
+given, in terms of the ya by (64). In particular, if T ∗ �
+C Sz denotes the cotangent bundle to �
+C Sz(p),
+we can locally introduce the differential
+(82)
+dζ(z) =
+∂ζb
+(z)
+∂ya dya ⊗
+∂
+∂ζb
+(z)
+,
+and interpret it as a section of the product bundle T ∗�[C S]z ⊗ ζ−1
+(z) TC Sz. To provide a comparison
+between the geometrical information gathered from the astrophysical data, let us recall that on the
+screens T �
+C Sz and TC Sz we have the inner products respectively defined by the pull-back metrics
+(55) and (27), i.e.
+(83)
+�h(�r(L(z)), �θ, �φ) :=
+�
+�
+exp∗
+p �g|�Σz
+�
+ab dyadyb���
+�r(L(z)) ,
+a, b = 1, 2,
+y1 := �θ, y2 := �φ .
+and
+(84)
+h(r(L(z)), θ, φ) :=
+�
+exp∗
+p g|Σz
+�
+ab dxadxb���
+r(L(z)) ,
+a, b = 1, 2,
+x1 := θ, x2 := φ .
+11In what follows the (�θ, �φ), corresponding to (y2, y2) in the normal coordinates string {yα}, are relabelled as
+{ya}, with a = 1, 2; a similar relabeling is also adopted for the normal coordinates (θ, φ) on C Sz(p).
+12In what follows we freely refer to the excellent [22], [32], and [36] for a detailed analysis of the geometry of the
+computations involved in harmonic map theory.
+
+18
+M. CARFORA AND F. FAMILIARI
+The Riemannian metric in the pull-back screen
+�
+ζ−1
+(z) TC Sz
+�
+y over y ∈ �
+C Sz(p) is provided by
+h(ζ(z)(y)), hence the tensor bundle T ∗ �
+C Sz ⊗ ζ−1
+(z) TC Sz over the celestial sphere �
+C Sz(p) is endowed
+with the pointwise inner product
+(85)
+⟨·, ·⟩T ∗�[C S]z⊗ζ−1
+(z) TC Sz := �h−1(y) ⊗ h(ζ(z)(y))(·, ·) ,
+where �h−1(y) := �hab(y) ∂a ⊗ ∂b is the metric tensor in T ∗
+y �
+C Sz. The corresponding Levi-Civita
+connection will be denoted by ∇⟨,⟩. Explicitly, if W = W b
+a dya ⊗
+∂
+∂ζb
+(z) is a section of T ∗ �
+C Sz ⊗
+ζ−1
+(z) TC Sz, the covariant derivative of W in the direction
+∂
+∂yb is provided by
+∇⟨,⟩
+b W = ∇⟨,⟩
+b
+�
+W c
+a dya ⊗
+∂
+∂ζc
+(z)
+�
+(86)
+=
+∂
+∂yb W c
+a dya ⊗
+∂
+∂ζc
+(z)
++ W c
+a
+�
+�∇b dya�
+⊗
+∂
+∂ζc
+(z)
++ W c
+a dya ⊗ ∇∗
+b
+�
+∂
+∂ζc
+(z)
+�
+,
+where �∇ denotes the Levi–Civita connection on ( �
+C Sz(p), �h), and ∇∗ is the pull back on ζ−1
+(z) TC Sz of
+the Levi–Civita connection of (C Sz, h). If �Γa
+bc(�h) and Γa
+bc(h) respectively denote the Christoffel sym-
+bols of ( �
+C Sz(p), �h) and (C Sz(p), h), then �∇b dya = − �Γa
+bc(�h) dyc and ∇∗
+b
+�
+∂
+∂ζc
+(z)
+�
+=
+∂ζi
+(z)
+∂yb Γk
+ci(h)
+∂
+∂ζk
+(z) ,
+and one computes
+(87)
+∇⟨,⟩
+b W =
+�
+∂
+∂yb W i
+a − W i
+c�Γc
+ba(�h) + W k
+a
+∂ζj
+(z)
+∂yb Γi
+kj(h)
+�
+dya ⊗
+∂
+∂ζi
+(z)
+.
+These remarks on the geometry of the map (80) allow us to compare the data on the screens TC Sz
+and T �
+C Sz. For this purpose, the relevant quantity is the norm, evaluated with respect to the inner
+product (85), of the differential (82) of the PSL(2, C) map ζ(z). Direct computation provides
+e(�h, ζ(z); h)
+:=
+⟨dζ(z), dζ(z)⟩T ∗�[C S]z⊗ζ−1
+(z) TC Sz
+(88)
+=
+�hab(y)
+∂ζi
+(z)(y)
+∂ya
+∂ζj
+(z)(y)
+∂yb
+hij(ζ(z)(y)) = tr�h(y) (ζ∗
+(z) h) ,
+where tr�h(y) (ζ∗
+(z) h) denotes the trace, with respect to the metric �h of the pull-back metric ζ∗
+(z) h.
+In other words, at any point y, e(�h, ζ(z); h)(y) is the sum of the eigenvalues of the metric ζ∗
+(z) h,
+thus providing the sum of the squares of the length stretching generated by the (pull-back of) the
+physical metric ζ∗
+(z) h along the orthogonal directions (�θ, �φ). To such stretching, we can associate
+the tension field of the map ζ(z), defined by
+(89)
+τ i(ζ(z)) := ∆(�h) ζi
+(z) + �hkj Γi
+ab(h)
+∂ζa
+(z)
+∂yk
+∂ζb
+(z)
+∂yj .
+To provide some intuition on these geometrical quantities, we can adapt to our case a nice heuristic
+remark by J. Eells and L. Lemaire described in their classical paper on harmonic map theory [22].
+Let us imagine the FLRW celestial sphere ( �
+C Sz(p), �h) as a rubber balloon, decorated with dots
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+19
+representing the astrophysical sources recorded from the sky section �Σz.
+This balloon has the
+geometry described by the round metric �h(z, �θ, �φ) defined by (83), explicitly (see (60))
+(90)
+�h(�r(z), �θ, �φ) =
+a2
+0
+(1 + zL)2 f 2 (�r(z))
+�
+d�θ2 + sin2 �θd�φ2�
+,
+where zL is the redshift associated with the length scale L. Conversely, let us imagine the physical
+celestial sphere (C Sz(p), h) as a rigid surface with the geometry induced by the metric h(r(z), θ, φ)
+defined by (84), i.e., (see (30)),
+h (r(z), θ, φ)
+(91)
+= D2(r(z), θ, φ)
+�
+dθ2 + sin2 θdφ2 + Lab(r(z), θ, φ) dxadxb�
+,
+x1 := θ, x2 := φ ,
+providing the geometric landscape of the astrophysical sources reaching us along null geodesics
+from the physical sky section Σz. We can think of the PSL(2, C) map ζ(z) as stretching the elastic
+surface ( �
+C Sz(p), �h) on the rigid surface (C Sz(p), h). The purpose of this stretching is to overlap the
+images of the astrophysical sources recorded on ( �
+C Sz(p), �h) with the images of the corresponding
+sources as registered on (C Sz(p), h). In general, this overlap is not successful without stretching
+the surface, and to any point y ∈ ( �
+C Sz(p), �h) we can associate a corresponding vector measuring
+the stretch necessary for connecting the images of the same source on the two celestial spheres13
+( �
+C Sz(p), �h) and (C Sz(p), h). To leading order, the required stretching is provided by the tension
+vector τ i(ζ(z), y) at y. Both the Hilbert-Schmidt norm (88) and the tension vector field (89) of
+the map ζ(z) are basic quantities in harmonic map theory, and to understand the strategy we will
+follow in comparing, at a given length scale L, the FLRW past light cone �C(p, �g) with the physical
+observational past light cone C(p, g) we need to look into the harmonic map theory associated with
+ζ(z). Let us start by associating with ⟨dζ(z), dζ(z)⟩T ∗�[C S]z⊗ζ−1
+(z) TC Sz the density
+(92)
+e(�h, ζ(z), h) dµ�h := ⟨dζ(z), dζ(z)⟩T ∗�[C S]z⊗ζ−1
+(z) TC Sz dµ�h = tr�h(y) (ζ∗
+(z) h) dµ�h ,
+where dµ�h is the volume element defined by the metric �h on the FLRW celestial sphere �
+C Sz(p). An
+important property of the density e(�h, ζ(z); h) dµ�h is that it is invariant under the two-dimensional
+conformal transformations
+(93)
+( �
+C Sz(p), �hab) �−→ ( �
+C Sz(p), e−f �hab) ,
+where f is a smooth function on �
+C Sz(p). In this connection, it is worthwhile to recall that conformal
+invariance is strictly related to the action of the Lorentz group on the celestial spheres (and it is
+ultimately the rationale for the relation between Lorentz transformations and the fractional linear
+transformations of PSL(2, C)).
+The expression 1
+2 e(�h, ζ(z); h) dµ�h characterizes the harmonic map energy functional associated to
+the map ζ(z), viz.
+(94)
+E[�h, ζ(z), h] := 1
+2
+�
+�
+C Sz
+e(�h, ζ(z), h) dµ�h .
+It is worthwhile to put forward a more explicit characterization of the nature of the harmonic map
+functional E[�h, ζ(z); h] by making explicit, together with the celestial spheres �
+C Sz(p) and C Sz(p),
+13This is not to be confused with the phenomenon of strong gravitational lensing that occurs in a given celestial
+sphere. It is simply a mismatch due to the comparison between the description of the same astrophysical source on
+two distinct celestial spheres.
+
+20
+M. CARFORA AND F. FAMILIARI
+the role of the corresponding sky sections �Σz and Σz. To this end, let us consider the map (79)
+acting between the sky sections �Σz and Σz,
+ψ(z) : (�Σz, �g|ˆΣz)
+−→
+(Σz, g|Σz)
+(95)
+y
+�−→
+ψ(z)(q) := expp ◦ ζ(z) ◦ �
+exp −1
+p (y) .
+The corresponding harmonic map functional is provided by
+(96)
+E
+�
+�g(z), ψ(z), g(z)
+�
+:= 1
+2
+�
+�Σz
+(�g(z))ab ∂ψi
+(z)(y)
+∂ya
+∂ψk
+(z)(y)
+∂yb
+(g(z))ik dµ�g(z)
+where, for notational ease, we have set �g(z) := �g ˆΣz and g(z) := g Σz. We can equivalently write
+E
+�
+�g(z), ψ(z), g(z)
+�
+in terms of pull-backs of the relevant maps, and get the following chain of relations
+E
+�
+�g(z), ψ(z), g(z)
+�
+=
+1
+2
+�
+�Σz
+(�g(z))ab �
+ψ∗
+(z)g(z)
+�
+ab dµ�g(z)
+(97)
+=
+1
+2
+�
+�
+expp( �
+C Sz)
+(�g(z))ab �
+ψ∗
+(z)g(z)
+�
+ab dµ�g(z)
+=
+1
+2
+�
+�
+C Sz
+�
+expp
+∗ �
+(�g(z))ab �
+ψ∗
+(z)g(z)
+�
+ab
+�
+�
+expp
+∗(dµ�g(z))
+=
+1
+2
+�
+�
+C Sz
+�hab �
+�
+expp
+∗ �
+ψ∗
+(z)g(z)
+��
+ab dµ�h
+=
+1
+2
+�
+�
+C Sz
+�hab �
+�
+expp
+∗ �
+expp ◦ ζ(z) ◦ �
+exp −1
+p
+�∗
+g(z)
+�
+ab dµ�h
+=
+1
+2
+�
+�
+C Sz
+�hab �
+ζ∗
+(z)h
+�
+ab dµ�h = E[�h, ζ(z), h] ,
+from which it follows that the harmonic map energy functional associated with the localized
+PSL(2, C) map ζ(z) and with the map ψ(z), defined by (95), can be identified. This is not sur-
+prising since ψ(z) := expp ◦ ζ(z) ◦ �
+exp −1
+p
+can be seen as the representation of ζ(z) on the sky
+sections �Σz := �
+expp
+�
+�
+C Sz(p)
+�
+and Σz := expp (C Sz(p)). From the conformal nature of the map
+ζ(z) : �
+C Sz(p) −→ C Sz(p), it follows that ψ(z) acts as a conformal diffeomorphism between ˆΣz
+and Σz as long as the exponential maps are diffeomorphisms from �
+C Sz(p) and C Sz(p) onto their
+respective images �Σz and Σz. Later we shall see how this result can be extended, under suitable
+hypotheses, to the less regular case of Lipschitzian exponential map. Here, we restrict our attention
+to the stated regularity assumptions on the exponential maps �
+expp and expp. They imply that the
+sky sections ˆΣz and Σz have the topology of a 2-sphere. Moreover, we can take advantage of the fact
+that (�Σz, �g(z)) is a (rescaled) round sphere, thus we can apply the Poincar´e–Koebe uniformization
+theorem, to the effect that there is a positive scalar function Φ�Σ Σ ∈ C∞(�Σz, R>0) such that
+(98)
+�
+ψ∗
+(z)g(z)
+�
+ab =
+∂ψi
+(z)(y)
+∂ya
+∂ψk
+(z)(y)
+∂yb
+(g(z))ik = Φ2
+�Σ Σ (�g(z))ab .
+The required conformal factor Φ�Σ Σ ∈ C∞(�Σz, R>0) is the solution, (unique up to the PSL(2, C)
+action on (�Σz, �g(z))), of the elliptic partial differential equation on (�Σz, ˆg(z)) defined by [2]
+(99)
+− ∆�g(z) ln(Φ2
+�ΣΣ) + R(�g(z)) = R(ψ∗
+(z)g(z)) Φ2
+�ΣΣ ,
+where ∆�g(z) := �gab
+(z)∇a∇b is the Laplace-Beltrami operator on (�Σz, ˆg(z)), and where we respectively
+denoted by R(�g(z)) and R(ψ∗
+(z)g(z)) the scalar curvature of the metrics �g(z) and ψ∗
+(z)g(z). Notice that
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+21
+the scalar curvature R(ˆg(z)) is associated with the metric (60) evaluated for �r = �r(L) and hence is
+given by the constant R(ˆg(z)) =
+�
+a2
+0
+(1 + z)2 f 2 (�r)
+�−1
+. Similarly, R(g(z)) is associated with the metric
+(30) evaluated for r = r(z), and as such it depends on the area distance D2(r(z), θ, φ) and the
+lensing distortion Lab.
+By tracing (98) with respect to �gab
+(z), we get tr�g(z)(y)
+�
+ψ∗
+(z)g(z)
+�
+= 2Φ2
+�Σ Σ, and we can wite
+(100)
+Φ2
+�ΣΣ = 1
+2 tr�g(z)(y)
+�
+ψ∗
+(z)g(z)
+�
+= 1
+2 �gab
+(z)
+∂ψi
+(z)(y)
+∂ya
+∂ψk
+(z)(y)
+∂yb
+(g(z))ik .
+From (98) we also get det
+�
+ψ∗
+(z)g(z)
+�
+= Φ4
+�ΣΣ det(�g(z)), hence we can equivalently express the
+conformal factor Φ2
+�ΣΣ as the Radon-Nikodym derivative of the Riemannian measure dµψ∗g(z) :=
+ψ∗
+(z)dµ of the pulled back metric ψ∗
+(z)g(z) on the sky section �Σz, with respect to the Riemannian
+measure dµ�g(z) of the round metric �g(z) on �Σz, i.e.,
+(101)
+Φ2
+�ΣΣ =
+dµψ∗
+(z)g(z)
+dµ�g(z)
+=
+ψ∗
+(z)dµg(z)
+dµ�g(z)
+.
+Directly from this latter relation and from E
+�
+�g(z), ψ(z), g(z)
+�
+= E
+�
+�h, ζ(z), h
+�
+(see (97)), we get
+(102)
+E
+�
+�h, ζ(z), h
+�
+=
+�
+�Σz
+Φ2
+�ΣΣ dµˆh ,
+which expresses the harmonic map functional E
+�
+�h, ζ(z), h
+�
+in terms of the conformal factor Φ2
+�ΣΣ.
+As the PSL(2, C)-localized map ζ(z) varies with the scale L(z), relation (102) shows that E
+�
+�h, ζ(z), h
+�
+describes the ζ(z)-dependent total ”energy” associated with the conformal stretching of ( �
+C Sz(p), �h)
+over (C Sz(p), h).
+5.1. A local expression for Φ2
+�ΣΣ. It is worthwhile to provide a local expression for Φ2
+�ΣΣ show-
+ing the explicit dependence from the celestial coordinates (θ, φ), the area distances �D(�r(L)),
+D(r(L), θ, φ), and the distortion tensor L (see (30)). We proceed as follows. Let us consider one
+of the coordinate bin �B(y(I), δ) (see (75)) in the celestial sphere �
+C Sz(p). For y = (r(z), �θ, �φ) ∈
+�B(y(I), δ) let q := �
+expp(y) the point in the sky section �Σz reached, at the scale L(z), along the
+past-directed null geodesics associated with the observational direction y = (�θ, �φ). From the ex-
+pression (101) of the conformal factor Φ2
+�ΣΣ in terms of the measure ψ∗
+(z)dµg(z) we get, by massaging
+pull-backs,
+Φ2
+�ΣΣ dµ�g(z)(q)
+=
+ψ∗
+(z)dµg(z)(q)
+(103)
+=
+�
+expp ◦ ζ(z) ◦ �
+exp −1
+p
+�∗
+dµg(z)
+=
+(�
+exp −1
+p )∗(ζ∗
+(z)dµh)
+⇒
+�
+exp∗
+p
+�
+Φ2
+�ΣΣ dµ�g(z)(q)
+�
+= ζ∗
+(z)dµh(y)
+Φ2
+�ΣΣ(y) dµ�h(y)
+=
+ζ∗
+(z)dµh(y) .
+
+22
+M. CARFORA AND F. FAMILIARI
+Hence, on ( �
+C S(p), �h), we need to compute the Radon-Nicodym derivative
+(104)
+Φ2
+�ΣΣ(y) =
+ζ∗
+(z)dµh
+dµ�h
+(y) .
+If we take into account the characterization
+�
+det(h(r(z), θ, φ)) = D2(r(z), θ, φ)
+�
+det(�h(S2)) of
+the area distance D2(r(z), θ, φ) (see (29)), we compute
+(105)
+ζ∗
+(z)dµh(y) =
+��Jacy(ζ(z))
+�� D2(y) dµS2 ,
+where |Jacy(ζ(z))| is the Jacobian determinant associated with the localized PSL(2, C) map ζ(z),
+and where D2(y) is a shorthand notation for the area distance D2(ζ(z)(�r(z), �θ, �φ)) pulled back at y ∈
+( �
+C Sz(p), �h) by the localized ζ(z). Similarly, from (61) we compute dµ�h(y) =
+a2
+0
+(1 + zL)2 f 2 (�r(L)) dµS2 .
+Thus, we can write
+(106)
+Φ2
+�ΣΣ(�r(z), �θ, �φ) =
+���Jac
+�
+ζ(z)(�r(z), �θ, �φ)
+����
+D2(ζ(z)
+�
+�r(z), �θ, �φ)
+�
+(1 + z)2
+a2
+0 f 2 (�r(z))
+.
+In terms of the FLRW area distance
+(107)
+�D(�r(z)) =
+a0
+1 + z f (�r) ,
+we can equivalently write (106) in the simpler form (where, to have handy the formula for later
+use, we have taken the square root)
+(108)
+Φ�ΣΣ(�r(z), �θ, �φ) =
+���Jac
+�
+ζ(z)(�r(z), �θ, �φ)
+����
+1
+2 D
+�
+ζ(z)(�r(z), �θ, �φ)
+�
+�D(�r(z))
+.
+This clearly shows that the conformal factor Φ�ΣΣ is an explicit and, at least in principle, measurable
+quantity associated with the local Lorentz mapping (described by the localized PSL(2, C) map
+ζ(z)) needed for adjusting the three reference null directions in the chosen celestial coordinates
+bin �B(y(I), δ) in the celestial sphere �
+C Sz(p).
+This adjustment allows to transfer to �B(y(I), δ)
+the actual area distance, namely, compute D(ζ(z)(�r(z), �θ, �φ)), and compare its distribution on the
+FLRW celestial sphere �
+C Sz(p) with respect to the isotropic FLRW area distance �D(�r(z)). The
+anisotropies in the angular distribution with respect to �D(�r(z)) give rise to fluctuations in Φ�ΣΣ.
+It may appear somewhat surprising that, after all, the conformal factor does not explicitly depend
+also from the distortion tensor Lab defined by (30). This dependence is implicit in the definition
+of the area distance (29) and of the coordinate parametrization (30) characterizing Lab. These
+definitions give rise to the relation (34) that, as can be easily checked, remove the explicit Lab
+dependence from Φ�ΣΣ. As we shall see, this fact will turn to our advantage when extending our
+analysis to the more general case of fractal-like sky sections.
+6. The sky section comparison functional at scale L
+The harmonic energy E
+�
+�h, ζ(z), h
+�
+, or equivalently E
+�
+�g(z), ψ(z), g(z)
+�
+, associated with the maps
+ζ(z) and ψ(z), cannot be used directly as comparison functional between the sky sections (�Σz, �g(z))
+and (Σz, g(z)). This follows directly as a consequence of the conformal invariance (93) which implies
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+23
+E
+�
+�g(z), ψ(z), g(z)
+�
+= 1
+2
+�
+�Σz
+(�g(z))ab ∂ψi
+(z)(y)
+∂ya
+∂ψk
+(z)(y)
+∂yb
+(g(z))ik dµ�g(z)
+(109)
+= 1
+2
+�
+�Σz
+�
+a2
+0 f 2 �
+�r(z)
+�
+(1 + zL)2
+�−1
+(��h(S2))ab ∂ψi
+(z)(y)
+∂ya
+∂ψk
+(z)(y)
+∂yb
+(g(z))ik
+�
+a2
+0 f 2 �
+�r(z)
+�
+(1 + zL)2
+�
+dµS2
+= 1
+2
+�
+�Σz
+(��h(S2))ab ∂ψi
+(z)(y)
+∂ya
+∂ψk
+(z)(y)
+∂yb
+(g(z))ik dµS2 ,
+where, as usual, ��h(S2)) is the round metric on the unit 2-sphere S2. From the above relation it
+follows that E
+�
+�g(z), ψ(z), g(z)
+�
+, (and similarly for E
+�
+�h, ζ(z), h
+�
+), does not depend from the area
+distance
+a2
+0
+(1 + z)2 f 2 (�r(z)) on the FLRW past lightcone �C−(p). Thus, E
+�
+�g(z), ψ(z), g(z)
+�
+cannot be a
+good candidate for the role of the functional that compares the sky sections (�Σz, �g(z)) and (Σz, g(z)).
+For this role, we introduced in [12] a functional whose structure was suggested by the rich reper-
+toire of functionals used in the problem of comparing shapes of surfaces in relation to computer
+graphic and visualization problems (see e.g. [35] and [28], to quote two relevant papers in a vast
+literature). In particular, we were inspired by an energy functional introduced, under the name of
+elastic energy, in a remarkable paper by J. Hass and P. Koehl [29], who use it as a powerful means
+of comparing the shapes of genus-zero surfaces in problems relevant to surface visualization.
+In the more complex framework addressed in cosmography, we found it useful to define the sky
+section comparison functional at scale L(z) according to
+(110)
+E�ΣΣ[ψ(z)] :=
+�
+�Σz
+(Φ�ΣΣ − 1)2 dµˆg(z) ,
+that can be, more expressively, rewritten as (see (108))
+(111)
+E�ΣΣ[ψ(z)] :=
+�
+�Σz
+
+
+��Jac
+�
+ζ(z)(�r(z))
+���
+1
+2 D
+�
+ζ(z)(�r(z), �θ, �φ)
+�
+− �D(�r(z))
+�D(�r(z))
+
+
+2
+dµˆg(z) .
+Thus, from the physical point of view, E�ΣΣ[ψ(z)] describes the mean square fluctuations of the
+physical area distance D
+�
+ζ(z)(�r(z), �θ, �φ)
+�
+(biased by the localized PSL(2, C) mapping ζ(z)) with
+respect to the reference FLRW isotropic area distance �D(�r(z)).
+Notice that, whereas the harmonic map energy E
+�
+�g(z), ψ(z), g(z)
+�
+is a conformal invariant quantity,
+the functional E�ΣΣ[ψ(z)] is not conformally invariant. Under a conformal transformation ˆh −→
+e2f ˆh we get
+(112)
+�
+�Σz
+�
+e − fΦ�ΣΣ − 1
+�2
+e2f dµˆh .
+Since we can also write
+(113)
+Φ�ΣΣ =
+�ψ∗
+(z)dµg(z)
+dµ�g(z)
+� 1
+2
+,
+(see (101)), it is also clear from its definition that corresponding to large linear ”stretches” in con-
+formally mapping ψ∗
+(z)g(z) on �g(z), E�ΣΣ[ψ(z)] tends to the harmonic map energy.
+
+24
+M. CARFORA AND F. FAMILIARI
+In our particular framework, the functional E�ΣΣ[ψ(z)] has many important properties that make
+it a natural candidate for comparing, at the given length scale L, the sky sections (�Σz, �g(z)) and
+(Σz, g(z)) and, as the length-scale L varies, the physical lightcone region C−
+L (p, g) with the FLRW
+reference region C−
+L (p, ˆg). These properties are discussed in detail in [12] (see Lemma 8 and Theorem
+9), here we recollect them, without presenting their proof, in the following14
+Theorem 1. The functional E�ΣΣ[ψ(z)] is symmetric
+(114)
+E�ΣΣ[ψ(z)] = EΣ�Σ[ψ−1
+(z)] ,
+where
+(115)
+EΣ�Σ[ψ−1
+(z)] :=
+�
+Σz
+(ΦΣ�Σ − 1)2 dµg(z) ,
+is the comparison functional associated with the inverse map ψ−1
+(z) : Σz −→ �Σz, and ΦΣ�Σ is the
+corresponding conformal factor.
+Let (M, �g) be another member of the FLRW family of spacetimes, distinct from (M, ˆg), that we may
+wish to use as a control in a best-fitting procedure for the physical spacetime (M, g). Let (�Σz, �g(z))
+denote the sky section on the past lightcone �C−
+L0(p, ˜g), with vertex at p, and let �ψ(z) : Σz �−→ �Σz,
+and ΦΣ�Σ respectively denote the corresponding diffeomorphism and conformal factor. Then to the
+composition of maps
+(116)
+�Σz −→
+ψ(z)
+Σz −→
+�ψ(z)
+�Σz
+we can associate the triangular inequality
+(117)
+E�ΣΣ[ψ(z)] + EΣ�Σ[ �ψ(z)] ≥ E�Σ�Σ[( �ψ(z) ◦ ψ(z))] ,
+where
+(118)
+E�Σ�Σ[( �ψ(z) ◦ ψ(z))] :=
+�
+�Σz
+(Φ�Σ�Σ − 1)2 dµ�g(z) .
+Moreover,
+(119)
+E�ΣΣ[ψ(z)] = 0
+iff the sky sections (�Σ, ˆg(z)) and (Σ, g(z)) are isometric. Finally, if we denote by W1,2
+ζ(z)( �
+C Sz(p), C Sz(p))
+the space of localized PSL(2, C)- maps ζ(z) which are of Sobolev class W1,2, ( i.e. square summable
+together with their first derivatives), then
+(120)
+d(z)
+�
+�Σz, Σz
+�
+:=
+inf
+ζ(z)∈W1,2
+ζ(z)( �
+C Sz(p), C Sz(p))
+E�ΣΣ[ψ(z)]
+defines a scale-dependent distance between the sky sections (�Σz, ˆg(z)) and (Σz, g(z)) on the lightcone
+regions C−
+L (p, ˆg) and C−
+L (p, g).
+We need to conclude our long lightcone journey addressing the real nature of the physical sky
+section Σz. This forces us to leave the comfort zone of the assumed smoothness of the past physical
+lightcone C−(p, �g).
+14In [12], the general notation is somehow at variance from the one adopted here, since we address the analysis of
+E�ΣΣ directly on the surfaces �Σ and Σ. In particular, we refer to �Σ and Σ as celestial spheres rather than sky sections.
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+25
+7. The Lipschitz geometry of the cosmological sky sections Σz
+The celestial sphere description of the sky sections Σz discussed above is inherently vulnerable
+to the vagaries of the local distribution of astrophysical sources, and the associated strong gravita-
+tional lensing phenomena15 imply that the actual past light cone C −(p, g) is not smooth as we have
+assumed16. In particular, C −(p, g) may fail to be the boundary ∂ I−(p, g) of the chronological past
+I−(p, g) of p, (the set of all events q ∈ M that can be connected to p by a past-directed timelike
+curve), because past-directed null geodesics generators of C −(p, g), λ : [0, δ) −→ (M, g), with
+λ(0) = p, may leave ∂I−(p, g) and, under the action of the local spacetime curvature, plunge into
+the interior I−(p, g). A spacetime description of this behaviour in connection with the phenomenol-
+ogy of gravitational lensing is discussed in detail in [45], with a rich repertoire of examples of the
+possible singular structure that C −(p, g) may induce on the cosmological sky sections Σ(p, r). As a
+matter of fact, the sections Σz may evolve into fractal-like surfaces, and to describe them from the
+point of view of geometric analysis, we need to introduce a framework tailored to the low-regularity
+landscape generated by the local inhomogeneities.
+7.1. The Lipschitz landscape. Given a past-directed null geodesic IW ∋ r �−→ expp(rk(n(θ, φ))),
+issued from p ∈ M in the direction n(θ, φ) ∈ C Sz, we follow [37] and define its terminal point as
+the last–point
+(121)
+q(r∗, n(θ, φ)) := expp(rk(n(θ, φ)))
+that lies on the boundary ∂I−(p, g) of the chronological past of p.
+Any such terminal point
+q(r∗, n(θ, φ)) is said to be: i) a conjugate terminal point if the exponential map expp is singu-
+lar at (r∗, n(θ, φ)); ii) a cut locus terminal point if the exponential map expp is non–singular at
+(r∗, n(θ, φ)) and there exists another null geodesic, issued from p, passing through q(r∗, n(θ, φ)),
+(see also [1], [45]). We denote [37] by T −(p) the set of all terminal points associated with the
+past null geodesic flow issuing from p. In presence of cut points, C −(p, g) fails to be an embedded
+submanifold of (M, g). Failure to be an immersed manifold is more directly related to conjugate
+points along the generators of C −(p, g) and of the associated conjugate locus [45]. It follows that
+in presence of terminal points the mapping
+(122)
+expp
+��
+C −(p,g) : C Sz −→ Σz := expp [C Sz]
+is no longer one-to-one, and the cosmological sky section Σz fails to be a smooth surface. From the
+physical point of view, this is the geometrical setting associated with the generation of multiple
+images of astrophysical sources17 in the observer celestial sphere C Sz. The mathematical framework
+for handling such a scenario is to assume that the past null cone C −(p, g) has the regularity of a
+Lipschitz manifold, characterized by a maximal atlas A = {(Uα, ϕα)} such that all transition maps
+between the coordinate charts (Uα, ϕα) of C −(p, g),
+(123)
+ϕαβ := ϕβ ◦ ϕ−1
+α
+: ϕα (Uα ∩ Uβ) −→ ϕβ (Uα ∩ Uβ) ,
+are locally Lipschitz maps between domains of the Euclidean space (R3, δ).
+On C −(p, g), the
+condition of being Lipschitz can be viewed as a weakened version of the differentiability. In par-
+ticular, if f : C −(p, g) ∋ U −→ R3 is a continuous map between open sets, then f is Lipschitz
+if and only if it admits distributional partial derivatives that are in L∞(U) with respect to the
+15See [45] for a thorough analysis of the geometry of gravitational lensing.
+16The restrictive nature of the smoothness assumption on the metric g, typically represented by functions gab ∈
+Ck(R4, R), k ≥ 2, and of the associated light cone, has been pointed out by many authors, mainly in the context of
+the proof of singularity theorems and in causality theory, (see e.g. [13], [17], [38], [42], [51]).
+17If the sources are not pointlike, we also have the more complex ring patterns typical of strong gravitational
+lensing.
+
+26
+M. CARFORA AND F. FAMILIARI
+Lebesgue measure. This statement of Rademacher’s theorem [23], [48] implies that the transition
+maps ϕαβ on C −(p, g) have differentials dϕαβ that are defined almost everywhere, and which are
+locally bounded an measurable on their domains. In such a low-regularity setting the exponential
+map is quite delicate to handle. However, a key result, geometrically proved by M. Kunzinger,
+R. Steinbauer, M. Stojkovic [40], (based on work by B.-L. Chen and P. LeFloch [13]), and by E.
+Minguzzi [42], implies that the exponential map associated with a C1, 1 metric can still be defined
+as a local bi-Lipschitz homeomorphism, namely a bijective map which along with its inverse is
+Lipschitz continuous in a sufficiently small neighborhood of p. Thus, the exponential map retains
+an appropriate form of regularity in the sense that locally, for each point p ∈ M, there exist open
+star-shaped neighborhoods, N0(p) of 0 ∈ TpM and Up ⊂ (M, g), such that expp : N0(p) −→ Up is
+a bi-Lipschitz homeomorphism [40]. In particular, each point p ∈ (M, g) possesses a basis of totally
+normal neighborhoods. It is worthwhile to stress that geodesic normal coordinates (see (22)) can be
+still defined, but the transition from the current smooth coordinate systems18 used around p ∈ M
+to the normal coordinates associated with expp is only continuous.
+7.2. The fractal-like sky section Σz. We are interested in the geometry that such past light
+cone scenario induces on the cosmological sky section Σz := expp [C Sz] of C−(p, g). As long as expp
+is bi-Lipschitz, the sky sections Σz are topological 2-spheres, and the results above seem to suggest
+that after all there is no such a strong motivation to abandon the comforts of the smooth framework
+in favor of a Lipschitzian rugged landscape. However, as the length scale L varies, the development
+of caustics in C −(p, g) generates cusps and crossings in the surfaces Σz, to the effect that they are
+no longer homeomorphic to 2-spheres. In such a setting, the restriction of the exponential map to
+the celestial sphere C Sz, characterizing the surface Σz, (see (71)),
+(124)
+expp : C Sz ⊂ TpM −→ Σz := expp [C Sz] ⊂ C −(p, g) ,
+is only a Lipschitz map between the metric spaces
+�
+C Sz, dS2r
+�
+and
+�
+Σz, dg|Σ
+�
+, where dS2r is the
+standard distance function on the round 2-sphere S2
+r or radius r, and dg|Σ is the distance function
+induced (almost everywhere) on Σz by the metric g|Σz defined19 by (26). In general, the sky section
+Σz can be topologically very complex since it may contain terminal points of the exponential map
+expp, giving rise to cusps and swallow-tail points associated with self-intersections of Σz. Even if
+this may evolve in a very complex picture of Σz, we still have quite a geometric control over its
+metric structure. The Lipschitz regularity of expp implies that there is a constant cr, depending
+on the parameter r, such that
+(125)
+dΣ(p,r)
+�
+expp(x), expp(y)
+�
+≤ cr dS2r(x, y),
+∀ x, y ∈ S2
+r ,
+and we can define the pull-back on the celestial sphere C Sz ∈ TpM of the distance function dΣz
+according to
+(126)
+exp∗
+p dΣz = dgΣ
+�
+expp(x), expp(y)
+�
+,
+∀ x, y ∈ C Sz .
+We can also pull-back the metric g|g|Σz to C Sz. By Rademacher’s theorem expp is differentiable
+almost everywhere, and
+(127)
+h(θ, φ) :=
+�
+exp∗
+p g|Σz
+�
+αβ dxαdxβ ,
+is a metric defined, almost everywhere on the celestial sphere C Sz, (by a slight abuse of language, we
+have used the same notation as for the smooth version(27)). We can also define almost everywhere
+18Recall that M is a smooth manifold, and that the low Lipschitz C1, 1 regularity is caused by the metric g, and
+not by the differentiable structure of M.
+19In presence of cut points the inclusion map ιr : Σz ֒→ C −(p, g) of the sky section Σz into C −(p, g) is Lipschitz,
+thus Rademacher’s theorem allows us to define the pull-back metric g|Σz := ι∗
+r g|C −(p,g) only almost-everywhere
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+27
+the volume element dµh associated with the metric (127), i.e.
+(128)
+dµh := exp∗
+p dµg|Σz =
+�
+det(h(r(z), θ, φ)) dθdϕ ,
+in full analogy with its smooth version (28). All this implies that with the proviso of the almost
+everywhere meaning, the characterization (29) of the angular diameter distance D(r, θ, φ) and of
+the shear-inducing distortion Lαβ defined by (30), carry over to the bi-Lipschitz case.
+To put these geometrical remarks at work, let us stress that we cannot have reasonable control
+over the very complex topological structure of the sky section Σz induced by a cascade of (strong)
+lensing events. Moreover, the corresponding caustics and singularities at the terminal points on
+Σz provide a level of detail that is not relevant to the present analysis. Thus, as a reasonable
+compromise, we assume that the exponential map expp is bi-Lipschitz, that Σz is topologically a
+2-sphere, and we mimic the effect of the many lensing events that may affect Σz by assuming that
+the sky section Σz has the irregularities of a metric surface with the fractal geometry of a 2-sphere
+with the locally-finite Hausdorff 2-measure associated with (128). Under such assumptions, it can
+be shown that our smooth analysis can be safely extended, (in particular, we can still exploit
+the Poincar´e–Koebe uniformization theorem [44]), and the results obtained hold also in the more
+general setting of a Lipschitz description of the cosmographic past lightcone C−(p, g).
+8. Concluding remarks: d(z)
+�
+�Σz, Σz
+�
+as a scale-dependent field
+According to the physical characterization (111) of E�ΣΣ[ψ(z)], and the results described in Theo-
+rem 1, the distance function d(z)
+�
+�Σz, Σz
+�
+, (for simplicity, one may work with the E�ΣΣ[ψ(z)] realizing
+the minimum), can be interpreted as defining a z-dependent field on the FLRW past light cone
+�C−(p, �g) describing the mean square fluctuations of the anisotropies of the physical area distance
+D(ζ(z)) with respect to the reference FLRW area distance �D(�r(z)).
+These fluctuations provide
+information on how much the local area element on the physical sky section Σz differs from the
+corresponding (round) area element on the reference FLRW sky section Σz. Since for 2-dimensional
+surfaces the local Riemannian geometry is fully described by the area element, the fluctuations in
+D(ζ(z)) give information on how much the geometries of the sky sections �Σz and Σz differ. When
+we reach the scale of homogeneity, the physical area distance D(ζ(z)) becomes isotropic and can be
+identified with the reference FLRW �D(�r(z)). The localized null-directions alignment between the
+corresponding celestial spheres C Sz(p) and �
+C Sz(p) reduces to a global kinematical Lorentz boost
+(and a rotation). Thus, corresponding to this homogeneity scale, the distance function d(z)
+�
+�Σz, Σz
+�
+field vanishes.
+Thus, we have an interesting scenario whereby it is possible to associate with the distance functional
+d(z)
+�
+�Σz, Σz
+�
+a scale-dependent field that describes a global effect that the reference FLRW past
+lightcone �C−(p, �g) misses in describing the pre-homogeneity anisotropies of the actual past lightcone
+C−(p, �g). This pre-homogeneity field is, in line of principle, measurable since it is the mean-square
+variation of the physical area distance D(ζ(z)). The delicate question concerns its possible role in
+selecting the large-scale FLRW model that best fits the cosmological observations on large scales. A
+few qualitative indications in this direction, mainly of a perturbative nature, are discussed in [12].
+The results presented here are however more precise since they connect directly the distance func-
+tional d(z)
+�
+�Σz, Σz
+�
+to the area distance D(ζ(z)). To describe an important consequence of these
+results, let us consider the light cone regions C−
+L (p, ˆg) and C−
+L (p, g) over a sufficiently small length
+scale L(z). If ζ(z) and the corresponding ψ(z) denote the minimizing maps characterized in Theorem
+
+28
+M. CARFORA AND F. FAMILIARI
+1, then we can write [12]
+E�ΣΣ[ψ(z)]
+=
+�
+�Σz
+(Φ�ΣΣ − 1)2 dµ�g(z) =
+�
+�Σz
+Φ2
+�ΣΣ dµ�g(z) +
+�
+�Σz
+dµ�g(z) − 2
+�
+�Σz
+Φ�ΣΣ dµ�g(z)
+(129)
+=
+�
+�Σz
+ψ∗
+g(z)dµg(z)
+dµ�g(z)
+dµ�g(z) + A
+�
+�Σz
+�
+− 2
+�
+�Σz
+Φ�ΣΣ dµ�g(z)
+=
+�
+ψ(z)(�Σz)
+dµg(z) + A
+�
+�Σz
+�
+− 2
+�
+�Σz
+Φ�ΣΣ dµ�g(z)
+=
+A(Σz) + A
+�
+�Σz
+�
+− 2
+�
+�Σz
+Φ�ΣΣ dµ�g(z) ,
+where we have exploited the Radon-Nikodyn characterization of �Φ2
+�ΣΣ, (see (101)), the identification
+ψ(z)(�Σz) = Σz, and the relation
+(130)
+�
+�Σz
+ψ∗
+(z)dµg(z)
+dµ�g(z)
+dµ�g(z) =
+�
+�Σz
+ψ∗
+(z)dµg(z) =
+�
+ψ(�Σz)
+dµg(z) =
+�
+Σz
+dµg(z) = A(Σz) ,
+where A(Σz) and A
+�
+�Σz
+�
+respectively denote the area of the sky sections (ˆΣz, �g(z)) and (Σz, g(z)).
+Thus,
+(131)
+d(z)
+�
+�ΣL, ΣL
+�
+= E�ΣΣ[ψ(z)] := A
+�
+�Σz
+�
++ A(Σz) − 2
+�
+�Σz
+Φ�ΣΣ dµ�g(z) .
+To simplify matters, we assume that at the given length scale L(z) the corresponding region C−
+L (p, g)
+is caustic free. Let us rewrite ΦΣ�Σ as
+ΦΣ�Σ
+=
+�
+ΦΣ�Σ − 1
+�
++ 1
+(132)
+=
+��Jac
+�
+ζ(z)
+���
+1
+2 D(ζ(z)) − �D(�r(z))
+�D(�r(z))
++ 1 ,
+where we have simplified the notation used in (108). By introducing this in (131) we get
+(133)
+dL
+�
+�Σz, Σz
+�
+= A (Σz) − A(�Σz) − 2
+�
+�Σz
+
+
+��Jac
+�
+ζ(z)
+���
+1
+2 D(ζ(z)) − �D(�r(z))
+�D(�r(z))
+
+ dµ�g(z) .
+This expression can be further specialized if we exploit the asymptotic expressions of the area
+A
+�
+�Σz
+�
+and A (Σz) of the two surfaces (�Σz, �g(z)), (Σz, g(z)) on the corresponding lightcones C−
+L (p, �g)
+and C−
+L (p, g). These asymptotic expressions can be obtained if we consider the associated causal
+past regions J −
+L (p, �g) and J −
+L (p, g) sufficiently near the (common) observation point p, in particular
+when the length scale L(z) we are probing is small with respect to the ”cosmological” curvature
+scale. Under such assumption, there is a unique maximal 3-dimensional region V 3
+L(p), embedded
+in J −
+L (p, g), having the surface (Σz, h) as its boundary.
+This surface intersects the world line
+γ(τ) of the observer p at the point q = γ(τ0 = − L(z)) defined by the given length scale L(z).
+For the reference FLRW the analogous set up is associated to the constant-time slicing of the
+FLRW spacetime (M, �g) considered. The corresponding 3-dimensional region �V 3
+L(p), embedded in
+J −
+L (p, �g), has the surface (�Σz, ˆh) as its boundary. The FLRW observer �γ(�τ) will intersect �V 3
+L(p) at
+the point �q = �γ(�τ0 = − L(z)). By introducing geodesic normal coordinates {Xi} in J −
+L (p, g) and
+{Y k} in J −
+L (p, �g), respectively based at the point q and �q, we can pull back the metric tensors g
+and �g to TqM and T�qM, and obtain the classical normal coordinate development of the metrics g
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+29
+and �g valid in a sufficiently small convex neighborhood of q and �q. Explicitly, for the (more relevant
+case of the) metric g, we have (see e. g. Lemma 3.4 (p. 210) of [49] or [47])
+�
+(expq)∗ g
+�
+ef = ηef − 1
+3 Reabf|qXaXb − 1
+6 ∇cReabf|qXaXbXc
++
+�
+− 1
+20 ∇c∇dReabf + 2
+45 Reabm Rm
+fcd
+�
+q
+XaXbXcXd + . . . ,
+where Rabcd is the Riemann tensor of the metric g (evaluated at the point q). The induced expansion
+in the pulled-back measure
+�
+(exps(η))∗dµg
+�
+provides the Lorentzian analog of the familiar Bertrand-
+Puiseux formulas associated with the geometrical interpretation of the sectional, Ricci and scalar
+curvature for a Riemannian manifold in terms of the length, area, and volume measures of small
+geodesic balls. In the Lorentzian case the relevant formulas are more delicate to derive, [3], [25],
+[26], [43]. This asymptotics provides [25], to leading order in L(z), the following expressions for the
+area of (Σz, g(z)) and (�Σz, �g(z)),
+(134)
+A (Σz) = π L2(z)
+�
+1 − 1
+72 L2(z) R(q) + . . .
+�
+,
+and
+(135)
+A
+�
+�Σz
+�
+= π L2(z)
+�
+1 − 1
+72 L2(z) �R(�q) + . . .
+�
+,
+Introducing these expressions in (133) we eventually get
+(136)
+�R(ˆq) = R(q) + 72
+π
+d(z)
+�
+�Σz, Σz
+�
+L4(z)
++
+144
+πL4(z)
+�
+�Σz
+
+
+��Jac
+�
+ζ(z)
+���
+1
+2 D(ζ(z)) − �D(�r(z))
+�D(�r(z))
+
+ dµ�g(z) + . . . .
+Notice that the integral is the average value over the sky section (�Σz, �g(z)), of the fluctuations of
+��Jac
+�
+ζ(z)
+���
+1
+2 D(ζ(z)) with respect to �D(�r(z)), average that for notational ease we write as
+(137)
+�
+D(ζ(z))
+�� �D(�r(z))
+�
+�Σz := A−1(�Σz)
+�
+�Σz
+
+
+��Jac
+�
+ζ(z)
+���
+1
+2 D(ζ(z)) − �D(�r(z))
+�D(�r(z))
+
+ dµ�g(z) ,
+while, as we have already stressed, the distance functional is (up to the A(�Σz) normalization) the
+square mean deviation of this average, i. e.,
+��
+D(ζ(z))
+�� �D(�r(z))
+�2�
+�Σz
+:
+=
+A−1(�Σz)
+�
+�Σz
+
+
+��Jac
+�
+ζ(z)
+���
+1
+2 D(ζ(z)) − �D(�r(z))
+�D(�r(z))
+
+
+2
+dµ�g(z)
+(138)
+=
+A−1(�Σz) d(z)
+�
+�Σz, Σz
+�
+.
+To put these results at work, let us assume the conservative and quite a reasonable scenario where
+the fluctuations in the area distance D(ζ(z)), even if locally large in the various celestial coordinates
+bins, average out to zero over �Σz.
+However, the corresponding square mean deviation of the
+fluctuations
+��
+D(ζ(z))
+�� �D(�r(z))
+�2�
+�Σz
+= A−1(�Σz) d(z)
+�
+�Σz, Σz
+�
+can be significantly different from
+
+30
+M. CARFORA AND F. FAMILIARI
+zero, and from (136) we get
+(139)
+�R(ˆq) = R(q) + 72
+π
+d(z)
+�
+�Σz, Σz
+�
+L4(z)
++ . . . .
+The physical scalar curvature we measure (hard to!) in such a scenario is R(q), and if we decide
+to modeling with a FLRW solution a cosmological spacetime, homogeneous on large scale but
+highly inhomogeneous at smaller scale, then (139) shows that we cannot identify R(q) with the
+corresponding FLRW scalar curvature �R(ˆq). Such an identification is possible, with a rigorous level
+of scale dependence precision, only if we take into account the term
+(140)
+72
+π
+d(z)
+�
+�Σz, Σz
+�
+L4(z)
+.
+According to Theorem 1, this term vanishes once L(z) probes the homogeneity scales, conversely, it
+is clear from (139) that in pre-homogeneity region its presence is forced on us and plays the role of
+a scale-dependent effective positive contribution to the cosmological constant. As long as the local
+inhomogeneities give rise to significant fluctuations in the area distance D(ζ(z)), this contribution
+cannot be considered a priori negligible in high-precision cosmology.
+References
+[1] J. Beem, P. Ehrlich, K. Easley, Global Lorentzian Geometry, Monographs and Textbooks in Pure and Applied
+Mathematics Vol. 202, 2nd ed., Dekker, New York, (1996).
+[2] M. S. Berger, On Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds, J. Diff. Geo.
+5 325-332 (1971).
+[3] C. Berthiere, G. Gibbons, and S. N. Solodukhin, Comparison theorems for causal diamonds, Phys. Rev. D 92,
+064036 (2015).
+[4] T. Buchert, M. Carfora, Regional averaging and scaling in relativistic cosmology, Class. Quantum Grav. 19 6109
+(2002) DOI 10.1088/0264-9381/19/23/314.
+[5] T. Buchert, M. Carfora, Cosmological Parameters Are Dressed, Phys. Rev. Lett. 90, 031101, (2003).
+[6] T. Buchert, M. Carfora, On the curvature of the present-day Universe, Class.Quant.Grav.25:195001, (2008)
+https://doi.org/10.1088/0264-9381/25/19/195001, arXiv:0803.1401v2 [gr-qc].
+[7] T. Buchert, H. van Elst, A. Heinesen The averaging problem on the past null cone in inhomogeneous dust
+cosmologies, arXiv:2202.10798v1 [gr-qc].
+[8] M. Carfora, A. Marzuoli, Smoothing Out Spatially Closed Cosmologies, Phys. Rev. Lett. 53, 2445 (1984)
+https://doi.org/10.1103/PhysRevLett.53.2445.
+[9] M. Carfora, K. Piotrkowska, Renormalization group approach to relativistic cosmology, Phys. Rev. D 52, 4393
+(1995) https://doi.org/10.1103/PhysRevD.52.4393.
+[10] M. Carfora, A. Marzuoli, Einstein Constraints and Ricci Flow: A Geometrical Averaging of Initial Data Sets,
+Mathematical Physics Studies (MPST), Springer (2023) ISBN: 978-981-19-8539-3.
+[11] T. Buchert, M. Carfora, G. F. R. Ellis, E. W. Kolb, M. MacCallum, J. Ostrowski, S. Rasanen, B. Roukema, L.
+Andersson, A. Coley, D. Wiltshire, Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?.
+Classical and Quantum Gravity 32 (21), (2015).
+[12] M. Carfora, F. Familiari, A comparison theorem for cosmological lightcones, Letters in Mathematical Physics,
+111:53 (2021), https://doi.org/10.1007/s11005-021-01393-2
+[13] B.-L. Chen and P. LeFloch, Injectivity Radius of Lorentzian Manifolds, Commun. Math. Phys. 278 (2008)
+[14] Y. Choquet-Bruhat, P. T. Chrusciel, J. M. Mart´ın-Garc´ıa, The light-cone theorem, Class. Quantum Grav. 26,
+135011 (22pp) (2009).
+[15] Y. Choquet-Bruhat, General relativity and the Einstein Equations, Oxford Mathematical Monographs, Oxford
+University Press, Oxford, (2009).
+[16] Y. Choquet-Bruhat, P. T. Chrusciel, J. M. Mart´ın-Garc´ıa, The Cauchy Problem on a Characteristic Cone for
+the Einstein Equations in Arbitrary Dimensions, Annales Henri Poincar´e 12, 419–482 (2011)
+[17] P. Chrusciel and J. Grant, On Lorentzian causality with continuous metrics, Class. Quantum Grav. 29 (2012)
+[18] G.F.R. Ellis, The Domain of Cosmology and the Testing of Cosmological Theories, pp. 3-39 in The Philosophy
+of Cosmology, Eds. K. Chamcham, J. Silk, J. D. Barrow, S. Saunders, Cambridge Univ. Press (2017).
+
+A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY
+31
+[19] G.F.R. Ellis and H. van Elst, Deviation of geodesics in FLRW spacetime geometries, p. 203-225 in A. Harvey
+ed.,On Einstein’s path-Essays in Honor of Engelbert Sch¨ucking, Springer, New York, (1999).
+[20] G.F.R. Ellis, S.D. Nel, R. Maartens, W.R. Stoeger, and A.P. Whitman, Ideal observational cosmology, Phys.
+Reports 124, 315-417 (1985).
+[21] G.F.R. Ellis, R. Maartens and M. A. H. MacCallum, Relativistic Cosmology, Cambridge Univ. Press (2012).
+[22] J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc., 10, 1–68 (1978).
+[23] L. C. Evans, R. F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics,
+CRC Press (Boca Raton, Florida) (1992).
+[24] M. Gasperini, G. Marozzi3, F. Nugier and G. Veneziano, Light-cone averaging in cosmology:
+formalism
+and applications, Journal of Cosmology and Astroparticle Physics JCAP07(2011)008, DOI 10.1088/1475-
+7516/2011/07/008.
+[25] G. W. Gibbons and S. N. Solodukhin, The geometry of small causal diamonds, Phys. Lett. B 649 (2007) 317
+[hep-th/0703098]
+[26] G. W. Gibbons and S. N. Solodukhin, The geometry of large causal diamonds and the No-Hair property of
+asymptotically DeSitter spacetimes, Phys. Lett. B 652 (2007) 103 [arXiv: 0706.0603]
+[27] J. R. Gott, III, M. Juric, D. Schlegel, F. Hoyle, M. Vogeley, M. Tegmark, N. Bahcall, J. Brinkmann, A Map of
+the Universe, Astrophys.J.624:463,(2005) (arXiv:astro-ph/0310571).
+[28] X. Gu, S.-T. Yau, Computing conformal structure of surfaces, Communications in Information and Systems, Vol.
+2 (2002) 121-146.
+[29] J. Hass and P. Koehl, Comparing shapes of genus-zero surfaces, Journal of Applied and Computational Topology,
+Vol. 1, (2017) 57–87.
+[30] A. Heinesen, Multipole decomposition of the general luminosity distance ’Hubble law’ – a new framework for obser-
+vational cosmology, Journal of Cosmology and Astroparticle Physics 05(2021)008 https://doi.org/10.1088/1475-
+7516/2021/05/008, arXiv:2010.06534v2 [astro-ph.CO].
+[31] A. Heinesen, Redshift drift cosmography for model-independent cosmological inference, Phys. Rev. D 104 (2021),
+123527 https://doi.org/10.1103/PhysRevD.104.123527, arXiv:2107.08674v2 [astro-ph.CO].
+[32] F. H´elein and J. C. Wood, Harmonic maps, in Handbook of Global Analysis, Elsevier (2007).
+[33] D. W. Hogg, Distance measures in cosmology, arXiv: astro-ph/9905116v4 (2000).
+[34] D. W. Hogg, D. J. Eisenstein, M. R. Blanton, N. A. Bahcall, J. Brinkmann, J. E. Gunn, and D. P. Schneider,
+Cosmic Homogeneity Demonstrated with Luminous Red Galaxies, The Astrophysical Journal, Vol. 624, (2005)
+54-58.
+[35] M. Jin, Y. Wang, S.-T. Yau, X. Gu, Optimal global conformal surface parametrization for visualization, Com-
+munications in Information and Systems, (2005) 117-134.
+[36] J. Jost, Riemannian geometry and geometric analysis, 2nd ed. Springer Universitext, Springer–Verlag (1998).
+[37] S. Klainerman and I. Rodnianski, On the radius of injectivity of null hypersurfaces, Journal of the American
+Mathematical Society, Vol. 21 (2008), 775–795, S 0894-0347(08)00592-4
+[38] M. Kunzinger, R. Steinbauer, J. A. Vickers, The Penrose singularity theorem in regularity C1, 1, Classical and
+Quantum Gravity, 32 (15), 1-13, [155010]. (doi:10.1088/0264-9381/32/15/155010) (2015).
+[39] E. W. Kolb, V. Marra, S. Matarrese, Cosmological background solutions and cosmological backreactions,
+Gen.Rel.Grav. 42 (2010) 1399-1412.
+[40] M. Kunzinger, R. Steinbauer, M. Stojkovic, The exponential map of a C1,1−metric, Differential Geometry and
+its Applications 34 (2014) 14-24.
+[41] R. Maartens, Is the Universe homogeneous?
+Philosophical Transactions of the Royal Society, A 369 (2011),
+5115-37.
+[42] E. Minguzzi, Convex neighborhoods for Lipschitz connections and sprays, Monatsh. Math. 177, 569-625 (2015),
+https://doi.org/10.1007/s00605-014-0699-y. See also arXiv:1308.6675v2 [math.DG].
+[43] J. Myrheim, Statistical Geometry, Report No. CERN-TH-2538, (1978) (unpublished).
+[44] D. Ntalampekos and M. Romney, Polyhedral approximation and uniformization for non-length surfaces,
+arXiv:2206.01128v1[math. MG] (2022).
+[45] V.
+Perlick,
+Gravitational
+Lensing
+from
+a
+Spacetime
+Perspective,
+Living
+Reviews
+in
+Relativity,
+Livingreviews.org/lrr-2004-9.
+[46] R. Penrose and W. Rindler, Spinors and Space Time Vol I, Cambridge Monographs on Mathematical Physics,
+Cambridge Univ. Press (1984).
+[47] P. Petersen, Riemannian Geometry, Graduate Text in Mathematics 171 Springer (1998).
+[48] J. Rosenberg, Applications of Analysis on Lipschitz Manifolds, Proc. Centre Math. Appl., 16: 349pp. (1987)
+269-283, Miniconference on Harmonic Analysis and Operator Algebras (August 5-8 and December 2-3, 1987,
+Australian National University, Canberra). Eds. M. Cowling, C. Meaney, W. Moran.
+[49] R. Schoen, S-T. Yau, Lectures on differental geometry, Vol.I, International Press, Cambridge, MA, (1994).
+
+32
+M. CARFORA AND F. FAMILIARI
+[50] M. Scrimgeour M et al., The WiggleZ Dark Energy Survey: the transition to large-scale cosmic homogeneity
+Mon. Not. R. Astr. Soc. 425 (2012) 116 [arXiv:1205.6812].
+[51] J. M. M. Senovilla, Singularity Theorems and Their Consequences, Gen. Rel. and Gravitation, 30 (1998) 701-848,
+(this is available with updates in arXiv:1801.04912v1 [gr-qc] https://doi.org/10.48550/arXiv.1801.04912).
+[52] J.-P. Uzan, Emergent Structures of Effective Field Theories, pp. 109-135 in The Philosophy of Cosmology, Eds.
+K. Chamcham, J. Silk, J. D. Barrow, S. Saunders, Cambridge Univ. Press (2017).
+[53] D. L., Wiltshire, P. R. Smale, T. Mattsson, and R. Watkins, Hubble flow variance and the cosmic rest frame,
+Physical Review D, 88(8), (2013), doi:10.1103/physrevd.88.083529
+[54] D.Wiltshire, Comment on ”Hubble flow variations as a test for inhomogeneous cosmology”, Atronomy and As-
+trophysics 624 (2019) A12.
+[55] P. Zhang and A. Stebbins, Confirmation of the Copernican principle through the anisotropic kinetic Sunyaev
+Zel’dovich effect, Philosophical Transactions of the Royal Society, A 369 (2011), 5138-45.
+(Department of Physics, University of Pavia) University of Pavia
+(GNFM and INFN) Italian National Group of Mathematical Physics, and INFN Pavia Section
+Email address: mauro.carfora@unipv.it
+(Department of Physics, University of Pavia) University of Pavia
+(GNFM and INFN) Italian National Group of Mathematical Physics, and INFN Pavia Section
+Email address: francesca.familiari01@universitadipavia.it
+
diff --git a/edE3T4oBgHgl3EQfewrM/content/tmp_files/load_file.txt b/edE3T4oBgHgl3EQfewrM/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cf1d04d85d4a341171b80194b6562bbba9dc4b8e
--- /dev/null
+++ b/edE3T4oBgHgl3EQfewrM/content/tmp_files/load_file.txt
@@ -0,0 +1,1065 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf,len=1064
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='04547v1  [gr-qc]  11 Jan 2023  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN  PAST-LIGHTCONES IN COSMOLOGY  MAURO CARFORA AND FRANCESCA FAMILIARI  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We discuss a rigorous procedure for quantifying the difference between our past light-  cone and the past lightcone of the fiducial Friedmann-Lemaitre-Robertson-Walker spacetime mod-  eling the large scale description of cosmological data in the standard ΛCDM scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This result  is made possible by exploiting the scale-dependent distance functional between past lightcones re-  cently introduced by us in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We express this harmonic map type functional in terms of the  physical quantities that characterize the actual measurements along our past lightcone, namely the  area distance and the lensing distortion, also addressing the very delicate problem of the presence  of lightcone caustics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This analysis works beautifully and seems to remove several of the difficulties  encountered in comparing the actual geometry of our past lightcone with the geometry of the fidu-  cial FLRW lightcone of choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We also discuss how, from the point of view of the FLRW geometry,  this distance functional may be interpreted as a scale-dependent effective field, the pre-homogeneity  field, that may be of relevance in selecting the FLRW model that best fits the observational data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' INTRODUCTION  It is a pleasure to dedicate this paper to Maurizio Gasperini who has always liked it best on the  past light cone even if the routes are tough,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' but in such a rugged landscape that is to be expected  The ΛCDM model and the Friedman-Lemaitre-Robertson-Walker (FLRW) spacetimes provide a  rather accurate physical and geometrical representation of the universe in the present era1 and over  spatial scales ranging from2 ≈ 100 h−1 Mpc to the visual horizon of our past light cone [27],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' [34],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' [50],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  where h is the dimensionless parameter describing the relative uncertainty of the true value of the  present-epoch Hubble-Lemaitre constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Within such observational range, and on scales signif-  icantly smaller than the Hubble scale3, we have a testable ground for statistical isotropy in the  distribution of the dark and visible matter components on our past light cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Homogeneity of  this distribution is difficult to test directly via astronomical surveys, but a number of observational  results [41] and in particular the kinematic Sunyaev-Zeldovich effect [55], [18] imply that fluctu-  ations around spatial homogeneity cannot be too large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, without resorting to an axiomatic  use of the Copernican principle, we have an observational ground for assuming that spatial ho-  mogeneity holds, in a statistically averaged sense, over large scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It must be stressed that it is  in a statistical sense and only over large scales that this weak form of the cosmological principle  provides observational support for best fitting the description of spacetime geometry in terms of  a member of the FLRW family of solutions of the Einstein equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  In particular, to what-  ever degree one accepts this FLRW scenario, one has to address the fact that the role of FLRW  spacetime geometry becomes delicate to interpret when past light cone data are gathered in our  1Characterized by the actual temperature of the cosmic microwave background TCMB = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='725 K as measured in  the frame centered on us but stationary with respect to the CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  2The actual averaging scale marking the statistical onset of isotropy and homogeneity is still much debated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' For  the sake of the argument presented in this paper, we adopt the rather conservative estimate of the scales over which  an average isotropic expansion is seen to emerge, namely 70 − 120 h−1Mpc, and ideally extending to a few times this  scale [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  3At the Hubble scale, the problem of cosmic variance may alter the statistical significance of the data samples we  gather.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  1  2  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  cosmological neighborhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  As we probe spatial regions in the range ≲ 100h−1 Mpc, the ac-  tual distribution of matter (dark and visible) becomes extremely anisotropic with a high density  contrast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, gravitational clustering gives rise to a complex network of structures, char-  acterized by the presence of a foam-like web of voids and galaxy filaments often extending well into  the 100h−1 Mpc range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' At these scales, the Einstein evolution of the FLRW geometry uncouples  from the dynamics of the matter sources and survives more as a useful computational assumption  (often assisted by Newtonian theory) rather than as a bona fide perturbative background gravi-  tationally determined by the actual matter distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FLRW is thus a very strong assumption  and not a correct representation of spacetime geometry at the pre-homogeneity scales, not even  in a statistical sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' If we want or need to go beyond FLRW perturbation theory and enter into  a fully relativistic regime, it is fair to say that we have little mathematical control over the ac-  tual spacetime at these pre-homogeneity scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, the transition from the large-scale  FLRW to the actual inhomogeneous and anisotropic spacetime geometry emergent at these local  scales is poorly understood in a model-independent way, and the idea that around 100h−1 Mpc  we have a gradual and smooth transition between these two regimes is somewhat illusive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To wit,  we may have non-perturbative correction terms due to the coupling between gravitationally bound  structures and the emergent spacetime geometry (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' structure formation-induced curvature) that  can be significant in cosmological modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' For instance, they can back-react, in a top-down cau-  sation way [52], on the choice of the large-scale FLRW spacetime that best fits the observational  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This complex scenario gives rise to a number of delicate and to some extent controversial  issues that are currently much debated in discussing the existence of possible tensions between  cosmological observations and the standard ΛCDM model and in preparation to the coming era of  high-precision cosmology [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Some of the very delicate reasons4 motivating this tension is that  large-scale isotropy can hold for a much wider class of models, the so-called effective model [30], [31]  that need not even be a solution of Einstein’s equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As an illustrative example, one may con-  sider inhomogeneous spatial sections that can be smoothed into a constant-curvature space, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  with Ricci flow deformation techniques [4–6, 8–10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' While spatially, such slices can be identified  with spatial sections of a FLRW model, their Einstein time-evolution in general does not follow  the FLRW class of solutions, a backreaction is present [4–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, at least in principle, one may  actually deal with an effective model with global backreaction that can be large-scale isotropic and  homogeneous, or almost so, and it is not necessarily perturbatively away from a FLRW model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Thus, restricting a priori the ”best-fit” to the class of FLRW models is indeed a strong assumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  By its very nature, a discussion of this very complex scenario should be related, as far as possible,  to a model–independent direct observational cosmology approach, namely to the analysis of data  determined on our past lightcone without using any theory of gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since the dark matter and  dark energy components cannot be measured yet via direct observations, it must be stressed that  a full model-independent cosmographic approach is not actually possible [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Model hypotheses  must be imposed for the dark components, in particular on how they interact with observed matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The simplest assumptions made are that the dark matter component follows the baryonic compo-  nent, namely that: i) we know the primordial ratio of cold dark matter (CDM) density to baryonic  density;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ii) they have the same 4-velocity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' iii) we know their relative concentration in matter  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To these, one typically adds the working assumption that the dark energy component is  described in the form of a cosmological constant Λ, the value of which should be known from non–  cosmological physics and independently from cosmological observations (for a thorough discussion  of the implications of these assumptions in cosmography see Chap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 8 of [21]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' However, although  there are efforts to derive Λ from non-cosmological physics, it remains a fitting parameter of the  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The appropriate cosmographical framework was put forward in the ’80s by G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ellis,  4We wish to thank one of the referees for pointing this out to us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  3  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Maartens, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Stoeger, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Whitman [20] (see also [21]) by characterizing the set of cosmo-  logical observables on the past lightcone which, together with the Einstein field equations, allows  to reconstruct the spacetime geometry in a way adapted to the process of observation [20], [15], [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  In this paper we address an important step in this cosmographical framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular we  discuss a rigorous procedure for quantifying the difference between our past lightcone and the  reference past lightcone that, for consistency, we associate with the fiducial large-scale FLRW  spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This result is made possible by exploiting the scale-dependent (harmonic map type)  distance functional between past lightcones recently introduced by us in [12], and which extended  the light-cone theorem [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We express this functional in terms of the physical quantities that  characterize measurements along our past lightcone, namely the area distance and the lensing dis-  tortion, also briefly addressing the very delicate problem of the presence of lightcone caustics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This  analysis works beautifully and seems to remove several of the difficulties encountered in comparing  the actual geometry of our past lightcone with the geometry of a fiducial FLRW lightcone of choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  We also discuss how, from the point of view of the FLRW geometry, this distance functional may  be interpreted as a scale-dependent effective field that may be of relevance in selecting the FLRW  model that best fits the observative data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In this connection and in line with the introductory  remarks above its worthwhile to stress that our choice of a reference FLRW spacetime is strictly  related to the prevalence of this family of metrics in discussing the ΛCDM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The results  presented here can be easily extended to more general reference metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It is also important to  make clear that in this paper we are not addressing the extremely delicate averaging problem on  the past lightcone, a problem to which Maurizio Gasperini has significantly contributed with the  seminal paper [24], and that has seen importat recent progress in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' but the past lighcone routes  are still tough and the landscape rugged .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The past light cone and the celestial sphere  Throughout this paper (M, g) denotes a cosmological spacetime where g is a Lorentzian metric,  and where M is a smooth 4-dimensional manifold which for our purposes we can assume diffeo-  morphic to R4 (or to V 3 × R, for some smooth compact or complete 3–manifold V 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In local  coordinates {xi}4  i=1, we write g = gikdxi ⊗ dxk, where the metric components gik := g(∂i, ∂k) in  the coordinate basis {∂i := ∂/∂xi}4  i=1 have the Lorentzian signature (+, +, +, −), and the Einstein  summation convention is in effect5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We assume that (M, g) is associated with the evolution of  a universe which is (statistically) isotropic and homogeneous on sufficiently large scales L > L0  where, according to the introductory remarks, we indicatively assume L0 ∼= 100h−1 Mpc, and let  local inhomogeneities dominate for L < L0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The matter content in (M, g) is phenomenologically  described by a (multi-component) energy-momentum tensor T = Tik dxi ⊗ dxk, (typically in the  form of a perfect fluid, dust, and radiation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' If not otherwise stated, the explicit expression of T is  not needed for our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We assume that in (M, g) the motion of the matter components charac-  terize a phenomenological Hubble flow that generates a family of preferred world-lines parametrized  by proper time τ  γs : R>0  −→  (M, g)  (1)  τ  �−→  γs(τ) ,  and labeled by suitable comoving (Lagrangian) coordinates s adapted to the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We denote by  ˙γs :=  dγs(τ)  dτ  , g(˙γs, ˙γs) = −1, the corresponding 4-velocity field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' For simplicity, we assume that  at the present era these worldlines are geodesics, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ∇ ˙γs ˙γs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This phenomenological Hubble  flow is strongly affected by the peculiar motion of the astrophysical sources and by the complex  spacetime geometry that dominates on the pre-homogeneity scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  In particular, it exhibits a  5If not otherwise stated we adopt geometrical units, c = 1 = G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  4  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  complex pattern of fluctuations with respect to the linear FLRW Hubble flow that sets in, relatively  to the standard of rest provided by the cosmic microwave background (CMB), when we probe the  homogeneity scales, L ≳ 100h−1 Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Again, we stress that the transitional region between the  phenomenological Hubble flow and the statistical onset of the large-scale FLRW linear Hubble flow  is quite uncertain and still actively debated [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' If we adopt the weak form of the cosmological  principle described in the introduction, (M, g, γs) can be identified with the phenomenological  background spacetime or Phenomenological Background Solution (PBS) [39] associated with the  actual cosmological data gathered from our past lightcone observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In the same vein, we define  Phenomenological Observers the collection of observers {γs} comoving with the phenomenological  Hubble flow (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since in our analysis we fix our attention on a given observer, we drop the subscript  s in (1), and describe a finite portion of the observer’s world-line with the timelike geodesic segment  τ �−→ γ(τ), −δ < τ < δ, for some δ > 0, where p := γ(τ = 0) is the selected event corresponding  to which the cosmological data are gathered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To organize and describe these data in the local rest  frame of the observer p := γ(τ = 0), let  �  TpM, gp, {E(i)}  �  be the tangent space to M at p endowed  with a g-orthonormal frame {E(i)}i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',4, gp  �  E(i), E(k)  �  = ηik, where ηik is the Minkowski metric,  and where we identify E(4) with the observer 4-velocity ˙γ(τ)|τ=0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  E(4) := ˙γ(τ)|τ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, if  we denote by { ˘E (i)}i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',4, the 1-forms basis dual to {E(i)}i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',4, we write  gp = ηik ˘E (i) ⊗ ˘E (k) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (2)  Since we have the distinguished choice E(4) := ˙γ(τ)|τ=0 for the timelike basis vector E(4), we can  also introduce in  �  TpM, {E(i)}  �  a reference positive definite metric g(δ)  p  associated with the frame  {E(i)}i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',4 by setting  g(δ)  p  := δik ˘E (i) ⊗ ˘E (k) ,  (3)  where δik denote the components of the standard Euclidean metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As discussed in detail by Chen  and LeFloch [13], this reference metric comes in handy in the characterization of the functional  Lipschitz and Banach space norms of tensor fields defined on the past lightcone6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The celestial sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Let  (4)  C− �  TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' {E(i)}  �  :=  �  X = XiE(i) ̸= 0 ∈ TpM | gp(X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' X) = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' X4 + r = 0  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (5)  C− �  TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' {E(i)}  �  :=  �  X = XiE(i) ̸= 0 ∈ TpM | gp(X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' X) ≤ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' X4 + r ≤ 0  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  respectively denote the set of past-directed null vectors and the set of past-directed causal vectors  in (TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' {E(i)}),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' where  (6)  r := (  3  �  a=1  (Xa)2)1/2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  is the radial coordinate in the hyperplane X4 = 0 ⊂ TpM parametrizing the one-parameter family  of 2-spheres  (7)  S2  r(TpM) := {X ∈ C− �  TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' {E(i)}  �  | X4 = − r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  3  �  a=1  (Xa)2 = r2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' r ∈ R>0} ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  6The indefinite character of a Lorentzian metric makes it unsuitable for defining integral norms of tensor fields,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  and for such a purpose one is forced to introduce a reference positive definite metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, by exploiting the  Nash embedding theorem, one typically uses the Euclidean metric and the associated definitions of the functional  space of choice, say a Sobolev space of tensor fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Different choices of reference metrics, as long as they are of  controlled geometry, induce equivalent Banach space norms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In our case, we can exploit the natural choice provided  by (3) by using normal coordinates and identifying (TpM, {E(i)}, gδ  p) with the Euclidean space (R4, gδ  p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  5  that foliates C− �  TpM, {E(i)}  �  /{p}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The sphere S2  r(TpM) can be thought of as providing a rep-  resentation of the sky directions, at a given value of r, in the rest space  �  TpM, {E(i)}  �  of the  (instantaneous) observer (p, ˙γ(0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, the 2-sphere S2  r(TpM)  ��  r=1 or, equivalently, its  projection on the hyperplane X4 = 0 in TpM,  (8)  S2 (TpM) :=  �  X = XiE(i) ̸= 0 ∈ TpM | X4 = 0,  3  �  a=1  (Xa)2 = 1  �  ,  can be used to parametrize the (spatial) past directions of sight constituting the field of vision  of the observer (p, ˙γ(0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In the sense described by R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Penrose [46], this is a representation of  the abstract sphere S−(p) of past null directions parameterizing the past-directed null geodesics  through p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Explicitly, let  n(θ, φ)  :=  3  �  a=1  na(θ, φ) E(a)  (9)  =  cos φ sin θ E(1) + sin φ sin θ E(2) + cos θ E(3) ,  0 ≤ θ ≤ π, 0 ≤ φ < 2π ,  denote the spatial direction in TpM associated with the point (θ, φ) ∈ S2 (TpM), (by abusing nota-  tion, we often write n(θ, φ) ∈ S2 (TpM)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Any such spatial direction characterizes a corresponding  past-directed null vector ℓ(θ, φ) ∈  �  TpM, {E(i)}  �  ,  (10)  ℓ(θ, φ) = (n(θ, φ), − ˙γ(τ)|τ=0) =  3  �  a=1  na(θ, φ)E(a) − E(4) ,  normalized according to  (11)  gp (ℓ(θ, φ), ˙γ(τ)|τ=0) = gp  �  ℓ(θ, φ), E(4)  �  = 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The corresponding past-directed null rays  (12)  R≥0 ∋ r �−→ r ℓ(n(θ, φ)) ,  (θ, φ) ∈ S2 (TpM) ,  generate C− �  TpM, {E(i)}  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Note that in such a kinematical setup for the instantaneous rest space  �  TpM, {E(a)}  �  of the observer (p, ˙γ(0)), a photon reaching p from the past-directed null direction  ℓ(θ, φ), is characterized by the (future-pointing) wave vector  (13)  k(θ, φ) := − ν ℓ(θ, φ) ∈ TpM ,  where ν = − gp  �  k, E(4)  �  is the photon frequency as measured by the instantaneous observer  γ(τ)|τ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The spherical surface S2 (TpM) endowed with the standard round metric  (14)  �h(S2) = dθ2 + sin2 θ dφ2 ,  and the associated area form dµS2 =  �  det(�h(S2)) dθdφ = sin θ dθdφ, defines [46] the celestial  sphere  (15)  C S(p) :=  �  S2 (TpM) , �h(S2)  �  providing, in the instantaneous rest space  �  TpM, {E(i)}  �  , the geometrical representation of the set  of all directions towards which the observer can look at astrophysical sources from her instanta-  neous location in (M, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In this connection, dµS2 can be interpreted as the element of solid angle  subtended on the celestial sphere C S(p) by the observed astrophysical sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It is also useful  to keep track of the radial coordinate7 r as a possible parametrization of the past-directed null  7To avoid any misunderstanding we stress that r is not a distance parameter on the past light cone with vertex in  p ∈ (M, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  6  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  geodesics, and introduce a celestial sphere that provides also this information according to  (16)  C Sr(p) :=  �  S2  r (TpM) , r2�h(S2)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Lacking a better name, we shall refer to C Sr(p) as the celestial sphere at radius r in  �  TpM, {E(i)}  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The celestial sphere C S(p) plays a basic role in what follows since it provides the logbook where  astrophysical data are recorded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Let m(α)(θ, φ) ∈ TpM, with α = 2, 3, denote two spatial gp-orthonormal vectors spanning the  tangent space T(θ,φ)S2 (TpM) to S2 (TpM) at the point (θ, φ), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',  (17)  gp  �  m(α), n  �  = 0 = gp  �  m(α), E(4)  �  , gp  �  m(α), m(β)  �  = δαβ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The tetrad  (18)  �  n, m(2), m(3), ℓ(n)  �  provides a basis for TpM (the Sachs basis), and the pair  �  T(θ,φ)S2 (TpM) , m(α)(θ, φ)  �  defines the  screen plane TnC S(p) associated with the direction of sight n(θ, φ) ∈ C S(p) in the celestial sphere  C S(p), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (19)  TnC S(p) :=  �  T(θ,φ)S2 (TpM) , m(α)(θ, φ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  In the instantaneous rest space of the observer, the screen T(θ,φ)C S(p) is the (spatial) 2-plane on  which the apparent image of the astrophysical source, pointed by the direction n ∈ C S(p), is by  convention displayed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Sky sections and observational coordinates on the past light cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We transfer the  above kinematical setup from TpM to (M, g) by using the exponential map based at p,  expp : Wp ⊆ TpM  −→  M  (20)  X  �−→  expp (X) := λX(1) ,  where λX : IW −→ (M, g), for some maximal interval IW ⊆ R≥0, is the past-directed causal  geodesic emanating from the point p with initial tangent vector ˙λX(0) = X ∈ Wp, and where  Wp ⊆ TpM is the maximal domain of expp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, the past lightcone C −(p, g) ∈ (M, g) with the  vertex at p, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' the set of all events q ∈ (M, g) that can be reached from p along the past-pointing  null geodesics r �−→ expp(rℓ(n(θ, φ))), r ∈ IW , (θ, φ) ∈ C S(p), can be represented as  (21)  C −(p, g) := expp  �  Wp ∩ C− (TpM, gp)  �  ,  and the portion of C −(p, g) accessible to observations for a given value r0 ∈ IW of the affine  parameter r is given by  C −(p, g;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' r0) :=  �  q ∈ M | q = expp(rℓ(n(θ, φ))), 0 ≤ r < r0, (θ, φ) ∈ C S(p)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The exponential map representation, on the celestial spheres C S(p) and C Sr(p), provides a natural  setup for a description of observational data gathered from C −(p, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It emphasizes the basic role  of past-directed null geodesics and provides the framework for interpreting the physical data in  the local rest frame of the observer at p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, it allows us to represent on C S(p) and  C Sr(p) the actual geometry of the observed sky at a given length scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This role is quite effective  in a neighborhood of p, where we can introduce normal coordinates associated with expp, but it  is delicate to handle in regions where expp is not a diffeomorphism of Wp ∩ C− (TpM, gp) onto  its image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  To set notation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' our strategy is to start with the standard description [20],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' [21] of  observational coordinates on C −(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' g) associated with the usual assumption that the exponential  map is a diffeomorphism8 in a sufficiently small neighborhood of p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' and then we move to the more  8From an observational point of view,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' this is the geometrical set-up proper of the weak lensing regime describing  the alteration,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' due to the effect of gravity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' of the apparent shape and brightness of astrophysical sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  7  general, low regularity, Lipschitz case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In this connection, it is worthwhile to stress that the standard  normal coordinates description is strictly associated with the assumption that the metric of (M, g)  is sufficiently regular, with components gij(xℓ) which are at least twice continuously differentiable,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' gij(xℓ) ∈ Ck(R4, R),  for k ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Under this hypothesis, there is a star-shaped neighborhood  N0(g) of 0 in Wp ⊆ TpM and a corresponding geodesically convex neighborhood of p, Up ⊆ (M, g),  restricted to which expp : N0 ⊆ TpM −→  Up ⊆ M is a diffeomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In such Up we can  introduce geodesic normal coordinates (xi) according to  xi := Xi ◦ exp−1  p  : M ∩ Up  −→  R4  (22)  q  �−→  xi(q) := Xi �  exp−1  p (q)  �  where Xi �  exp−1  p (q)  �  are the components, in the g-orthonormal frame {E(i)}, (or with respect to  the corresponding basis (18)), of the vector exp−1  p (q) ∈ Wp ⊆ TpM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, in C −(p, g) ∩ Up we  can write,  expp  : C− �  TpM, {E(i)}  �  ∩ N0(g)  −→  C −(p, g) ∩ Up  (23)  rℓ(n(θ, φ)) = r  �  na(θ, φ)E(a) − E(4)  �  �−→  expp(rℓ(n)) = q  =⇒ q  �−→  {xi(q) := exp−1  p (q) = (r na(θ, φ), − r)} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  According to (21) and to the Gauss lemma applied to expp : C− �  TpM, {E(i)}  �  ∩ N0(g) −→  C −(p, g) ∩ Up, the past ligh cone region C −(p, g) ∩ Up \\ {p} is foliated by the r-dependent family  of 2–dimensional surfaces Σ(p, r), the cosmological sky sections, defined by  (24)  Σ(p, r) := expp [C Sr(p)] =  �  expp (r ℓ(n(θ, φ)))  �� (θ, φ) ∈ C S(p)  �  ,  and g-orthogonal to all null geodesics originating at p, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (25)  g  �  d(r,θ,φ) expp(ℓ(r, n)), d(r,θ,φ) expp(v)  ���  expp(ℓ(r,n)) = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Here d(r,θ,φ) expp(.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=') denotes the tangent mapping associated to expp evaluated at the point (θ, φ) ∈  S2  r(p), and v ∈ Tθ,φ S2  r(p) is the generic vector tangent to S2  r(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In C −(p, g) ∩ Up\\{p}, each surface  Σ(p, r) is topologically a 2-sphere endowed with the r-dependent two-dimensional Riemannian  metric  (26)  g|Σ(p,r) := ι∗  r g|C −(p,g)  induced by the inclusion ιr : Σ(p, r) ֒→ C −(p, g) of Σ(p, r) into C −(p, g) ∩ Up \\ {p}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We can pull  back this metric to the celestial sphere C Sr(p) :=  �  S2  r (TpM) , r2�h(S2)  �  by using the exponential  map according to  (27)  h(r, θ, φ) :=  �  exp∗  p g|Σ(p,r)  �  αβ dxαdxβ���  r ,  α, β = 2, 3,  x2 := θ, x3 := φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  This metric can be profitably compared with the pre-existing round metric r2�h(S2) on C Sr(p) (see  (14) and (16)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To this end, let r n(θ, φ) ∈ C Sr(p) be the direction of sight pointing, in the celestial  sphere C Sr(p), to the (extended) astrophysical source located around the point q ∈ Σ(p, r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' If  rℓ(n(θ, φ)) = r  �  na(θ, φ)E(a) − E(4)  �  is the corresponding null direction in C− �  TpM, {E(i)}  �  , then  according to (23) we have expp(rℓ(n)) = q and, via the exponential map along the past-directed  null geodesic reaching the observer located at p from the astrophysical source located at q, we can  pull-back the area element of  �  Σ(p, r), g|Σ(p,r)  �  on the celestial sphere C Sr(p) of the observer at p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  We have  (28)  dµh(r)(p, n(θ, φ), r) := exp∗  p dµg|Σ(p,r) ◦ expp(rℓ(n)) =  �  det(h(r, θ, φ)) dθdφ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  This defines the area element associated with the metric (27), and can be interpreted [21] as the  cross-sectional area element at the source location as seen by the observer at p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since the round  8  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  measure dµS2r = r2 dµS2 = r2 sin θ dθ dϕ and the actual physical measure dµh(r) are both defined  over the celestial sphere C Sr(p) ∈ TpM, we can introduce the relative density of dµh(r) with respect  to the Euclidean solid angle measure dµS2, viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' the function D(r, θ, φ) defined by the relation  (29)  dµh(r) = D2(r, θ, φ) dµS2 ,  or equivalently,  �  det(h(r, θ, φ)) = D2(r, θ, φ)  �  det(�h(S2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The function D(r, θ, φ) is the observer  area distance [20], [21], [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' By definition, it provides the ratio of an object’s cross sectional area  to its (apparent) angular size as seen on the celestial sphere S2(p) ⊂ TpM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Roughly speaking,  it converts the angular separations as seen in the images of an astrophysical source, gathered by  the observer at p, into proper separations at the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In general, D(r) := D(r, θ, φ)|θ,φ=const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  cannot be used as an affine parameter along the past-directed null geodesic r �→ expp(k(r, n))  since it is not a monotonic function of r, (for instance in FLRW models, monotonicity fails around  z ∼ 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' However, if we have an accurate knowledge of the brightness and of the spectrum of  the astrophysical source seen at the past light cone location q := expp(ℓ(r, n)) ∈ C −(p, g), then  D(r, θ, φ) is, at least in principle, a measurable quantity (see paragraph 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='3 of [20] and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='3 of  [21] for a discussion of this point9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As stressed above, we can also compare the physical metric  (27), h(r, θ, φ) :=  �  exp∗  p g|Σ(p,r)  �  αβ dxαdxβ���  r,  with the round metric r2�h(S2) pre-existing on the  celestial sphere C Sr(p), and introduce [20], [21] the set of functions Lαβ(r, θ, φ), α, β = 2, 3,  implicitly defined by representing (27) in the distorted polar form  (30)  hαβ|S2r = D2(r, θ, φ)  �  �hαβ(S2) + Lαβ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  We normalize this representation by imposing [20] that, in the limit r ց 0, the distortion,  Lαβ(r, θ, φ) = hαβ(r,θ,φ)  D2(r,θ φ − �hαβ(S2), of the normalized metric h(r)/D2(r) with respect to the round  metric �h(S2) goes to zero uniformly, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',  (31)  lim  rց0  ����  x4=0  hαβ(r, θ, φ) dxαdxβ  D2(r, θ, φ)  = dθ2 + sin2 θ dφ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  From the relation D− 2 hαβ = �hαβ(S2) + Lαβ we also compute  (32)  D− 2 �hµβ hαβ = δµ  α + Lµ  α =⇒ det (δµ  α + Lµ  α) = 1 ,  where, for rising indexes, we used the inverse round metric �hµβ(S2) to write Lµ  α := �hµβ(S2) Lαβ,  and where we have exploited the relation det  �  �hµβ hαβ  �  = D4, direct consequence of det(h) =  D4 det(�h(S2)) (see (29)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since  (33)  det (δµ  α + Lµ  α) = 1 + trS2 (Lµ  α) + det (Lµ  α) ,  from relation (32) it follows that  (34)  trS2 (Lµ  α) + det (Lµ  α) = 0 ,  which implies that Lµ  α cannot be trace-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Roughly speaking, Lαβ(r) can be interpreted as the  image distortion of the sources on (Σ(p, r), h(r)) as seen by the observer at p on her celestial sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  It can in principle be directly observed and it can be related to the gravitational lensing shear [20],  (see also chap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 8 of [21]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Explicitly, let us compute the deformation tensor Θαβ defined by the rate  9Beware that in [20], the observer area distance D2(r, θ, φ) is denoted by r, whereas our r corresponds to their y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  9  of variation of the metric tensor h(r) as r varies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Dropping the angular dependence for notational  ease, we get  Θαβ := d  dr hαβ(r)  =  d  dr  �  D2(r)  �  �hαβ(S2) + Lαβ(r)  ��  (35)  =  2hαβ(r) d  dr ln D(r) + D2(r) d  dr Lαβ(r) ,  where we exploited d�hαβ(S2)/dr = 0 and rewrote D(r)dD(r)/dr as D2(r)d ln D(r)/dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Similarly,  from the defining relation  �  det(h(r, θ, φ)) = D2(r, θ, φ)  �  det(�h(S2)), (see (29)), we compute  d  dr  �  det(h(r))  =  d  dr  �  D2(r)  �  det(�h(S2))  �  = 2  �  det(h(r)) d  dr ln D(r)  (36)  ⇒  d  dr ln  �  det(h(r))  =  2 d  dr ln D(r) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Inserting this relation in (35) we obtain  (37)  Θαβ := hαβ(r) d  dr ln  �  det(h(r)) + D2(r) d  dr Lαβ(r) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The shear �σαβ is the trace-free part of this expression, �σαβ := Θαβ − 1  2hαβ hµνΘµν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since  (38)  1  2hαβ hµνΘµν = 1  2hαβ hµν d  drhµν = hαβ  d  dr ln  �  det(h(r)) ,  we eventually get  (39)  �σαβ = D2(r) dLαβ(r)  dr  ,  as might have been expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Note that, in contrast to Lαβ, �σαβ is trace-free (but with respect to  the physical metric hαβ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Now, let us introduce the other basic player of our narrative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The background FLRW past light cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  As already pointed out, the standard ΛCDM model is built on the assumption that over scales  L > 100 h−1 Mpc, the phenomenological background spacetime (M, g, γs) follows on average the  dynamics of a FLRW model with a (linear) Hubble expansion law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It is also assumed that below  the scale of statistical homogeneity, deviations from this average scenario can be described by  FLRW perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since there is no smooth transition between the large-scale FLRW  Hubble flow and the phenomenological Hubble flow, this latter assumption rests on quite delicate  ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' For instance, the field of peculiar velocities {˙γs(τ)} of the phenomenological observers  {τ −→ γs(τ)} shows a significant statistical variance [53] with respect to the average FLRW Hubble  flow and the standard of rest provided by the cosmic microwave background (CMB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This remark  has an important effect on the relation between the celestial sphere C Sr(p) of the phenomenological  observer (p, ˙γ(0)) and the corresponding celestial sphere �  C S�r(p) of the idealized FLRW observer  (p, �˙γ(0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' They cannot be identified and must be connected by a Lorentz boost that takes into  account the origin of this statistical variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The actual scenario is significantly constrained by the  coupling of the matter inhomogeneities with a spacetime geometry that is no longer Friedmannian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  As a consequence, the peculiar velocity field of the phenomenological observer may have a rather  complex origin, and its variance with respect to the FLRW average expansion may become a variable  of relevance in cosmography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This scenario naturally calls into play a delicate comparison between  the geometry of C−(p, g) and the geometry of the associated FLRW past light cone that sets in at  scales L > 100 h−1 Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' For this purpose, along with the physical metric g, we consider on the  spacetime manifold M a reference FLRW metric ˆg and the associated family of global Friedmannian  observers ˆτ �−→ ˆγs(ˆτ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Strictly speaking, the FLRW model (M, ˆg, ˆγs(ˆτ)) should be used only over  10  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  the scales L > L0 ≃ 100 h−1 Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We need to consider it also over the inhomogeneity scales  L < L0 where it plays the role of the geometrical background used to interpret the data according  to the standard perturbative FLRW point of view recalled above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In such an extended role, the  chosen FLRW is the Global Background Solution (GBS according to [39]) we need to check against  the physical metric g representing the phenomenological background solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In this section, we set  up the kinematical aspects for such a comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' First some standard verbiage for introducing the  FLRW model (M, ˆg, ˆγs(ˆτ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In terms of the radial,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' and angular FRLW coordinates yα :=  �  ˆr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ˆθ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ˆϕ  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  and of the proper time of the comoving fundamental observers y4 := ˆτ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' we set  �g  :=  −dˆτ 2 + a2(ˆτ)  �  dˆr2 + f 2(ˆr)  �  dˆθ2 + sin2 ˆθ d ˆϕ2��  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  �˙γ  h = δh  4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (40)  f(ˆr)  :=  \uf8f1  \uf8f4  \uf8f2  \uf8f4  \uf8f3  sin ˆr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  k = +1  ˆr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  k = 0  sinh ˆr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' k = −1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  where a(ˆτ) is the time-dependent scale factor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' k is the normalized dimensionless spatial curvature  constant,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' and �˙γ  h are the components of the 4-velocity �˙γ of the fundamental FLRW observers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ac-  cording to the above remarks, the geodesics τ �−→ γ(τ), and ˆτ �−→ ˆγ(ˆτ), −δ < τ, ˆτ < δ, associated  with the corresponding Hubble flow in (M, g, γ) and (M, ˆg, ˆγ), are assumed to be distinct, but  in line with the scale-dependent cosmographic approach adopted here we assume that they share  a common observational event p ∈ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We denote by  �  C −(p, ˆg) the associated FLRW past light  cone, and normalize the proper times τ and ˆτ along γ(τ) and ˆγ(ˆτ) so that at τ = 0 = ˆτ we  have γ(0) = p = ˆγ(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As stressed, the two instantaneous observers (p, ˙γ(0)) and (p, �˙γ(0)) have  different 4-velocities, ˙γ(0) ̸= �˙γ(0), and their respective celestial spheres, C S(p) and �  C S  2(p) are  quite distinct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' They are related by a Lorentz trasformation describing the aberration of the sky  mapping of one instantaneous observer with respect to the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This mapping will play a basic  role in our analysis, and to provide an explicit description of its properties, we start by adapting  to the FLRW instantaneous observer (p, �˙γ(0)) ∈ (M, ˆg, ˆγ) the setup characterizing the celestial  spheres C S(p) and C Sr(p) of the instantaneous observer (p, ˙γ(0)) ∈ (M, g, γ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The FLRW celestial sphere and the associated sky sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Let  �  �TpM, �gp, { �E(i)}  �  be  the tangent space to (M, ˆg, ˆγ) at p endowed with a �g-orthonormal frame { �E(i)}i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',4, �gp  �  �E(i), �E(k)  �  =  ηik, where ηik is the Minkowski metric, and where we identify �E(4) with the FLRW-observer’s 4-  velocity �˙γ(τ)|τ=0, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  �E(4) := �˙γ(τ)|τ=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' For ease of notation, we shall often use the shorthand  �TpM when referring to the tangent space to (M, ˆg, ˆγ) at p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Let  (41)  C− �  �TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' { �E(i)}  �  :=  �  Y = Yi �E(i) ̸= 0 ∈ �TpM | �gp(Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Y ) = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Y4 + �r = 0  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (42)  C−  �  �TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' { �E(i)}  �  :=  �  Y = Yi �E(i) ̸= 0 ∈ �TpM | �gp(Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Y ) ≤ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Y4 + �r ≤ 0  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  respectively denote the set of past-directed null vectors and the set of past-directed causal vectors  in ( �TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' { �E(i)}),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' where �r := (�3  a=1(Ya)2)1/2 is the radial coordinate (see (6)) in the hyperplane  Y4 = 0 ⊂ �TpM parametrizing the one-parameter family of 2-spheres  (43)  S2  �r( �TpM) := {Y ∈ C− �  �TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' { �E(i)}  �  | Y4 = − �r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  3  �  a=1  (Ya)2 = �r2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' �r ∈ R>0} ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  11  that foliate C− �  �TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' { �E(i)}  �  /{p}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The 2-spheres S2  �r( �TpM), endowed with the round metric  (44)  ��h(S2) = ��hαβ(S2)dyαdyβ = d�θ2 + sin2 �θ d�φ2 ,  0 ≤ �θ ≤ π, 0 ≤ �φ < 2π  can be thought of as providing a representation of the sky, at a given value of the radial coordinate  �r, in the instantaneous rest space  �  �TpM, { �E(i)}  �  of the FLRW observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  In analogy with the  characterization (8) of the celestial sphere C S(p),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' we use the projection of S2  �r( �TpM)  ���  �r=1 on the  hyperplane Y4 = 0 in �TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' to define the FLRW celestial sphere  (45)  �  C S(p)  �  S2  �r( �TpM)  ���  �r=1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ��h(S2)(p)  �  :=  �  Y = YiE(i) ̸= 0 ∈ �TpM | Y4 = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  3  �  a=1  (Ya)2 = 1  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  parametrizing the directions of sight  (46)  �n(�θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' �φ) := (cos �φ sin �θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' sin �φ sin �θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' cos �θ) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  0 ≤ �θ ≤ π,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 0 ≤ �φ < 2π  in the instantaneous rest space  �  �TpM,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' { �E(i)}  �  of the FLRW observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In full analogy with (16),  we define the FLRW celestial sphere at radius �r in  �  �TpM, { �E(i)}  �  according to  (47)  �  C S�r(p) :=  �  S2  �r  �  �TpM  �  , �r2��h(S2(p))  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  With a straightforward adaptation to the FLRW geometry of the definitions (10), (18), and (19),  we also introduce in �TpM the tetrad  (48)  �  �n, �m(2), �m(3), �ℓ(�n)  �  and associate with the pair  �  �T(�θ,�φ)S2 �  �TpM  �  , �m(α)(�θ, �φ)  �  the screen plane T�n �  C S(p) associated  with the direction of sight �n(�θ, �φ) in the FLRW celestial sphere �  C S(p),  (49)  T�n �  C S(p) :=  �  T(�θ,�φ)S2 �  �TpM  �  , �m(α)(�θ, �φ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Together with the observational normal coordinates {Xi} in (M, g, γ), describing the local geometry  on the past lightcone C −(p, g) ∩ Up, we introduce corresponding (normal) coordinates {Y k} on  the past light cone �  C −(p, ˆg) in the reference FLRW spacetime (M, ˆg, ˆγ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To begin with, let �  expp  denote the exponential mapping based at the event p = ˆγ(0), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  �  expp : �  Wp ⊆ �TpM  −→  (M, ˆg),  (50)  Y  �−→  expp (Y) := λY(1) ,  where �  Wp is the maximal domain of �  expp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To keep on with the notation set by (21) and (22), we  characterize the past lightcone �  C −(p, ˆg) ∈ (M, �g), with vertex at p, according to  (51)  �  C −(p, ˆg) := �  expp  �  �  Wp ∩ C− �  �TpM, �gp  ��  ,  and we denote by  �  C −(p, �g;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' �r0) :=  �  q ∈ M | q = �  expp(�r�ℓ(�n(�θ, �φ))), 0 ≤ �r < �r0, (�θ, �φ) ∈ �  C S(p)  �  ,  the portion of  �  C −(p, ˆg) accessible to observations for a given value �r0 of the radial parameter �r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  That said, if ˆUp ⊂ (M, ˆg) denotes the region of injectivity of �  expp, then normal coordinates are  12  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  defined by  (52)  yi := Yi ◦ �  exp−1  p  : (M, �g) ∩ �Up −→ R ,  where Yi are the components of the vectors Y ∈  �TpM with respect to a ˆg-orthonormal frame  { ˆE(i)}i=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',4 with ˆE(4) := ˆ˙γ(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We can parametrize �  C −(p, �g) ∩ �Up in terms of the 2-dimensional  FLRW sky sections  (53)  �Σ(p, ˆr) := �  expp  �  �  C S�r(p)  �  =  �  �  expp  �  �r �ℓ(�n(�θ, �φ))  � ��� (�θ, �φ) ∈ �  C S(p)  �  ,  endowed with the metric induced by the inclusion of �Σ(p, ˆr) into �  C −(p, ˆg), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (54)  �g|�Σ(p,ˆr) := (�g)αβ dyαdyβ���  ˆr = a2(�τ(�r)) f 2 (�r)  �  d�θ2 + sin2 �θd�φ2�  ,  where a(�τ(�r)) is the FLRW expansion factor a(�τ) (see (40)) evaluated in correspondence of the  given value of the radial coordinate �r ∈ �TpM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We proceed as in Subsection 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='2, and exploit the  exponential map �  expp to pull back �g|�Σ(p,ˆr) on the celestial sphere �  C S�r(p),  (55)  �h(�r, �θ, �φ) :=  �  �  exp∗  p �g|�Σ(p,�r)  �  αβ dyαdyβ  ����  �r  ,  α, β = 2, 3,  y2 := �θ, y3 := �φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  This pull-back can be explicitly computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To wit, let yi  q = (�rq, �θq, �φq, �τq) the normal coordinates  of the event q ∈  �  C −(p, ˆg) associated with the observation of a given astrophysical source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The  equation for the radial, past-directed, null geodesic connecting q to the observation event p reduces  in the FLRW case to [19]  (56)  d�r = − d�τ  a(�τ) ,  �τ(p) = 0 = �r(p) ,  that integrates to the expression providing the (matter-comoving) radial coordinate distance be-  tween p and q  (57)  �rq =  � �τq  0  d�τ  a(�τ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Thus, the metric (55), evaluated at �  expp  −1(q), can be written in terms of �τq as  (58)  �hq := �h(�rq, �θq, �φq) = a2(�τq) f 2 (�rq)  �  d�θ2  q + sin2 �θqd�φ2  q  �  ,  If we introduce the dimensionless FLRW cosmological redshift corresponding to the event q,  (59)  zq := z (�τq) =  a0  a(�τq) − 1 ,  where a0 := a(�τ = 0), then we can rewrite �h(�rq, �θq, �φq) as  (60)  �hq =  a2  0  (1 + zq)2 f 2 (�rq)  �  d�θ2  q + sin2 �θqd�φ2  q  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Note that the area element associated with the metric �hq,  (61)  dµ�hq =  a2  0  (1 + zq)2 f 2 (�rq) dµS2  characterizes the FLRW observer area distance (see (29)) of the event q ∈  �  C −(p, ˆg) according to  (62)  �D(�rq) =  a0  1 + zq  f (�rq) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  13  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Comparing the celestial spheres C S(p) and �  C S(p)  As stressed in the previous Section, the celestial sphere C S(p) of the phenomenological observer  (p, ˙γ(0)), and the celestial sphere �  C S(p) of the FLRW ideal observer (p, �˙γ(0)) cannot be directly  identified as they stand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The velocity fields ˙γ(0) and �˙γ(0) are distinct and to compensate for the  induced aberration, the celestial spheres C S(p) and �  C S(p) can be identified only up to Lorentz  boosts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In the standard FLRW view, this is the familiar global boost taking care of the kinematical  dipole component in the CMB spectrum due to our peculiar motion with respect to the standard  of rest provided by the CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' However, in a cosmographic setting and presence of a complex  pattern of local inhomogeneities coupled with a non-FLRW spacetime geometry over scales ≲  100h−1 Mpc, the peculiar motion of the phenomenological observer has a dynamical origin, driven  by the gravitational interaction and not just by a kinematical velocity effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Even if we factor out  the effect of coherent bulk flows due to the non-linear local gravitational dynamics, and average  the rate of expansion over spherical shells at increasing distances from (p, ˙γ(0)), the variance in  the peculiar velocity of (p, ˙γ(0)) with respect to the average rate of expansion is significant [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  These remarks imply that the Lorentz boosts connecting C S(p) and �  C S(p) acquire a dynamical  meaning that plays a basic role in what follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As a first step, we describe the Lorentz boost in  the idealized pure kinematical situation where we need to compensate for a well-defined velocity  field of the celestial sphere C S(p) with respect to the celestial sphere �  C S(p) taken as providing  a well-defined standard of rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As a second step, we move to the more general setting required  in the pre-homogeneity region where we sample scales ≲ 100h−1 Mpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In this latter case, a pure  kinematical Lorentz boost will not suffice, the large fluctuations in the sources distribution require  a suitable localization of the Lorentz boosts to compare the data on C S(p) with those on �  C S(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The kinematical setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To describe a kinematical Lorentz boost acting between �  C S(p)  and C S(p), we find it convenient to use in this section the well-known correspondence between  the restricted Lorentz group and the six-dimensional projective special linear group PSL(2, C)  describing the automorphisms of the Riemann sphere S2 ≃ C ∪ {∞}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' More expressively, PSL(2, C)  can be viewed as the group of the conformal transformations of the celestial spheres that correspond  to the restricted Lorentz transformations connecting C S(p) to �  C S(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In oder to set notation, let us  recall that the elements of PSL(2, C) can be identified with the set of the M¨obius transformations  of the Riemann sphere S2 ≃ C ∪ {∞}, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' the fractional linear transformations of the form  ζ : C ∪ {∞}  −→  C ∪ {∞}  (63)  w  �−→  ζ(w) := aw + b  cw + d ,  a, b, c, d ∈ C , ad − bc ̸= 0 ,  where, to avoid a notational conflict with the redshift parameter z, we have labeled the complex  coordinate in C ∪ {∞} with w rather than with the standard z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Let Y = �n(�θ, �φ) denote a point on  the celestial sphere �  C S(p), and let �w denote its stereographic projection10 on the Riemann sphere  C ∪ {∞}, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',  PS2 : �  C S(p) −→ C ∪ {∞}  (64)  Yα �−→ PS2(Yα) = �w := Y1 + i Y2  1 − Y3  = cos �φ sin �θ + i sin �φ sin �θ  1 − cos �θ  ,  with 0 < θ ≤ π, 0 ≤ φ < 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It is worthwhile to stress once more that the celestial spheres �  C S(p)  and C S(p) play the role of a mapping frame, a celestial globe where astrophysical positions are  registered, and where the Lorentz boost �  C S(p) −→ C S(p) must be interpreted actively as affecting  only the recorded astrophysical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In other words, the Lorentz boost affects the null directions  10From the north pole θ = 0 ∈ �  C S(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  14  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  in �  C S(p), mapping them in the corresponding directions in C S(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To quote a few illustrative  examples [46] of the PSL(2, C) transformations associated to the Lorentz group action between  the celestial spheres �  C S(p) and C S(p), let v denote the modulus of the relative 3-velocity of the  FLRW ideal observer (p, �˙γ(0)) with respect to the phenomenological observer (p, ˙γ(0)), (where  E4 is identified with the observer’s 4-velocity ˙γ(0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' If the map between �  C S(p) and C S(p) is a  pure Lorentz boost in a common direction, say E3, then the associated PSL(2, C) transformation  is provided by  PSL(2, C) × �  C S(p)  −→  C S(p)  (65)  (ζ boost, �w)  �−→  ζ( �w) = w =  �  1 + v  1 − v �w ,  where  �  1 + v  1 − v is the relativistic Doppler factor and w is the point in the Riemann sphere corre-  sponding, under stereographic projection, to the direction n(θ, φ) ∈ C S(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Similarly, if �  C S(p) and  C S(p) differ by a pure rotation through an angle α about the E3 direction, then the associated  PSL(2, C) transformation is given by  PSL(2, C) × �  C S(p)  −→  C S(p)  (66)  (ζ rot, �w)  �−→  ζ( �w) = w = ei α �w .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (67)  By composing them, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' by considering a rotation through an angle α about the E3 direction,  followed by a boost with rapidity β := log  �  1 + v  1 − v along the E3 axis, we get  PSL(2, C) × �  C S(p)  −→  C S(p)  (68)  (ζ, �w)  �−→  ζ( �w) = w =  �  1 + v  1 − v ei α �w ,  describing the general fractional linear transformation mapping �  C S(p) and C S(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' From the phys-  ical point of view, this corresponds to the composition of the adjustment of the relative orienta-  tion of the spatial bases {E(α)} with respect to { �E(α)}, α = 1, 2, 3, followed by a Lorentz boost  adjusting for the relative velocity of (p, ˙γ(0)) with respect to (p, �˙γ(0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since the spatial direc-  tions n(θ, φ) ∈ C S(p) and �n(�θ, �φ) ∈ �  C S(p) characterize corresponding past-directed null vectors  ℓ(θ, φ) ∈  �  TpM, {E(i)}  �  and �ℓ(�θ, �φ) ∈  �  �TpM, { �E(i)}  �  (see (10) and (48)), we can associate with  the spatial directions {E(α)} and { �E(α)} the respective null directions  ℓ(α)  =  E(α) − E(4) = E(α) − ˙γ(0) ,  (69)  �ℓ(α)  =  �E(α) − �E(4) = �E(α) − �˙γ(0) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The pre-homogeneity setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' From the above remarks, it follows that the Lorentz map-  ping from �  C S(p) to C S(p) is fully determined if we specify the three distinct null directions on the  FLRW celestial sphere �  C S(p) that are the images, under the PSL(2, C)-transformation, of three  chosen distinct sources on C S(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The selection of these three distinct sources of choice and of the  corresponding null directions on C S(p) will depend on the scale L we are probing in our cosmo-  logical observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This is a particularly delicate matter when looking at the pre-homogeneity  scales L ≲ 100 h−1 Mpc, where astrophysical sources are characterized by a complex distribution of  peculiar velocities with respect to the assumed Hubble flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To keep track of this scale dependence,  let us consider the celestial spheres C Sr(p) and �  C S�r(p) defined by (16) and (47), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' For  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  15  L > 0, let �r(L) be the value of �r such that the FLRW sky section (53)  (70)  �Σ(p, ˆr(L)) := �  expp  �  �  C S�r(L)(p)  �  =  �  �  expp  �  �r(L) �ℓ(�n(�θ, �φ))  � ��� (�θ, �φ) ∈ �  C S(p)  �  ,  probes the length scale L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Similarly, we let r(L) denote the value of r such that the physical sky  section (71)  (71)  Σ(p, r(L)) := expp  �  C Sr(L)(p)  �  =  �  expp (r(L) ℓ(n(θ, φ)))  �� (θ, φ) ∈ C S(p)  �  ,  probes the length scale L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since the FLRW area distance (62),  (72)  �D(�r) =  a0  1 + z f (�r) ,  is isotropic and may be directly expressed in terms of z, we may well use the redshift parameter  z as the reference L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Given z, we denote by L(z) the corresponding length-scale of choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As  long as �D(�r) is an increasing function, we can identify L(z) with the area distance �D(�r), but in  general, we leave the selection of the most appropriate L(z) to the nature of the cosmographical  observations one wants to perform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Given ζ ∈ PSL(2, C) and a value of the redshift z, we have a  corresponding relation between the ”radial” variables �r(L(z)) and r(L(z)) in (70) and (71).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We can  take advantage of this relation to simplify the notation for the celestial spheres and the associated  sky sections according to  (73)  �  C Sz(p) := �  C S�r(L(z))(p) =⇒ �Σz := �Σ(p, ˆr(L(z))) := �  expp  �  �  C Sz(p)  �  ,  and  (74)  C Sz(p) := C Sr(L(z))(p) =⇒ Σz := Σ(p, r(L(z))) := expp [C Sz(p)] ,  a notation that, if not otherwise stated, we adopt henceforth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since in the pre-homogeneity region  L(z) ≲ 100 h−1 Mpc, the large variance in peculiar velocities of the astrophysical sources implies a  great variability in the selection of the three reference null directions that fix the PSL(2, C) action,  we localize this action according to the following construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  We assume that there is a finite collection of points {y(I)} ∈ �  C Sz(p) and a corresponding  collection of open disks { �B(y(I), δ)} of radius δ, centered at the points {y(I)}, and defined  by  (75)  �B(y(I), δ) := {y′ ∈ �  C Sz(p) | dS2(y′, y(I)) ≤ δ} ⊂ �  C Sz(p)  where dS2(y′, y(I)) denotes the distance in the round unit metric on S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We also assume that  any such �B(y(I), δ) contains the images of three reference astrophysical sources of choice, call  them A(I, k), k = 1, 2, 3,, with celestial coordinates in �  C Sz(p) given by y(I, k) =: �n(I, k)(�θ, �φ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  We adopt a similar partition on the celestial sphere C Sz(p), to the effect that associated  with each disk �B(y(I), δ) there is, in C Sz(p), a corresponding metric disk  (76)  B(x(y(I)), δ) = {x′ ∈ C Sz(p) | dS2(x′, x(y(I))) ≤ δ} ⊂ C Sz(p) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  We require that the images A(I, k) of the three reference astrophysical sources of choice,  that in �B(y(I), δ) have celestial coordinates y(I, k), are represented in B(x(y(I)), δ) by three  distinct points with celestial coordinates x(I, k) =: n(I, k)(θ, φ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  We further assume that the past null directions �ℓ(I, k) = �n(I, k)(�θ, �φ) − �˙γ(0), associated with  the location of the reference sources A(I, k) in the portion of the celestial sphere �B(y(I), δ) ∩  16  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  �  C Sz(p),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' are related to the corresponding null directions ℓ(I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' k) = n(I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' k)(θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' φ) − ˙γ(0),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' locating  the sources A(I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' k) in B(x(y(I)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' δ) ∩ C Sz(p),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' by the PSL(2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' C) map  ζ(I) : �B(y(I),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' δ) ∩ �  C Sz(p)  −→  B(x(y(I)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' δ) ∩ C Sz(p)  (77)  �w  �−→  ζI( �w) = w =  �  1 + v  1 − v ei α(A(I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' k)) �w ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  where  �  1 + v  1 − v ei α(A(I,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' k)) is the composition of the Lorentz boost (v being the relative 3-  velocity of ˙γ(0) with respect to �˙γ(0)) and of the spatial rotation that,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' at the given scale  L(z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' allow us to align the portion of the celestial sphere C Sz(p) described by B(x(y(I)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' δ)  with the portion of the FLRW celestial sphere �  C Sz(p) described by �B(y(I),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Finally, we require that the finite collections of celestial coordinate bins { �B(y(I), δ)} and  �  B(x(y(I)), δ)  �  cover the respective celestial spheres �  C Sz(p) and C Sz(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  It is worthwhile to stress that the collections of bins { �B(y(I), δ)} and  �  B(x(y(I)), δ)  �  can be chosen  in many distinct ways, according to the cosmographic observations one wishes to carry out (we use  disks for mathematical convenience).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Whatever choice of the above type we make, we can extend the  localized PSL(2, C) maps (77) by using a smooth partition of unity  �  χ(I)  �  subordinated to the finite  covering { �B(y(I), δ)} of �  C Sz(p), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' a collection of smooth functions χ(I) : �B(y(I), δ) −→ [0, 1]  whose support is such that supp χ(I) ⊆ �B(y(I), δ) and such that �  y∈ �  C Sz(p) χ(I)(y) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We define  the localized PSL(2, C) map connecting, at scale L(z), the celestial spheres �  C Sz(p) and C Sz(p),  decorated with the respective coordinate bins { �B(y(I)} and {B(x(y(I)), δ)}, according to  ζ(z) : �  C Sz(p)  −→  C Sz(p)  (78)  �w  �−→  ζ(z)( �w) :=  �  y∈ �  C Sz(p)  χ(I)(y) ζ(I)(w) ,  where ζ(I)(w) is provided by (77).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Note that, when necessary, this localized PSL(2, C) map can  be further generalized by completing it in the Sobolev space of maps which together with their  derivatives are square-summable over �  C Sz(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This completion requires some care which we do not  enter here (see [12] for details), and it is needed when discussing the distance between the FLRW  and the cosmographic lightcones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  It is worthwhile to stress that in the pre-homogeneity region L(z) ≲ 100 h−1 Mpc, the large  variance in peculiar velocities of the astrophysical sources implies a great variability in the selection  of the three reference null directions that fix the local PSL(2, C) action characterizing the map ζ(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  This implies that ζ(z) may vary considerably with L(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Recall that the role of the celestial spheres  C Sz(p) and �  C Sz(p) is simply that of representing past null directions at the observational event  p ∈ M, directions that respectively point to the astrophysical sources on the sky section Σz, as  seen by (p, ˙γ(0)), and on �Σz, as seen according to (p, �˙γ(0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' These data are transferred from these  sky sections to the respective celestial spheres through null geodesics, thus we can associate with  the localized PSL(2, C) action the map between the sky sections �Σz and Σz given by  ψ(z) : �Σz  −→  Σz  (79)  q  �−→  ψ(z)(q) := expp ◦ ζ(z) ◦ �  exp −1  p (q) ,  for any point q ∈ �Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  17  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The comparison between the screen planes T�n�  C Sz(p) and TnC Sz(p)  The localized PSL(2, C) map ζ(z) induces a corresponding map between the screen plane T�n �  C S(p)z  associated with the direction of sight �n(�θ, �φ) in the FLRW celestial sphere �  C Sz(p) (see (49)), and  the screen plane TnC Sz(p) associated with the direction of sight n(θ, φ) = ζ(z)  �  �n(�θ, �φ)  �  in the  celestial sphere C Sz(p) (see (19)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The geometry of this correspondence is quite sophisticated since  it is strictly related to harmonic map theory and it will be described here in some detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To begin  with, we denote by T �  C Sz and by TC Sz the screen bundles associated with the screen planes on  �  C Sz(p) and C Sz(p), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' These are just two copies of the usual tangent bundle TS2 of the  2-sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' If there is no danger of confusion, we use both notations in what follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Under such  notational assumptions, we can associate with the map (78),  (80)  ζ(z) : �  C Sz(p) −→ C Sz(p) ,  the pull–back bundle ζ−1  (z) TC Sz whose sections v ≡ ζ−1  (z)V := V ◦ζ(z), V ∈ C∞(C Sz(p), TC Sz), are  the vector fields over C Sz(p) covering the map ζ(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In physical terms, the vectors v are the tangent  vector on the celestial sphere C Sz(p) that describe the (active) effect of the combination of rotation  and Lorentz boost induced by ζ(z) on the null direction �ℓ(�n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' More expressively, let us remark that  for a given direction of sight ζ(z)(�n) = n(θ, φ) ∈ C Sz(p), the vectors V ∈ TnC Sz(p) can be used  to describe the geometrical characteristics of the astrophysical images on the screen TnC Sz(p), for  instance, the apparent diameters of the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, the vectors v ≡ ζ−1  (z)V := V ◦ ζ(z), sections of  the pull–back bundle ζ−1  (z) TC Sz, can be interpreted as transferring the ”images” of the screens in  TC Sz back to �  C Sz(p) so as to be able to compare them with the reference screen-shots in T �  C Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  In terms of the local coordinates ya :=  �  �θ, �φ  �  , a = 1, 2, on �  C Sz(p) (see (52))11, we can write the  section v ≡ ζ−1  (z)V := V ◦ ζ(z) as12  (81)  C Sz(p) ∋ ya �−→ v(ya) = vb(y)  ∂  ∂ζb  (z)(y) ∈ ζ−1  (z)TC Sz  ���  y ,  where ζb  (z)(y), b = 1, 2, are the coordinates of the point (direction of sight) in ζ(z)(y) ∈ C Sz(p)  given, in terms of the ya by (64).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, if T ∗ �  C Sz denotes the cotangent bundle to �  C Sz(p),  we can locally introduce the differential  (82)  dζ(z) =  ∂ζb  (z)  ∂ya dya ⊗  ∂  ∂ζb  (z)  ,  and interpret it as a section of the product bundle T ∗�[C S]z ⊗ ζ−1  (z) TC Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To provide a comparison  between the geometrical information gathered from the astrophysical data, let us recall that on the  screens T �  C Sz and TC Sz we have the inner products respectively defined by the pull-back metrics  (55) and (27), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (83)  �h(�r(L(z)), �θ, �φ) :=  �  �  exp∗  p �g|�Σz  �  ab dyadyb���  �r(L(z)) ,  a, b = 1, 2,  y1 := �θ, y2 := �φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  and  (84)  h(r(L(z)), θ, φ) :=  �  exp∗  p g|Σz  �  ab dxadxb���  r(L(z)) ,  a, b = 1, 2,  x1 := θ, x2 := φ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  11In what follows the (�θ, �φ), corresponding to (y2, y2) in the normal coordinates string {yα}, are relabelled as  {ya}, with a = 1, 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' a similar relabeling is also adopted for the normal coordinates (θ, φ) on C Sz(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  12In what follows we freely refer to the excellent [22], [32], and [36] for a detailed analysis of the geometry of the  computations involved in harmonic map theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  18  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  The Riemannian metric in the pull-back screen  �  ζ−1  (z) TC Sz  �  y over y ∈ �  C Sz(p) is provided by  h(ζ(z)(y)), hence the tensor bundle T ∗ �  C Sz ⊗ ζ−1  (z) TC Sz over the celestial sphere �  C Sz(p) is endowed  with the pointwise inner product  (85)  ⟨·, ·⟩T ∗�[C S]z⊗ζ−1  (z) TC Sz := �h−1(y) ⊗ h(ζ(z)(y))(·, ·) ,  where �h−1(y) := �hab(y) ∂a ⊗ ∂b is the metric tensor in T ∗  y �  C Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The corresponding Levi-Civita  connection will be denoted by ∇⟨,⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Explicitly, if W = W b  a dya ⊗  ∂  ∂ζb  (z) is a section of T ∗ �  C Sz ⊗  ζ−1  (z) TC Sz, the covariant derivative of W in the direction  ∂  ∂yb is provided by  ∇⟨,⟩  b W = ∇⟨,⟩  b  �  W c  a dya ⊗  ∂  ∂ζc  (z)  �  (86)  =  ∂  ∂yb W c  a dya ⊗  ∂  ∂ζc  (z)  + W c  a  �  �∇b dya�  ⊗  ∂  ∂ζc  (z)  + W c  a dya ⊗ ∇∗  b  �  ∂  ∂ζc  (z)  �  ,  where �∇ denotes the Levi–Civita connection on ( �  C Sz(p), �h), and ∇∗ is the pull back on ζ−1  (z) TC Sz of  the Levi–Civita connection of (C Sz, h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' If �Γa  bc(�h) and Γa  bc(h) respectively denote the Christoffel sym-  bols of ( �  C Sz(p), �h) and (C Sz(p), h), then �∇b dya = − �Γa  bc(�h) dyc and ∇∗  b  �  ∂  ∂ζc  (z)  �  =  ∂ζi  (z)  ∂yb Γk  ci(h)  ∂  ∂ζk  (z) ,  and one computes  (87)  ∇⟨,⟩  b W =  �  ∂  ∂yb W i  a − W i  c�Γc  ba(�h) + W k  a  ∂ζj  (z)  ∂yb Γi  kj(h)  �  dya ⊗  ∂  ∂ζi  (z)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  These remarks on the geometry of the map (80) allow us to compare the data on the screens TC Sz  and T �  C Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' For this purpose, the relevant quantity is the norm, evaluated with respect to the inner  product (85), of the differential (82) of the PSL(2, C) map ζ(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Direct computation provides  e(�h, ζ(z);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' h)  :=  ⟨dζ(z), dζ(z)⟩T ∗�[C S]z⊗ζ−1  (z) TC Sz  (88)  =  �hab(y)  ∂ζi  (z)(y)  ∂ya  ∂ζj  (z)(y)  ∂yb  hij(ζ(z)(y)) = tr�h(y) (ζ∗  (z) h) ,  where tr�h(y) (ζ∗  (z) h) denotes the trace, with respect to the metric �h of the pull-back metric ζ∗  (z) h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  In other words, at any point y, e(�h, ζ(z);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' h)(y) is the sum of the eigenvalues of the metric ζ∗  (z) h,  thus providing the sum of the squares of the length stretching generated by the (pull-back of) the  physical metric ζ∗  (z) h along the orthogonal directions (�θ, �φ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To such stretching, we can associate  the tension field of the map ζ(z), defined by  (89)  τ i(ζ(z)) := ∆(�h) ζi  (z) + �hkj Γi  ab(h)  ∂ζa  (z)  ∂yk  ∂ζb  (z)  ∂yj .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  To provide some intuition on these geometrical quantities, we can adapt to our case a nice heuristic  remark by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Eells and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Lemaire described in their classical paper on harmonic map theory [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Let us imagine the FLRW celestial sphere ( �  C Sz(p), �h) as a rubber balloon, decorated with dots  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  19  representing the astrophysical sources recorded from the sky section �Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  This balloon has the  geometry described by the round metric �h(z, �θ, �φ) defined by (83), explicitly (see (60))  (90)  �h(�r(z), �θ, �φ) =  a2  0  (1 + zL)2 f 2 (�r(z))  �  d�θ2 + sin2 �θd�φ2�  ,  where zL is the redshift associated with the length scale L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Conversely, let us imagine the physical  celestial sphere (C Sz(p), h) as a rigid surface with the geometry induced by the metric h(r(z), θ, φ)  defined by (84), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=', (see (30)),  h (r(z), θ, φ)  (91)  = D2(r(z), θ, φ)  �  dθ2 + sin2 θdφ2 + Lab(r(z), θ, φ) dxadxb�  ,  x1 := θ, x2 := φ ,  providing the geometric landscape of the astrophysical sources reaching us along null geodesics  from the physical sky section Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We can think of the PSL(2, C) map ζ(z) as stretching the elastic  surface ( �  C Sz(p), �h) on the rigid surface (C Sz(p), h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The purpose of this stretching is to overlap the  images of the astrophysical sources recorded on ( �  C Sz(p), �h) with the images of the corresponding  sources as registered on (C Sz(p), h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In general, this overlap is not successful without stretching  the surface, and to any point y ∈ ( �  C Sz(p), �h) we can associate a corresponding vector measuring  the stretch necessary for connecting the images of the same source on the two celestial spheres13  ( �  C Sz(p), �h) and (C Sz(p), h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To leading order, the required stretching is provided by the tension  vector τ i(ζ(z), y) at y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Both the Hilbert-Schmidt norm (88) and the tension vector field (89) of  the map ζ(z) are basic quantities in harmonic map theory, and to understand the strategy we will  follow in comparing, at a given length scale L, the FLRW past light cone �C(p, �g) with the physical  observational past light cone C(p, g) we need to look into the harmonic map theory associated with  ζ(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Let us start by associating with ⟨dζ(z), dζ(z)⟩T ∗�[C S]z⊗ζ−1  (z) TC Sz the density  (92)  e(�h, ζ(z), h) dµ�h := ⟨dζ(z), dζ(z)⟩T ∗�[C S]z⊗ζ−1  (z) TC Sz dµ�h = tr�h(y) (ζ∗  (z) h) dµ�h ,  where dµ�h is the volume element defined by the metric �h on the FLRW celestial sphere �  C Sz(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' An  important property of the density e(�h, ζ(z);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' h) dµ�h is that it is invariant under the two-dimensional  conformal transformations  (93)  ( �  C Sz(p), �hab) �−→ ( �  C Sz(p), e−f �hab) ,  where f is a smooth function on �  C Sz(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In this connection, it is worthwhile to recall that conformal  invariance is strictly related to the action of the Lorentz group on the celestial spheres (and it is  ultimately the rationale for the relation between Lorentz transformations and the fractional linear  transformations of PSL(2, C)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The expression 1  2 e(�h, ζ(z);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' h) dµ�h characterizes the harmonic map energy functional associated to  the map ζ(z), viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (94)  E[�h, ζ(z), h] := 1  2  �  �  C Sz  e(�h, ζ(z), h) dµ�h .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  It is worthwhile to put forward a more explicit characterization of the nature of the harmonic map  functional E[�h, ζ(z);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' h] by making explicit, together with the celestial spheres �  C Sz(p) and C Sz(p),  13This is not to be confused with the phenomenon of strong gravitational lensing that occurs in a given celestial  sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It is simply a mismatch due to the comparison between the description of the same astrophysical source on  two distinct celestial spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  20  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  the role of the corresponding sky sections �Σz and Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To this end, let us consider the map (79)  acting between the sky sections �Σz and Σz,  ψ(z) : (�Σz, �g|ˆΣz)  −→  (Σz, g|Σz)  (95)  y  �−→  ψ(z)(q) := expp ◦ ζ(z) ◦ �  exp −1  p (y) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The corresponding harmonic map functional is provided by  (96)  E  �  �g(z), ψ(z), g(z)  �  := 1  2  �  �Σz  (�g(z))ab ∂ψi  (z)(y)  ∂ya  ∂ψk  (z)(y)  ∂yb  (g(z))ik dµ�g(z)  where, for notational ease, we have set �g(z) := �g ˆΣz and g(z) := g Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We can equivalently write  E  �  �g(z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ψ(z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' g(z)  �  in terms of pull-backs of the relevant maps,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' and get the following chain of relations  E  �  �g(z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ψ(z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' g(z)  �  =  1  2  �  �Σz  (�g(z))ab �  ψ∗  (z)g(z)  �  ab dµ�g(z)  (97)  =  1  2  �  �  expp( �  C Sz)  (�g(z))ab �  ψ∗  (z)g(z)  �  ab dµ�g(z)  =  1  2  �  �  C Sz  �  expp  ∗ �  (�g(z))ab �  ψ∗  (z)g(z)  �  ab  �  �  expp  ∗(dµ�g(z))  =  1  2  �  �  C Sz  �hab �  �  expp  ∗ �  ψ∗  (z)g(z)  ��  ab dµ�h  =  1  2  �  �  C Sz  �hab �  �  expp  ∗ �  expp ◦ ζ(z) ◦ �  exp −1  p  �∗  g(z)  �  ab dµ�h  =  1  2  �  �  C Sz  �hab �  ζ∗  (z)h  �  ab dµ�h = E[�h,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ζ(z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' h] ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  from which it follows that the harmonic map energy functional associated with the localized  PSL(2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' C) map ζ(z) and with the map ψ(z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' defined by (95),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' can be identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This is not sur-  prising since ψ(z) := expp ◦ ζ(z) ◦ �  exp −1  p  can be seen as the representation of ζ(z) on the sky  sections �Σz := �  expp  �  �  C Sz(p)  �  and Σz := expp (C Sz(p)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' From the conformal nature of the map  ζ(z) : �  C Sz(p) −→ C Sz(p), it follows that ψ(z) acts as a conformal diffeomorphism between ˆΣz  and Σz as long as the exponential maps are diffeomorphisms from �  C Sz(p) and C Sz(p) onto their  respective images �Σz and Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Later we shall see how this result can be extended, under suitable  hypotheses, to the less regular case of Lipschitzian exponential map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Here, we restrict our attention  to the stated regularity assumptions on the exponential maps �  expp and expp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' They imply that the  sky sections ˆΣz and Σz have the topology of a 2-sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Moreover, we can take advantage of the fact  that (�Σz, �g(z)) is a (rescaled) round sphere, thus we can apply the Poincar´e–Koebe uniformization  theorem, to the effect that there is a positive scalar function Φ�Σ Σ ∈ C∞(�Σz, R>0) such that  (98)  �  ψ∗  (z)g(z)  �  ab =  ∂ψi  (z)(y)  ∂ya  ∂ψk  (z)(y)  ∂yb  (g(z))ik = Φ2  �Σ Σ (�g(z))ab .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The required conformal factor Φ�Σ Σ ∈ C∞(�Σz, R>0) is the solution, (unique up to the PSL(2, C)  action on (�Σz, �g(z))), of the elliptic partial differential equation on (�Σz, ˆg(z)) defined by [2]  (99)  − ∆�g(z) ln(Φ2  �ΣΣ) + R(�g(z)) = R(ψ∗  (z)g(z)) Φ2  �ΣΣ ,  where ∆�g(z) := �gab  (z)∇a∇b is the Laplace-Beltrami operator on (�Σz, ˆg(z)), and where we respectively  denoted by R(�g(z)) and R(ψ∗  (z)g(z)) the scalar curvature of the metrics �g(z) and ψ∗  (z)g(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Notice that  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  21  the scalar curvature R(ˆg(z)) is associated with the metric (60) evaluated for �r = �r(L) and hence is  given by the constant R(ˆg(z)) =  �  a2  0  (1 + z)2 f 2 (�r)  �−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Similarly, R(g(z)) is associated with the metric  (30) evaluated for r = r(z), and as such it depends on the area distance D2(r(z), θ, φ) and the  lensing distortion Lab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  By tracing (98) with respect to �gab  (z), we get tr�g(z)(y)  �  ψ∗  (z)g(z)  �  = 2Φ2  �Σ Σ, and we can wite  (100)  Φ2  �ΣΣ = 1  2 tr�g(z)(y)  �  ψ∗  (z)g(z)  �  = 1  2 �gab  (z)  ∂ψi  (z)(y)  ∂ya  ∂ψk  (z)(y)  ∂yb  (g(z))ik .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  From (98) we also get det  �  ψ∗  (z)g(z)  �  = Φ4  �ΣΣ det(�g(z)), hence we can equivalently express the  conformal factor Φ2  �ΣΣ as the Radon-Nikodym derivative of the Riemannian measure dµψ∗g(z) :=  ψ∗  (z)dµ of the pulled back metric ψ∗  (z)g(z) on the sky section �Σz, with respect to the Riemannian  measure dµ�g(z) of the round metric �g(z) on �Σz, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',  (101)  Φ2  �ΣΣ =  dµψ∗  (z)g(z)  dµ�g(z)  =  ψ∗  (z)dµg(z)  dµ�g(z)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Directly from this latter relation and from E  �  �g(z), ψ(z), g(z)  �  = E  �  �h, ζ(z), h  �  (see (97)), we get  (102)  E  �  �h, ζ(z), h  �  =  �  �Σz  Φ2  �ΣΣ dµˆh ,  which expresses the harmonic map functional E  �  �h, ζ(z), h  �  in terms of the conformal factor Φ2  �ΣΣ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  As the PSL(2, C)-localized map ζ(z) varies with the scale L(z), relation (102) shows that E  �  �h, ζ(z), h  �  describes the ζ(z)-dependent total ”energy” associated with the conformal stretching of ( �  C Sz(p), �h)  over (C Sz(p), h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' A local expression for Φ2  �ΣΣ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It is worthwhile to provide a local expression for Φ2  �ΣΣ show-  ing the explicit dependence from the celestial coordinates (θ, φ), the area distances �D(�r(L)),  D(r(L), θ, φ), and the distortion tensor L (see (30)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We proceed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Let us consider one  of the coordinate bin �B(y(I), δ) (see (75)) in the celestial sphere �  C Sz(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' For y = (r(z), �θ, �φ) ∈  �B(y(I), δ) let q := �  expp(y) the point in the sky section �Σz reached, at the scale L(z), along the  past-directed null geodesics associated with the observational direction y = (�θ, �φ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' From the ex-  pression (101) of the conformal factor Φ2  �ΣΣ in terms of the measure ψ∗  (z)dµg(z) we get, by massaging  pull-backs,  Φ2  �ΣΣ dµ�g(z)(q)  =  ψ∗  (z)dµg(z)(q)  (103)  =  �  expp ◦ ζ(z) ◦ �  exp −1  p  �∗  dµg(z)  =  (�  exp −1  p )∗(ζ∗  (z)dµh)  ⇒  �  exp∗  p  �  Φ2  �ΣΣ dµ�g(z)(q)  �  = ζ∗  (z)dµh(y)  Φ2  �ΣΣ(y) dµ�h(y)  =  ζ∗  (z)dµh(y) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  22  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  Hence, on ( �  C S(p), �h), we need to compute the Radon-Nicodym derivative  (104)  Φ2  �ΣΣ(y) =  ζ∗  (z)dµh  dµ�h  (y) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  If we take into account the characterization  �  det(h(r(z), θ, φ)) = D2(r(z), θ, φ)  �  det(�h(S2)) of  the area distance D2(r(z), θ, φ) (see (29)), we compute  (105)  ζ∗  (z)dµh(y) =  ��Jacy(ζ(z))  �� D2(y) dµS2 ,  where |Jacy(ζ(z))| is the Jacobian determinant associated with the localized PSL(2, C) map ζ(z),  and where D2(y) is a shorthand notation for the area distance D2(ζ(z)(�r(z), �θ, �φ)) pulled back at y ∈  ( �  C Sz(p), �h) by the localized ζ(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Similarly, from (61) we compute dµ�h(y) =  a2  0  (1 + zL)2 f 2 (�r(L)) dµS2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Thus, we can write  (106)  Φ2  �ΣΣ(�r(z), �θ, �φ) =  ���Jac  �  ζ(z)(�r(z), �θ, �φ)  ����  D2(ζ(z)  �  �r(z), �θ, �φ)  �  (1 + z)2  a2  0 f 2 (�r(z))  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  In terms of the FLRW area distance  (107)  �D(�r(z)) =  a0  1 + z f (�r) ,  we can equivalently write (106) in the simpler form (where, to have handy the formula for later  use, we have taken the square root)  (108)  Φ�ΣΣ(�r(z), �θ, �φ) =  ���Jac  �  ζ(z)(�r(z), �θ, �φ)  ����  1  2 D  �  ζ(z)(�r(z), �θ, �φ)  �  �D(�r(z))  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  This clearly shows that the conformal factor Φ�ΣΣ is an explicit and, at least in principle, measurable  quantity associated with the local Lorentz mapping (described by the localized PSL(2, C) map  ζ(z)) needed for adjusting the three reference null directions in the chosen celestial coordinates  bin �B(y(I), δ) in the celestial sphere �  C Sz(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  This adjustment allows to transfer to �B(y(I), δ)  the actual area distance, namely, compute D(ζ(z)(�r(z), �θ, �φ)), and compare its distribution on the  FLRW celestial sphere �  C Sz(p) with respect to the isotropic FLRW area distance �D(�r(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The  anisotropies in the angular distribution with respect to �D(�r(z)) give rise to fluctuations in Φ�ΣΣ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  It may appear somewhat surprising that, after all, the conformal factor does not explicitly depend  also from the distortion tensor Lab defined by (30).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This dependence is implicit in the definition  of the area distance (29) and of the coordinate parametrization (30) characterizing Lab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' These  definitions give rise to the relation (34) that, as can be easily checked, remove the explicit Lab  dependence from Φ�ΣΣ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As we shall see, this fact will turn to our advantage when extending our  analysis to the more general case of fractal-like sky sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The sky section comparison functional at scale L  The harmonic energy E  �  �h, ζ(z), h  �  , or equivalently E  �  �g(z), ψ(z), g(z)  �  , associated with the maps  ζ(z) and ψ(z), cannot be used directly as comparison functional between the sky sections (�Σz, �g(z))  and (Σz, g(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This follows directly as a consequence of the conformal invariance (93) which implies  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  23  E  �  �g(z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ψ(z),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' g(z)  �  = 1  2  �  �Σz  (�g(z))ab ∂ψi  (z)(y)  ∂ya  ∂ψk  (z)(y)  ∂yb  (g(z))ik dµ�g(z)  (109)  = 1  2  �  �Σz  �  a2  0 f 2 �  �r(z)  �  (1 + zL)2  �−1  (��h(S2))ab ∂ψi  (z)(y)  ∂ya  ∂ψk  (z)(y)  ∂yb  (g(z))ik  �  a2  0 f 2 �  �r(z)  �  (1 + zL)2  �  dµS2  = 1  2  �  �Σz  (��h(S2))ab ∂ψi  (z)(y)  ∂ya  ∂ψk  (z)(y)  ∂yb  (g(z))ik dµS2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  where,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' as usual,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ��h(S2)) is the round metric on the unit 2-sphere S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' From the above relation it  follows that E  �  �g(z), ψ(z), g(z)  �  , (and similarly for E  �  �h, ζ(z), h  �  ), does not depend from the area  distance  a2  0  (1 + z)2 f 2 (�r(z)) on the FLRW past lightcone �C−(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, E  �  �g(z), ψ(z), g(z)  �  cannot be a  good candidate for the role of the functional that compares the sky sections (�Σz, �g(z)) and (Σz, g(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  For this role, we introduced in [12] a functional whose structure was suggested by the rich reper-  toire of functionals used in the problem of comparing shapes of surfaces in relation to computer  graphic and visualization problems (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' [35] and [28], to quote two relevant papers in a vast  literature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, we were inspired by an energy functional introduced, under the name of  elastic energy, in a remarkable paper by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Hass and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Koehl [29], who use it as a powerful means  of comparing the shapes of genus-zero surfaces in problems relevant to surface visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  In the more complex framework addressed in cosmography, we found it useful to define the sky  section comparison functional at scale L(z) according to  (110)  E�ΣΣ[ψ(z)] :=  �  �Σz  (Φ�ΣΣ − 1)2 dµˆg(z) ,  that can be, more expressively, rewritten as (see (108))  (111)  E�ΣΣ[ψ(z)] :=  �  �Σz  \uf8ee  \uf8ef\uf8f0  ��Jac  �  ζ(z)(�r(z))  ���  1  2 D  �  ζ(z)(�r(z), �θ, �φ)  �  − �D(�r(z))  �D(�r(z))  \uf8f9  \uf8fa\uf8fb  2  dµˆg(z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Thus, from the physical point of view, E�ΣΣ[ψ(z)] describes the mean square fluctuations of the  physical area distance D  �  ζ(z)(�r(z), �θ, �φ)  �  (biased by the localized PSL(2, C) mapping ζ(z)) with  respect to the reference FLRW isotropic area distance �D(�r(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Notice that, whereas the harmonic map energy E  �  �g(z), ψ(z), g(z)  �  is a conformal invariant quantity,  the functional E�ΣΣ[ψ(z)] is not conformally invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Under a conformal transformation ˆh −→  e2f ˆh we get  (112)  �  �Σz  �  e − fΦ�ΣΣ − 1  �2  e2f dµˆh .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Since we can also write  (113)  Φ�ΣΣ =  �ψ∗  (z)dµg(z)  dµ�g(z)  � 1  2  ,  (see (101)), it is also clear from its definition that corresponding to large linear ”stretches” in con-  formally mapping ψ∗  (z)g(z) on �g(z), E�ΣΣ[ψ(z)] tends to the harmonic map energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  24  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  In our particular framework, the functional E�ΣΣ[ψ(z)] has many important properties that make  it a natural candidate for comparing, at the given length scale L, the sky sections (�Σz, �g(z)) and  (Σz, g(z)) and, as the length-scale L varies, the physical lightcone region C−  L (p, g) with the FLRW  reference region C−  L (p, ˆg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' These properties are discussed in detail in [12] (see Lemma 8 and Theorem  9), here we recollect them, without presenting their proof, in the following14  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The functional E�ΣΣ[ψ(z)] is symmetric  (114)  E�ΣΣ[ψ(z)] = EΣ�Σ[ψ−1  (z)] ,  where  (115)  EΣ�Σ[ψ−1  (z)] :=  �  Σz  (ΦΣ�Σ − 1)2 dµg(z) ,  is the comparison functional associated with the inverse map ψ−1  (z) : Σz −→ �Σz, and ΦΣ�Σ is the  corresponding conformal factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Let (M, �g) be another member of the FLRW family of spacetimes, distinct from (M, ˆg), that we may  wish to use as a control in a best-fitting procedure for the physical spacetime (M, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Let (�Σz, �g(z))  denote the sky section on the past lightcone �C−  L0(p, ˜g), with vertex at p, and let �ψ(z) : Σz �−→ �Σz,  and ΦΣ�Σ respectively denote the corresponding diffeomorphism and conformal factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Then to the  composition of maps  (116)  �Σz −→  ψ(z)  Σz −→  �ψ(z)  �Σz  we can associate the triangular inequality  (117)  E�ΣΣ[ψ(z)] + EΣ�Σ[ �ψ(z)] ≥ E�Σ�Σ[( �ψ(z) ◦ ψ(z))] ,  where  (118)  E�Σ�Σ[( �ψ(z) ◦ ψ(z))] :=  �  �Σz  (Φ�Σ�Σ − 1)2 dµ�g(z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Moreover,  (119)  E�ΣΣ[ψ(z)] = 0  iff the sky sections (�Σ, ˆg(z)) and (Σ, g(z)) are isometric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Finally, if we denote by W1,2  ζ(z)( �  C Sz(p), C Sz(p))  the space of localized PSL(2, C)- maps ζ(z) which are of Sobolev class W1,2, ( i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' square summable  together with their first derivatives), then  (120)  d(z)  �  �Σz, Σz  �  :=  inf  ζ(z)∈W1,2  ζ(z)( �  C Sz(p), C Sz(p))  E�ΣΣ[ψ(z)]  defines a scale-dependent distance between the sky sections (�Σz, ˆg(z)) and (Σz, g(z)) on the lightcone  regions C−  L (p, ˆg) and C−  L (p, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  We need to conclude our long lightcone journey addressing the real nature of the physical sky  section Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This forces us to leave the comfort zone of the assumed smoothness of the past physical  lightcone C−(p, �g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  14In [12], the general notation is somehow at variance from the one adopted here, since we address the analysis of  E�ΣΣ directly on the surfaces �Σ and Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, we refer to �Σ and Σ as celestial spheres rather than sky sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  25  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The Lipschitz geometry of the cosmological sky sections Σz  The celestial sphere description of the sky sections Σz discussed above is inherently vulnerable  to the vagaries of the local distribution of astrophysical sources, and the associated strong gravita-  tional lensing phenomena15 imply that the actual past light cone C −(p, g) is not smooth as we have  assumed16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, C −(p, g) may fail to be the boundary ∂ I−(p, g) of the chronological past  I−(p, g) of p, (the set of all events q ∈ M that can be connected to p by a past-directed timelike  curve), because past-directed null geodesics generators of C −(p, g), λ : [0, δ) −→ (M, g), with  λ(0) = p, may leave ∂I−(p, g) and, under the action of the local spacetime curvature, plunge into  the interior I−(p, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' A spacetime description of this behaviour in connection with the phenomenol-  ogy of gravitational lensing is discussed in detail in [45], with a rich repertoire of examples of the  possible singular structure that C −(p, g) may induce on the cosmological sky sections Σ(p, r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As a  matter of fact, the sections Σz may evolve into fractal-like surfaces, and to describe them from the  point of view of geometric analysis, we need to introduce a framework tailored to the low-regularity  landscape generated by the local inhomogeneities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The Lipschitz landscape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Given a past-directed null geodesic IW ∋ r �−→ expp(rk(n(θ, φ))),  issued from p ∈ M in the direction n(θ, φ) ∈ C Sz, we follow [37] and define its terminal point as  the last–point  (121)  q(r∗, n(θ, φ)) := expp(rk(n(θ, φ)))  that lies on the boundary ∂I−(p, g) of the chronological past of p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Any such terminal point  q(r∗, n(θ, φ)) is said to be: i) a conjugate terminal point if the exponential map expp is singu-  lar at (r∗, n(θ, φ));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ii) a cut locus terminal point if the exponential map expp is non–singular at  (r∗, n(θ, φ)) and there exists another null geodesic, issued from p, passing through q(r∗, n(θ, φ)),  (see also [1], [45]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We denote [37] by T −(p) the set of all terminal points associated with the  past null geodesic flow issuing from p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In presence of cut points, C −(p, g) fails to be an embedded  submanifold of (M, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Failure to be an immersed manifold is more directly related to conjugate  points along the generators of C −(p, g) and of the associated conjugate locus [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It follows that  in presence of terminal points the mapping  (122)  expp  ��  C −(p,g) : C Sz −→ Σz := expp [C Sz]  is no longer one-to-one, and the cosmological sky section Σz fails to be a smooth surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' From the  physical point of view, this is the geometrical setting associated with the generation of multiple  images of astrophysical sources17 in the observer celestial sphere C Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The mathematical framework  for handling such a scenario is to assume that the past null cone C −(p, g) has the regularity of a  Lipschitz manifold, characterized by a maximal atlas A = {(Uα, ϕα)} such that all transition maps  between the coordinate charts (Uα, ϕα) of C −(p, g),  (123)  ϕαβ := ϕβ ◦ ϕ−1  α  : ϕα (Uα ∩ Uβ) −→ ϕβ (Uα ∩ Uβ) ,  are locally Lipschitz maps between domains of the Euclidean space (R3, δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  On C −(p, g), the  condition of being Lipschitz can be viewed as a weakened version of the differentiability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In par-  ticular, if f : C −(p, g) ∋ U −→ R3 is a continuous map between open sets, then f is Lipschitz  if and only if it admits distributional partial derivatives that are in L∞(U) with respect to the  15See [45] for a thorough analysis of the geometry of gravitational lensing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  16The restrictive nature of the smoothness assumption on the metric g, typically represented by functions gab ∈  Ck(R4, R), k ≥ 2, and of the associated light cone, has been pointed out by many authors, mainly in the context of  the proof of singularity theorems and in causality theory, (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' [13], [17], [38], [42], [51]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  17If the sources are not pointlike, we also have the more complex ring patterns typical of strong gravitational  lensing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  26  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  Lebesgue measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This statement of Rademacher’s theorem [23], [48] implies that the transition  maps ϕαβ on C −(p, g) have differentials dϕαβ that are defined almost everywhere, and which are  locally bounded an measurable on their domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In such a low-regularity setting the exponential  map is quite delicate to handle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' However, a key result, geometrically proved by M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Kunzinger,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Steinbauer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Stojkovic [40], (based on work by B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Chen and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' LeFloch [13]), and by E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Minguzzi [42], implies that the exponential map associated with a C1, 1 metric can still be defined  as a local bi-Lipschitz homeomorphism, namely a bijective map which along with its inverse is  Lipschitz continuous in a sufficiently small neighborhood of p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, the exponential map retains  an appropriate form of regularity in the sense that locally, for each point p ∈ M, there exist open  star-shaped neighborhoods, N0(p) of 0 ∈ TpM and Up ⊂ (M, g), such that expp : N0(p) −→ Up is  a bi-Lipschitz homeomorphism [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In particular, each point p ∈ (M, g) possesses a basis of totally  normal neighborhoods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' It is worthwhile to stress that geodesic normal coordinates (see (22)) can be  still defined, but the transition from the current smooth coordinate systems18 used around p ∈ M  to the normal coordinates associated with expp is only continuous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The fractal-like sky section Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We are interested in the geometry that such past light  cone scenario induces on the cosmological sky section Σz := expp [C Sz] of C−(p, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As long as expp  is bi-Lipschitz, the sky sections Σz are topological 2-spheres, and the results above seem to suggest  that after all there is no such a strong motivation to abandon the comforts of the smooth framework  in favor of a Lipschitzian rugged landscape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' However, as the length scale L varies, the development  of caustics in C −(p, g) generates cusps and crossings in the surfaces Σz, to the effect that they are  no longer homeomorphic to 2-spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In such a setting, the restriction of the exponential map to  the celestial sphere C Sz, characterizing the surface Σz, (see (71)),  (124)  expp : C Sz ⊂ TpM −→ Σz := expp [C Sz] ⊂ C −(p, g) ,  is only a Lipschitz map between the metric spaces  �  C Sz, dS2r  �  and  �  Σz, dg|Σ  �  , where dS2r is the  standard distance function on the round 2-sphere S2  r or radius r, and dg|Σ is the distance function  induced (almost everywhere) on Σz by the metric g|Σz defined19 by (26).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In general, the sky section  Σz can be topologically very complex since it may contain terminal points of the exponential map  expp, giving rise to cusps and swallow-tail points associated with self-intersections of Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Even if  this may evolve in a very complex picture of Σz, we still have quite a geometric control over its  metric structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The Lipschitz regularity of expp implies that there is a constant cr, depending  on the parameter r, such that  (125)  dΣ(p,r)  �  expp(x), expp(y)  �  ≤ cr dS2r(x, y),  ∀ x, y ∈ S2  r ,  and we can define the pull-back on the celestial sphere C Sz ∈ TpM of the distance function dΣz  according to  (126)  exp∗  p dΣz = dgΣ  �  expp(x), expp(y)  �  ,  ∀ x, y ∈ C Sz .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  We can also pull-back the metric g|g|Σz to C Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' By Rademacher’s theorem expp is differentiable  almost everywhere, and  (127)  h(θ, φ) :=  �  exp∗  p g|Σz  �  αβ dxαdxβ ,  is a metric defined, almost everywhere on the celestial sphere C Sz, (by a slight abuse of language, we  have used the same notation as for the smooth version(27)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' We can also define almost everywhere  18Recall that M is a smooth manifold, and that the low Lipschitz C1, 1 regularity is caused by the metric g, and  not by the differentiable structure of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  19In presence of cut points the inclusion map ιr : Σz ֒→ C −(p, g) of the sky section Σz into C −(p, g) is Lipschitz,  thus Rademacher’s theorem allows us to define the pull-back metric g|Σz := ι∗  r g|C −(p,g) only almost-everywhere  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  27  the volume element dµh associated with the metric (127), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (128)  dµh := exp∗  p dµg|Σz =  �  det(h(r(z), θ, φ)) dθdϕ ,  in full analogy with its smooth version (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' All this implies that with the proviso of the almost  everywhere meaning, the characterization (29) of the angular diameter distance D(r, θ, φ) and of  the shear-inducing distortion Lαβ defined by (30), carry over to the bi-Lipschitz case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  To put these geometrical remarks at work, let us stress that we cannot have reasonable control  over the very complex topological structure of the sky section Σz induced by a cascade of (strong)  lensing events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Moreover, the corresponding caustics and singularities at the terminal points on  Σz provide a level of detail that is not relevant to the present analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, as a reasonable  compromise, we assume that the exponential map expp is bi-Lipschitz, that Σz is topologically a  2-sphere, and we mimic the effect of the many lensing events that may affect Σz by assuming that  the sky section Σz has the irregularities of a metric surface with the fractal geometry of a 2-sphere  with the locally-finite Hausdorff 2-measure associated with (128).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Under such assumptions, it can  be shown that our smooth analysis can be safely extended, (in particular, we can still exploit  the Poincar´e–Koebe uniformization theorem [44]), and the results obtained hold also in the more  general setting of a Lipschitz description of the cosmographic past lightcone C−(p, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Concluding remarks: d(z)  �  �Σz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Σz  �  as a scale-dependent field  According to the physical characterization (111) of E�ΣΣ[ψ(z)],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' and the results described in Theo-  rem 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' the distance function d(z)  �  �Σz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Σz  �  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' (for simplicity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' one may work with the E�ΣΣ[ψ(z)] realizing  the minimum),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' can be interpreted as defining a z-dependent field on the FLRW past light cone  �C−(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' �g) describing the mean square fluctuations of the anisotropies of the physical area distance  D(ζ(z)) with respect to the reference FLRW area distance �D(�r(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  These fluctuations provide  information on how much the local area element on the physical sky section Σz differs from the  corresponding (round) area element on the reference FLRW sky section Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Since for 2-dimensional  surfaces the local Riemannian geometry is fully described by the area element, the fluctuations in  D(ζ(z)) give information on how much the geometries of the sky sections �Σz and Σz differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' When  we reach the scale of homogeneity, the physical area distance D(ζ(z)) becomes isotropic and can be  identified with the reference FLRW �D(�r(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The localized null-directions alignment between the  corresponding celestial spheres C Sz(p) and �  C Sz(p) reduces to a global kinematical Lorentz boost  (and a rotation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Thus, corresponding to this homogeneity scale, the distance function d(z)  �  �Σz, Σz  �  field vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Thus, we have an interesting scenario whereby it is possible to associate with the distance functional  d(z)  �  �Σz, Σz  �  a scale-dependent field that describes a global effect that the reference FLRW past  lightcone �C−(p, �g) misses in describing the pre-homogeneity anisotropies of the actual past lightcone  C−(p, �g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This pre-homogeneity field is, in line of principle, measurable since it is the mean-square  variation of the physical area distance D(ζ(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The delicate question concerns its possible role in  selecting the large-scale FLRW model that best fits the cosmological observations on large scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' A  few qualitative indications in this direction, mainly of a perturbative nature, are discussed in [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The results presented here are however more precise since they connect directly the distance func-  tional d(z)  �  �Σz, Σz  �  to the area distance D(ζ(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' To describe an important consequence of these  results, let us consider the light cone regions C−  L (p, ˆg) and C−  L (p, g) over a sufficiently small length  scale L(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' If ζ(z) and the corresponding ψ(z) denote the minimizing maps characterized in Theorem  28  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' then we can write [12]  E�ΣΣ[ψ(z)]  =  �  �Σz  (Φ�ΣΣ − 1)2 dµ�g(z) =  �  �Σz  Φ2  �ΣΣ dµ�g(z) +  �  �Σz  dµ�g(z) − 2  �  �Σz  Φ�ΣΣ dµ�g(z)  (129)  =  �  �Σz  ψ∗  g(z)dµg(z)  dµ�g(z)  dµ�g(z) + A  �  �Σz  �  − 2  �  �Σz  Φ�ΣΣ dµ�g(z)  =  �  ψ(z)(�Σz)  dµg(z) + A  �  �Σz  �  − 2  �  �Σz  Φ�ΣΣ dµ�g(z)  =  A(Σz) + A  �  �Σz  �  − 2  �  �Σz  Φ�ΣΣ dµ�g(z) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  where we have exploited the Radon-Nikodyn characterization of �Φ2  �ΣΣ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' (see (101)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' the identification  ψ(z)(�Σz) = Σz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' and the relation  (130)  �  �Σz  ψ∗  (z)dµg(z)  dµ�g(z)  dµ�g(z) =  �  �Σz  ψ∗  (z)dµg(z) =  �  ψ(�Σz)  dµg(z) =  �  Σz  dµg(z) = A(Σz) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  where A(Σz) and A  �  �Σz  �  respectively denote the area of the sky sections (ˆΣz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' �g(z)) and (Σz,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' g(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Thus,  (131)  d(z)  �  �ΣL, ΣL  �  = E�ΣΣ[ψ(z)] := A  �  �Σz  �  + A(Σz) − 2  �  �Σz  Φ�ΣΣ dµ�g(z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  To simplify matters, we assume that at the given length scale L(z) the corresponding region C−  L (p, g)  is caustic free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Let us rewrite ΦΣ�Σ as  ΦΣ�Σ  =  �  ΦΣ�Σ − 1  �  + 1  (132)  =  ��Jac  �  ζ(z)  ���  1  2 D(ζ(z)) − �D(�r(z))  �D(�r(z))  + 1 ,  where we have simplified the notation used in (108).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' By introducing this in (131) we get  (133)  dL  �  �Σz, Σz  �  = A (Σz) − A(�Σz) − 2  �  �Σz  \uf8ee  \uf8f0  ��Jac  �  ζ(z)  ���  1  2 D(ζ(z)) − �D(�r(z))  �D(�r(z))  \uf8f9  \uf8fb dµ�g(z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  This expression can be further specialized if we exploit the asymptotic expressions of the area  A  �  �Σz  �  and A (Σz) of the two surfaces (�Σz, �g(z)), (Σz, g(z)) on the corresponding lightcones C−  L (p, �g)  and C−  L (p, g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' These asymptotic expressions can be obtained if we consider the associated causal  past regions J −  L (p, �g) and J −  L (p, g) sufficiently near the (common) observation point p, in particular  when the length scale L(z) we are probing is small with respect to the ”cosmological” curvature  scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Under such assumption, there is a unique maximal 3-dimensional region V 3  L(p), embedded  in J −  L (p, g), having the surface (Σz, h) as its boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  This surface intersects the world line  γ(τ) of the observer p at the point q = γ(τ0 = − L(z)) defined by the given length scale L(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  For the reference FLRW the analogous set up is associated to the constant-time slicing of the  FLRW spacetime (M, �g) considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The corresponding 3-dimensional region �V 3  L(p), embedded in  J −  L (p, �g), has the surface (�Σz, ˆh) as its boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The FLRW observer �γ(�τ) will intersect �V 3  L(p) at  the point �q = �γ(�τ0 = − L(z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' By introducing geodesic normal coordinates {Xi} in J −  L (p, g) and  {Y k} in J −  L (p, �g), respectively based at the point q and �q, we can pull back the metric tensors g  and �g to TqM and T�qM, and obtain the classical normal coordinate development of the metrics g  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  29  and �g valid in a sufficiently small convex neighborhood of q and �q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Explicitly, for the (more relevant  case of the) metric g, we have (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='4 (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 210) of [49] or [47])  �  (expq)∗ g  �  ef = ηef − 1  3 Reabf|qXaXb − 1  6 ∇cReabf|qXaXbXc  +  �  − 1  20 ∇c∇dReabf + 2  45 Reabm Rm  fcd  �  q  XaXbXcXd + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' ,  where Rabcd is the Riemann tensor of the metric g (evaluated at the point q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' The induced expansion  in the pulled-back measure  �  (exps(η))∗dµg  �  provides the Lorentzian analog of the familiar Bertrand-  Puiseux formulas associated with the geometrical interpretation of the sectional, Ricci and scalar  curvature for a Riemannian manifold in terms of the length, area, and volume measures of small  geodesic balls.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' In the Lorentzian case the relevant formulas are more delicate to derive, [3], [25],  [26], [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' This asymptotics provides [25], to leading order in L(z), the following expressions for the  area of (Σz, g(z)) and (�Σz, �g(z)),  (134)  A (Σz) = π L2(z)  �  1 − 1  72 L2(z) R(q) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  �  ,  and  (135)  A  �  �Σz  �  = π L2(z)  �  1 − 1  72 L2(z) �R(�q) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  �  ,  Introducing these expressions in (133) we eventually get  (136)  �R(ˆq) = R(q) + 72  π  d(z)  �  �Σz, Σz  �  L4(z)  +  144  πL4(z)  �  �Σz  \uf8ee  \uf8f0  ��Jac  �  ζ(z)  ���  1  2 D(ζ(z)) − �D(�r(z))  �D(�r(z))  \uf8f9  \uf8fb dµ�g(z) + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Notice that the integral is the average value over the sky section (�Σz, �g(z)), of the fluctuations of  ��Jac  �  ζ(z)  ���  1  2 D(ζ(z)) with respect to �D(�r(z)), average that for notational ease we write as  (137)  �  D(ζ(z))  �� �D(�r(z))  �  �Σz := A−1(�Σz)  �  �Σz  \uf8ee  \uf8f0  ��Jac  �  ζ(z)  ���  1  2 D(ζ(z)) − �D(�r(z))  �D(�r(z))  \uf8f9  \uf8fb dµ�g(z) ,  while, as we have already stressed, the distance functional is (up to the A(�Σz) normalization) the  square mean deviation of this average, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',  ��  D(ζ(z))  �� �D(�r(z))  �2�  �Σz  :  =  A−1(�Σz)  �  �Σz  \uf8ee  \uf8f0  ��Jac  �  ζ(z)  ���  1  2 D(ζ(z)) − �D(�r(z))  �D(�r(z))  \uf8f9  \uf8fb  2  dµ�g(z)  (138)  =  A−1(�Σz) d(z)  �  �Σz, Σz  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  To put these results at work, let us assume the conservative and quite a reasonable scenario where  the fluctuations in the area distance D(ζ(z)), even if locally large in the various celestial coordinates  bins, average out to zero over �Σz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  However, the corresponding square mean deviation of the  fluctuations  ��  D(ζ(z))  �� �D(�r(z))  �2�  �Σz  = A−1(�Σz) d(z)  �  �Σz, Σz  �  can be significantly different from  30  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  zero, and from (136) we get  (139)  �R(ˆq) = R(q) + 72  π  d(z)  �  �Σz, Σz  �  L4(z)  + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  The physical scalar curvature we measure (hard to!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=') in such a scenario is R(q), and if we decide  to modeling with a FLRW solution a cosmological spacetime, homogeneous on large scale but  highly inhomogeneous at smaller scale, then (139) shows that we cannot identify R(q) with the  corresponding FLRW scalar curvature �R(ˆq).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Such an identification is possible, with a rigorous level  of scale dependence precision, only if we take into account the term  (140)  72  π  d(z)  �  �Σz, Σz  �  L4(z)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  According to Theorem 1, this term vanishes once L(z) probes the homogeneity scales, conversely, it  is clear from (139) that in pre-homogeneity region its presence is forced on us and plays the role of  a scale-dependent effective positive contribution to the cosmological constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' As long as the local  inhomogeneities give rise to significant fluctuations in the area distance D(ζ(z)), this contribution  cannot be considered a priori negligible in high-precision cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  References  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Beem, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ehrlich, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Easley, Global Lorentzian Geometry, Monographs and Textbooks in Pure and Applied  Mathematics Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 202, 2nd ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=', Dekker, New York, (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Berger, On Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Diff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Geo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  5 325-332 (1971).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Berthiere, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Gibbons, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Solodukhin, Comparison theorems for causal diamonds, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' D 92,  064036 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Buchert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Carfora, Regional averaging and scaling in relativistic cosmology, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Quantum Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 19 6109  (2002) DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1088/0264-9381/19/23/314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Buchert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Carfora, Cosmological Parameters Are Dressed, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 90, 031101, (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [6] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Buchert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Carfora, On the curvature of the present-day Universe, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='25:195001, (2008)  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1088/0264-9381/25/19/195001, arXiv:0803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1401v2 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [7] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Buchert, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' van Elst, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Heinesen The averaging problem on the past null cone in inhomogeneous dust  cosmologies, arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='10798v1 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Carfora, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Marzuoli, Smoothing Out Spatially Closed Cosmologies, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 53, 2445 (1984)  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='2445.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Carfora, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Piotrkowska, Renormalization group approach to relativistic cosmology, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' D 52, 4393  (1995) https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='4393.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Carfora, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Marzuoli, Einstein Constraints and Ricci Flow: A Geometrical Averaging of Initial Data Sets,  Mathematical Physics Studies (MPST), Springer (2023) ISBN: 978-981-19-8539-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [11] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Buchert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Carfora, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ellis, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Kolb, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' MacCallum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ostrowski, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rasanen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Roukema, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Andersson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Coley, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Wiltshire, Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='.  Classical and Quantum Gravity 32 (21), (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [12] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Carfora, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Familiari, A comparison theorem for cosmological lightcones, Letters in Mathematical Physics,  111:53 (2021), https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1007/s11005-021-01393-2  [13] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Chen and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' LeFloch, Injectivity Radius of Lorentzian Manifolds, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 278 (2008)  [14] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Choquet-Bruhat, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Chrusciel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Mart´ın-Garc´ıa, The light-cone theorem, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Quantum Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 26,  135011 (22pp) (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [15] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Choquet-Bruhat, General relativity and the Einstein Equations, Oxford Mathematical Monographs, Oxford  University Press, Oxford, (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [16] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Choquet-Bruhat, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Chrusciel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Mart´ın-Garc´ıa, The Cauchy Problem on a Characteristic Cone for  the Einstein Equations in Arbitrary Dimensions, Annales Henri Poincar´e 12, 419–482 (2011)  [17] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Chrusciel and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Grant, On Lorentzian causality with continuous metrics, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Quantum Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 29 (2012)  [18] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ellis, The Domain of Cosmology and the Testing of Cosmological Theories, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 3-39 in The Philosophy  of Cosmology, Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Chamcham, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Silk, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Barrow, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Saunders, Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Press (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  A SCALE-DEPENDENT DISTANCE FUNCTIONAL BETWEEN PAST-LIGHTCONES IN COSMOLOGY  31  [19] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ellis and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' van Elst, Deviation of geodesics in FLRW spacetime geometries, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 203-225 in A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Harvey  ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=',On Einstein’s path-Essays in Honor of Engelbert Sch¨ucking, Springer, New York, (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [20] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ellis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Nel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Maartens, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Stoeger, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Whitman, Ideal observational cosmology, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Reports 124, 315-417 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [21] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ellis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Maartens and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' MacCallum, Relativistic Cosmology, Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Press (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Eells and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Lemaire, A report on harmonic maps, Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=', 10, 1–68 (1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [23] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Evans, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics,  CRC Press (Boca Raton, Florida) (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Gasperini, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Marozzi3, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Nugier and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Veneziano, Light-cone averaging in cosmology:  formalism  and applications, Journal of Cosmology and Astroparticle Physics JCAP07(2011)008, DOI 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1088/1475-  7516/2011/07/008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [25] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Gibbons and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Solodukhin, The geometry of small causal diamonds, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' B 649 (2007) 317  [hep-th/0703098]  [26] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Gibbons and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Solodukhin, The geometry of large causal diamonds and the No-Hair property of  asymptotically DeSitter spacetimes, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' B 652 (2007) 103 [arXiv: 0706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='0603]  [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Gott, III, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Juric, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Schlegel, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Hoyle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Vogeley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Tegmark, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Bahcall, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Brinkmann, A Map of  the Universe, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='624:463,(2005) (arXiv:astro-ph/0310571).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [28] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Gu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Yau, Computing conformal structure of surfaces, Communications in Information and Systems, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  2 (2002) 121-146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Hass and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Koehl, Comparing shapes of genus-zero surfaces, Journal of Applied and Computational Topology,  Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 1, (2017) 57–87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [30] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Heinesen, Multipole decomposition of the general luminosity distance ’Hubble law’ – a new framework for obser-  vational cosmology, Journal of Cosmology and Astroparticle Physics 05(2021)008 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1088/1475-  7516/2021/05/008, arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='06534v2 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [31] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Heinesen, Redshift drift cosmography for model-independent cosmological inference, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' D 104 (2021),  123527 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='123527, arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='08674v2 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='CO].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [32] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' H´elein and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Wood, Harmonic maps, in Handbook of Global Analysis, Elsevier (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [33] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Hogg, Distance measures in cosmology, arXiv: astro-ph/9905116v4 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [34] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Hogg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Eisenstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Blanton, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Bahcall, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Brinkmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Gunn, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Schneider,  Cosmic Homogeneity Demonstrated with Luminous Red Galaxies, The Astrophysical Journal, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 624, (2005)  54-58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [35] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Jin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Yau, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Gu, Optimal global conformal surface parametrization for visualization, Com-  munications in Information and Systems, (2005) 117-134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [36] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Jost, Riemannian geometry and geometric analysis, 2nd ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Springer Universitext, Springer–Verlag (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [37] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Klainerman and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rodnianski, On the radius of injectivity of null hypersurfaces, Journal of the American  Mathematical Society, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 21 (2008), 775–795, S 0894-0347(08)00592-4  [38] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Kunzinger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Steinbauer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Vickers, The Penrose singularity theorem in regularity C1, 1, Classical and  Quantum Gravity, 32 (15), 1-13, [155010].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' (doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1088/0264-9381/32/15/155010) (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [39] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Kolb, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Marra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Matarrese, Cosmological background solutions and cosmological backreactions,  Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 42 (2010) 1399-1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Kunzinger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Steinbauer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Stojkovic, The exponential map of a C1,1−metric, Differential Geometry and  its Applications 34 (2014) 14-24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [41] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Maartens, Is the Universe homogeneous?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Philosophical Transactions of the Royal Society, A 369 (2011),  5115-37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [42] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Minguzzi, Convex neighborhoods for Lipschitz connections and sprays, Monatsh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 177, 569-625 (2015),  https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1007/s00605-014-0699-y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' See also arXiv:1308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='6675v2 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='DG].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [43] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Myrheim, Statistical Geometry, Report No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CERN-TH-2538, (1978) (unpublished).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [44] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Ntalampekos and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Romney, Polyhedral approximation and uniformization for non-length surfaces,  arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='01128v1[math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' MG] (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [45] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  Perlick,  Gravitational  Lensing  from  a  Spacetime  Perspective,  Living  Reviews  in  Relativity,  Livingreviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='org/lrr-2004-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [46] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Penrose and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rindler, Spinors and Space Time Vol I, Cambridge Monographs on Mathematical Physics,  Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Press (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [47] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Petersen, Riemannian Geometry, Graduate Text in Mathematics 171 Springer (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [48] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rosenberg, Applications of Analysis on Lipschitz Manifolds, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Centre Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=', 16: 349pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' (1987)  269-283, Miniconference on Harmonic Analysis and Operator Algebras (August 5-8 and December 2-3, 1987,  Australian National University, Canberra).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Cowling, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Meaney, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Moran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [49] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Schoen, S-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Yau, Lectures on differental geometry, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='I, International Press, Cambridge, MA, (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  32  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' CARFORA AND F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' FAMILIARI  [50] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Scrimgeour M et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=', The WiggleZ Dark Energy Survey: the transition to large-scale cosmic homogeneity  Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Astr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 425 (2012) 116 [arXiv:1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='6812].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [51] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Senovilla, Singularity Theorems and Their Consequences, Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' and Gravitation, 30 (1998) 701-848,  (this is available with updates in arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='04912v1 [gr-qc] https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='48550/arXiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='04912).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [52] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Uzan, Emergent Structures of Effective Field Theories, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' 109-135 in The Philosophy of Cosmology, Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Chamcham, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Silk, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Barrow, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Saunders, Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Press (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [53] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=', Wiltshire, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Smale, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Mattsson, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Watkins, Hubble flow variance and the cosmic rest frame,  Physical Review D, 88(8), (2013), doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='1103/physrevd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='083529  [54] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='Wiltshire, Comment on ”Hubble flow variations as a test for inhomogeneous cosmology”, Atronomy and As-  trophysics 624 (2019) A12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  [55] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Zhang and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content=' Stebbins, Confirmation of the Copernican principle through the anisotropic kinetic Sunyaev  Zel’dovich effect, Philosophical Transactions of the Royal Society, A 369 (2011), 5138-45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='  (Department of Physics, University of Pavia) University of Pavia  (GNFM and INFN) Italian National Group of Mathematical Physics, and INFN Pavia Section  Email address: mauro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='carfora@unipv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='it  (Department of Physics, University of Pavia) University of Pavia  (GNFM and INFN) Italian National Group of Mathematical Physics, and INFN Pavia Section  Email address: francesca.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='familiari01@universitadipavia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
+page_content='it' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edE3T4oBgHgl3EQfewrM/content/2301.04547v1.pdf'}
diff --git a/edFRT4oBgHgl3EQfVDdZ/content/tmp_files/2301.13538v1.pdf.txt b/edFRT4oBgHgl3EQfVDdZ/content/tmp_files/2301.13538v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..131a9f66ff37d3ff1742f3e5333dcc5d38a50c87
--- /dev/null
+++ b/edFRT4oBgHgl3EQfVDdZ/content/tmp_files/2301.13538v1.pdf.txt
@@ -0,0 +1,1095 @@
+AMD: Adaptive Masked Distillation for Object
+Detection
+Guang Yanga, Yin Tangb, Jun Lia�,Jianhua Xua,Xili Wanb
+a School of Computer and Electronic Information, Nanjing Normal University, Nanjing, China
+b School of Computer Science and Technology, Nanjing Tech University, Nanjing, China
+{Jun Li}lijuncst@njnu.edu.cn
+Abstract—As a general model compression paradigm, feature-
+based knowledge distillation allows the student model to learn
+expressive features from the teacher counterpart. In this paper,
+we mainly focus on designing an effective feature-distillation
+framework and propose a spatial-channel adaptive masked distil-
+lation (AMD) network for object detection. More specifically, in
+order to accurately reconstruct important feature regions, we first
+perform attention-guided feature masking on the feature map of
+the student network, such that we can identify the important
+features via spatially adaptive feature masking instead of random
+masking in the previous methods. In addition, we employ a simple
+and efficient module to allow the student network channel to
+be adaptive, improving its model capability in object perception
+and detection. In contrast to the previous methods, more crucial
+object-aware features can be reconstructed and learned from
+the proposed network, which is conducive to accurate object
+detection. The empirical experiments demonstrate the superiority
+of our method: with the help of our proposed distillation method,
+the student networks report 41.3%, 42.4%, and 42.7% mAP
+scores when RetinaNet, Cascade Mask-RCNN and RepPoints are
+respectively used as the teacher framework for object detection,
+which outperforms the previous state-of-the-art distillation meth-
+ods including FGD and MGD.
+Index Terms—Feature-based Knowledge Distillation, Object
+Detection, Adaptive Masked Distillation, Object-Aware Features
+I. INTRODUCTION
+Recent years have witnessed successful and pervasive ap-
+plications of Deep Convolutional Neural Networks (CNNs) in
+various computer vision tasks. However, deep CNNs usually
+cost a huge amount of computational resources in pursuit
+of higher performance, which adversely affects their deploy-
+ment in practical applications and leads to severe parameter
+redundancy. It is therefore necessary to transfer the dark
+knowledge learned in the complex networks (teacher) to
+another lightweight network (student). This is also termed as
+knowledge distillation [1] which allows the student model to
+generate expressive features learned from the teacher model.
+Thus, it is more preferable to deploy the student model
+with compact network architecture sacrificing minimal loss of
+performance.
+The earliest distillation algorithms function mainly at the
+output head. The representative examples include logit-based
+distillation for classification and head-based distillation for
+detection [2]. Recently, a more common distillation strategy
+emerges as feature-based distillation mechanism. Since only
+0.3
+0.4
+0.8
+0.4
+3.6
+2.3
+1.2
+1.1
+0.8
+0.5
+0.3
+0.1
+1.8
+1.0
+1.3
+0.7
+1.2
+1.0
+0.4
+1.8
+0.8
+0.5
+1.8
+1.2
+0.8
+0.7
+0.3
+0.2
+0.3
+1.1
+0.4
+0.7
+1.3
+1.2
+0.5
+Fig. 1: Different regions are quantified with varying attention
+scores in the feature map of teacher model. The regions
+with higher scores encode the region importance and should
+outweigh the low-score regions in the feature masking.
+the head or projector after the generated feature varies within
+different networks, the feature-based distillation approaches
+can potentially be employed in a variety of tasks. There-
+fore, it has become a prominent line of research for both
+model compression and performance improvement due to
+its simplicity and efficacy. In object detection, in particular,
+a variety of feature-based distillation approaches have been
+developed. The earlier research, such as FitNet [3], performs
+distillation at the global level. FGFI [4] operates by distilling
+the features of high IoU between ground truth and anchors.
+FGD [5] was developed to separate distillation of foreground
+and background. Recent research suggests it is preferable for
+the student model to reconstruct and learn expressive features
+from the teacher model in the first place instead of following
+the teacher for generating competitive representations. For
+instance, MGD [6] was proposed to randomly mask pixels in
+the feature map of student network, leading to reconstructed
+features of the teacher model via a simple block.
+Although MGD further improves the feature distillation
+by reconstructing the features of masked areas, the masked
+regions are generated in a random manner. This random
+operation fails to identify the region-specific importance, and
+is likely to cause the student model to generate features of
+the teacher in unimportant regions. As illustrated in Fig. 1,
+arXiv:2301.13538v1  [cs.CV]  31 Jan 2023
+
+Spatial Attention
+Mask
+Feature
+Mask
+Backbone
+(Neck)
+SE block
+3×3
+3×3
+Distillation
+Teacher
+Spatial Attention
+R
+1× H× W
+R
+C×H× W
+R
+C×1× 1
+R
+C×H× W
+R
+C×H× W
+Avg pooling
+RELU
+FC
+FC
+Sigmoid
+Backbone
+(Neck)
+SE block
+ReLU
+Student
+Teacher
+Generation 
+Block
+.
+Fig. 2: The proposed AMD distillation framework. It first learns the adaptive Region-of-Interest (RoI) via attention-guided
+feature masking, generating the spatial mask clue from the teacher model imposed on the student feature. Furthermore, we
+apply the simple and efficient SE layer to the feature of the teacher model, leading to the channel adaptive clues. The auxiliary
+clues are then fused with the output from the generation block via a Hadamard product, such that the generated feature from
+the student model is channel adaptive.
+the importance of different regions in the feature map of
+a teacher model can be quantified using the region-specific
+attention scores. Only the regions with higher scores play
+critical role in feature masking while the low-score regions
+should be downplayed.
+To alleviate the above-mentioned drawback, we propose an
+adaptive masked distillation (AMD) framework which enjoys
+object-aware spatial and channel adaptivity. On the one hand,
+we perform attention-guided spatial masking instead of ran-
+dom masking on the feature map of the student network. More
+specifically, we first learn a spatial attention map from the
+feature map of the teacher model, producing a region-specific
+mask. Then, the feature of the student network is adaptively
+masked by using this attention map. Benefiting from this
+selective feature masking, it allows subsequent generation
+block to focus on those adaptively masked important areas,
+leading to robust and expressive representations. On the other
+hand, to further explore the object-awareness capability, we
+leverage a simple and effective SE layer [7] for modeling the
+channel attention of the resulting feature of the teacher model.
+The learned clue and the output from the generation block
+of students will be fused via a Hadamard product, achieving
+desirable object-aware channel adaptivity.
+To summarize, the contributions of this paper are threefold.
+• First, we develop a spatially adaptive feature masking
+mechanism for the student model, such that the region-
+specific importance can be encoded in the features recon-
+structed and learned from the teacher network.
+• Second, we further explore the channel adaptivity by
+introducing a simple and efficient SE module to improve
+the object-aware capability of the student model.
+• Third, we evaluate our proposed feature distillation net-
+work AMD using various detection frameworks includ-
+ing one-stage detector RetinaNet [8], two-stage detec-
+tor Faster-RCNN [9], and anchor free model RepPoint
+[10]. Extensive experimental results demonstrate that
+our method can help to learn features with sufficient
+descriptive capability and achieve significant performance
+gains over the previous state-of-the-art methods.
+The remainder of this paper is structured as follows. After
+reviewing the related work in Section II, we elaborate on our
+method in Section III. Next, we conduct extensive experi-
+mental evaluations in Section IV before the paper is finally
+concluded in Section V.
+II. RELATED WORK
+In this section, we comprehensively review the recent ad-
+vance in object detection and knowledge distillation, both of
+which are closely related to our method.
+A. Object Detection
+As one fundamental vision task, object detection aims to
+determine the category and location of the objects in an
+image. Over recent years, the success of CNNs has enormously
+advanced the research in object detection. In general, the
+detectors based on deep CNNs can be classified into three
+categories including anchor-based detectors [9, 11], anchor-
+free detectors [12] and end-to-end detectors [13]. In particular,
+anchor-based detection models are divided into two-stage
+[9, 14–16] and one-stage detectors [11, 17, 18]. The former
+detection method, represented by R-CNN like [9, 19] algo-
+rithms, has a higher detection accuracy, whereas its inference
+speed is usually unsatisfactory due to expensive computational
+costs incurred by region proposal network (RPN). As a result,
+
+it is impractical for some real-time scenarios. In contrast, one-
+stage detectors directly perform classification and regression
+on the anchors without generating proposals beforehand. Thus,
+they run faster with guaranteed detection performance.
+While recent deep networks achieve high detection accu-
+racy, they usually rely on complex backbone structure and
+significant computational resources [13, 20–22]. In this sense,
+designing lightweight and efficient backbone networks has
+emerged as a major line of research in object detection. In
+particular, knowledge distillation, which can transfer sufficient
+descriptive power from a large network to a small network, is
+beneficial for designing lightweight backbone with maintained
+performance close to the large network.
+B. Knowledge Distillation
+Recently, knowledge distillation has received increasing
+attention in model compression, since it is capable of retaining
+compact model structure with promoted performance. Hinton
+et al. [1] first came up with the concept of knowledge
+distillation by introducing the soft label of the teacher network
+as part of the loss of the student network, allowing the student
+network to learn probability distribution fitting of the teacher
+model for classification task. Moreover, Romero et al. [3]
+demonstrated that semantic information in the intermediate
+layer can also be learned as dark knowledge by student
+networks. Thus, knowledge distillation can therefore be widely
+applied to a wide range of downstream tasks. Chen et al. [2]
+distilled the neck feature, classification head, and regression
+head by setting up three loss functions, respectively. Tang
+et al. [23] carefully designed the distillation weights and
+distillation loss functions such that they are automatically
+adjusted between samples for the single-stage object detector.
+Li et al. [24] used region proposals of the larger network to
+help the smaller network learn higher semantic information.
+Zheng et al. [25] transferred the knowledge distillation of the
+classification head to the location head of object detection,
+leading to a new distillation mechanism termed Localization
+Distillation (LD). LD makes logit mimicking become a better
+alternative to feature imitation, and reveals the knowledge
+of object category and object location should be handled
+separately. Dai et al. [26] developed GID framework which
+selects distillation areas based on differences between the
+student and teacher networks. Yang et al. proposed FGD [5]
+which separates the foreground and background, enabling the
+student model to learn from the teacher network areas of
+interest and global knowledge via local and global distillation
+respectively. Besides, MGD [6] imposes random masking on
+the feature map of the student model, and then generates
+the feature map reconstructing from the teacher network.
+However, the uncertainty of random masking may introduce
+additional noise, producing biased feature map with compro-
+mised representation capability.
+III. THE PROPOSED APPROACH
+Recently, a massive amount of distillation methods are
+carefully designed for various model architectures and tasks.
+Typically, the feature maps used for distillation usually have
+high-level semantics and spatial information about adjacent
+pixels. Therefore, learning these features from the teacher
+model can significantly improve the performance of the stu-
+dent model. Mathematically, basic feature distillation can be
+formulated as:
+Lfea =
+1
+CHW
+C
+�
+k=1
+H
+�
+i=1
+W
+�
+j=1
+�
+F T
+k,i,j − f
+�
+F S
+k,i,j
+��2
+(1)
+where C, H, and W denote the channel, height, and width of
+the feature map, respectively. F T and F S denote the feature
+generated from the teacher model and its counterpart from the
+student model. f represents the adaptation layer that aligns the
+shape of F S and F T .
+Recent research suggests learning and reconstructing the
+features of the teacher model is a desirable alternative to
+feature imitation [6]. More specifically, expressive features
+can be generated from the masked regions on the feature
+map of the student network. However, previous state-of-the-
+art method mainly performs random feature masking without
+identifying the importance of different regions on the feature
+map. In this paper, we attempt to make the student model
+generate features corresponding to the important areas on the
+feature map of the teacher network. Towards this end, we
+propose a spatial-channel adaptive masked distillation strategy
+termed AMD. In contrast to the random masking strategy in
+the previous method, we perform feature masking via region-
+aware attention for identifying the important areas in the
+feature map of the teacher network. In order to improve the
+object-aware capability, we further introduce a simple and
+efficient SE module such that the resulting features are channel
+adaptive. The framework of our proposed method is illustrated
+in Fig. 2.
+A. Spatially adaptive feature masking
+Using random pixels to recover the complete feature map,
+MGD allows the masked features of the student model to
+generate features of the teacher model. Thus, it is beneficial for
+the student network to obtain a better representation. However,
+the region-specific importance is discarded due to the random
+masking in MGD. To alleviate this drawback, we carefully
+design the region-aware feature masking with the help of
+spatial attention. To begin with, we calculate the absolute mean
+value of the teacher network along the channel dimension:
+GS(F) = 1
+C
+C
+�
+k=1
+��F T
+k
+��
+(2)
+where C denotes the channel number of the feature. F T is the
+feature of the teacher. GS(F) is the spatial representation map.
+Then, the spatial attention mask resulting from the teacher
+model can be formulated as:
+AS(F) = H · W · softmax
+�
+GS(F)/T
+�
+(3)
+where T is a hyper-parameter introduced in [1] to change the
+probability distribution such that the shape of the resulting AS
+
+FGD
+mAP:40.7
+MGD
+mAP:41.0
+Ours
+mAP:41.3
+Fig. 3: Visualisation of the feature maps obtained by different distillation methods. Teacher detector is RetinaNet-ResNeXt101
+while student detector is RetinaNet-ResNet50.
+is 1×H ×W. The attention score for each location represents
+the level of interest in the teacher network. Furthermore, the
+mask value is set to 0 when the attention score is greater than
+λ and the rest are set to 1. This can be expressed as:
+Mi,j =
+� 0,
+if AS
+i,j > λ
+1,
+Otherwise
+(4)
+where AS
+i,j is the spatial attention score at the point with
+coordinates (i, j) on the feature map of the teacher network.
+λ is a hyper-parameter to control the number of pixels in the
+mask. Next, we cover the feature map of the student model
+with the mask M, which can be formulated as follows:
+F S
+mask = F S · M
+(5)
+In a nutshell, with the help of this attention-guided feature
+masking, we can mask out the student feature map according
+to the important regions of interest on the teacher counterpart,
+and the resulting feature will contain more important semantic
+information.
+B. Channel adaptive clues generation
+Different from single-object recognization tasks such as
+image classification, object detection is a dense prediction task
+focusing on detecting multiple objects. Except for the effective
+receptive field (ERF), the capability of capturing the object
+information in different scales can also bring a significant
+performance fluctuation for a detector, which is not considered
+in the previous work [5, 6, 13]. Therefore, we utilize a simple
+and lightweight SE layer [7] to learn the channel adaptive clue
+from the teacher feature. The resulting channel adaptive clue
+will be applied to enhance the student’s feature, and further
+improve the object-awareness capability:
+F T
+clue = σ
+�
+WL1
+�
+WL2
+�
+F T
+avg; θ1
+�
+; θ2
+��
+,
+GS(F S
+mask) = WC1
+�
+ReLU
+�
+WC2(F S
+mask; θ1)
+�
+; θ2
+�
+⊙ F T
+clue,
+(6)
+where F T
+clue ∈ R1×1×C denotes the learned channel adaptive
+clue for the student feature. It is fused with the output
+from the generation block via a Hadamard product denoted
+as ⊙. The WL(·; θ) and WC(·; θ) are weight matrices of
+linear projection and convolution layer for SE and generation
+modules, respectively.
+Benefiting from this design, our model further explores the
+object-aware potential, resulting in a significant improvement
+over those vanilla counterparts, i.e., models with no channel-
+adaptive design. More interestingly, we observe that our AMD
+can achieve a remarkable mAP improvement in the case of
+detecting small objects, demonstrating the effectiveness of our
+proposed method. We also provide the visualization results of
+the feature map derived from different distillation models as
+shown in Fig 3. It can be easily observed that the object feature
+produced from our AMD is more distinguishable than those
+of methods.
+C. Loss function
+Based on the proposed distillation method, we design the
+following distillation loss for AMD:
+Lfea =
+C
+�
+k=1
+H
+�
+i=1
+W
+�
+j=1
+�
+F T
+k,i,j − GS(F S
+mask)
+�2
+(7)
+where C, H, and W respectively denote the channel number,
+height and width of the feature map. F S
+mask denotes the
+masked student feature map. Thus, the overall loss function
+is as follows:
+Loverall
+�
+F T , F S�
+= α · Lfea + Loriginal
+(8)
+where α is a hyper-parameter to balance distillation loss and
+original loss, and Loriginal is the original loss of the detection
+task.
+IV. EXPERIMENT
+A. Experimental Setting
+To verify the effectiveness of our AMD for object detection,
+we evaluate our method on MS COCO2017 [27] benchmark
+dataset, which contains 80 object categories and over 160k
+images. We use 120k training images for training and 5k
+validation images for testing. For performance measures, we
+use Average Precision (AP) and Average Recall (AR) to
+evaluate the performance of different object detectors. Three
+mainstream detectors including the anchor-based one-stage
+detector RetinaNet [8], the two-stage detector Faster-RCNN
+[9], and the anchor-free detector RepPoint [10] are involved
+in our comprehensive experiments. In addition, ResNeXt101
+and ResNet50 are respectively used as the backbone of the
+teacher network and its student counterpart.
+We also conduct a series of ablation studies to ex-
+plore the effects of individual components on the per-
+formance
+of
+our
+AMD
+framework.
+In
+implementation,
+
+TABLE I: Comparison of our method with other distillation methods for object detection on COCO.
+Teacher
+Student
+mAP
+APS
+APM
+APL
+mAR
+ARS
+ARM
+ARL
+RetinaNet-Res50
+37.4
+20.6
+40.7
+49.7
+53.9
+33.1
+57.7
+70.2
+FKD [28]
+39.6 (+2.2)
+22.7
+43.3
+52.5
+56.1 (+2.2)
+36.8
+60.0
+72.1
+FGD [5]
+40.7 (+3.3)
+22.9
+45.0
+54.7
+56.8 (+2.9)
+36.5
+61.4
+72.8
+MGD [6]
+41.0 (+3.6)
+23.4
+45.3
+55.7
+57.0 (+3.1)
+37.2
+61.7
+72.8
+RetinaNet
+ResNeXt101
+(41.0)
+AMD (ours)
+41.3 (+3.9)
+23.9
+45.4
+55.7
+57.4 (+3.5)
+38.2
+61.7
+73.5
+RepPoints-Res50
+38.6
+22.5
+42.2
+50.4
+55.1
+34.9
+59.4
+70.3
+FKD [28]
+40.6 (+2.0)
+23.4
+44.6
+53.0
+56.9 (+1.8)
+37.3
+60.9
+71.4
+FGD [5]
+42.0 (+3.4)
+24.0
+45.7
+55.6
+58.2 (+3.1)
+37.8
+62.2
+73.3
+MGD [6]
+42.3 (+3.7)
+24.4
+46.2
+55.9
+58.4 (+3.3)
+40.4
+62.3
+73.9
+RepPoints
+ResNeXt101
+(44.2)
+AMD (ours)
+42.7 (+4.1)
+24.8
+46.5
+56.3
+58.8 (+3.7)
+40.6
+62.4
+74.1
+Faster RCNN-Res50
+38.4
+21.5
+42.1
+50.3
+52.0
+32.6
+55.8
+66.1
+FKD [28]
+41.5 (+3.1)
+23.5
+45.0
+55.3
+54.4 (+2.4)
+34.0
+58.2
+69.9
+FGD [5]
+42.0 (+3.6)
+23.8
+46.4
+55.5
+55.4 (+3.4)
+35.5
+60.0
+70.0
+MGD [6]
+42.1 (+3.7)
+23.7
+46.4
+56.1
+55.5 (+3.5)
+35.4
+60.0
+70.5
+Cascade
+Mask RCNN
+ResNeXt101
+(47.3)
+AMD (ours)
+42.4 (+4.0)
+24.1
+46.5
+56.2
+55.8 (+3.8)
+35.3
+60.0
+70.8
+all the experiments are conducted on a server with one
+RTX3090 GPU using MMdetection toolbox [29] and Py-
+torch framework [30]. Besides, the hyper-parameters are
+empirically set to
+�
+α = 2.5 × 10−7, λ = 1, T = 0.5
+�
+and
+�
+α = 4 × 10−6, λ = 1.2, T = 0.5
+�
+for the one-stage models
+and the two-stage models respectively. During the training
+process, SGD optimizer is used for training all the detectors
+within 24 epochs. Meanwhile, momentum is set as 0.9 whilst
+weight decay is set to 0.0001. Moreover, single-scale training
+strategy is utilized in our experiments.
+B. Results
+In our comparative studies, we carry out three groups of
+experiments to evaluate different distillation methods with the
+three popular detectors involved. The corresponding experi-
+mental results are shown in Table I.
+In the first group of experiments, RetinaNet is used as the
+detection framework for both the teacher and the student.
+The corresponding experimental results demonstrate that our
+distillation method provides significant performance boosts of
+3.9% in mAP over the baseline student network by reporting
+the highest accuracy at 41.3%. This result consistently outper-
+forms the state-of-the-art methods FGD and MGD by 0.6%
+and 0.3%, while it even surpasses the teacher model achieving
+41.0% mAP. Similar performance improvement can also be ob-
+served with respect to mAR metric. The experimental setting
+in the second group is analogous to the first one except that the
+RetinaNet framework is replaced with RepPoints. Consistent
+with the results in the first group, dramatic performance gains
+of 4.1% in mAP and 3.7% in mAR are reported, and similar
+performance superiority to the competing distillation methods
+is also demonstrated. The results reveal that our method can
+adaptively learn more important information from the teacher
+and significantly contribute to the improvement of the student
+model.
+To further assess the generalization capability of our pro-
+posed method, we make use of different detection frameworks
+for the teacher and student models. To be specific, the more
+powerful detector Cascade Mask-RCNN is used as the teacher
+network while the Faster-RCNN for the student model. As
+shown in Table I, our method boosts the baseline student
+model from 38.4% to 42.4% in mAP and from 52.0% to 55.8%
+in mAR, outperforming MGD 0.3% both in mAP and mAR. It
+sufficiently suggests our method is independent of the specific
+detector and shows consistent advantages in cross-framework
+scenarios.
+C. Ablation Study
+In this section, we conduct extensive ablation experiments
+to explore the effect of different configurations on the pro-
+posed AMD. Consistent with the above setting, the ablation
+experiments with different configurations are conducted based
+on the three popular detectors, i.e., RetinaNet, Faster-RCNN,
+and RepPoint.
+As shown in Table II, when RetinaNet is used for the
+detection framework for both the teacher and the student, we
+explore two primary modules in our AMD model, namely
+the spatially adaptive masking (Ada-Mask) and the channel
+adaptive clues generation (Ada-Channel). It is observed that
+the complete AMD model including both the Ada-Mask and
+Ada-Channel components achieves the best results. Further-
+more, when we remove either component, there is a clear
+performance drop in particular in the small-object detection
+scenario (0.3%↓ w/o Ada-Mask and 0.5%↓ w/o Ada-Channel).
+This implies that our AMD method can improve object-
+awareness capability which is crucial for dense prediction
+tasks.
+When the RetinaNet is replaced with the RepPoint, similar
+results can be obtained. As displayed in Table III, both the
+Ada-Mask and Ada-Channel components play critical roles
+in our AMD model. Specifically, single Ada-Mask module
+reports 24.4%, 46.3% and 56.0% in APS, APM and APL
+scores. With the help of additional channel adaptive clues, fur-
+ther performance gains of 0.4%, 0.2% and 0.3% are reported
+for the respective metrics.
+Furthermore, we also perform ablation studies in cross-
+framework scenarios. Specifically, the Cascade Mask-RCNN
+is used as the teacher network, while the Faster-RCNN as the
+student counterpart. As shown in Table IV, the complete AMD
+model achieves the highest accuracy. In particular, the highest
+
+TABLE II: Ablation studies using RetinaNet [8] framework for both the teacher and the student. The backbone of the teacher
+network is ResNeXt-101 whilst its student counterpart is ResNet-50. Ada-Mask and Ada-channel respectively denote spatially
+adaptive masking and channel adaptive clue generation module. They constitute two main components in our proposed AMD
+model.
+Ada-Mask
+Ada-Channel
+Student: RetinaNet + Res50
+AP b
+AP b
+50
+AP b
+75
+APS
+APM
+APL
+
+
+41.3
+61.0
+44.1
+23.9
+45.4
+55.7
+
+41.0
+61.0
+43.8
+23.7
+45.3
+55.6
+
+41.2
+60.8
+44.0
+23.4
+45.2
+55.6
+TABLE III: Ablation studies using RepPoint [10] framework for both the teacher and the student. ResNeXt-101 and ResNet-50
+are respective backbones.
+Ada-Mask
+Ada-Channel
+Student: RepPoint + Res50
+AP b
+AP b
+50
+AP b
+75
+APS
+APM
+APL
+
+
+42.7
+63.5
+46.5
+24.8
+46.5
+56.3
+
+42.4
+63.2
+46.4
+24.6
+46.5
+56.1
+
+42.4
+63.3
+46.2
+24.4
+46.3
+56.0
+TABLE IV: Ablation studies in a cross-framework scenario. The Cascade Mask-RCNN [31] is employed for the teacher
+framework, while the Faster R-CNN is for the student counterpart.
+Ada-Mask
+Ada-Channel
+Student: Faster-RCNN + Res50
+AP b
+AP b
+50
+AP b
+75
+APS
+APM
+APL
+
+
+42.4
+63.1
+46.2
+24.1
+46.5
+56.2
+
+42.1
+62.8
+46.0
+23.8
+46.4
+56.3
+
+42.3
+63.0
+46.2
+23.6
+46.6
+56.3
+APS score 24.1% is reported, outperforming the other settings
+w/o either Ada-Mask or Ada-Channel. This indicates that our
+AMD model benefits small-object detection with improved
+object-awareness capability.
+TABLE V: Comparison of different generation blocks. For
+MBConv [32], we use 5 × 5 depthwise convolution.
+Student: RetinaNet-Res50
+Generation Block
+MBConv
+3 × 3 Dense Conv * 1
+3 × 3 Dense Conv * 2
+mAP
+41.0
+41.2
+41.3
+In addition to the above ablation studies, we also discuss the
+effect of different generation blocks on the performance of our
+method. As illustrated in Table V, three different generation
+blocks are compared within the RetinaNet framework. The
+results reveal that a slightly inferior performance is reported
+by the advanced MBConv [32]. In contrast, a better result
+is achieved by simply stacking two vanilla convolutional
+layers. We assume that the channel adaptive clues learned
+from the teacher network is not compatible with MBConv
+block, because MBConv somewhat encodes the channel clues
+from the student model. This incompatibility results from the
+difference of the channel clues between the teacher and the
+student network.
+To gain a deeper insight into the effect of the Ada-Channel
+module on feature generation, we explore the following two
+TABLE VI: Comparison of different locations of Ada-channel.
+After and Within denote that we apply the channel adaptive
+clues after the generation block and between the two convo-
+lution layers, respectively.
+Student: Faster-RCNN + Res50
+Location
+After
+Within
+mAP
+42.4
+42.2
+cases with Cascade Mask-RCNN and Faster-RCNN respec-
+tively used as the teacher and the student. In the first case,
+Ada-Channel follows the generation block, and the two com-
+ponents function separately. In the other case, Ada-Channel
+is embedded within two consecutive convolution layers of the
+generation block, which implies that two modules are coupled.
+As shown in Table VI, decoupling the two components brings
+an improvement of 0.2% in mAP, suggesting that the genera-
+tion process working on the masked feature of the student is
+repulsive with other exotic clues, even the informative ones.
+D. Parameter Analysis
+In our AMD method, the hyper-parameter λ in Eq. 4
+controls the coverage of feature mask. A larger λ value
+indicates that only the points with higher attention scores of
+the teacher model are masked, and most of the pixel points
+are in the object-specific ground-truth region. In contrast, it
+
+is likely that masked points appear in the background region
+when decreasing λ. In our experiments, we discuss the effect
+of λ using RepPoints as the detection framework. It is observed
+from Fig. 4 that the highest mAP 42.7% and mAR 58.8%
+are reported when λ = 1.0, suggesting it helps the model to
+better compromise between encoding low-score and high-score
+regions.
+40
+45
+50
+55
+60
+0.7
+1
+1.5
+42.5
+42.7
+42.3
+58.4
+58.8
+58.5
+λ
+Accuracy(%)
+mAR
+mAP
+Fig. 4: Parameter λ analysis on one-stage RepPoints frame-
+work.
+V. CONCLUSION
+In this paper, we focus on the topic of feature-based masked
+distillation and propose spatial-channel adaptive masked dis-
+tillation termed AMD for object detection. On the one hand,
+we perform spatially adaptive feature masking to encode
+the region-specific importance, such that more important and
+expressive features can be learned from the teacher net-
+work. On the other hand, to improve the object-awareness
+capability, we utilize the simple and efficient SE block to
+generate informative channel-adaptive clues for the student
+model. Extensive experiments demonstrate the superiority and
+effectiveness of our method, showing that the proposed AMD
+model not only significantly boosts the performance of the
+baseline student model but also outperforms the other state-
+of-the-art distillation approaches.
+In our proposed AMD, the spatial attention map generated
+from the feature of the teacher model lacks information
+interaction. Our future work will focus on exploring alternative
+strategies to enhance the interaction among different locations
+on the attention map.
+REFERENCES
+[1] G. Hinton, O. Vinyals, J. Dean et al., “Distilling the
+knowledge in a neural network,” in Proceedings of the
+International Conference on Neural Information Process-
+ing Systems Workshop, 2014, pp. 1–9.
+[2] G. Chen, W. Choi, X. Yu, T. Han, and M. Chandraker,
+“Learning efficient object detection models with knowl-
+edge distillation,” in Proceedings of the International
+Conference on Neural Information Processing Systems
+Workshop, 2017, pp. 1–10.
+[3] A. Romero, N. Ballas, S. E. Kahou, A. Chassang,
+C. Gatta, and Y. Bengio, “Fitnets: Hints for thin deep
+nets,” in Proceedings of the International Conference on
+Learning Representations, 2015, pp. 1–13.
+[4] T. Wang, L. Yuan, X. Zhang, and J. Feng, “Distilling
+object detectors with fine-grained feature imitation,” in
+Proceedings of the IEEE Conference on Computer Vision
+and Pattern Recognition, 2019, pp. 4933–4942.
+[5] Z. Yang, Z. Li, X. Jiang, Y. Gong, Z. Yuan, D. Zhao,
+and C. Yuan, “Focal and global knowledge distillation
+for detectors,” in Proceedings of the IEEE Conference
+on Computer Vision and Pattern Recognition, 2022, pp.
+4643–4652.
+[6] Z. Yang, Z. Li, M. Shao, D. Shi, Z. Yuan, and C. Yuan,
+“Masked generative distillation,” in Proceedings of the
+European Conference on Computer Vision, 2022, pp. 1–
+17.
+[7] J. Hu, L. Shen, and G. Sun, “Squeeze-and-excitation
+networks,” in Proceedings of the IEEE Conference on
+Computer Vision and Pattern Recognition, 2018, pp.
+7132–7141.
+[8] T.-Y. Lin, P. Goyal, R. Girshick, K. He, and P. Doll´ar,
+“Focal loss for dense object detection,” in Proceedings of
+the IEEE International Conference on Computer Vision,
+2017, pp. 2980–2988.
+[9] S. Ren, K. He, R. Girshick, and J. Sun, “Faster r-cnn:
+Towards real-time object detection with region proposal
+networks,” in Proceedings of the International Confer-
+ence on Neural Information Processing Systems, 2015,
+pp. 1–9.
+[10] Z. Yang, S. Liu, H. Hu, L. Wang, and S. Lin, “Rep-
+points: Point set representation for object detection,” in
+Proceedings of the IEEE/CVF International Conference
+on Computer Vision, 2019, pp. 9657–9666.
+[11] C.-Y. Fu, W. Liu, A. Ranga, A. Tyagi, and A. C.
+Berg, “Dssd: Deconvolutional single shot detector,” arXiv
+preprint arXiv:1701.06659, 2017.
+[12] Z. Tian, C. Shen, H. Chen, and T. He, “Fcos: Fully con-
+volutional one-stage object detection,” in Proceedings of
+the IEEE International Conference on Computer Vision,
+2019, pp. 9627–9636.
+[13] N. Carion, F. Massa, G. Synnaeve, N. Usunier, A. Kir-
+illov, and S. Zagoruyko, “End-to-end object detection
+with transformers,” in Proceedings of the European Con-
+ference on Computer Vision.
+Springer, 2020, pp. 213–
+229.
+[14] S. Gidaris and N. Komodakis, “Object detection via
+a multi-region and semantic segmentation-aware cnn
+model,” in Proceedings of the IEEE International Con-
+ference on Computer Vision, 2015, pp. 1134–1142.
+[15] T. Kong, A. Yao, Y. Chen, and F. Sun, “Hypernet:
+Towards accurate region proposal generation and joint
+object detection,” in Proceedings of the IEEE Conference
+on Computer Vision and Pattern Recognition, 2016, pp.
+845–853.
+
+[16] K. He, G. Gkioxari, P. Doll´ar, and R. Girshick, “Mask
+r-cnn,” in Proceedings of the IEEE International Confer-
+ence on Computer Vision, 2017, pp. 2961–2969.
+[17] J. Redmon and A. Farhadi, “Yolov3: An incremental
+improvement,” arXiv preprint arXiv:1804.02767, 2018.
+[18] Z. Ge, S. Liu, F. Wang, Z. Li, and J. Sun, “Yolox:
+Exceeding yolo series in 2021,” in Proceedings of the
+IEEE/CVF Conference on Computer Vision and Pattern
+Recognition, 2021, pp. 1–7.
+[19] R. Girshick, “Fast r-cnn,” in Proceedings of the IEEE
+International Conference on Computer Vision, 2015, pp.
+1440–1448.
+[20] Z. Liu, Y. Lin, Y. Cao, H. Hu, Y. Wei, Z. Zhang, S. Lin,
+and B. Guo, “Swin transformer: Hierarchical vision
+transformer using shifted windows,” in Proceedings of
+the IEEE International Conference on Computer Vision,
+2021, pp. 10 012–10 022.
+[21] H. Zhang, F. Li, S. Liu, L. Zhang, H. Su, J. Zhu,
+L. M. Ni, and H.-Y. Shum, “Dino: Detr with improved
+denoising anchor boxes for end-to-end object detection,”
+in Proceedings of the IEEE Conference on Computer
+Vision and Pattern Recognition, 2022, pp. 1–23.
+[22] X. Zhu, W. Su, L. Lu, B. Li, X. Wang, and J. Dai,
+“Deformable detr: Deformable transformers for end-to-
+end object detection,” in Proceedings of the International
+Conference on Learning Representations, 2021, pp. 1–16.
+[23] S. Tang, L. Feng, W. Shao, Z. Kuang, W. Zhang,
+and Y. Chen, “Learning efficient detector with semi-
+supervised adaptive distillation,” in Proceedings of the
+IEEE Conference on Computer Vision and Pattern
+Recognition, 2019, pp. 1–9.
+[24] Q. Li, S. Jin, and J. Yan, “Mimicking very efficient
+network for object detection,” in Proceedings of the IEEE
+Conference on Computer Vision and Pattern Recognition,
+2017, pp. 6356–6364.
+[25] Z. Zheng, R. Ye, P. Wang, D. Ren, W. Zuo, Q. Hou,
+and M.-M. Cheng, “Localization distillation for dense
+object detection,” in Proceedings of the IEEE Conference
+on Computer Vision and Pattern Recognition, 2022, pp.
+9407–9416.
+[26] X. Dai, Z. Jiang, Z. Wu, Y. Bao, Z. Wang, S. Liu,
+and E. Zhou, “General instance distillation for object
+detection,” in Proceedings of the IEEE Conference on
+Computer Vision and Pattern Recognition, 2021, pp.
+7842–7851.
+[27] T.-Y. Lin, M. Maire, S. Belongie, J. Hays, P. Perona,
+D. Ramanan, P. Doll´ar, and C. L. Zitnick, “Microsoft
+coco: Common objects in context,” in European Confer-
+ence on Computer Vision.
+Springer, 2014, pp. 740–755.
+[28] L. Zhang and K. Ma, “Improve object detection with
+feature-based knowledge distillation: Towards accurate
+and efficient detectors,” in International Conference on
+Learning Representations, 2020.
+[29] K. Chen, J. Wang, J. Pang, Y. Cao, Y. Xiong, X. Li,
+S. Sun, W. Feng, Z. Liu, J. Xu et al., “Mmdetection:
+Open mmlab detection toolbox and benchmark,” arXiv
+preprint arXiv:1906.07155, 2019.
+[30] A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury,
+G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga
+et al., “Pytorch: An imperative style, high-performance
+deep learning library,” in Proceedings of the International
+Conference on Neural Information Processing Systems,
+2019, pp. 1–12.
+[31] Z. Cai and N. Vasconcelos, “Cascade r-cnn: high quality
+object detection and instance segmentation,” IEEE Trans-
+actions on Pattern Analysis and Machine Intelligence,
+vol. 43, no. 5, pp. 1483–1498, 2019.
+[32] M. Tan and Q. Le, “Efficientnet: Rethinking model scal-
+ing for convolutional neural networks,” in Proceedings
+of the International Conference on Machine Learning.
+PMLR, 2019, pp. 6105–6114.
+
diff --git a/edFRT4oBgHgl3EQfVDdZ/content/tmp_files/load_file.txt b/edFRT4oBgHgl3EQfVDdZ/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a503a4a5b82bfa9d4c227025a0b4947262aea122
--- /dev/null
+++ b/edFRT4oBgHgl3EQfVDdZ/content/tmp_files/load_file.txt
@@ -0,0 +1,760 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf,len=759
+page_content='AMD: Adaptive Masked Distillation for Object  Detection  Guang Yanga, Yin Tangb, Jun Lia�,Jianhua Xua,Xili Wanb  a School of Computer and Electronic Information, Nanjing Normal University, Nanjing, China  b School of Computer Science and Technology, Nanjing Tech University, Nanjing, China  {Jun Li}lijuncst@njnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='cn  Abstract—As a general model compression paradigm, feature-  based knowledge distillation allows the student model to learn  expressive features from the teacher counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In this paper,  we mainly focus on designing an effective feature-distillation  framework and propose a spatial-channel adaptive masked distil-  lation (AMD) network for object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' More specifically, in  order to accurately reconstruct important feature regions, we first  perform attention-guided feature masking on the feature map of  the student network, such that we can identify the important  features via spatially adaptive feature masking instead of random  masking in the previous methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In addition, we employ a simple  and efficient module to allow the student network channel to  be adaptive, improving its model capability in object perception  and detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In contrast to the previous methods, more crucial  object-aware features can be reconstructed and learned from  the proposed network, which is conducive to accurate object  detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The empirical experiments demonstrate the superiority  of our method: with the help of our proposed distillation method,  the student networks report 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3%, 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4%, and 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7% mAP  scores when RetinaNet, Cascade Mask-RCNN and RepPoints are  respectively used as the teacher framework for object detection,  which outperforms the previous state-of-the-art distillation meth-  ods including FGD and MGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Index Terms—Feature-based Knowledge Distillation, Object  Detection, Adaptive Masked Distillation, Object-Aware Features  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' INTRODUCTION  Recent years have witnessed successful and pervasive ap-  plications of Deep Convolutional Neural Networks (CNNs) in  various computer vision tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' However, deep CNNs usually  cost a huge amount of computational resources in pursuit  of higher performance, which adversely affects their deploy-  ment in practical applications and leads to severe parameter  redundancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' It is therefore necessary to transfer the dark  knowledge learned in the complex networks (teacher) to  another lightweight network (student).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' This is also termed as  knowledge distillation [1] which allows the student model to  generate expressive features learned from the teacher model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Thus, it is more preferable to deploy the student model  with compact network architecture sacrificing minimal loss of  performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  The earliest distillation algorithms function mainly at the  output head.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The representative examples include logit-based  distillation for classification and head-based distillation for  detection [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Recently, a more common distillation strategy  emerges as feature-based distillation mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Since only  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1: Different regions are quantified with varying attention  scores in the feature map of teacher model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The regions  with higher scores encode the region importance and should  outweigh the low-score regions in the feature masking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  the head or projector after the generated feature varies within  different networks, the feature-based distillation approaches  can potentially be employed in a variety of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' There-  fore, it has become a prominent line of research for both  model compression and performance improvement due to  its simplicity and efficacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In object detection, in particular,  a variety of feature-based distillation approaches have been  developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The earlier research, such as FitNet [3], performs  distillation at the global level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' FGFI [4] operates by distilling  the features of high IoU between ground truth and anchors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  FGD [5] was developed to separate distillation of foreground  and background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Recent research suggests it is preferable for  the student model to reconstruct and learn expressive features  from the teacher model in the first place instead of following  the teacher for generating competitive representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' For  instance, MGD [6] was proposed to randomly mask pixels in  the feature map of student network, leading to reconstructed  features of the teacher model via a simple block.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Although MGD further improves the feature distillation  by reconstructing the features of masked areas, the masked  regions are generated in a random manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' This random  operation fails to identify the region-specific importance, and  is likely to cause the student model to generate features of  the teacher in unimportant regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' As illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1,  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='13538v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='CV]  31 Jan 2023  Spatial Attention  Mask  Feature  Mask  Backbone  (Neck)  SE block  3×3  3×3  Distillation  Teacher  Spatial Attention  R  1× H× W  R  C×H× W  R  C×1× 1  R  C×H× W  R  C×H× W  Avg pooling  RELU  FC  FC  Sigmoid  Backbone  (Neck)  SE block  ReLU  Student  Teacher  Generation  Block  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 2: The proposed AMD distillation framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' It first learns the adaptive Region-of-Interest (RoI) via attention-guided  feature masking, generating the spatial mask clue from the teacher model imposed on the student feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Furthermore, we  apply the simple and efficient SE layer to the feature of the teacher model, leading to the channel adaptive clues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The auxiliary  clues are then fused with the output from the generation block via a Hadamard product, such that the generated feature from  the student model is channel adaptive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  the importance of different regions in the feature map of  a teacher model can be quantified using the region-specific  attention scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Only the regions with higher scores play  critical role in feature masking while the low-score regions  should be downplayed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  To alleviate the above-mentioned drawback, we propose an  adaptive masked distillation (AMD) framework which enjoys  object-aware spatial and channel adaptivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' On the one hand,  we perform attention-guided spatial masking instead of ran-  dom masking on the feature map of the student network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' More  specifically, we first learn a spatial attention map from the  feature map of the teacher model, producing a region-specific  mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Then, the feature of the student network is adaptively  masked by using this attention map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Benefiting from this  selective feature masking, it allows subsequent generation  block to focus on those adaptively masked important areas,  leading to robust and expressive representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' On the other  hand, to further explore the object-awareness capability, we  leverage a simple and effective SE layer [7] for modeling the  channel attention of the resulting feature of the teacher model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  The learned clue and the output from the generation block  of students will be fused via a Hadamard product, achieving  desirable object-aware channel adaptivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  To summarize, the contributions of this paper are threefold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  First, we develop a spatially adaptive feature masking  mechanism for the student model, such that the region-  specific importance can be encoded in the features recon-  structed and learned from the teacher network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Second, we further explore the channel adaptivity by  introducing a simple and efficient SE module to improve  the object-aware capability of the student model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Third, we evaluate our proposed feature distillation net-  work AMD using various detection frameworks includ-  ing one-stage detector RetinaNet [8], two-stage detec-  tor Faster-RCNN [9], and anchor free model RepPoint  [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Extensive experimental results demonstrate that  our method can help to learn features with sufficient  descriptive capability and achieve significant performance  gains over the previous state-of-the-art methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  The remainder of this paper is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' After  reviewing the related work in Section II, we elaborate on our  method in Section III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Next, we conduct extensive experi-  mental evaluations in Section IV before the paper is finally  concluded in Section V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' RELATED WORK  In this section, we comprehensively review the recent ad-  vance in object detection and knowledge distillation, both of  which are closely related to our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Object Detection  As one fundamental vision task, object detection aims to  determine the category and location of the objects in an  image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Over recent years, the success of CNNs has enormously  advanced the research in object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In general, the  detectors based on deep CNNs can be classified into three  categories including anchor-based detectors [9, 11], anchor-  free detectors [12] and end-to-end detectors [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In particular,  anchor-based detection models are divided into two-stage  [9, 14–16] and one-stage detectors [11, 17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The former  detection method, represented by R-CNN like [9, 19] algo-  rithms, has a higher detection accuracy, whereas its inference  speed is usually unsatisfactory due to expensive computational  costs incurred by region proposal network (RPN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' As a result,  it is impractical for some real-time scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In contrast, one-  stage detectors directly perform classification and regression  on the anchors without generating proposals beforehand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Thus,  they run faster with guaranteed detection performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  While recent deep networks achieve high detection accu-  racy, they usually rely on complex backbone structure and  significant computational resources [13, 20–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In this sense,  designing lightweight and efficient backbone networks has  emerged as a major line of research in object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In  particular, knowledge distillation, which can transfer sufficient  descriptive power from a large network to a small network, is  beneficial for designing lightweight backbone with maintained  performance close to the large network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Knowledge Distillation  Recently, knowledge distillation has received increasing  attention in model compression, since it is capable of retaining  compact model structure with promoted performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Hinton  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' [1] first came up with the concept of knowledge  distillation by introducing the soft label of the teacher network  as part of the loss of the student network, allowing the student  network to learn probability distribution fitting of the teacher  model for classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Moreover, Romero et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' [3]  demonstrated that semantic information in the intermediate  layer can also be learned as dark knowledge by student  networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Thus, knowledge distillation can therefore be widely  applied to a wide range of downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' [2]  distilled the neck feature, classification head, and regression  head by setting up three loss functions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Tang  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' [23] carefully designed the distillation weights and  distillation loss functions such that they are automatically  adjusted between samples for the single-stage object detector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' [24] used region proposals of the larger network to  help the smaller network learn higher semantic information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Zheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' [25] transferred the knowledge distillation of the  classification head to the location head of object detection,  leading to a new distillation mechanism termed Localization  Distillation (LD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' LD makes logit mimicking become a better  alternative to feature imitation, and reveals the knowledge  of object category and object location should be handled  separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' [26] developed GID framework which  selects distillation areas based on differences between the  student and teacher networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' proposed FGD [5]  which separates the foreground and background, enabling the  student model to learn from the teacher network areas of  interest and global knowledge via local and global distillation  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Besides, MGD [6] imposes random masking on  the feature map of the student model, and then generates  the feature map reconstructing from the teacher network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  However, the uncertainty of random masking may introduce  additional noise, producing biased feature map with compro-  mised representation capability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' THE PROPOSED APPROACH  Recently, a massive amount of distillation methods are  carefully designed for various model architectures and tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Typically, the feature maps used for distillation usually have  high-level semantics and spatial information about adjacent  pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Therefore, learning these features from the teacher  model can significantly improve the performance of the stu-  dent model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Mathematically, basic feature distillation can be  formulated as:  Lfea =  1  CHW  C  �  k=1  H  �  i=1  W  �  j=1  �  F T  k,i,j − f  �  F S  k,i,j  ��2  (1)  where C, H, and W denote the channel, height, and width of  the feature map, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' F T and F S denote the feature  generated from the teacher model and its counterpart from the  student model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' f represents the adaptation layer that aligns the  shape of F S and F T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Recent research suggests learning and reconstructing the  features of the teacher model is a desirable alternative to  feature imitation [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' More specifically, expressive features  can be generated from the masked regions on the feature  map of the student network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' However, previous state-of-the-  art method mainly performs random feature masking without  identifying the importance of different regions on the feature  map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In this paper, we attempt to make the student model  generate features corresponding to the important areas on the  feature map of the teacher network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Towards this end, we  propose a spatial-channel adaptive masked distillation strategy  termed AMD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In contrast to the random masking strategy in  the previous method, we perform feature masking via region-  aware attention for identifying the important areas in the  feature map of the teacher network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In order to improve the  object-aware capability, we further introduce a simple and  efficient SE module such that the resulting features are channel  adaptive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The framework of our proposed method is illustrated  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Spatially adaptive feature masking  Using random pixels to recover the complete feature map,  MGD allows the masked features of the student model to  generate features of the teacher model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Thus, it is beneficial for  the student network to obtain a better representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' However,  the region-specific importance is discarded due to the random  masking in MGD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' To alleviate this drawback, we carefully  design the region-aware feature masking with the help of  spatial attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' To begin with, we calculate the absolute mean  value of the teacher network along the channel dimension:  GS(F) = 1  C  C  �  k=1  ��F T  k  ��  (2)  where C denotes the channel number of the feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' F T is the  feature of the teacher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' GS(F) is the spatial representation map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Then, the spatial attention mask resulting from the teacher  model can be formulated as:  AS(F) = H · W · softmax  �  GS(F)/T  �  (3)  where T is a hyper-parameter introduced in [1] to change the  probability distribution such that the shape of the resulting AS  FGD  mAP:40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  MGD  mAP:41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  Ours  mAP:41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 3: Visualisation of the feature maps obtained by different distillation methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Teacher detector is RetinaNet-ResNeXt101  while student detector is RetinaNet-ResNet50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  is 1×H ×W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The attention score for each location represents  the level of interest in the teacher network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Furthermore, the  mask value is set to 0 when the attention score is greater than  λ and the rest are set to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' This can be expressed as:  Mi,j =  � 0,  if AS  i,j > λ  1,  Otherwise  (4)  where AS  i,j is the spatial attention score at the point with  coordinates (i, j) on the feature map of the teacher network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  λ is a hyper-parameter to control the number of pixels in the  mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Next, we cover the feature map of the student model  with the mask M, which can be formulated as follows:  F S  mask = F S · M  (5)  In a nutshell, with the help of this attention-guided feature  masking, we can mask out the student feature map according  to the important regions of interest on the teacher counterpart,  and the resulting feature will contain more important semantic  information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Channel adaptive clues generation  Different from single-object recognization tasks such as  image classification, object detection is a dense prediction task  focusing on detecting multiple objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Except for the effective  receptive field (ERF), the capability of capturing the object  information in different scales can also bring a significant  performance fluctuation for a detector, which is not considered  in the previous work [5, 6, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Therefore, we utilize a simple  and lightweight SE layer [7] to learn the channel adaptive clue  from the teacher feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The resulting channel adaptive clue  will be applied to enhance the student’s feature, and further  improve the object-awareness capability:  F T  clue = σ  �  WL1  �  WL2  �  F T  avg;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' θ1  �  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' θ2  ��  ,  GS(F S  mask) = WC1  �  ReLU  �  WC2(F S  mask;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' θ1)  �  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' θ2  �  ⊙ F T  clue,  (6)  where F T  clue ∈ R1×1×C denotes the learned channel adaptive  clue for the student feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' It is fused with the output  from the generation block via a Hadamard product denoted  as ⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The WL(·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' θ) and WC(·;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' θ) are weight matrices of  linear projection and convolution layer for SE and generation  modules, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Benefiting from this design, our model further explores the  object-aware potential, resulting in a significant improvement  over those vanilla counterparts, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=', models with no channel-  adaptive design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' More interestingly, we observe that our AMD  can achieve a remarkable mAP improvement in the case of  detecting small objects, demonstrating the effectiveness of our  proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' We also provide the visualization results of  the feature map derived from different distillation models as  shown in Fig 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' It can be easily observed that the object feature  produced from our AMD is more distinguishable than those  of methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Loss function  Based on the proposed distillation method, we design the  following distillation loss for AMD:  Lfea =  C  �  k=1  H  �  i=1  W  �  j=1  �  F T  k,i,j − GS(F S  mask)  �2  (7)  where C, H, and W respectively denote the channel number,  height and width of the feature map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' F S  mask denotes the  masked student feature map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Thus, the overall loss function  is as follows:  Loverall  �  F T , F S�  = α · Lfea + Loriginal  (8)  where α is a hyper-parameter to balance distillation loss and  original loss, and Loriginal is the original loss of the detection  task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' EXPERIMENT  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Experimental Setting  To verify the effectiveness of our AMD for object detection,  we evaluate our method on MS COCO2017 [27] benchmark  dataset, which contains 80 object categories and over 160k  images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' We use 120k training images for training and 5k  validation images for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' For performance measures, we  use Average Precision (AP) and Average Recall (AR) to  evaluate the performance of different object detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Three  mainstream detectors including the anchor-based one-stage  detector RetinaNet [8], the two-stage detector Faster-RCNN  [9], and the anchor-free detector RepPoint [10] are involved  in our comprehensive experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In addition, ResNeXt101  and ResNet50 are respectively used as the backbone of the  teacher network and its student counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  We also conduct a series of ablation studies to ex-  plore the effects of individual components on the per-  formance  of  our  AMD  framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  In  implementation,  TABLE I: Comparison of our method with other distillation methods for object detection on COCO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Teacher  Student  mAP  APS  APM  APL  mAR  ARS  ARM  ARL  RetinaNet-Res50  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9  33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  FKD [28]  39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2)  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2)  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  FGD [5]  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3)  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9)  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  MGD [6]  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1)  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  RetinaNet  ResNeXt101  (41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0)  AMD (ours)  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5)  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  RepPoints-Res50  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9  59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  FKD [28]  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9 (+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8)  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9  71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  FGD [5]  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4)  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1)  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  MGD [6]  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7)  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3)  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9  RepPoints  ResNeXt101  (44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2)  AMD (ours)  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7 (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1)  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7)  40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  Faster RCNN-Res50  38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  FKD [28]  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4 (+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4)  34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9  FGD [5]  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4)  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  MGD [6]  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7)  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5)  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  Cascade  Mask RCNN  ResNeXt101  (47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3)  AMD (ours)  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4 (+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0)  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8 (+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8)  35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  all the experiments are conducted on a server with one  RTX3090 GPU using MMdetection toolbox [29] and Py-  torch framework [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Besides, the hyper-parameters are  empirically set to  �  α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5 × 10−7, λ = 1, T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  �  and  �  α = 4 × 10−6, λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2, T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  �  for the one-stage models  and the two-stage models respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' During the training  process, SGD optimizer is used for training all the detectors  within 24 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Meanwhile, momentum is set as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9 whilst  weight decay is set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Moreover, single-scale training  strategy is utilized in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Results  In our comparative studies, we carry out three groups of  experiments to evaluate different distillation methods with the  three popular detectors involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The corresponding experi-  mental results are shown in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  In the first group of experiments, RetinaNet is used as the  detection framework for both the teacher and the student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  The corresponding experimental results demonstrate that our  distillation method provides significant performance boosts of  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9% in mAP over the baseline student network by reporting  the highest accuracy at 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' This result consistently outper-  forms the state-of-the-art methods FGD and MGD by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6%  and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3%, while it even surpasses the teacher model achieving  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0% mAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Similar performance improvement can also be ob-  served with respect to mAR metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The experimental setting  in the second group is analogous to the first one except that the  RetinaNet framework is replaced with RepPoints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Consistent  with the results in the first group, dramatic performance gains  of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1% in mAP and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7% in mAR are reported, and similar  performance superiority to the competing distillation methods  is also demonstrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The results reveal that our method can  adaptively learn more important information from the teacher  and significantly contribute to the improvement of the student  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  To further assess the generalization capability of our pro-  posed method, we make use of different detection frameworks  for the teacher and student models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' To be specific, the more  powerful detector Cascade Mask-RCNN is used as the teacher  network while the Faster-RCNN for the student model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' As  shown in Table I, our method boosts the baseline student  model from 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4% to 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4% in mAP and from 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0% to 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8%  in mAR, outperforming MGD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3% both in mAP and mAR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' It  sufficiently suggests our method is independent of the specific  detector and shows consistent advantages in cross-framework  scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ablation Study  In this section, we conduct extensive ablation experiments  to explore the effect of different configurations on the pro-  posed AMD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Consistent with the above setting, the ablation  experiments with different configurations are conducted based  on the three popular detectors, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=', RetinaNet, Faster-RCNN,  and RepPoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  As shown in Table II, when RetinaNet is used for the  detection framework for both the teacher and the student, we  explore two primary modules in our AMD model, namely  the spatially adaptive masking (Ada-Mask) and the channel  adaptive clues generation (Ada-Channel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' It is observed that  the complete AMD model including both the Ada-Mask and  Ada-Channel components achieves the best results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Further-  more, when we remove either component, there is a clear  performance drop in particular in the small-object detection  scenario (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3%↓ w/o Ada-Mask and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5%↓ w/o Ada-Channel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  This implies that our AMD method can improve object-  awareness capability which is crucial for dense prediction  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  When the RetinaNet is replaced with the RepPoint, similar  results can be obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' As displayed in Table III, both the  Ada-Mask and Ada-Channel components play critical roles  in our AMD model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Specifically, single Ada-Mask module  reports 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4%, 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3% and 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0% in APS, APM and APL  scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' With the help of additional channel adaptive clues, fur-  ther performance gains of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4%, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2% and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3% are reported  for the respective metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Furthermore, we also perform ablation studies in cross-  framework scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Specifically, the Cascade Mask-RCNN  is used as the teacher network, while the Faster-RCNN as the  student counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' As shown in Table IV, the complete AMD  model achieves the highest accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In particular, the highest  TABLE II: Ablation studies using RetinaNet [8] framework for both the teacher and the student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The backbone of the teacher  network is ResNeXt-101 whilst its student counterpart is ResNet-50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ada-Mask and Ada-channel respectively denote spatially  adaptive masking and channel adaptive clue generation module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' They constitute two main components in our proposed AMD  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Ada-Mask  Ada-Channel  Student: RetinaNet + Res50  AP b  AP b  50  AP b  75  APS  APM  APL  \x14  \x14  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='9  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  \x14  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  \x14  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  TABLE III: Ablation studies using RepPoint [10] framework for both the teacher and the student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' ResNeXt-101 and ResNet-50  are respective backbones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Ada-Mask  Ada-Channel  Student: RepPoint + Res50  AP b  AP b  50  AP b  75  APS  APM  APL  \x14  \x14  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  \x14  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  \x14  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  TABLE IV: Ablation studies in a cross-framework scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The Cascade Mask-RCNN [31] is employed for the teacher  framework, while the Faster R-CNN is for the student counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Ada-Mask  Ada-Channel  Student: Faster-RCNN + Res50  AP b  AP b  50  AP b  75  APS  APM  APL  \x14  \x14  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  \x14  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  \x14  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='6  56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  APS score 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='1% is reported, outperforming the other settings  w/o either Ada-Mask or Ada-Channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' This indicates that our  AMD model benefits small-object detection with improved  object-awareness capability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  TABLE V: Comparison of different generation blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' For  MBConv [32], we use 5 × 5 depthwise convolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Student: RetinaNet-Res50  Generation Block  MBConv  3 × 3 Dense Conv * 1  3 × 3 Dense Conv * 2  mAP  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  In addition to the above ablation studies, we also discuss the  effect of different generation blocks on the performance of our  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' As illustrated in Table V, three different generation  blocks are compared within the RetinaNet framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' The  results reveal that a slightly inferior performance is reported  by the advanced MBConv [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In contrast, a better result  is achieved by simply stacking two vanilla convolutional  layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' We assume that the channel adaptive clues learned  from the teacher network is not compatible with MBConv  block, because MBConv somewhat encodes the channel clues  from the student model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' This incompatibility results from the  difference of the channel clues between the teacher and the  student network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  To gain a deeper insight into the effect of the Ada-Channel  module on feature generation, we explore the following two  TABLE VI: Comparison of different locations of Ada-channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  After and Within denote that we apply the channel adaptive  clues after the generation block and between the two convo-  lution layers, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Student: Faster-RCNN + Res50  Location  After  Within  mAP  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2  cases with Cascade Mask-RCNN and Faster-RCNN respec-  tively used as the teacher and the student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In the first case,  Ada-Channel follows the generation block, and the two com-  ponents function separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In the other case, Ada-Channel  is embedded within two consecutive convolution layers of the  generation block, which implies that two modules are coupled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  As shown in Table VI, decoupling the two components brings  an improvement of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='2% in mAP, suggesting that the genera-  tion process working on the masked feature of the student is  repulsive with other exotic clues, even the informative ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Parameter Analysis  In our AMD method, the hyper-parameter λ in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 4  controls the coverage of feature mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' A larger λ value  indicates that only the points with higher attention scores of  the teacher model are masked, and most of the pixel points  are in the object-specific ground-truth region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In contrast, it  is likely that masked points appear in the background region  when decreasing λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' In our experiments, we discuss the effect  of λ using RepPoints as the detection framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' It is observed  from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 4 that the highest mAP 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7% and mAR 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8%  are reported when λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='0, suggesting it helps the model to  better compromise between encoding low-score and high-score  regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  40  45  50  55  60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='7  42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='3  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='4  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='8  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='5  λ  Accuracy(%)  mAR  mAP  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 4: Parameter λ analysis on one-stage RepPoints frame-  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' CONCLUSION  In this paper, we focus on the topic of feature-based masked  distillation and propose spatial-channel adaptive masked dis-  tillation termed AMD for object detection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' On the one hand,  we perform spatially adaptive feature masking to encode  the region-specific importance, such that more important and  expressive features can be learned from the teacher net-  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' On the other hand, to improve the object-awareness  capability, we utilize the simple and efficient SE block to  generate informative channel-adaptive clues for the student  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Extensive experiments demonstrate the superiority and  effectiveness of our method, showing that the proposed AMD  model not only significantly boosts the performance of the  baseline student model but also outperforms the other state-  of-the-art distillation approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  In our proposed AMD, the spatial attention map generated  from the feature of the teacher model lacks information  interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Our future work will focus on exploring alternative  strategies to enhance the interaction among different locations  on the attention map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  REFERENCES  [1] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Hinton, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Vinyals, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Dean et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=', “Distilling the  knowledge in a neural network,” in Proceedings of the  International Conference on Neural Information Process-  ing Systems Workshop, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [2] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Chen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Choi, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Han, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Chandraker,  “Learning efficient object detection models with knowl-  edge distillation,” in Proceedings of the International  Conference on Neural Information Processing Systems  Workshop, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Romero, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ballas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Kahou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Chassang,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Gatta, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Bengio, “Fitnets: Hints for thin deep  nets,” in Proceedings of the International Conference on  Learning Representations, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yuan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Feng, “Distilling  object detectors with fine-grained feature imitation,” in  Proceedings of the IEEE Conference on Computer Vision  and Pattern Recognition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 4933–4942.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [5] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Jiang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Gong, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yuan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhao,  and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yuan, “Focal and global knowledge distillation  for detectors,” in Proceedings of the IEEE Conference  on Computer Vision and Pattern Recognition, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  4643–4652.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [6] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Shao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Shi, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yuan, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yuan,  “Masked generative distillation,” in Proceedings of the  European Conference on Computer Vision, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Hu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Shen, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Sun, “Squeeze-and-excitation  networks,” in Proceedings of the IEEE Conference on  Computer Vision and Pattern Recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  7132–7141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [8] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Lin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Goyal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Girshick, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' He, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Doll´ar,  “Focal loss for dense object detection,” in Proceedings of  the IEEE International Conference on Computer Vision,  2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 2980–2988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ren, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' He, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Girshick, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Sun, “Faster r-cnn:  Towards real-time object detection with region proposal  networks,” in Proceedings of the International Confer-  ence on Neural Information Processing Systems, 2015,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [10] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Hu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Wang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Lin, “Rep-  points: Point set representation for object detection,” in  Proceedings of the IEEE/CVF International Conference  on Computer Vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 9657–9666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [11] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Fu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ranga, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Tyagi, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Berg, “Dssd: Deconvolutional single shot detector,” arXiv  preprint arXiv:1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='06659, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [12] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Tian, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Shen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Chen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' He, “Fcos: Fully con-  volutional one-stage object detection,” in Proceedings of  the IEEE International Conference on Computer Vision,  2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 9627–9636.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [13] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Carion, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Massa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Synnaeve, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Usunier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Kir-  illov, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zagoruyko, “End-to-end object detection  with transformers,” in Proceedings of the European Con-  ference on Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Springer, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 213–  229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Gidaris and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Komodakis, “Object detection via  a multi-region and semantic segmentation-aware cnn  model,” in Proceedings of the IEEE International Con-  ference on Computer Vision, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1134–1142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [15] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Kong, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Chen, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Sun, “Hypernet:  Towards accurate region proposal generation and joint  object detection,” in Proceedings of the IEEE Conference  on Computer Vision and Pattern Recognition, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  845–853.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [16] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' He, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Gkioxari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Doll´ar, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Girshick, “Mask  r-cnn,” in Proceedings of the IEEE International Confer-  ence on Computer Vision, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 2961–2969.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Redmon and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Farhadi, “Yolov3: An incremental  improvement,” arXiv preprint arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='02767, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [18] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ge, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Liu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Li, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Sun, “Yolox:  Exceeding yolo series in 2021,” in Proceedings of the  IEEE/CVF Conference on Computer Vision and Pattern  Recognition, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Girshick, “Fast r-cnn,” in Proceedings of the IEEE  International Conference on Computer Vision, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  1440–1448.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [20] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Cao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Wei, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Lin,  and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Guo, “Swin transformer: Hierarchical vision  transformer using shifted windows,” in Proceedings of  the IEEE International Conference on Computer Vision,  2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 10 012–10 022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [21] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Su, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhu,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ni, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Shum, “Dino: Detr with improved  denoising anchor boxes for end-to-end object detection,”  in Proceedings of the IEEE Conference on Computer  Vision and Pattern Recognition, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [22] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Su, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Lu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Wang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Dai,  “Deformable detr: Deformable transformers for end-to-  end object detection,” in Proceedings of the International  Conference on Learning Representations, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [23] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Tang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Feng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Shao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Kuang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhang,  and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Chen, “Learning efficient detector with semi-  supervised adaptive distillation,” in Proceedings of the  IEEE Conference on Computer Vision and Pattern  Recognition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [24] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Jin, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Yan, “Mimicking very efficient  network for object detection,” in Proceedings of the IEEE  Conference on Computer Vision and Pattern Recognition,  2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 6356–6364.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [25] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zheng, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ye, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ren, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zuo, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Hou,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Cheng, “Localization distillation for dense  object detection,” in Proceedings of the IEEE Conference  on Computer Vision and Pattern Recognition, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  9407–9416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [26] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Dai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Jiang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Bao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Liu,  and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhou, “General instance distillation for object  detection,” in Proceedings of the IEEE Conference on  Computer Vision and Pattern Recognition, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  7842–7851.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [27] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Lin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Maire, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Belongie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Hays, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Perona,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ramanan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Doll´ar, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zitnick, “Microsoft  coco: Common objects in context,” in European Confer-  ence on Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  Springer, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 740–755.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [28] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Zhang and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Ma, “Improve object detection with  feature-based knowledge distillation: Towards accurate  and efficient detectors,” in International Conference on  Learning Representations, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [29] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Pang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Xiong, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Li,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Sun, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Feng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=', “Mmdetection:  Open mmlab detection toolbox and benchmark,” arXiv  preprint arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='07155, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [30] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Paszke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Gross, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Massa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Lerer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Bradbury,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Chanan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Killeen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Lin, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Gimelshein, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Antiga  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=', “Pytorch: An imperative style, high-performance  deep learning library,” in Proceedings of the International  Conference on Neural Information Processing Systems,  2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [31] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Cai and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Vasconcelos, “Cascade r-cnn: high quality  object detection and instance segmentation,” IEEE Trans-  actions on Pattern Analysis and Machine Intelligence,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 43, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 1483–1498, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  [32] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Tan and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' Le, “Efficientnet: Rethinking model scal-  ing for convolutional neural networks,” in Proceedings  of the International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content='  PMLR, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
+page_content=' 6105–6114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/edFRT4oBgHgl3EQfVDdZ/content/2301.13538v1.pdf'}
diff --git a/hNAyT4oBgHgl3EQfXffW/content/tmp_files/2301.00186v1.pdf.txt b/hNAyT4oBgHgl3EQfXffW/content/tmp_files/2301.00186v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5509f61a332be764f1544c97c01e717e4467fe52
--- /dev/null
+++ b/hNAyT4oBgHgl3EQfXffW/content/tmp_files/2301.00186v1.pdf.txt
@@ -0,0 +1,3782 @@
+QUANTITATIVE MEAN ERGODIC INEQUALITIES: POWER
+BOUNDED OPERATORS ACTING ON ONE SINGLE
+NONCOMMUTATIVE Lp SPACE
+GUIXIANG HONG, WEI LIU, AND BANG XU
+Abstract. In this paper, we establish the quantitative mean ergodic theorems for
+two subclasses of power bounded operators on a fixed noncommutative Lp-space
+with 1 < p < ∞, which mainly concerns power bounded invertible operators and
+Lamperti contractions. Our approach to the quantitative ergodic theorems is the
+noncommutative square function inequalities. The establishment of the latter involves
+several new ingredients such as the almost orthogonality and Calder´on-Zygmund
+arguments for non-smooth kernels from semi-commutative harmonic analysis, the
+extension properties of the operators under consideration from operator theory, and
+a noncommutative version of the classical transference method due to Coifman and
+Weiss.
+1. Introduction
+In classical ergodic theory, there are many papers related to the convergence prop-
+erties of certain averages along the orbits with respect to the transformations. Let
+(X, F, µ) be a σ-finite measure space. The celebrated von Neumann’s mean ergodic
+theorem [47] stated that when T is a unitary operator on L2(X, µ) induced by a µ-
+preserving measurable transformation on X, the ergodic averages Mnf defined by
+(1.1)
+Mnf(x) =
+1
+n + 1
+n
+�
+k=0
+T kf(x) n ∈ N,
+converges in L2(X) for any f ∈ L2(X). Later on, Riesz [43] greatly generalized the von
+Neumann’s mean ergodic theorem; he proved that the convergence of ergodic averages
+is also valid for contractive operators defined simultaneously on all Lp(X, µ) (1 ≤
+p ≤ ∞) spaces, where (X, µ) is a probability space. Also, Riesz gave a simple proof
+when T is a contraction operator on some Hilbert space [44]. Furthermore, the mean
+ergodic theorem for Lp (1 ≤ p ≤ ∞)-contractions acting on general Banach spaces was
+established by Dunford and Schwartz [11, VIII.5].
+It is then natural to ask for the speed of the convergence of the ergodic averages.
+Unfortunately, Krengel [28] proved that the speed of the ergodic convergence can be
+arbitrarily slow. On the other hand, one can not capture any information on the rate
+of the convergence from the classical proofs of aforementioned works. With the aid of
+Date: January 3, 2023.
+2010 Mathematics Subject Classification. Primary 46L52; Secondary 46L53, 46L51, 46L55.
+Key words and phrases. Mean ergodic theorems, Noncommutative square functions, Noncommuta-
+tive Lp spaces.
+This work was partially supported by Natural Science Foundation of China (Grant: 12071355).
+1
+arXiv:2301.00186v1  [math.FA]  31 Dec 2022
+
+2
+G. HONG, W. LIU, AND B. XU
+the spectral theorem and the dilation theorem developed in [46], Jones, Ostrovskii and
+Rosenblatt [22] established the square function inequalities for ergodic averages (1.1)
+associated with a contraction on L2(X). More precisely, they proved that for a L2-
+contraction T and any sequence of finite positive integers n0 < n1 < · · · < nm
+(1.2)
+� m
+�
+i=1
+��Mni(T)f − Mni−1(T)f
+��2
+L2(X)
+�1/2
+≤ 25∥f∥L2(X).
+This result can be viewed as a quantitative and finer version of the mean ergodic the-
+orem. Indeed, (1.2) implies that for any ε > 0, the sequence (Mn(f))∞
+n=1 admits at
+most 625(ε−2∥f∥2
+2) jumps of size at least ε in L2 norm, and as a consequence the se-
+quence converges. Moreover, many variants of the inequality (1.2) have been obtained.
+Avigad and Rute [3] extended (1.2) with the power 2 of (1.2) replaced by q (q ≥ 2) to
+q-uniformly convex Banach spaces and specific power bounded operators. Bourgain [5]
+(see also Jones et al [23]) considered the variational inequalities, which may deduce the
+inequality (1.2) and the pointwise convergence of ergodic averages. We remark that
+Calder´on’s transference principle plays an important role in the above papers which
+reduces (1.2) to the study of the related operators in harmonic analysis where more
+tools are available.
+Motivated by quantum physics, the convergence of the ergodic averages in von Neu-
+mann algebras has attracted much attention.
+For instance, Kov´acs and Sz¨ucs [27]
+considered the mean ergodic theorem for an automorphism T on von Neumann alge-
+bras equipped with a faithful T-invariant semifinite normal state, and Lance [30] gave a
+complete discussion of this subject. Later on, Yeadon [48, 49] established the mean er-
+godic theorem for positive Dunford-Schwartz operators on noncommutative Lp spaces.
+For more results about the mean ergodic theorem in von Neumann algebras we refer
+the reader to [19, 20]. On the other hand, on the study of pointwise ergodic theorems
+in noncommutative Lp, after the work in the case p = ∞ [30, 29, 9] and in the case
+p = 1 [48], a breakthrough was made by Junge and Xu [26], where they established
+the noncommutative maximal ergodic inequalities for positive Dunford-Schwartz op-
+erators. This celebrated work motivated further research on noncommutative ergodic
+theory, such as [2, 4, 16, 18, 31]. In particular, the first author and his collaborators
+broke the framework of Junge and Xu by establishing the maximal and pointwise er-
+godic theorems for a large subclass of positive operators on one single noncommutative
+Lp space, see [13, 15] for more details.
+However, to the best of the authors’ knowledge, there is no quantitative estimate of
+noncommutative ergodic theorems in the literature. This paper is devoted to the first
+study of quantitative mean ergodic theorem (1.2) under the noncommutative framwork.
+To better state our results, we need to introduce some notions. Let M be a semifinite
+von Neumann algebra equipped with a normal semifinite faithful (abbrieviated as n.s.f )
+trace τ. Let Lp(M) be the associated noncommutative Lp space and Lp(M; ℓrc
+2 ) be
+one noncommutative analogue of Hilbert-valued Lp space (see Section 2 for the precise
+definition). Throughout the paper, T stands for a bounded linear operator on Lp(M).
+The one-sided ergodic averages Mn(T) is defined as
+Mn(T) =
+1
+n + 1
+n
+�
+k=0
+T k,
+∀ n ∈ N;
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+3
+and if T is invertible, one defines the two-sided ergodic averages Bn(T) by
+Bn(T) =
+1
+2n + 1
+n
+�
+k=−n
+T k,
+∀ n ∈ N.
+Theorem 1.1. Let 1 < p < ∞. Suppose that T satisfy
+(1.3)
+sup
+k∈Z
+∥T k : Lp(M) → Lp(M)∥ < ∞.
+Then there exists a positive constant Cp such that
+sup
+���
+Bni(T)x − Bni+1(T)x
+�
+i∈N
+��
+Lp(M;ℓrc
+2 ) ≤ Cp∥x∥Lp(M), ∀x ∈ Lp(M)
+where the supremum is taken over all the increasing subsequence (ni)i∈N of positive
+integers. Similar inequality holds for one-sided ergodic averages (Mn(T))n∈N.
+Remark 1.2. Theorem 1.1 is a noncommutative version of [22, Theorem 1.2]. Note
+also that Theorem 1.1 can be viewed as an ergodic theorem with respect to a bounded
+Lp(M)-representation of the group Z.
+And for the bounded noncommuative Lp-
+representations of other groups such as the ones of polynomial growth that appeard in
+[13], similar quantitative mean ergodic theorems still hold. These results will appear
+in a forthcoming paper [14].
+The second main result concerns the quantitative mean theorem for Lamperti oper-
+ators.
+Definition 1.3. An operator T is called a Lamperti operator (or supports separating)
+if for any two τ-finite projections e, f ∈ M satisfies ef = 0, we have
+(Te)∗Tf = Te(Tf)∗ = 0.
+In [15], the authors derived the maximal inequalities for the convex combinations
+of positive Lamperti contraction on one single noncommutative Lp spaces, which can
+be viewed as the first Akcoglu’s maximal ergodic inequalities in the noncommutative
+setting.
+In this paper, we establish the quantitative mean ergodic theorem for Lamperti
+operators where the positivity assumption can be relaxed.
+Theorem 1.4. Let 1 < p < ∞. Suppose that T belong to the family
+(1.4)
+S = convsot{S : Lp(M) → Lp(M) Lamperti contractions},
+that is, the closed convex hull of all Lamperti contractions on Lp(M) with respect to
+strong operator topology. For 2 ≤ p < ∞, there exists a positive constant Cp such that
+for any increasing subsequence of positive integers (ni)i∈N,
+���
+Mni(T)x − Mni+1(T)x
+�
+i∈N
+��
+Lp(M;ℓrc
+2 ) ≤ Cp∥x∥Lp(M) ∀x ∈ Lp(M).
+For 1 < p < 2, if T ∈ S is positive, then the above conclusion holds too.
+Theorem 1.1 and Theorem 1.4 seem new even in the commutative case since the
+quantitative mean ergodic inequalities are deduced for a large class of operators acting
+on a fixed Lp spaces with 1 < p ̸= 2 < ∞.
+It should be pointed out that when
+M is commutative, the class of operators in the two theorems should be able to be
+
+4
+G. HONG, W. LIU, AND B. XU
+enlarged. We left this to the interested reader. With a moment’s thought, there are
+many difficulties to apply the classical methods exploited in [1, 3, 22, 23] to our setting.
+Our approach is mainly motivated by the study of maximal ergodic inequalities and
+semi-commutative harmonic analysis.
+The proof of Theorem 1.1 and Theorem 1.4 rely on several auxiliary results. Our first
+key ingredient is the operator-valued square function inequalities related to the Hardy-
+Littlewood averages on Z. Let (ni)i∈N be an increasing sequence in N. A sequence of
+intervals (Ani)i∈N ⊂ Z is called nested if it satisfies one of the following two cases:
+(a) each Ani can be written as [−ni, ni];
+(b) each Ani can be written as [0, ni].
+Let A ⊂ Z be an interval and f : Z → SM be a bounded operator-valued function,
+where SM is the subset of M with τ-finite support. The averaging operator over A is
+defined by
+MAf(v) = 1
+|A|
+�
+y∈A
+f(v + y),
+v ∈ Z.
+Theorem 1.5. Let (ni)i∈N be an increasing sequence of positive integers and (Ani)i be
+the associated nested sequence. Let Ti = MAni − MAni+1. Then for 1 ≤ p ≤ ∞ the
+following assertions are true with a positive constant Cp depending only on p:
+(i) for p = 1,
+∥(Tif)i∈N∥L1,∞(N,ℓrc
+2 ) ≤ Cp∥f∥1, ∀f ∈ L1(N);
+(ii) for p = ∞,
+���
+�
+i:i∈N
+Tif ⊗ e1i
+���
+BMOd(R) +
+���
+�
+i:i∈N
+Tif ⊗ ei1
+���
+BMOd(R) ≤ Cp ∥f∥∞, ∀f ∈ L∞(N);
+(iii) for 1 < p < ∞,
+∥(Tif)i∈N∥Lp(N;ℓrc
+2 ) ≤ Cp∥f∥p, ∀f ∈ Lp(N).
+Here N = L∞(Z)⊗M is equipped with the tensor trace ϕ = �
+Z ⊗τ and R = N⊗B(ℓ2)
+with the tensor trace ϕ ⊗ tr, where tr is the canonical trace on B(ℓ2).
+We refer to Section 5 for the definition of the dyadic BMO space BMOd(R) intro-
+duced by Mei [34].
+Our second key ingredient is to explore the following noncommutative version of the
+classical transference principle due to Coifman and Weiss [8].
+Proposition 1.6. Let (Ani)i be a nested sequence and set Ti = MAni − MAni+1. As-
+sume that the operator T satisfies (1.3) with 1 < p < ∞ in Theorem 1.1. Under the
+assumption Ani = [−ni, ni]: if there exists a positive constant Cp such that
+(1.5)
+∥(Tif)i∈N∥Lp(N;ℓrc
+2 ) ≤ Cp∥f∥Lp(N) ∀f ∈ Lp(N),
+then there exists a positive constant C such that
+���
+Bni(T)x − Bni+1(T)x
+�
+i∈N
+��
+Lp(M;ℓrc
+2 ) ≤ CCp∥x∥Lp(M) ∀ x ∈ Lp(M).
+Under the assumption (Ani)i = [0, ni], we have the similar transference result for one-
+sided ergodic averages (Mn(T))n∈N.
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+5
+This noncommutative transference technique is partly motivated by the noncommu-
+tative Calder´on’s transference principle developed in [13]. In the course of establishing
+Proposition 1.6, we need the following extension property of the bounded linear oper-
+ators.
+Lemma 1.7. Let 1 ≤ p < ∞. Assume that T is a bounded linear operator on Lp(M).
+Then T extends to a bounded operator on Lp(M; ℓrc
+2 ).
+Lemma 1.7 follows from the noncommutative Khintchine inequalities—Proposition
+2.2—without surprise, see Section 6 for the details. However, to exploit the transference
+technique in showing Theorem 1.4 is much more complicated. To this end, we start with
+a reduction. More precisely, we reduce Lamperti operators to isometric operators by
+applying the structural characterizations and dilation properties of Lamperti operators
+recently developed in [15] (see Section 7). With this reduction, we give our effort to
+the strong type (p, p) estimate of the square function for isometric operators. This will
+be achieved by using a similar noncommutative Calder´on’s transference principle as
+Proposition 1.6 for isometries, once there holds the following property that concerns
+the isometric extension of isometries to Lp(M; ℓrc
+2 ).
+Proposition 1.8. Let 1 ≤ p < ∞ and T : Lp(M) → Lp(M) be an isometry. Then
+T extends to an isometry (resp. a contraction) on Lp(M; ℓrc
+2 ) if 2 ≤ p < ∞ (resp.
+1 ≤ p < 2). If T is morevoer positive, then T extends also to an isometry on Lp(M; ℓrc
+2 )
+for 1 < p < 2.
+When M is commutative, the above extension is almost plain. The truly noncommu-
+tative case is highly non-trivial. Our argument depends on the structural description
+of isometries, see e.g. [25, 50]. Moreover, for 1 < p < 2, some complicated duality argu-
+ment are explored, and similar one has appeared in [15] in dealing with noncommutative
+maximal inequalities. For more details we refer to Section 6.
+Remark 1.9. What we need to point out here is that the estimates stated in all
+the aforementioned theorems for infinite summations should be understood as a con-
+sequence of the corresponding uniform boundedness for all finite summations by the
+standard approximation arguments (see e.g. [24, Section 6.A]). For this reason, as in
+[17], we are not going to explain the convergence of infinite sums appearing in the whole
+paper if there is no ambiguity.
+We end the introduction by mentioning the organization of the paper. In Section 2,
+we recall the necessary background including noncommutative Lp spaces and Hilbert-
+valued Lp spaces, as well as the noncommutative Calder´on-Zygmund decomposition
+recently developed in [7].
+Section 3-5 is devoted to the proof of Theorem 1.5.
+In
+Section 6, we prove Lemma 1.7, Proposition 1.6 and Theorem 1.1. Finally, in Section 7,
+we prove Proposition 1.8 and Theorem 1.4, which involves the intermediate square
+function inequalities for isometries—Lemma 7.5.
+Notation: In all what follows, we use the same letter C to denote various positive
+constants that may change at each occurrence. Also, we write X ≲ Y for non-negative
+quantities X and Y to mean that X ≤ CY for some inessential constant C > 0.
+Similarly, we use the notation X ≈ Y if both X ≲ Y and Y ≲ X hold.
+
+6
+G. HONG, W. LIU, AND B. XU
+2. Preliminaries
+2.1. Noncommutative Lp spaces.
+Throughout this paper, M denotes a semifinite von Neumann algebra equipped with
+a n.s.f trace τ. Let M+ be the cone of positive elements in M. Given x ∈ M+, the
+support projection of x, denoted by suppx, is defined as the least projection e in M
+such that ex = xe = x. Let SM+ be the set of all x ∈ M+ such that τ(suppx) < ∞
+and SM be the linear span of SM+. Then SM is a w∗-dense ∗-subalgebra of M. Given
+0 < p < ∞ and x ∈ SM, if we set
+∥x∥p =
+�
+τ(|x|p)
+�1/p,
+where |x| = (x∗x)
+1
+2 is the modulus of x, then it turns out that ∥ · ∥p is a norm in SM
+for 1 ≤ p < ∞, and a p-norm for 0 < p < 1. The completion of (SM, ∥ · ∥p) is the
+noncommutative Lp space associated to the pair (M, τ), which is simply denoted by
+Lp(M). As usual, we set L∞(M) = M equipped with the operator norm.
+We also work with noncommutative weak Lp spaces. Let M′ be the commutant of
+M. A closed densely defined operator on H (H being the Hilbert space on which M
+acts) is said to be affiliated with M if it commutes with any unitary in M′. Given a
+densely defined selfadjoint operator x, its spectral projection
+�
+I dγx(λ) will be simply
+denoted by χI(x), where I is a measurable subset of R. A closed and densely defined
+operator x affiliated with M is said to be τ-measurable if there is λ ∈ R+ such that
+τ
+�
+χ(λ,∞)(|x|)
+�
+< ∞.
+Let L0(M) be the set of the ∗-algebra of τ-measurable operators. For 0 < p < ∞, the
+weak Lp space Lp,∞(M) is defined as the set of all x in L0(M) with the following finite
+quasi-norm
+∥x∥p,∞ = sup
+λ>0
+λτ
+�
+χ(λ,∞)(|x|)
+� 1
+p .
+The following property has already been proved in [21, Lemma 2.1] that for any x1, x2 ∈
+L1,∞(M) and any λ ∈ R+
+τ
+�
+(χ(λ,∞)(|x1 + x2|)
+�
+≤ τ
+�
+χ(λ/2,∞)(|x1|)
+�
++ τ
+�
+χ(λ/2,∞)(|x2|)
+�
+.
+(2.1)
+The reader is referred to e.g. [12, 40] for a comprehensive study of noncommutative
+Lp spaces.
+2.2. Noncommutative Hilbert-valued Lp spaces.
+In this subsection, we recall the noncommutative Hilbert-valued Lp spaces [40]. Let
+(xn) be a finite sequence in Lp(M). Define
+∥(xn)∥Lp(M;ℓr
+2) = ∥(
+�
+n
+|x∗
+n|2)
+1
+2 ∥p, ∥(xn)∥Lp(M;ℓc
+2) = ∥(
+�
+n
+|xn|2)
+1
+2 ∥p.
+Then Lp(M; ℓr
+2) (resp. Lp(M; ℓc
+2)) is defined as the completion of all finite sequences
+in Lp(M) with respect to ∥ · ∥Lp(M;ℓr
+2) (resp. ∥ · ∥Lp(M;ℓc
+2)). The space Lp(M; ℓrc
+2 ) is
+defined as follows.
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+7
+• If 2 ≤ p ≤ ∞,
+Lp(M; ℓrc
+2 ) = Lp(M; ℓc
+2) ∩ Lp(M; ℓr
+2)
+equipped with the intersection norm:
+∥(xn)∥Lp(M;ℓrc
+2 ) =
+�
+∥(xn)∥p
+Lp(M;ℓc
+2) + ∥(xn)∥p
+Lp(M;ℓr
+2)
+� 1
+p .
+• If 1 ≤ p < 2,
+Lp(M; ℓrc
+2 ) = Lp(M; ℓc
+2) + Lp(M; ℓr
+2)
+equipped with the sum norm:
+∥(xn)∥Lp(M;ℓrc
+2 ) = inf
+�
+∥(yn)∥p
+Lp(M;ℓc
+2) + ∥(zn)∥p
+Lp(M;ℓr
+2)
+� 1
+p ,
+where the infimum runs over all possible decompositions xn = yn + zn with yn
+and zn in Lp(M).
+This procedure is also used to define the spaces L1,∞(M; ℓr
+2) (resp. L1,∞(M; ℓc
+2)) and
+L1,∞(M; ℓrc
+2 ) with the sum norm,
+∥(xn)∥L1,∞(M;ℓrc
+2 ) =
+inf
+xn=yn+zn
+�
+∥(yn)∥L1,∞(M;ℓc
+2) + ∥(zn)∥L1,∞(M;ℓr
+2)
+�
+.
+We remark that the definition of space Lp(M; ℓrc
+2 ) equals the classical one [40], and
+one can easily see that the following basic properties related to space Lp(M; ℓrc
+2 ) are
+also valid.
+Proposition 2.1. Let 1 ≤ p < ∞ and p′ be its conjugate index. Then
+(Lp(M; ℓc
+2))∗ = Lp′(M; ℓc
+2),
+(Lp(M; ℓr
+2))∗ = Lp′(M; ℓr
+2)
+and
+(Lp(M; ℓrc
+2 ))∗ = Lp′(M; ℓrc
+2 ).
+The duality bracket is given by
+⟨(xn), (yn)⟩ =
+�
+n
+τ(xny∗
+n),
+(xn) ⊂ Lp(M), (yn) ⊂ Lp′(M).
+The following noncommutative Khintchine inequalities will be frequently used. See
+e.g. [32, 33, 38, 6] for the proof.
+Proposition 2.2. Let (εn) be a sequence of independent Rademarcher random variables
+on a probability space (Ω, P). Let 1 ≤ p < ∞ and (xn) be a sequence in Lp(M; ℓrc
+2 ).
+For 1 ≤ p < ∞, there exist two positive constants cp and Cp such that
+cp∥(xn)∥Lp(M;ℓrc
+2 ) ≤
+����
+�
+n
+εnxn
+����
+Lp(L∞(Ω)⊗M)
+≤ Cp∥(xn)∥Lp(M;ℓrc
+2 ).
+The above estimate is still true if one replaces the Lp spaces by the weak Lp spaces.
+
+8
+G. HONG, W. LIU, AND B. XU
+2.3. Noncommutative Calder´on-Zygmund decomposition.
+In this subsection, we introduce the noncommutative Calder´on-Zygmund decompo-
+sition developed in [7], whose construction is based on the noncommutative martingale
+theory. To this end, we first introduce the related notions. For each n ∈ N, let Fn be
+the set of dyadic intervals with length of 2n in Z, that is each interval in Fn can be
+written as [s2n, (s + 1)2n), where s is an integer. Let σn be the n-th σ-algebra gener-
+ated by Fn and Nn = L∞(Z, σn)⊗M. Recall that N = L∞(Z)⊗M. Then (Nn)n∈N
+is a sequence of decreasing von Neumann subalgebras of N. Hence, (Nn)n∈N forms a
+filtration and the resulting conditional expectations (En)n∈N satisfy
+∀ m, n ∈ N,
+EmEn = EnEm = Emax(m,n)
+and for f ∈ Lp(N) with 1 ≤ p < ∞,
+(2.2)
+fn := En(f) =
+�
+I∈Fn
+fIχI,
+where χI is the characteristic function of I and
+fI = 1
+|I|
+�
+y∈I
+f(y).
+It is easy to check that (fn)n∈N is a Lp-reverse martingale, namely supn∈N ∥fn∥Lp(N) <
+∞. The resulting martingale difference sequence df = (dfn)n∈N is defined by dfn =
+fn−1 − fn for n ≥ 1 and df0 = 0.
+To give the content of noncommutative Calder´on-Zygmund decomposition, consider
+Nc,+ =
+�
+f : Z → M ∩ L1(M)
+�� f ≥ 0, −−→
+suppf is compact
+�
+,
+which is dense in L1(N)+. Here −−→
+suppf = supp∥f∥L1(M). Observe that for any given
+f ∈ Nc,+ and λ > 0, there exists mλ(f) ∈ N such that fn ≤ λ1N for all n ≥ mλ(f)
+(see [37, Lemma 3.1]), where 1N denotes the unit element in N.
+The following modified Cuculescu’s theorem [10] was obtained in [37, Lemma 3.1].
+Lemma 2.3. Let f ∈ Nc,+ and consider its related dyadic martingale (fn)n∈N. Given
+λ > 0, there exists an increasing sequence of projections (qn)n∈N defined by qn = 1N
+for n ≥ mλ(f) and recursively for n < mλ(f)
+qn = qn(f, λ) = χ(0,λ](qn+1fnqn+1)
+such that the following conclusions hold:
+(i) qn commutes with qn+1fnqn+1 for each n;
+(ii) qn belongs to Nn and qnfnqn ≤ λqn for each n;
+(iii) set q0 := q = �mλ(f)
+n=0
+qn, then λϕ(1N − q) ≤ ∥f∥1.
+In fact, for each n, qn admits the following expression (see e.g. [37])
+qn =
+�
+I∈Fn
+qIχI,
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+9
+with qI projections in M defined by
+qI =
+�
+�
+�
+�
+�
+1M
+if n > mλ(f),
+χ(0,λ](fI)
+if n = mλ(f),
+χ(0,λ]
+�
+q�IfIq�I
+�
+if 0 ≤ n < mλ(f),
+where �I is the dyadic father of I. Accordingly, these projections satisfy
+(2.3)
+qI ≤ q�I,
+qI commutes with q�IfIq�I,
+qIfIqI ≤ λqI.
+If we define the sequence (pn)n of pairwise disjoint projections by
+(2.4)
+pn = qn+1 − qn =
+�
+I∈Fn
+(q�I − qI)χI ≜
+�
+I∈Fn
+pIχI
+for each n, then
+(2.5)
+�
+n
+pn = 1N − q = q⊥
+and for each n
+(2.6)
+∥pnfnpn∥∞ ≤ 2λ.
+Based on the previous notation, the noncommutative analogue for the Calder´on-
+Zygmund decomposition was recently found by Caldilhac et al [7].
+Proposition 2.4. Fix f ∈ Nc,+ and λ > 0. Let (qn)n and (pn)n be the two sequences
+of projections appeared in the above Cuculescu’s construction. Then there exist a pro-
+jection ζ ∈ N defined by
+(2.7)
+ζ =
+� �
+I∈F
+pIχ5I
+�⊥,
+where 5I denotes the interval with the same center as I with length |5I| = 5|I|, and a
+decomposition of f,
+(2.8)
+f = g + b
+such that the following assertions hold.
+(i) λϕ(1N − ζ) ≤ 5∥f∥1.
+(ii) g = qfq + �
+n pnfnpn satisfies ∥g∥1 ≤ ∥f∥1
+and
+∥g∥∞ ≤ 2λ.
+(iii) b = �
+n bn, where
+(2.9)
+bn = pn(f − fn)qn + qn+1(f − fn)pn.
+Each bn satisfies two cancellation conditions: Enbn = 0; and for all x, y ∈ Z with
+y ∈ 5Ix,n, ζ(x)bn(y)ζ(x) = 0, where Ix,n is the unique interval in Fn containing x.
+3. Proof of Theorem 1.5: one reduction
+To prove Theorem 1.5, we give a reduction in the present section. Motivated by
+the study of the variational inequalities [5], we split the square function into the ‘long
+one’ and the ‘short one’. To be more precise, fix an increasing sequence (ni)i∈N and let
+(Ani)i∈N be the associated nested sequence. For an interval Ii = [ni, ni+1), one can see
+that there are two cases:
+• Case 1: Ii contains no dyadic point, that is, for any k ∈ N, 2k /∈ Ii;
+
+10
+G. HONG, W. LIU, AND B. XU
+• Case 2: Ii contains at least one dyadic point 2k for k ∈ N.
+According to the above classification, for each interval Ii = [ni, ni+1), we split it into
+at most three disjoint parts
+(3.1)
+Ii := [ni, ˜ni) ∪ [˜ni, ˜˜ni) ∪ [˜˜ni, ni+1)
+by the law: if Ii belongs to Case 1, then set ˜ni = ˜˜ni = ni+1; if Ii belongs to Case 2,
+we set ˜ni = 2ki := min{2k : 2k ∈ Ii} and ˜˜ni = 2li := max{2k : 2k ∈ ¯Ii} where ¯Ii is the
+closure of Ii.
+By above decomposition of intervals and using the quasi-triangle inequality for weak
+L1 norm ∥ · ∥L1,∞(N;ℓrc
+2 ), we have
+∥(MAnif − MAni+1f)i∈N∥L1,∞(N;ℓrc
+2 )
+≤ 3∥(MAnif − MA˜nif)i∈N∥L1,∞(N;ℓrc
+2 ) + 3∥(MA˜nif − MA˜˜nif)i∈N∥L1,∞(N;ℓrc
+2 )
++ 3∥(MA˜˜nif − MAni+1f)i∈N∥L1,∞(N;ℓrc
+2 ).
+(3.2)
+On the other hand, by (3.1), we introduce two collections of intervals with respect
+to {[ni, ni+1)}i:
+• S consists of all intervals Ii belonging to Case 1, or [ni, ˜ni), [˜˜ni, ni+1) in (3.1).
+• L consists of all intervals [˜ni, ˜˜ni) in (3.1).
+It is not difficult to check that L ∪ S is a disjoint family of intervals and forms a finer
+partition of
+�
+[ni, ni+1)
+�
+i∈N. By (3.2), we have
+∥(MAnif − MAni+1f)i∈N∥L1,∞(N;ℓrc
+2 )
+≤ 3∥(MA˜nif − MA˜˜ni:f)i:[˜ni,˜˜ni)∈L∥L1,∞(N;ℓrc
+2 )
++ 6∥(MAmif − MA �
+mif)i:[mi, �mi)∈S∥L1,∞(N;ℓrc
+2 ).
+(3.3)
+We now focus on the first term on the right hand side of the above inequality. Fix an
+interval [˜ni, ˜˜ni). By (3.1), we write [˜ni, ˜˜ni) = [2ki, 2li). Decompose
+(MA2ki f − MA2li f) = (MA2ki f − Ekif) + (Ekif − Elif) + (Elif − MA2li f),
+where (Ek)k is the dyadic conditional expectations defined in the preliminary section.
+As a consequence, there exists a sequence of positive integers k0 < l0 ≤ k1 < l1 < · · · ≤
+ki < li ≤ · · · such that
+∥(MA˜nif − MA˜˜nif)i:[˜ni,˜˜ni)∈L∥L1,∞(N;ℓrc
+2 ) ≤ 3∥(MA2ki f − Ekif)i∥L1,∞(N;ℓrc
+2 )
++ 3∥(Ekif − Elif)i∥L1,∞(N;ℓrc
+2 ) + 3∥(MA2li f − Elif)i∥L1,∞(N;ℓrc
+2 ).
+Using the fact that n �→ (�n
+k=1 |xk|2)
+1
+2 is increasing, one easily checks that
+∥(MA˜nif − MA˜˜nif)i:[˜ni,˜˜ni)∈L∥L1,∞(N;ℓrc
+2 )
+≤ 3∥(Ekif − Elif)i∥L1,∞(N;ℓrc
+2 ) + 6∥(MA2kf − Ekf)k∈Z∥L1,∞(N;ℓrc
+2 ).
+(3.4)
+Together with (3.3) and (3.4), we obtain
+∥(MAnif − MAni+1f)i∈N∥L1,∞(N;ℓrc
+2 )
+≤ 6∥(MAmif − MA �
+mif)i:[mi, �mi)∈S∥L1,∞(N;ℓrc
+2 )
++ 9∥(Ekif − Elif)i∥L1,∞(N;ℓrc
+2 ) + 18∥(MA2kf − Ekf)k∈Z∥L1,∞(N;ℓrc
+2 ).
+(3.5)
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+11
+Remark 3.1. By applying the same arguments as above, it is clear that there exist
+similar dominations as (3.5) for ∥·∥Lp(N;ℓrc
+2 ) and ∥·∥BMOd(R) via the triangle inequalities
+with possibly different constants.
+Concerning the sequence (MA2kf − Ekf)k∈Z, the first and third authors [17] estab-
+lished the following results.
+Lemma 3.2 ([17]). Let 1 ≤ p ≤ ∞. Set Lkf = MA2kf − Ekf. Then the following
+assertions are true with a positive constant Cp depending only on p:
+(i) for p = 1,
+∥(Lkf)k∈Z∥L1,∞(N;ℓrc
+2 ) ≤ Cp∥f∥1, ∀f ∈ L1(N);
+(ii) for p = ∞,
+���
+�
+k∈Z
+Lkf ⊗ e1k
+���
+BMOd(R) +
+���
+�
+k∈Z
+Lkf ⊗ ek1
+���
+BMOd(R) ≤ Cp ∥f∥∞, ∀f ∈ L∞(N);
+(iii) for 1 < p < ∞,
+∥(Lkf)k∈Z∥Lp(N;ℓrc
+2 ) ≤ Cp∥f∥p, ∀f ∈ Lp(N).
+On the other hand, (Ekif − Elif)i forms a new sequence of martingale differences,
+and the dyadic martingale analogue of Lemma 3.2 have been established in [35]. See
+also [39, 41, 42] for more on noncommutative Burkholder-Gundy inequalities.
+Hence, we give our main efforts to the first term on the right hand side of (3.5),
+namely the sequence (MAmif − MA �
+mif)i:[mi, �mi)∈S. We denote, by abuse of notation,
+the sequence {m0, �m0, m1, · · · , mi, �mi, · · · } as {m0, m1, m2 · · · , mi, mi+1, · · · }. Then if
+[mi, mi+1) ∈ S, we denote it as i ∈ S. Setting Tif = MAmif − MAmi+1f, and thus we
+get (Tif)i∈S standing for (MAmif − MA �
+mif)i:[mi, �mi)∈S. Combining (3.5), Remark 3.1,
+Lemma 3.2 with the fact that n �→ (�n
+k=1 |xk|2)
+1
+2 is increasing, to establish Theorem
+1.5, it suffices to show the following result.
+Theorem 3.3. Let S and (Tif)i∈S be defined as above. Let 1 ≤ p ≤ ∞. Then the
+following assertions are true with a positive constant Cp depending only on p:
+(i) for p = 1,
+∥(Tif)i∈S∥L1,∞(N;ℓrc
+2 ) ≤ Cp∥f∥1, ∀f ∈ L1(N);
+(ii) for p = ∞,
+���
+�
+i∈S
+Tif ⊗ e1i
+���
+BMOd(R) +
+���
+�
+i∈S
+Tif ⊗ ei1
+���
+BMOd(R) ≤ Cp ∥f∥∞, ∀f ∈ L∞(N);
+(iii) for 1 < p < ∞,
+∥(Tif)i∈S∥Lp(N;ℓrc
+2 ) ≤ Cp∥f∥p, ∀f ∈ Lp(N).
+4. Proof of Theorem 3.3: Weak type (1, 1) estimate
+In this section, we show the weak type (1, 1) estimate stated in Theorem 3.3.
+
+12
+G. HONG, W. LIU, AND B. XU
+4.1. Some technical lemmas.
+Recall that (εi) is a Rademacher sequence on a fixed probability space (Ω, P). Define
+(4.1)
+Tf(x) =
+�
+i∈S
+εiTif(x) =
+�
+i∈S
+εi(MAni − MAni+1)f(x).
+Then Proposition 2.2(ii) immediately implies the following result.
+Lemma 4.1. Let h ∈ Nc,+. Then
+∥(Tih)i∈S∥L1,∞(N;ℓrc
+2 ) ≈ ∥Th∥L1,∞(L∞(Ω)⊗N).
+Lemma 4.2. Let (Sk,i)k,i∈Z be a sequence of bounded linear operators on L2(N). Let
+h ∈ L2(N). If (un)n∈Z and (vn)n∈Z are two sequences of operators in L2(N) such that
+h = �
+n∈Z un and �
+n∈Z ∥vn∥2
+2 < ∞, then
+�
+k∈Z
+∥(Sk,ih)i∥2
+L2(N;ℓrc
+2 ) ≤ w2 �
+n∈Z
+∥vn∥2
+2
+provided that there exists a sequence (σ(j))j∈Z of positive numbers with w = �
+j∈Z σ(j) <
+∞ such that
+∥(Sk,iun)i∥L2(N;ℓrc
+2 ) ≤ σ(n − k)∥vn∥2
+(4.2)
+for every n, k.
+Proof. By the triangle inequality in L2(N; ℓrc
+2 ), (4.2) and the Young inequality in ℓ2,
+we deduce that
+�
+k∈Z
+∥(Sk,ih)i∥2
+L2(N;ℓrc
+2 ) ≤
+�
+k∈Z
+� �
+n∈Z
+∥(Sk,iun)i∥L2(N;ℓrc
+2 )
+�2
+≤
+�
+k∈Z
+� �
+n∈Z
+σ(n − k)∥vn∥2
+�2
+≤
+� �
+n∈Z
+σ(n)
+�2� �
+k∈Z
+∥vk∥2
+2
+�
+,
+which finishes the proof.
+□
+Let A be a subset of Z, define
+I(A, n) =
+�
+I∈Fn
+∂A∩I̸=∅
+A ∩ I
+(4.3)
+and
+I1(A, n) =
+�
+I∈Fn
+∂A∩I̸=∅
+I,
+(4.4)
+where ∂A means the boundary of A.
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+13
+Lemma 4.3. Let h ∈ L2(N). Then for any x ∈ Z, n ∈ N and subset B ⊆ Z,
+���
+�
+y∈I(x+B,n)
+h(y)
+���
+2
+L2(M) ≤ |I1(x + B, n)|
+�
+y∈I1(x+B,n)
+∥En(h1x+B)(y)∥2
+L2(M);
+���
+�
+y∈I(x+B,n)
+h(y)
+���
+2
+L2(M) ≤ |I(x + B, n)|
+�
+y∈I(x+B,n)
+∥h(y)∥2
+L2(M).
+Proof. We first prove the first inequality. It is easy to check that
+�
+y∈I(x+B,n)
+h(y) =
+�
+I∈Fn
+I∩∂(x+B)̸=∅
+�
+y∈I
+En(h1x+B)(y) =
+�
+y∈I1(x+B,n)
+En(h1x+B)(y).
+By the Minkowski and the Cauchy-Schwarz inequalities, we obtain
+���
+�
+y∈I(x+B,n)
+h(y)
+���
+2
+L2(M) ≤
+�
+�
+y∈I1(x+B,n)
+∥En(h1x+B)(y)∥L2(M)
+�2
+≤ |I1(x + B, n)|
+�
+y∈I1(x+B,n)
+∥En(h1x+B)(y)∥2
+L2(M).
+The same argument gives
+���
+�
+y∈I(x+B,n)
+h(y)
+���
+2
+L2(M) ≤
+�
+�
+y∈I(x+B,n)
+∥h(y)∥L2(M)
+�2
+≤ |I(x + B, n)|
+�
+y∈I(x+B,n)
+∥h(y)∥2
+L2(M).
+This completes the proof.
+□
+Now we are ready to prove the weak type (1, 1) estimate in Theorem 3.3. Note that
+we just consider the case that each Ani is written as [0, ni], since another case Ani of
+the form [−ni, ni] can be handled in the same way.
+By decomposing f = f1 − f2 + i(f3 − f4) with fj ≥ 0 such that ∥fj∥1 ≤ ∥f∥1
+for j = 1, 2, 3, 4, we may assume that f is positive. Moreover, since Nc,+ is dense in
+L1(N)+, by the standard approximation argument, it suffices to consider f ∈ Nc,+.
+Now fix one f ∈ Nc,+ and a λ ∈ (0, +∞). Using Theorem 2.4, we can decompose f as
+f = g + b. Then the distribution inequality gives (2.1),
+�ϕ
+�
+χ(λ,∞)(|Tf|)
+�
+≤ �ϕ
+�
+χ(λ/2,∞)(|Tg|)
+�
++ �ϕ
+�
+χ(λ/2,∞)(|Tb|)
+�
+,
+where �ϕ =
+�
+Ω ⊗ϕ. Therefore, by Lemma 4.1, it suffices to show
+�ϕ(χ(λ/2,∞)(|Tb|)) ≲ ∥f∥1
+λ
+,
+(4.5)
+�ϕ(χ(λ/2,∞)(|Tg|)) ≲ ∥f∥1
+λ
+.
+(4.6)
+
+14
+G. HONG, W. LIU, AND B. XU
+4.2. Weak type estimate for the bad function: (4.5).
+Using the projection ζ introduced in Proposition 2.4, we decompose Tb as
+Tb = (1N − ζ)Tb(1N − ζ) + ζ Tb(1N − ζ) + (1N − ζ)Tbζ + ζ Tbζ.
+In particular, by Proposition 2.4(i), we find
+�ϕ
+�
+χ(λ/2,∞)(|Tb|)
+�
+≲ ϕ(1N − ζ) + �ϕ
+�
+χ(λ/8,∞)(|ζTbζ|)
+�
+≲ ∥f∥1
+λ
++ �ϕ
+�
+χ(λ/8,∞)(|ζTbζ|)
+�
+.
+Hence, we are reduced to showing
+�ϕ
+�
+χ(λ/8,∞)(|ζTbζ|)
+�
+≲ ∥f∥1
+λ
+.
+Note that the Chebychev inequality gives
+λ2 �ϕ
+�
+χ(λ/8,∞)(|ζTbζ|)
+�
+≲ ∥ζTbζ∥2
+L2(L∞(Ω)⊗N).
+Hence, it is enough to prove
+∥ζTbζ∥2
+L2(L∞(Ω)⊗N) ≲ λ2 �
+n
+∥pn∥2
+2,
+(4.7)
+due to Cuculescu’s construction and (2.5),
+�
+n
+∥pn∥2
+2 =
+�
+n
+∥pn∥1 ≲ ∥f∥1
+λ
+.
+To estimate (4.7), we first use the orthogonality of εi to get
+∥ζTbζ∥2
+L2(L∞(Ω)⊗N) =
+�
+i∈S
+∥ζ Tib ζ∥2
+2 =
+�
+i∈S
+∥ζ (MAni − MAni+1)b ζ∥2
+2.
+For each k ∈ Z, let Sk be the set of i such that [ni, ni+1) ⊆ [2k, 2k+1). Then clearly
+S = ∪k∈ZSk since for k < 0, Sk is empty. With this convention, we deduce that
+�
+i∈S
+∥ζ (MAni − MAni+1)b ζ∥2
+2 =
+�
+k
+�
+i∈Sk
+∥ζ (MAni − MAni+1)b ζ∥2
+2.
+Hence, (4.7) is reduced to showing
+�
+k
+�
+i∈Sk
+∥ζ (MAni − MAni+1)b ζ∥2
+2 ≲ λ2 �
+n
+∥pn∥2
+2.
+(4.8)
+To show (4.8), by noting the definition of mλ(f), we can express b as b = �
+n≤mλ(f) bn,
+where bn = pn(f − fn)qn + qn+1(f − fn)pn as in (2.9).
+On the other hand, let
+(Sk,ih)i∈Sk = (ζ(MAni − MAni+1)bζ)i∈Sk, un = bn and vn = pn in Lemma 4.2. Then it
+suffices to show �
+i∈Sk
+∥ζ(MAni − MAni+1)bnζ∥2
+2 ≲ 2−|k−n|λ2∥pn∥2
+2.
+(4.9)
+In the following, we divide the proof of (4.9) into several steps.
+Lemma 4.4. Fix i ∈ Sk. Then for k ≤ n,
+ζ(x)(MAni − MAni+1)bn(x)ζ(x) = 0, ∀x ∈ Z.
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+15
+Proof. This follows from the observation ζ(x)MAnibn(x)ζ(x) = ζ(x)MAni+1bn(x)ζ(x) =
+0, ∀x ∈ Z.
+To see this, fix one x ∈ Z.
+The cancellation property announced in
+Proposition 2.4(iii) implies
+ζ(x)MAni+1bn(x)ζ(x) = ζ(x)
+1
+|Ani+1|
+�
+y∈x+Ani+1
+bn(y)1y /∈5Ix,nζ(x) = 0
+since x+Ani+1 ⊂ 5Ix,n and k ≤ n. The same reasoning implies ζ(x)MAnibn(x)ζ(x) = 0.
+This finishes the proof.
+□
+With Lemma 4.4, since ζ is a projection, it suffices to show for n < k
+�
+i∈Sk
+∥(MAni − MAni+1)bn∥2
+2 ≲ 2n−kλ2∥pn∥2
+2.
+(4.10)
+To show (4.10), by applying the Minkowski inequality, we have
+�
+i∈Sk
+∥(MAni − MAni+1)bn∥2
+2 ≲
+�
+i∈Sk
+�
+x∈Z
+���
+1
+|Ani+1|
+�
+y∈x+Ani+1\Ani
+bn(y)
+���
+2
+L2(M)
++
+�
+i∈Sk
+�
+1
+|Ani| −
+1
+|Ani+1|
+�2 �
+x∈Z
+���
+�
+y∈x+Ani
+bn(y)
+���
+2
+L2(M)
+≜ I1
+k,n + I2
+k,n.
+4.2.1. Estimate of I1
+k,n.
+Lemma 4.5. For n < k, we have
+I1
+k,n ≲ 2n−kλ2∥pn∥2
+2.
+Proof. First, the cancellation property-Proposition 2.4(iii) of bn gives
+I1
+k,n =
+�
+i∈Sk
+�
+x∈Z
+���
+1
+|Ani+1|
+�
+y∈I(x+Ani+1\Ani,n)
+bn(y)
+���
+2
+L2(M).
+On the other hand, observe that
+bn = pnfqn + qn+1fpn − qn+1fnpn.
+(4.11)
+Indeed, by (2.4), pn = qn+1−qn ≤ qn+1; moreover, by Cuculescu’s construction-Lemma
+2.3(i), we obtain
+pnfnqn = pnqn+1fnqn+1qn = pnqnqn+1fnqn+1 = 0.
+This gives the desired expression (4.11).
+With the observation (4.11) and the Minkowski inequality, we see that to obtain the
+desired inequality for the term I1
+k,n, it suffices to estimate the following three terms
+I1
+k,n,1
+≜
+�
+i∈Sk
+�
+x∈Z
+���
+1
+|Ani+1|
+�
+y∈I(x+Ani+1\Ani,n)
+(pnfqn)(y)
+���
+2
+L2(M)
+I1
+k,n,2
+≜
+�
+i∈Sk
+�
+x∈Z
+���
+1
+|Ani+1|
+�
+y∈I(x+Ani+1\Ani,n)
+(qn+1fpn)(y)
+���
+2
+L2(M)
+
+16
+G. HONG, W. LIU, AND B. XU
+I1
+k,n,3
+≜
+�
+i∈Sk
+�
+x∈Z
+���
+1
+|Ani+1|
+�
+y∈I(x+Ani+1\Ani,n)
+(qn+1fnpn)(y)
+���
+2
+L2(M),
+We first deal with the term I1
+k,n,1. By Lemma 4.3, we have
+���
+1
+|Ani+1|
+�
+y∈I(x+Ani+1\Ani,n)
+(pnfqn)(y)
+���
+2
+L2(M)
+≲ 2n−2k
+�
+y∈I1(x+Ani+1\Ani,n)
+τ(|En(pnfqn1x+Ani+1\Ani)(y)|2),
+(4.12)
+where we used the fact that for all i ∈ Sk, 2k ≤ |Ani| ≤ 2k+1 and |I1(x + Ani+1 \
+Ani, n)| ≲ 2n.
+Note that f1x+Ani+1\Ani is positive in N and f1x+Ani+1\Ani ≤ f. Since En is a posi-
+tive map, we obtain En(f1x+Ani+1\Ani) ≤ fn. Moreover, applying the H¨older inequality,
+we find
+τ(|pn(y)En(f1x+Ani+1\Ani)(y)qn(y)|2)
+= τ
+�
+pn(y)En(f1x+Ani+1\Ani)(y)qn(y)En(f1x+Ani+1\Ani)(y)pn(y)
+�
+≤ τ
+�
+pn(y)En(f1x+Ani+1\Ani)(y)pn(y)
+�
+∥qn(y)En(f1x+Ani+1\Ani)(y)qn(y)∥M
+≤ τ
+�
+pn(y)En(f1x+Ani+1\Ani)(y)pn(y)
+�
+∥qn(y)fn(y)qn(y)∥M
+≤ λτ
+�
+pn(y)En(f1x+Ani+1\Ani)(y)pn(y)
+�
+,
+(4.13)
+where the last inequality follows from Lemma 2.3(ii).
+Combining above estimate
+with (4.12), we get
+I1
+k,n,1 ≲ λ2n−2k �
+x∈Z
+�
+i∈Sk
+�
+y∈I1(x+Ani+1\Ani,n)
+τ(pn(y)En(f1x+Ani+1\Ani)(y)pn(y)).
+Note that for any fixed x ∈ Z, ∪i∈SkI(x + Ani+1 \ Ani, n) ⊆ x + A2k+1, which implies
+�
+i∈Sk
+�
+y∈I1(x+Ani+1\Ani,n)
+τ(pn(y)En(f1x+Ani+1\Ani)(y)pn(y))
+=
+�
+i∈Sk
+�
+I∈Fn,
+I∩∂(x+Ani+1\Ani)̸=∅
+�
+y∈I
+τ(En(pnf1x+Ani+1\Anipn)(y))
+=
+�
+i∈Sk
+�
+I∈Fn,
+I∩∂(x+Ani+1\Ani)̸=∅
+�
+y∈I∩(x+Ani+1\Ani)
+τ(pn(y)f(y)pn(y))
+=
+�
+i∈Sk
+�
+y∈I(x+Ani+1\Ani,n)
+τ(pn(y)f(y)pn(y))
+≤
+�
+y∈x+A2k+1
+τ(pn(y)f(y)pn(y)),
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+17
+where in the second equality we used the fact that the conditional expectation is trace-
+preserving. Therefore, putting these observations together, we finally get
+I1
+k,n,1 ≲ λ2n−2k �
+x∈Z
+�
+y∈x+A2k+1
+τ(pn(y)f(y)pn(y)) ≲ λ2n−k �
+x∈Z
+τ(pn(x)f(x)pn(x))
+≲ λ22n−k �
+x∈Z
+τ(pn(x)) = λ22n−k∥pn∥2
+2,
+where the second inequality followed from the Fubini theorem and the last inequality
+from (2.6). This finishes the proof of I1
+k,n,1.
+We now turn to the terms I1
+k,n,2 and I1
+k,n,3. Note that qn+1 ∈ Nn and
+qn+1fnqn+1 ≲ qn+1fn+1qn+1 ≤ λ.
+(4.14)
+Then the argument (4.13) also works for the terms I1
+k,n,2 and I1
+k,n,3. As a consequence,
+we can estimate these two terms in the similar way as in the proof of I1
+k,n,1. Hence, we
+omit the details and the proof is complete.
+□
+4.2.2. Estimate of I2
+k,n.
+Lemma 4.6. For n < k, we have
+I2
+k,n ≲ 2n−kλ2∥pn∥2
+2.
+Proof. By the same arguments of I1
+k,n, that is using the cancellation property and the
+definition of bn, we are reduced to estimating the following three terms:
+I2
+k,n,1
+≜
+�
+i∈Sk
+�
+1
+|Ani| −
+1
+|Ani+1|
+�2 �
+x∈Z
+���
+�
+y∈I(x+Ani,n)
+(pnfqn)(y)
+���
+2
+L2(M)
+I2
+k,n,2
+≜
+�
+i∈Sk
+�
+1
+|Ani| −
+1
+|Ani+1|
+�2 �
+x∈Z
+���
+�
+y∈I(x+Ani,n)
+(qn+1fpn)(y)
+���
+2
+L2(M)
+I2
+k,n,3
+≜
+�
+i∈Sk
+�
+1
+|Ani| −
+1
+|Ani+1|
+�2 �
+x∈Z
+���
+�
+y∈I(x+Ani,n)
+(qn+1fnpn)(y)
+���
+2
+L2(M).
+We begin with the term I2
+k,n,1. Using Lemma 4.3, the fact that I1(x + Ani, n) ⊆
+x + A2k+2 and |I1(x + Ani, n)| ≲ 2n for all i ∈ Sk, we deduce that
+���
+�
+y∈I(x+Ani,n)
+(pnfqn)(y)
+���
+2
+L2(M) ≲ 2n
+�
+y∈I1(x+Ani,n)
+τ(|En(pnfqn1x+Ani)(y)|2)
+≤ 2n
+�
+y∈I1(x+Ani,n)
+τ(|En(pnfqn1x+Ani)(y)|2)
+≤ 2n
+�
+y∈x+A2k+2
+τ(|En(pnfqn1x+Ani)(y)|2).
+Since En is a positive map, by applying (2.6) and the H¨older inequality, we obtain
+τ(|En(pnfqn1x+Ani)(y)|2) ≤ τ
+�
+pn(y)fn(y)pn(y)
+�
+∥qn(y)fn(y)qn(y)∥M ≲ λ2τ(pn(y)).
+
+18
+G. HONG, W. LIU, AND B. XU
+Combining the above observations with the fact that for i ∈ Sk, A2k ⊂ Ani ⊂ A2k+1,
+we have
+I2
+k,n,1 ≲ 2nλ2 �
+i∈Sk
+�
+1
+|Ani| −
+1
+|Ani+1|
+�2 �
+x∈Z
+�
+y∈x+A2k+2
+τ(pn(y))
+≤ 2nλ2�
+1
+|A2k| −
+1
+|A2k+1|
+�2 �
+x∈Z
+�
+z∈x+An2k+2
+τ(pn(z))
+≲ 2n−kλ2∥pn∥2
+2.
+The same arguments also work for the terms I2
+k,n,2 and I2
+k,n,3 just by noticing the
+relation (4.14) and qn+1 ∈ Nn, we omit the proofs. The lemma is proved.
+□
+Proof of estimate (4.9). By Lemmas 4.4, 4.5 and 4.6, we conclude the desired estimate
+(4.9) and complete the argument for Tb.
+□
+4.3. Weak type estimate for the good function: (4.6).
+In order to estimate the good part, we need the following proposition.
+Proposition 4.7. Let h ∈ L2(N). Then
+∥Th∥L2(L∞(Ω)⊗N) ≲ ∥h∥2.
+With this proposition at hand, we prove easily the estimate (4.6).
+Proof of estimate (4.6). We clearly have
+�ϕ(χ(λ/2,∞)(|Tg|)) ≤
+∥Tg∥2
+L2(L∞(Ω)⊗N)
+λ2
+≲ ∥g∥2
+2
+λ2
+≤ ∥g∥1∥g∥∞
+λ2
+≲ ∥f∥1
+λ
+,
+as a consequence of the Chebychev inequality, Proposition 4.7, the H¨older inequality
+and conclusion (ii) in Theorem 2.4. This completes the proof.
+□
+We now prove Proposition 4.7. The key idea is the almost orthogonality argument.
+Proof of Proposition 4.7. Let h ∈ L2(N). Without loss of generality, we can assume
+that h is positive. Let h = �
+n∈Z
+dhn, where dhn = hn−1 − hn for n > 1 and dhn = 0 for
+n ≤ 0. The property of martingale difference implies
+�
+n∈N
+∥dhn∥2
+2 = ∥h∥2
+2.
+Then by the orthogonality of εi and the definition of Sk, one has
+∥Th∥2
+L2(L∞(Ω)⊗N) =
+�
+i∈S
+∥(MAni − MAni+1)
+�
+n
+dhn∥2
+2
+=
+�
+k
+�
+i∈Sk
+���
+�
+MAni − MAni+1
+� �
+n
+dhn
+���
+2
+2.
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+19
+Hence, from Lemma 4.2, it is enough to prove
+�
+i∈Sk
+∥(MAni − MAni+1)dhn∥2
+2 ≲ 2−|n−k|∥dhn∥2
+2.
+(4.15)
+To prove (4.15), let us first assume n > k. Recalling that Fn−1 is the set of all atoms
+of n − 1-th dyadic σ-algebra, we may write
+�
+i∈Sk
+∥(MAni − MAni+1)dhn∥2
+2 =
+�
+I∈Fn−1
+�
+x∈I
+�
+i∈Sk
+∥(MAni − MAni+1)dhn(x)∥2
+L2(M).
+Fix one x ∈ I ∈ Fn−1.
+Since dhn is a constant operator on I, �
+i∈Sk ∥(MAni −
+MAni+1)dhn(x)∥2
+L2(M) may be nonzero only if for some i ∈ Sk, at least one of intervals
+x + Ani or x + Ani+1 intersects the boundary of I. Let Sk(dhn)(x) = �
+i∈Sk ∥(MAni −
+MAni+1)dhn(x)∥2
+L2(M). It can be easily seen that
+{x ∈ I : Sk(dhn)(x) ̸= 0} ⊆ {x ∈ I : x + A2k+1 ∩ ∂I ̸= ∅},
+and by a simple geometric argument
+|{x ∈ I : x + A2k+1 ∩ ∂I ̸= ∅}| ≲ 2k.
+On the other hand, we have the following crude estimate for x ∈ I
+� �
+i∈Sk
+∥(MAni − MAni+1)dhn(x)∥2
+L2(M)
+� 1
+2 ≤
+�
+i∈Sk
+∥(MAni − MAni+1)dhn(x)∥L2(M)
+≤
+�
+i∈Sk
+1
+|Ani+1|
+�
+y∈x+Ani+1\Ani
+∥dhn(y)∥L2(M)
++
+�
+i∈Sk
+�
+1
+|Ani| −
+1
+|Ani+1|
+�
+�
+y∈x+Ani
+∥dhn(y)∥L2(M)
+≲
+1
+|A2k|
+�
+y∈x+A2k+1
+∥dhn(y)∥L2(M).
+Set JI = ∪x∈I{J : J ∈ Fn−1&J ∩ x + A2k+1 ̸= ∅} and mI = maxJ∈JI ∥dhn(cJ)∥L2(M),
+where cJ stands for the left endpoint of the dyadic interval J. With these definitions,
+one can see at once that
+1
+|A2k|
+�
+y∈x+A2k+1 ∥dhn(y)∥L2(M) ≲ mI for every x ∈ I. It
+follows from the above observations that
+�
+I∈Fn−1
+�
+x∈I
+�
+i∈Sk
+∥(MAni − MAni+1)dhn(x)∥2
+L2(M)
+=
+�
+I∈Fn−1
+�
+x∈I
+x+A2k+1∩∂I̸=∅
+�
+i∈Sk
+∥(MAni − MAni+1)dhn(x)∥2
+L2(M)
+≲ 2k
+�
+I∈Fn−1
+m2
+I
+≲ 2k−n
+�
+I∈Fn−1
+�
+J∈JI
+�
+x∈J
+∥dhn(x)∥2
+L2(M)
+
+20
+G. HONG, W. LIU, AND B. XU
+≲ 2k−n∥dhn∥2
+2,
+where we used the fact that the number #{J : J ∈ JI} ≤ 4 for every I ∈ Fn−1 in the
+last inequality. So we finish the argument of (4.15) in the case n > k.
+Let us now estimate (4.15) for the case n ≤ k. By the Minkowski inequality,
+�
+i∈Sk
+∥(MAni − MAni+1)dhn∥2
+2 ≲
+�
+i∈Sk
+�
+x∈Z
+���
+1
+|Ani+1|
+�
+y∈x+Ani+1\Ani
+dhn(y)
+���
+2
+L2(M)
++
+�
+i∈Sk
+�
+x∈Z
+�
+1
+|Ani| −
+1
+|Ani+1|
+�2���
+�
+y∈x+Ani
+dhn(y)
+���
+2
+L2(M)
+≜ C1
+k,n + C2
+k,n.
+The cancellation property of dhn over atoms in Fn implies
+C1
+k,n =
+�
+i∈Sk
+�
+x∈Z
+���
+1
+|Ani+1|
+�
+y∈I(x+Ani+1\Ani,n)
+dhn(y)
+���
+2
+L2(M).
+Since 2k ≤ supi∈Sk |Ani| ≤ 2k+1, ∪i∈SkI(x+Ani+1\Ani, n) ⊆ x+A2k+1 and supi∈Sk |I(x+
+Ani+1 \ Ani, n)| ≲ 2n, we use Lemma 4.3 to get
+C1
+k,n ≤ 2n−2k �
+i∈Sk
+�
+x∈Z
+�
+y∈I(x+Ani+1\Ani,n)
+∥dhn(y)∥2
+L2(M)
+≤ 2n−2k �
+x∈Z
+�
+y∈x+A2k+1
+∥dhn(y)∥2
+L2(M) ≤ 2n−k∥dhn∥2
+2.
+It remains to estimate C2
+k,n. Using the cancellation property of dhn over atoms in Fn,
+I(x + Ani, n) ⊆ x + A2k+1, supi∈Sk |I(x + Ani, n)| ≲ 2n and Lemma 4.3 again, we find
+C2
+k,n ≲ sup
+i∈Sk
+�
+x∈Z
+���
+�
+y∈I(x+Ani,n)
+dhn(y)
+���
+2
+L2(M)
+� �
+i∈Sk
+1
+|Ani| −
+1
+|Ani+1|
+�2
+≲ 2n+k �
+x∈Z
+∥dhn(x)∥2
+L2(M) sup
+i∈Sk
+1
+|Ani|2
+≲2n−k∥dhn∥2
+2.
+This finishes the proof.
+□
+5. Proof of Theorem 3.3: (L∞, BMO) and strong type (p, p) estimates
+In this section, we examine the (L∞, BMO) and strong type (p, p) estimates stated
+in Theorem 3.3.
+5.1. (L∞, BMO) estimate.
+We first recall the definition of BMO spaces associated to the von Neumann algebra
+R = N⊗B(ℓ2) equipped with the tensor trace ψ = ϕ ⊗ tr where tr is the canonical
+trace on B(ℓ2). According to [35], the dyadic BMO space BMOd(R) is defined as a
+subspace of L∞(M⊗B(ℓ2); Lrc
+2 (Z; dx/(1 + |x|)2)) with
+∥f∥BMOd(R) = max
+�
+∥f∥BMOr
+d (R), ∥f∥BMOc
+d (R)
+�
+< ∞,
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+21
+where the row and column dyadic BMOd norms are given by
+∥f∥BMOr
+d (R)
+=
+sup
+I∈F
+���
+� 1
+|I|
+�
+x∈I
+���
+�
+f(x) − 1
+|I|
+�
+y∈I
+f(y)
+�∗���
+2� 1
+2 ���
+M⊗B(ℓ2),
+∥f∥BMOc
+d (R)
+=
+sup
+I∈F
+���
+� 1
+|I|
+�
+x∈I
+���f(x) − 1
+|I|
+�
+y∈I
+f(y)
+���
+2� 1
+2 ���
+M⊗B(ℓ2).
+By the definition of BMO spaces, we are reduced to showing
+���
+�
+i∈S
+Tif ⊗ ei1
+���
+BMOd(R) ≲ ∥f∥∞,
+(5.1)
+and
+���
+�
+i∈S
+Tif ⊗ e1i
+���
+BMOd(R) ≲ ∥f∥∞.
+(5.2)
+However, it suffices to estimate (5.1). Indeed, we assume (5.1). Notice that (5.1) is
+equivalent to
+���
+�
+i∈S
+Tif ⊗ ei1
+���
+BMOc
+d(R) ≲ ∥f∥∞
+(5.3)
+and
+���
+�
+i∈S
+Tif ⊗ ei1
+���
+BMOr
+d(R) ≲ ∥f∥∞.
+(5.4)
+Using the fact ∥g∥BMOc
+d(R) = ∥g∗∥BMOr
+d(R) and taking the adjoint of both sides of (5.3),
+we obtain���
+�
+i∈S
+Tif ⊗ e1i
+��
+BMOr
+d(R) =
+���
+� �
+i∈S
+Tif ⊗ e1i
+�∗���
+BMOc
+d(R)
+=
+���
+�
+i∈S
+Tif∗ ⊗ ei1
+���
+BMOc
+d(R) ≲ ∥f∗∥∞ = ∥f∥∞.
+Similarly, we use (5.4) to get
+���
+�
+i∈S
+Tif ⊗ e1i
+���
+BMOc
+d(R) ≲ ∥f∥∞.
+These two inequalities imply
+���
+�
+i∈S
+Tif ⊗ e1i
+���
+BMOd(R) ≲ ∥f∥∞,
+which is the desired estimate (5.2).
+Now let us prove (5.1).
+Proof of (5.1). Let f ∈ L∞(N) and I be a dyadic cube in Z. Decompose f as f =
+fχ3I + fχZ\3I ≜ f1 + f2, where 3I denotes the interval with the same center as I
+such that |3I| = 3|I|. If we set αI,i = Tif2(cI) where cI is the center of I or the left
+
+22
+G. HONG, W. LIU, AND B. XU
+neighborhood in Z of the center if the center does not belong to Z, and αI = �
+i
+αI,i⊗ei1,
+then
+Tif(x) − αI,i = Tif1(x) + (Tif2(x) − αI,i) ≜ Bi1f + Bi2f.
+We first prove (5.3). By the operator convexity of square function x �→ |x|2, we obtain
+�� �
+i∈S
+(Tif − αI,i) ⊗ ei1
+��2 ≤ 2
+�� �
+i∈S
+Bi1f ⊗ ei1
+��2 + 2
+�� �
+i∈S
+Bi2f ⊗ ei1
+��2.
+The first term B1f = �
+i
+Bi1f ⊗ ei1 is easy to estimate. Indeed,
+���
+� 1
+|I|
+�
+x∈I
+(B1f(x))∗(B1f(x))
+� 1
+2 ���
+2
+M⊗B(ℓ2)
+=
+���
+� 1
+|I|
+�
+x∈I
+�
+i∈S
+|Tif1(x)|2� 1
+2 ���
+2
+M
+= 1
+|I|
+���
+�
+x∈I
+�
+i∈S
+|Tif1(x)|2���
+M
+= 1
+|I|
+sup
+∥a∥L2(M)≤1
+τ
+�
+x∈I
+�
+i∈S
+|Tif1(x)a|2
+≤ 1
+|I|
+sup
+∥a∥L2(M)≤1
+τ
+�
+x∈Z
+�
+i∈S
+|Tif1(x)a|2
+= 1
+|I|
+sup
+∥a∥L2(M)≤1
+∥(Ti(fχ3Ia))i∈S∥2
+L2(N;ℓrc
+2 )
+≲ 1
+|I|
+sup
+∥a∥L2(M)≤1
+∥fχ3Ia∥2
+2 ≲ ∥f∥2
+∞,
+where in the third equality, we considered elements in M as bounded linear oper-
+ators on L2(M) via the left multiplication and the last inequality follows from the
+L2-boundedness of T, namely Proposition 4.7.
+Now we turn to the second term B2f = �
+i∈S
+Bi2f ⊗ ei1. Note that
+B2f(x)∗B2f(x)
+=
+�
+i∈S
+|Tif2(x) − Tif2(cI)|2
+=
+�
+i∈S
+|(MAnif2(x) − MAni+1f2(x)) − (MAnif2(cI) − MAni+1f2(cI))|2
+=
+�
+k
+�
+i∈Sk
+|(MAnif2(x) − MAni+1f2(x)) − (MAnif2(cI) − MAni+1f2(cI))|2
+≜
+�
+k
+�
+i∈Sk
+|Fk,i(x)|2.
+We claim that for any k satisfying 2k+1 < |I|, Fk,i(x) = 0 for any i ∈ Sk and x ∈ I.
+Indeed, fix i ∈ Sk and x ∈ I. Since 2k+1 < |I| and f2 is supported in Z \ 3I, a simple
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+23
+geometric observation implies that both MAni+1f2 and MAnif2 are supported in Z \ I.
+This is precisely the claim. Hence,
+B2f(x)∗B2f(x) =
+�
+k:2k+1≥|I|
+�
+i∈Sk
+|Fk,i(x)|2.
+In the following, we further spilt the summation over Sk to two parts by comparing
+ni+1 − ni and |I|. More precisely, we decompose B2f(x)∗B2f(x) as
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni<|I|
+|Fk,i(x)|2 +
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni≥|I|
+|Fk,i(x)|2.
+Let us estimate term of the case ni+1 −ni < |I|. By the operator-convexity of square
+function x �→ |x|2,
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni<|I|
+|Fk,i(x)|2 ≲
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni<|I|
+|MAnif2(x) − MAni+1f2(x)|2
++
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni<|I|
+|MAnif2(cI) − MAni+1f2(cI)|2.
+Now we claim that to complete the argument of the case ni+1 − ni < |I|, it is enough
+to show for any z ∈ I
+∥MAnif2(z) − MAni+1f2(z)∥M ≲ ∥f∥∞|I|
+1
+2
+� � |Ani+1|
+|Ani|
+1
+u2 du
+� 1
+2 .
+(5.5)
+Indeed, by (5.5) and the Minkowski inequality, we have
+���
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni<|I|
+|Fk,I(x)|2���
+M
+≤
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni<|I|
+∥Fk,I(x)∥2
+M
+≲
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni<|I|
+∥f∥2
+∞|I|
+� |Ani+1|
+|Ani|
+1
+u2 du
+≤ ∥f∥2
+∞|I|
+�
+k:2k+1≥|I|
+�
+i∈Sk
+� |Ani+1|
+|Ani|
+1
+u2 du
+≤ ∥f∥2
+∞|I|
+�
+k:2k+1≥|I|
+� 2k+1
+2k
+1
+u2 du
+≲ ∥f∥2
+∞|I|
+�
+k:2k+1≥|I|
+2−k−1 ≲ ∥f∥2
+∞.
+
+24
+G. HONG, W. LIU, AND B. XU
+Thus we deduce that
+���
+� 1
+|I|
+�
+x∈I
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni<|I|
+|Fk,i(x)|2� 1
+2 ���
+2
+M
+≤ 1
+|I|
+�
+x∈I
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni<|I|
+∥Fk,i(x)∥2
+M
+≲ ∥f∥2
+∞,
+which is the desired estimate. It remains to show (5.5). To this end, fix z ∈ I.
+∥MAnif2(z) − MAni+1f2(z)∥M
+=
+���
+�
+1
+|Ani| −
+1
+|Ani+1|
+�
+�
+y∈z+Ani
+f2(y) +
+1
+|Ani+1|
+�
+y∈z+Ani+1\Ani
+f2(y)
+���
+M
+≤
+�
+1
+|Ani| −
+1
+|Ani+1|
+�
+�
+y∈z+Ani
+∥f2(y)∥M +
+1
+|Ani+1|
+�
+y∈z+Ani+1\Ani
+∥f2(y)∥M
+≤
+�
+1
+|Ani| −
+1
+|Ani+1|
+�
+|Ani|∥f2∥∞ +
+1
+|Ani+1|(|Ani+1| − |Ani|)∥f2∥∞
+= 2(|Ani+1| − |Ani|)
+1
+|Ani+1|∥f∥∞
+≲ ∥f∥∞
+� |Ani+1|
+|Ani|
+1
+udu.
+Furthermore, by the H¨older inequality and the fact that ni+1 − ni < |I|, we see that
+∥MAnif2(z) − MAni+1f2(z)∥M ≲ ∥f∥∞(|Ani+1| − |Ani|)
+1
+2
+� � |Ani+1|
+|Ani|
+1
+u2 du
+� 1
+2
+≲ ∥f∥∞|I|
+1
+2
+� � |Ani+1|
+|Ani|
+1
+u2 du
+� 1
+2 .
+Let us now turn to the case ni+1 − ni ≥ |I|. Likewise, we use the operator-convexity
+of square function x �→ |x|2 to obtain
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni≥|I|
+|Fk,i(x)|2 ≲
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni≥|I|
+|MAnif2(x) − MAnif2(cI)|2
++
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni≥|I|
+|MAni+1f2(x) − MAni+1f2(cI)|2.
+In this case, observe that for any Ani,
+∥MAnif2(x) − MAnif2(cI)∥M =
+1
+|Ani|∥
+�
+y∈x+Ani
+f2(y) −
+�
+y∈cI+Ani
+f2(y)∥∞
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+25
+=
+1
+|Ani|
+�
+y∈Z
+∥f2(y)(χx+Ani(y) − χcI+Ani(y))∥∞
+≤
+1
+|Ani|∥f∥∞|(cI + Ani)∆(x + Ani)|,
+where ∆ denotes the usual symmetric difference of two sets. Note that |(cI +Ani)∆(x+
+Ani)| ≲ |x − cI|. Then
+∥MAnif2(x) − MAnif2(cI)∥∞ ≲
+1
+|Ani||x − cI|∥f∥∞.
+Moreover, it is not difficult to verify that the number of i ∈ Sk such that ni+1 −ni ≥ |I|
+is smaller than 2k
+|I|. Therefore,
+���
+� 1
+|I|
+�
+x∈I
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni≥|I|
+|Fk,i(x)|2� 1
+2 ���
+2
+∞
+≤ 1
+|I|
+�
+x∈I
+�
+k:2k+1≥|I|
+�
+i∈Sk
+ni+1−ni≥|I|
+∥Fk,i(x)∥2
+∞
+≲ ∥f∥2
+∞
+1
+|I|
+�
+x∈I
+�
+k:2k+1≥|I|
+2k
+|I|
+1
+|Ani|2 |x − cI|2
+≤ ∥f∥2
+∞
+�
+k:2k+1≥|I|
+2k
+|I|
+1
+|Ani|2 |I|2
+≤ ∥f∥2
+∞|I|
+�
+k:2k+1≥|I|
+2−k−1 ≲ ∥f∥2
+∞,
+where we used the relations |x − cI| ≤ |I| and |Ani| ≈ 2k+1. So we complete the proof
+of (5.3).
+We now consider (5.4). However, we just deal with the term B1f = �
+i∈S
+Bi1f ⊗ ei1,
+since B2f can be treated as before. We note that
+���
+� 1
+|I|
+�
+x∈I
+(B1f(x))(B1f(x))∗� 1
+2 ���
+2
+M⊗B(ℓ2)
+= 1
+|I|
+���
+�
+x∈I
+(B1f(x))(B1f(x))∗���
+M⊗B(ℓ2)
+= 1
+|I|
+���
+�
+i1,i2∈S
+� �
+x∈I
+Ti1f1(x)Ti2f∗
+1 (x)
+�
+⊗ ei1,i2
+���
+M⊗B(ℓ2)
+≜ 1
+|I|∥Λ∥M⊗B(ℓ2).
+
+26
+G. HONG, W. LIU, AND B. XU
+Note that Λ is a positive operator acting on ℓ2(L2(M)) (= L2(M; ℓrc
+2 )). Hence,
+1
+|I|
+���
+�
+x∈I
+(B1f(x))(B1f(x))∗���
+M⊗B(ℓ2)
+= 1
+|I|
+sup
+∥a∥L2(M;ℓrc
+2 )≤1
+�
+Λa, a
+�
+= 1
+|I|
+sup
+∥a∥L2(M;ℓrc
+2 )≤1
+τ
+�� �
+i1∈S
+a∗
+i1 ⊗ e1i1
+�
+Λ
+� �
+i2∈S
+ai2 ⊗ ei21
+��
+= 1
+|I|
+sup
+∥a∥L2(M;ℓrc
+2 )≤1
+τ
+�
+x∈I
+���
+�
+i∈S
+Tif∗
+1 (x)ai
+���
+2
+≤ 1
+|I|
+sup
+∥a∥L2(M;ℓrc
+2 )≤1
+τ
+�
+x∈Z
+���
+�
+i∈S
+Ti(f∗
+1 ai)(x)
+���
+2
+≲ 1
+|I|
+sup
+∥a∥L2(M;ℓrc
+2 )≤1
+τ
+�
+x∈Z
+�
+i∈S
+|f∗
+1 (x)ai|2
+≤ 1
+|I|
+sup
+∥a∥L2(M;ℓrc
+2 )≤1
+τ(
+�
+i:i∈S
+|ai|2)|3I| ∥f∥2
+∞ ≲ ∥f∥2
+∞,
+where in the second inequality we applied Proposition 4.7. This proves (5.4). Finally,
+putting all the estimates obtained so far together with their row analogues, we get
+max
+����
+�
+i∈S
+Tif ⊗ ei1
+���
+BMOd(R),
+���
+�
+i∈S
+Tif ⊗ e1i
+���
+BMOd(R)
+�
+≲ ∥f∥∞.
+This completes the proof of the (L∞, BMO) estimate.
+□
+5.2. Strong type (p, p) estimates.
+In this subsection, we complete the proof of Theorem 3.3 by showing the strong type
+(p, p) estimates.
+Proposition 5.1. Let 1 < p < ∞. Then (Ti)i∈S is bounded from Lp(N) to Lp(N; ℓrc
+2 ).
+Proof. Proposition 4.7 gives the result for p = 2. For the case 1 < p < 2, by applying
+the weak type (1, 1) estimate of T and Proposition 4.7, we conclude that T is bounded
+from Lp(N) to Lp(L∞(Ω)⊗N) by real interpolation [40].
+Thus (Ti)i∈S is bounded
+from Lp(N) to Lp(N; ℓrc
+2 ) according to noncommutative Khintchine’s inequalities—
+Proposition 2.2.
+Consider the case 2 < p < ∞. If we set Tcf = �
+i∈S Tif ⊗ ei1 and Trf = �
+i∈S Tif ⊗
+e1i, then Proposition 4.7 and (L∞, BMO) estimates yield that Tc and Tr are bounded
+from Lp(N) to Lp(N⊗B(ℓ2)) via complex interpolation [36]. Therefore, (Ti) is bounded
+from Lp(N) to Lp(N; ℓrc
+2 ) for all 2 < p < ∞.
+□
+6. Proof of Theorem 1.1
+In this section we prove the extension property—Lemma 1.7, the transference principle—
+Proposition 1.6 and Theorem 1.1 immediately.
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+27
+Proof of Lemma 1.7. Let (xn)n>0 be a sequence in Lp(M; ℓrc
+2 ). By the noncommutative
+Khintchine inequalities Proposition 2.2, there exist two positive constants C1, C2 such
+that
+∥(Txn)n∥Lp(M;ℓrc
+2 ) ≤ C−1
+1
+����
+�
+n
+εnTxn
+����
+Lp(Ω;Lp(M))
+≤ C−1
+1 ∥id ⊗ T∥Lp(Ω;Lp(M))→Lp(Ω;Lp(M))
+����
+�
+n
+εnxn
+����
+Lp(Ω;Lp(M))
+≤ C−1
+1 C2∥T∥Lp(M)→Lp(M)∥(xn)n∥Lp(M;ℓrc
+2 ),
+which completes the proof.
+□
+We now establish the following noncommutative variant of Coifman-Weiss’s trans-
+ference principle.
+Proof of Proposition 1.6. In the following we only consider the two-sided ergodic av-
+erages while the one-sided ones can be handled quite similarly. By the standard ap-
+proximation argument stated in Remark 1.9, it suffices to show for any fixed integer
+i0 ≥ 1
+���
+Bni(T)x − Bni+1(T)x
+�
+0≤i≤i0
+��
+Lp(M;ℓrc
+2 ) ≲ ∥x∥Lp(M).
+(6.1)
+For each n ∈ N, define
+B′
+n : Lp(Z; Lp(M)) → Lp(Z; Lp(M)), B′
+nf(k) =
+1
+2n + 1
+n
+�
+l=−n
+f(l + k), ∀k ∈ Z.
+Let m be a large integer bigger than N. Fix x ∈ Lp(M). Define a Lp(M)-valued
+function fm on Z as
+fm(l) = T lx,
+if |l| ≤ m + N;
+fm(l) = 0 otherwise,
+where N = ni0+1. Then for all −m ≤ k ≤ m and 1 ≤ n ≤ N,
+T kBn(T)x =
+1
+2n + 1
+n
+�
+l=−n
+T k+lx =
+1
+2n + 1
+n
+�
+l=−n
+fm(l + k) = B′
+nfm(k).
+Therefore, for −m ≤ k ≤ m and 0 ≤ i ≤ i0,
+T k(Bni(T)x − Bni+1(T)x) = B′
+nifm(k) − B′
+ni+1fm(k).
+Note that T is a power bounded operator, namely supk∈Z ∥T k∥Lp(M)→Lp(M) < ∞.
+Then for each k ∈ Z, Lemma 1.7 implies
+���
+Bni(T)x − Bni+1(T)x
+�
+0≤i≤i0
+��
+Lp(M;ℓrc
+2 )
+≲
+���
+T k(Bni(T)x − Bni+1(T)x)
+�
+0≤i≤i0
+��
+Lp(M;ℓrc
+2 )
+=
+���
+B′
+nifm(k) − B′
+ni+1fm(k)
+�
+0≤i≤i0
+��
+Lp(M;ℓrc
+2 ).
+(6.2)
+Now we prove (6.1).
+Consider the case 2 < p < ∞ firstly.
+In this case, by the
+assumption (1.5), we have
+���
+B′
+nifm − B′
+ni+1fm
+�
+0≤i≤i0
+��
+Lp(M⊗ℓ∞(N);ℓrc
+2 ) ≲ ∥fm∥Lp(M⊗ℓ∞(N)),
+
+28
+G. HONG, W. LIU, AND B. XU
+which is equivalent to
+m
+�
+k=−m
+���
+B′
+nifm(k) − B′
+ni+1fm(k)
+�
+0≤i≤i0
+��p
+Lp(M;ℓrc
+2 ) ≲ ∥fm∥p
+Lp(M⊗ℓ∞(N)).
+Hence, we use (6.2) to obtain that for any m ≥ 1,
+���
+Bni(T)x − Bni+1(T)x
+�
+0≤i≤i0
+��p
+Lp(M;ℓrc
+2 )
+≲
+1
+2m + 1
+m
+�
+k=−m
+���
+B′
+nifm(k) − B′
+ni+1fm(k)
+�
+0≤i≤i0
+��p
+Lp(M;ℓrc
+2 )
+≲
+1
+2m + 1∥fm∥p
+Lp(M⊗ℓ∞(N)).
+Then by the definition of fm, we see that
+���
+Bni(T)x − Bni+1(T)x
+�
+0≤i≤i0
+��p
+Lp(M;ℓrc
+2 ) ≲
+1
+2m + 1
+m+N
+�
+l=−m−N
+∥fm(l)∥p
+Lp(M)
+=
+1
+2m + 1
+m+N
+�
+l=−m−N
+∥T lx∥p
+Lp(M)
+≲ 2m + 2N + 1
+2m + 1
+∥x∥p
+Lp(M).
+Since m is arbitrarily chosen, we get
+���
+Bni(T)x − Bni+1(T)x
+�
+0≤i≤i0
+��
+Lp(M;ℓrc
+2 ) ≲ ∥x∥Lp(M).
+This gives the desired estimate for the case 2 < p < ∞.
+It remains to show the case 1 < p ≤ 2. In this case, for any ε > 0, there exists a
+factorization B′
+nifm − B′
+ni+1fm = gi + hi such that
+∥(gi)0≤i≤i0∥p
+Lp(M⊗ℓ∞(N);ℓr
+2) + ∥(hi)0≤i≤i0∥p
+Lp(M⊗ℓ∞(N);ℓc
+2)
+≤
+���
+B′
+nifm − B′
+ni+1fm
+�
+0≤i≤i0
+��p
+Lp(M⊗ℓ∞(N);ℓrc
+2 ) + ε.
+Then we have
+m
+�
+k=−m
+���
+B′
+nifm(k) − B′
+ni+1fm(k)
+�
+0≤i≤i0
+��p
+Lp(M;ℓrc
+2 )
+≤
+m
+�
+k=−m
+∥(gi(k))0≤i≤i0∥p
+Lp(M;ℓr
+2) +
+m
+�
+k=−m
+∥(hi(k))0≤i≤i0∥p
+Lp(M;ℓc
+2)
+≲
+���
+B′
+nifm − B′
+ni+1fm
+�
+0≤i≤i0
+��p
+Lp(M⊗ℓ∞(N);ℓrc
+2 ) + ε.
+Since ε is arbitrarily chosen, we obtain
+m
+�
+k=−m
+���
+B′
+nifm(k) − B′
+ni+1fm(k)
+�
+0≤i≤i0
+��p
+Lp(M;ℓrc
+2 )
+≲
+���
+B′
+nifm − B′
+ni+1fm
+�
+0≤i≤i0
+��p
+Lp(M⊗ℓ∞(N);ℓrc
+2 ).
+(6.3)
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+29
+Finally, by (6.2) and the assumption (1.5), we deduce that for any m ≥ 1,
+���
+Bni(T)x − Bni+1(T)x
+�
+0≤i≤i0
+��p
+Lp(M;ℓrc
+2 )
+≲
+1
+2m + 1
+m
+�
+k=−m
+���
+B′
+nifm(k) − B′
+ni+1fm(k)
+�
+0≤i≤i0
+��p
+Lp(M;ℓrc
+2 )
+≲
+1
+2m + 1
+���
+B′
+nifm − B′
+ni+1fm
+�
+0≤i≤i0
+��p
+Lp(M⊗ℓ∞(N);ℓrc
+2 )
+≲
+1
+2m + 1∥fm∥p
+Lp(M⊗ℓ∞(N)) ≲ 2m + 2N + 1
+2m + 1
+∥x∥p
+Lp(M).
+By the arbitrariness of m, we find
+���
+Bni(T)x − Bni+1(T)x
+�
+0≤i≤i0
+��
+Lp(M;ℓrc
+2 ) ≲ ∥x∥Lp(M).
+So we finish the proof of (6.1).
+□
+Now, we are able to conclude Theorem 1.1.
+Proof of Theorem 1.1. Actually, Theorem 1.1 follows immediately from Proposition 1.6
+and Theorem 1.5.
+□
+7. Proof of Theorem 1.4
+In this section, we prove Proposition 1.8 and Theorem 1.4. Before that, we give some
+notations and lemmas. We first recall the definitions of dilations and N-dilation in the
+noncommutative setting (see e.g. [15]).
+Definition 7.1. Let 1 ≤ p ≤ ∞ and T : Lp(M, τM) → Lp(M, τM) be a contrac-
+tion.
+We call the operator T has a dilation if there exist a von Neumann algebra
+A equipped with a normal faithful semifinite trace τA, two contraction linear opera-
+tors Q : Lp(A, τA) → Lp(M, τM), J : Lp(M, τM) → Lp(A, τA) and an isometry
+U : Lp(A, τA) → Lp(A, τA) such that
+(7.1)
+T n = QUnJ, ∀n ∈ N ∪ {0}.
+We can use the following diagrams to represent the above decomposition
+Lp(M, τM)
+T n �
+J
+�
+Lp(M, τM)
+Lp(A, τA)
+Un
+� Lp(A, τA)
+Q
+�
+for all n ≥ 0.
+We call the operator T has an N-dilation if (7.1) holds for all n ∈ {0, 1, · · · , N}.
+Let 1 ≤ p < ∞. Let SS(Lp(M)) denote the set of all Lamperti contractions on
+Lp(M). Moreover, for a given set A consisting of operators on Lp(M), we denote by
+conv{A} the convex hull of A, namely
+conv{A} =
+�
+n
+�
+i=1
+λiTi : Ti ∈ A,
+n
+�
+i=1
+λi = 1, λi ≥ 0, n ∈ N
+�
+.
+
+30
+G. HONG, W. LIU, AND B. XU
+The following result which can be seen as a N-dilation theorem for conv(SS(Lp(M)))
+was established in [15, Corollary 4.7].
+Lemma 7.2. Let 1 < p < ∞. Each operator T ∈ conv(SS(Lp(M))) has an N-dilation
+for all N ∈ N.
+Now we present a characterization theorem for isometric operators established in
+[50, 25]. Let M and A be two von Neumann algebras. A complex linear map J : M →
+A is called a Jordan ∗-homomorphism if J(x)∗ = J(x∗) and J(x2) = J(x)2 for all
+x ∈ M. Moreover, J is called the Jordan ∗-monomorphism if J is an injective Jordan
+∗-homomorphism.
+The following lemma was obtained by Størmer [45].
+Lemma 7.3. Let J : M → A be a normal (completely additive, ultraweakly continuous)
+Jordan ∗-homomorphism.
+Let
+�
+A denote the von Neumann subalgebra generated by
+J(M) in A, and Z �
+A be the center of �
+A. Then there are two projections e, f ∈ Z �
+A
+satisfying e + f = 1 �
+A, such that the map x → J(x)e is a ∗-homomorphism and x →
+J(x)f is a ∗-anti-homomorphism.
+The following characterization of isometric operators will be frequently used.
+Proposition 7.4. [50, 25] Let 1 ≤ p ̸= 2 < ∞.
+Assume that T : Lp(M, τM) →
+Lp(A, τA) is a bounded linear operator. Then T is an isometry if and only if there exist
+uniquely a partial isometry w ∈ A, a normal Jordan ∗-monomorphism J : M → A,
+and a positive self-adjoint operator b affiliated with A, such that
+(i) w∗w = suppb = J(1);
+(ii) For all x ∈ M, J(x) commutes with every spectral projection of b;
+(iii) T(x) = wbJ(x) for all x ∈ SM;
+(iv) τA(bpJ(x)) = τM(x) for all x ∈ M+.
+Now we are ready to prove Proposition 1.8.
+Proof of Proposition 1.8. Let (xn)1≤n≤N be a finite sequence in Lp(M; ℓrc
+2 ).
+By an
+approximation argument, without loss of generality, we may assume that xn ∈ SM for
+all 1 ≤ n ≤ N. For p = 2, the conclusion is trivially right. Indeed, in this case
+���
+T(xn)
+�
+n
+��2
+L2(M;ℓrc
+2 ) =
+�
+n
+∥Txn∥2
+L2(M) = ∥(xn)n∥L2(M;ℓrc
+2 ).
+We now focus on the case 2 < p < ∞. Since T is an isometric operator, there exist
+w, b, J such that T = wbJ satisfying properties (i)-(iii) in Proposition 7.4. Moreover,
+by Lemma 7.3, we may find projections e, f such that
+�
+T(xn)
+�∗�
+T(xn)
+�
+=
+���
+bJ(xn)e + bJ(xn)f
+���2
+=
+�
+bJ(xn)e + bJ(xn)f
+�∗�
+bJ(xn)e + bJ(xn)f
+�
+=
+�
+bJ(x∗
+n)e + bJ(x∗
+n)f
+��
+bJ(xn)e + bJ(xn)f
+�
+= b2J(x∗
+nxn)e + b2J(xnx∗
+n)f.
+(7.2)
+As a consequence,
+�
+n
+�
+T(xn)
+�∗�
+T(xn)
+�
+= b2J
+� �
+n
+x∗
+nxn
+�
+e + b2J
+� �
+n
+xnx∗
+n
+�
+f.
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+31
+Set y1 =
+� �
+n x∗
+nxn
+�1/2 and y2 =
+� �
+n xnx∗
+n
+�1/2. Then
+�
+n
+�
+T(xn)
+�∗�
+T(xn)
+�
+= b2J(y2
+1)e + b2J(y2
+2)f.
+Hence, we have
+���
+T(xn)
+�
+n
+��p
+Lp(M;ℓc
+2) = τ
+��
+b2J(y2
+1)e + b2J(y2
+2)f
+� p
+2
+�
+.
+According to Lemma 7.3 and Proposition 7.4(ii), we further have
+τ
+��
+b2J(y2
+1)e + b2J(y2
+2)f
+� p
+2
+�
+= τ(bpJ(yp
+1)e) + τ(bpJ(yp
+2)f).
+So, we obtain
+���
+T(xn)
+�
+n
+��p
+Lp(M;ℓc
+2) = τ(bpJ(yp
+1)e) + τ(bpJ(yp
+2)f).
+(7.3)
+On the other hand, applying the fact T = wbJ, we get
+�
+T(xn)
+��
+T(xn)
+�∗ = (wbJ(xn))(wbJ(xn))∗
+= wb2J(xn)J(xn)∗w∗ = wb2J(xnx∗
+n)ew∗ + wb2J(x∗
+nxn)fw∗,
+which gives rise to
+�
+n
+�
+T(xn)
+��
+T(xn)
+�∗ = wb2J(y2
+2)ew∗ + wb2J(y2
+1)fw∗.
+Then by the above observations and Proposition 7.4(i), we find
+���
+T(xn)
+�
+n
+��p
+Lp(M;ℓr
+2) = ∥w(b2J(y2
+2)e + b2J(y2
+1)f)w∗∥
+p
+2
+L p
+2 (M)
+= ∥(b2J(y2
+2)e + b2J(y2
+1)f)
+1
+2 w∗w(b2J(y2
+2)e + b2J(y2
+1)f)
+1
+2 ∥
+p
+2
+L p
+2 (M)
+= ∥b2J(y2
+2)e + b2J(y2
+1)f∥
+p
+2
+L p
+2 (M)
+= τ(bpJ(yp
+2)e) + τ(bpJ(yp
+1)f).
+(7.4)
+Therefore, combining (7.3) with (7.4), we arrive at
+���
+T(xn)
+�
+n
+��p
+Lp(M;ℓc
+2) +
+���
+T(xn)
+�
+n
+��p
+Lp(M;ℓr
+2)
+= τ(bpJ(yp
+1)e) + τ(bpJ(yp
+2)f) + τ(bpJ(yp
+2)e) + τ(bpJ(yp
+1)f)
+= τ(bpJ(yp
+1)) + τ(bpJ(yp
+2)).
+Moreover, by Proposition 7.4(iv), we have
+���
+T(xn)
+�
+n
+��p
+Lp(M;ℓc
+2) +
+���
+T(xn)
+�
+n
+��p
+Lp(M;ℓr
+2) = τ(yp
+1) + τ(yp
+2)
+= ∥(xn)n∥p
+Lp(M;ℓr
+2) + ∥(xn)n∥p
+Lp(M;ℓc
+2),
+which yields ∥
+�
+T(xn)
+�
+n∥Lp(M;ℓrc
+2 ) = ∥(xn)n∥Lp(M;ℓrc
+2 ). So T is an isometry on Lp(M; ℓrc
+2 )
+and we finish the proof of the case 2 < p < ∞.
+We then turn to the case 1 ≤ p < 2. Since (xn)n ∈ Lp(M; ℓrc
+2 ), for any given ε > 0,
+there are two finite sequences (gn)n and (hn)n such that xn = gn + hn and
+(7.5)
+∥(gn)n∥p
+Lp(M;ℓc
+2) + ∥(hn)n∥p
+Lp(M;ℓr
+2) ≤ ∥(xn)n∥p
+Lp(M;ℓrc
+2 ) + ε.
+
+32
+G. HONG, W. LIU, AND B. XU
+Then by Lemma 7.3, we may decompose T(xn) as
+T(xn) = T(gn)e + T(hn)f + (T(gn)f + T(hn)e).
+By the definition of the norm ∥ · ∥Lp(M;ℓrc
+2 ), we have
+���
+T(xn)
+�
+n
+��p
+Lp(M;ℓrc
+2 )
+≤
+���
+T(gn)e + T(hn)f
+�
+n
+��p
+Lp(M;ℓc
+2) +
+���
+T(gn)f + T(hn)e
+�
+n
+��p
+Lp(M;ℓr
+2).
+(7.6)
+On one hand, similar to (7.2), we have
+�
+n
+|T(gn)e + T(hn)f|2 =
+�
+n
+(wbJ(gn)e + wbJ(hn)f)∗(wbJ(gn)e + wbJ(hn)f)
+= b2J
+� �
+n
+g∗
+ngn
+�
+e + b2J
+� �
+n
+hnh∗
+n
+�
+f.
+(7.7)
+Set y3 =
+� �
+n g∗
+ngn
+�1/2 and y4 =
+� �
+n hnh∗
+n
+�1/2. Then
+(7.8)
+���
+T(gn)e + T(hn)f
+�
+n
+��p
+Lp(M;ℓc
+2) = τ(bpJ(yp
+3)e) + τ(bpJ(yp
+4)f).
+On the other hand, for the term
+���
+T(gn)f + T(hn)e
+�
+n
+��p
+Lp(M;ℓr
+2), similar to (7.7), we
+deduce that
+�
+n
+|(T(gn)f + T(hn)e)∗|2 =
+�
+n
+(wbJ(gn)f + wbJ(hn)e)(wbJ(gn)f + wbJ(hn)e)∗
+= wb2J
+� �
+n
+g∗
+ngn
+�
+fw∗ + wb2J
+� �
+n
+hnh∗
+n
+�
+ew∗
+= wb2J(y2
+3)fw∗ + wb2J(y2
+4)ew∗.
+Using the same argument as in (7.4), we have
+(7.9)
+���
+T(gn)f + T(hn)e
+�
+n
+��p
+Lp(M;ℓr
+2) = τ(bpJ(yp
+3)f) + τ(bpJ(yp
+4)e).
+Together (7.8), (7.9) and (7.6) with Proposition (7.4)(iv) and (7.5), we get
+���
+T(xn)
+�
+n
+��p
+Lp(M;ℓrc
+2 ) ≤ ∥(xn)n∥Lp(M;ℓrc
+2 ) + ε.
+By the arbitrariness of ε, we proved that T extends to a contraction on Lp(M; ℓrc
+2 ).
+Finally, we assume that T is positive. It is sufficient to consider the case 1 < p < 2.
+The following facts are taken from [15]. Note that T is a positive isometry. Then T is
+Lamperti and T = bJ, where b, J are defined in Lemma 7.3 (see [15, Theorem 3.3 and
+Remark 3.9]). Let A be the von Neumann algebra generated by J(M). By Lemma 7.3,
+we may decompose A = A1 ⊕ A2, where A1 and A2 are two von Neumann subalgebras
+of A, and write J = J1 + J2 such that J1 : M → A1 is a normal ∗-homomorphism
+and J2 : M → A2 is a normal ∗-anti-homomorphism. Let σ : A2 → Aop
+2 be the usual
+opposite map and define
+Σ : A → A1 ⊕ Aop
+2 ,
+Σ = IdA1 ⊕ σ.
+Then Σ ◦ J is a normal ∗-homomorphism and Σ(J(M)) is a von Neumann subalgebra
+of A1 ⊕ Aop
+2 . Define
+ϕ : Σ(J(M))+ → [0, ∞],
+x �→ τ(bpΣ−1x).
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+33
+Then ϕ becomes a normal semifinite trace on Σ(J(M)). Let Lp(Σ(J(M)), ϕ) be the
+associated noncommutative Lp space.
+Then Σ ◦ J extends to a positive surjective
+isometry
+˜J : Lp(M, τ) → Lp(Σ(J(M)), ϕ),
+x �→ Σ(J(x)),
+whence ˜J−1 is well defined, positive and isometric on Lp(Σ(J(M)), ϕ). We refer to [15,
+Proposition 5.3] for the detailed description of above facts.
+In the following, we claim that ˜J extends to an isometry from Lp(M, τ; ℓrc
+2 ) onto
+Lp(Σ(J(M)), ϕ; ℓrc
+2 ). To see this, we divide the proof of the claim into three steps.
+In the first step, we prove that for any finite sequence (xn) in Lp(M, τ; ℓrc
+2 ) and each
+xn ∈ SM,
+(7.10)
+∥( ˜J(xn))n∥p
+Lp(Σ(J(M)),ϕ;ℓc
+2) = ∥(xn)n∥p
+Lp(M,τ;ℓc
+2)
+and
+(7.11)
+∥( ˜J(xn))n∥p
+Lp(Σ(J(M)),ϕ;ℓr
+2) = ∥(xn)n∥p
+Lp(M,τ;ℓr
+2).
+To prove (7.10), note that for x ∈ M, ˜J(x)∗ = (Σ(J(x)))∗ = J1(x∗)⊕σ(J2(x∗)) = ˜J(x∗)
+which implies ˜J(x)∗ ˜J(x) = ˜J(x∗) ˜J(x) = ˜J(x∗x). Then
+∥( ˜J(xn))n∥p
+Lp(Σ(J(M)),ϕ;ℓc
+2) =
+���
+� �
+n
+| ˜J(xn)|2�1/2���
+p
+Lp(Σ(J(M)),ϕ)
+= ϕ
+�� �
+n
+˜J(xn)∗ ˜J(xn)
+�p/2�
+= τ
+�
+bpΣ−1�
+˜J
+� �
+n
+x∗
+nxn
+��p/2�
+= τ
+�
+bpΣ−1�
+Σ ◦ J
+� �
+n
+x∗
+nxn
+��p/2�
+= τ
+�
+bp�
+J
+�� �
+n
+|xn|2�1/2��p�
+= τ
+��
+bJ
+�� �
+n
+|xn|2�1/2��p�
+=
+���T
+�� �
+n
+|xn|2�1/2����
+p
+Lp(M,τ) = ∥(xn)n∥p
+Lp(M,τ;ℓc
+2),
+which gives (7.10). Replacing ˜J(xn) by ˜J(xn)∗ in the above argument, we obtain (7.11).
+In the second step, we show
+(7.12)
+��� ˜J(xn)
+�
+n
+��
+Lp(Σ(J(M)),ϕ;ℓrc
+2 ) ≤ ∥(xn)n∥Lp(M,τ;ℓrc
+2 ).
+To see this, since (xn) ∈ Lp(M, τ; ℓrc
+2 ), for any given ε > 0, there exist sequences (gn)n
+and (hn)n such that xn = gn + hn and
+∥(gn)n∥p
+Lp(M;ℓc
+2) + ∥(hn)n∥p
+Lp(M;ℓr
+2) ≤ ∥(xn)n∥p
+Lp(M;ℓrc
+2 ) + ε.
+Then by (7.10) and (7.11), we have
+��� ˜J(xn)
+�
+n
+��p
+Lp(Σ(J(M)),ϕ;ℓrc
+2 )
+≤
+��� ˜J(gn)
+�
+n
+��p
+Lp(Σ(J(M)),ϕ;ℓc
+2) +
+��� ˜J(hn)
+�
+n
+��p
+Lp(Σ(J(M)),ϕ;ℓr
+2)
+= ∥(gn)n∥p
+Lp(M;ℓc
+2) + ∥(hn)n∥p
+Lp(M;ℓr
+2)
+≤ ∥(xn)n∥p
+Lp(M;ℓrc
+2 ) + ε.
+By the arbitrariness of ε, we obtain (7.12).
+
+34
+G. HONG, W. LIU, AND B. XU
+In the last step, we prove
+(7.13)
+��� ˜J−1(xn)
+�
+n
+��
+Lp(M,τ;ℓrc
+2 ) ≤ ∥(xn)n∥Lp(Σ(J(M)),ϕ;ℓrc
+2 ).
+Indeed, notice that ˜J−1 is positive and isometric from Lp(Σ(J(M)), ϕ) to Lp(M, τ).
+Then
+∥( ˜J−1(xn))n∥p
+Lp(M,τ;ℓc
+2) = τ
+��
+˜J−1� �
+n
+x∗
+nxn
+��p/2�
+=
+��� ˜J−1�� �
+n
+|xn|2�1/2����
+p
+Lp(M,τ) = ∥(xn)n∥p
+Lp(Σ(J(M)),ϕ;ℓc
+2).
+Replacing ˜J−1(xn) by ˜J−1(xn)∗, we also have
+∥( ˜J−1(xn))n∥Lp(M,τ;ℓr
+2) = ∥(xn)n∥Lp(Σ(J(M)),ϕ;ℓr
+2).
+Therefore, repeating argument as in (7.12), we get (7.13).
+From (7.12) and (7.13), we deduce the claim.
+To complete the argument, there remains to verify that the embedding
+Lp(Σ(J(M)), ϕ; ℓrc
+2 ) → Lp(M, τ; ℓrc
+2 ),
+(xn)n �→ (bΣ−1xn)n
+is an isometry. Let p′ be the conjugate index of p, that is 1
+p + 1
+p′ = 1. Then 2 < p′ <
+∞. Let (xn) be a finite sequence in Lp′(Σ(J(M)), ϕ; ℓrc
+2 ). Write xn = (xn,1, xn,2) ∈
+Lp′(A1) ⊕ Lp′(Aop
+2 ). Then
+∥(bp/p′Σ−1xn)n∥p′
+Lp′(M,τ;ℓc
+2) =
+���
+� �
+n
+|bp/p′Σ−1xn|2�1/2���
+p′
+Lp′(M,τ)
+= τ
+�
+bp� �
+n
+Σ−1(x∗
+n)Σ−1(xn)
+�p′/2�
+= τ
+�
+bp� �
+n
+�
+x∗
+n,1xn,1 + σ−1(xn,2x∗
+n,2)
+��p′/2�
+= τ
+�
+bp� �
+n
+x∗
+n,1xn,1 + σ−1� �
+n
+xn,2x∗
+n,2
+��p′/2�
+= τ
+�
+bp� �
+n
+x∗
+n,1xn,1
+�p′/2�
++ τ
+�
+bp�
+σ−1� �
+n
+xn,2x∗
+n,2
+��p′/2�
+= ∥(xn,1)n∥p′
+Lp′(Σ(J(M)),ϕ;ℓc
+2) + ∥(xn,2)n∥p′
+Lp′(Σ(J(M)),ϕ;ℓr
+2).
+Note that (bp/p′Σ−1xn)∗ = bp/p′Σ−1x∗
+n. Then replacing bp/p′Σ−1xn by (bp/p′Σ−1xn)∗ in
+the above identities, we deduce that
+∥(bp/p′Σ−1xn)n∥p′
+Lp′(M,τ;ℓr
+2) = ∥(xn,1)n∥p′
+Lp′(Σ(J(M)),ϕ;ℓr
+2) + ∥(xn,2)n∥p′
+Lp′(Σ(J(M)),ϕ;ℓc
+2).
+Combining the above two identities, we have
+∥(bp/p′Σ−1xn)n∥p′
+Lp′(M,τ;ℓc
+2) + ∥(bp/p′Σ−1xn)n∥p′
+Lp′(M,τ;ℓr
+2)
+= ∥(xn,1)n∥p′
+Lp′(Σ(J(M)),ϕ;ℓr
+2) + ∥(xn,2)n∥p′
+Lp′(Σ(J(M)),ϕ;ℓr
+2)
++ ∥(xn,1)n∥p′
+Lp′(Σ(J(M)),ϕ;ℓc
+2) + ∥(xn,2)n∥p′
+Lp′(Σ(J(M)),ϕ;ℓc
+2)
+= ∥(xn)n∥p′
+Lp′(Σ(J(M)),ϕ;ℓrc
+2 ).
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+35
+Hence the map
+φ : Lp′(Σ(J(M)), ϕ; ℓrc
+2 ) → Lp′(M, τ; ℓrc
+2 ),
+(xn)n �→ (bp/p′Σ−1xn)n
+is an isometry.
+By Proposition 2.1, we know that (Lp(Σ(J(M)), ϕ; ℓrc
+2 ))∗ = Lp′(Σ(J(M)), ϕ; ℓrc
+2 ).
+Let φ∗ be the conjugate of φ. Then we can check that φ∗((bΣ−1xn)n) = (xn)n (see the
+proof of Proposition 5.3 in [15]).
+Therefore, recalling that T is a contraction on Lp(M, τ; ℓrc
+2 ) with T = bJ and together
+with above observations, we finally get
+∥(xn)n∥Lp(Σ(J(M)),ϕ;ℓrc
+2 ) = ∥φ∗((bΣ−1xn)n)∥Lp(Σ(J(M)),ϕ;ℓrc
+2 )
+≤ ∥(bΣ−1xn)n∥Lp(M,τ;ℓrc
+2 ) = ∥(T ˜J−1xn)n∥Lp(M,τ;ℓrc
+2 )
+≤ ∥( ˜J−1xn)n∥Lp(M,τ;ℓrc
+2 ) = ∥(xn)n∥Lp(Σ(J(M)),ϕ;ℓrc
+2 ),
+which gives ∥(xn)n∥Lp(Σ(J(M)),ϕ;ℓrc
+2 ) = ∥(bΣ−1xn)n∥Lp(M,τ;ℓrc
+2 ). So the proof of Proposi-
+tion 1.8 is complete.
+□
+Based on Proposition 1.8, a similar Coifman-Weiss’s transference principle as Propo-
+sition 1.6 holds also for isometries and we thus get the following quantitative mean
+ergodic theorem for isometries.
+Lemma 7.5. Let 1 ≤ p < ∞ and T : Lp(M) → Lp(M) be an isometry. Let (ni)i∈N be
+any increasing sequence of positive integers. Then for 2 ≤ p < ∞,
+���
+Mni(T)x − Mni+1(T)x
+�
+i∈N
+��
+Lp(M;ℓrc
+2 ) ≲ ∥x∥Lp(M), forallx ∈ Lp(M).
+If T is moreover positive, then the above inequality holds also for 1 < p < 2.
+Lemma 7.5 can be proved in a similar way as Proposition 1.6 by observing that the
+“≲” in (6.2) can be strengthened to “=” due to Proposition 1.8. We omit the details.
+By Lemma 7.5, we now can conclude the proof of Theorem 1.4.
+Proof of Theorem 1.4. Recall that Mn(T) =
+1
+n+1
+�n
+k=0 T k. By the density argument,
+it is enough to prove the theorem for any finite positive sequence (ni)0≤i≤N.
+Fix an arbitrary N ≥ 1. Note that T ∈ S. Then by definition, we can find (Tj) ⊆
+conv(SS(Lp(M))) such that Tj converges to T in the sense of strong operator topology.
+Moreover, according to Lemma 7.2, for each Tj, there exist two contractions Qj,N, Jj,N
+and one isometry Uj,N such that T ni
+j
+= Qj,NU ni
+j,NJj,N for every 0 ≤ ni ≤ nN. As a
+consequence, by Proposition 1.7, Qj,N and Jj,N extend to two bounded operators on
+Lp(M; ℓrc
+2 ). Therefore, for any fixed x ∈ Lp(M), together with Lemma 7.5, we get
+∥
+�
+Mni(Tj)x − Mni+1(Tj)x
+�
+0≤i≤N∥Lp(M;ℓrc
+2 )
+= ∥(Qj,N(Mni − Mni+1)(Uj,N)Jj,Nx)0≤i≤N∥Lp(M;ℓrc
+2 )
+≤ ∥((Mni − Mni+1)(Uj,N)Jj,Nx)0≤i≤N∥Lp(M;ℓrc
+2 )
+≲ ∥Jj,Nx∥Lp(M) ≲ ∥x∥Lp(M).
+Consequently, combined with the noncommutative Khintchine inequality in Lp space-
+Proposition 2.2, we finally deduce that
+∥
+�
+Mni(T)x − Mni+1(T)x
+�
+0≤i≤N∥Lp(M;ℓrc
+2 )
+
+36
+G. HONG, W. LIU, AND B. XU
+≤ ∥
+��
+Mni − Mni+1
+�
+Tjx)0≤i≤N∥Lp(M;ℓrc
+2 ) + ∥
+��
+Mni − Mni+1
+�
+(T − Tj)x
+�
+)0≤i≤N∥Lp(M;ℓrc
+2 )
+≲ ∥x∥Lp(M) + ∥
+��
+Mni − Mni+1
+�
+(T − Tj)x
+�
+)0≤i≤N∥Lp(M;ℓrc
+2 )
+≈ ∥x∥Lp(M) +
+����
+N
+�
+i=0
+εi
+�
+Mni − Mni+1
+�
+(T − Tj)x
+����
+Lp(Ω;Lp(M))
+≲ ∥x∥Lp(M) +
+N
+�
+i=0
+∥
+�
+Mni − Mni+1
+�
+(T − Tj)x∥Lp(M),
+By letting j → ∞, we obtain the desired conclusion.
+□
+By the argument of Corollary 5.4 in [15] and Theorem 1.4, we immediately obtain
+the quantitative mean ergodic theorem for operator-valued positive contractions.
+Corollary 7.6. Let 1 < p < ∞ and let (Ω, µ) be a σ-finite measure space. Suppose
+that T : Lp(Ω) → Lp(Ω) is a positive contraction. Define �T = T ⊗ ILp(M). Let (ni)i∈N
+be any increasing sequence of positive integers. Then there exists a positive constant
+Cp such that
+���
+Mni( �T)x − Mni+1( �T)x
+�
+i∈N
+��
+Lp(L∞(Ω)⊗M;ℓrc
+2 ) ≤ Cp∥x∥p ∀ x ∈ Lp(L∞(Ω)⊗M; ℓrc
+2 ).
+References
+[1] M .A. Akcoglu, A pointwise ergodic theorem in Lp-spaces, Canad. J. Math. 27 (1975), no. 5,
+1075-1082.
+[2] C. Anantharaman-Delaroche, On ergodic theorems for free group actions on noncommutative
+spaces, Probab. Theory Related Fields 135 (2006), no. 4, 520-546.
+[3] J. Avigad, J. Rute, Oscillation and the mean ergodic theorem for uniformly convex Banach spaces,
+Ergod. Th. & Dynam. Sys. 35 (2015), no. 4, 1009-1027.
+[4] T. N. Bekjan, Noncommutative maximal ergodic theorems for positive contractions, J. Funct. Anal.
+254 (2008), no. 9, 2401-2418.
+[5] J. Bourgain, Pointwise ergodic theorems for arithmetic sets, Publ. Math. IHES. 69 (1989), 5-41.
+[6] L. Cadilhac, Noncommutative Khintchine inequalities in interpolation spaces of Lp-spaces, Adv.
+Math. 352 (2019) 265-296.
+[7] L. Cadilhac, J. M. Conde-Alonso, J. Parcet, Spectral multipliers in group algebras and noncommu-
+tative Calder´on-Zygmund theory, J. Math. Pures Appl. (9) 163 (2022) 450-472.
+[8] R.R. Coifman, W. Weiss, Transference methods in Analysis, CBMS No. 31, Amer. Math. Soc.,
+Providence, R.I., 1997.
+[9] J. P. Conze, N. Dang-Ngoc, Ergodic theorems for noncommutative dynamical systems, Invent.
+Math., 46 (1978), 1-15.
+[10] I. Cuculescu, Martingales on von Neumann algebras, J. Multivariate Anal. 1 (1971), no. 1, 17-27.
+[11] N. Dunford, J. T. Schwartz, Linear Operators. I. General Theory, Applied Mathematics, Vol. 7.
+Interscience Publishers, Inc., New York, 1958.
+[12] T. Fack, H. Kosaki, Generalized s-numbers of τ-measurable operators, Pacific J. Math. 123 (1986),
+no. 2, 269-300.
+[13] G. Hong, B. Liao, S. Wang, Noncommutative maximal ergodic inequalities associated with dou-
+bling conditions, Duke Math. J. 170 (2021), no. 2, 205-246.
+[14] G. Hong, W. Liu, B. Xu, Quantitative mean ergodic inequalities II: power bounded operators
+acting on one noncommutative Lp space, prepare.
+[15] G. Hong, S. Ray, S. Wang, Maximal ergodic inequalities for some positive operators on noncom-
+mutative Lp-spaces, arXiv:1907,12967.
+[16] G. Hong, M. Sun, Noncommutative multi-parameter Wiener-Wintner type ergodic theorem, J.
+Funct. Anal. 275 (2018), no. 5, 1100-1137.
+
+QUANTITATIVE MEAN ERGODIC INEQUALITIES
+37
+[17] G. Hong, B. Xu, A noncommutative weak (1, 1) type estimate for a square function from ergodic
+theory, J. Funct. Anal. 280 (2021), no.9, 108959.
+[18] Y. Hu, Maximal ergodic theorems for some group actions, J. Funct. Anal. 254 (2008), no. 5,
+1282-1306.
+[19] R. Jajte, Strong limit theorems in noncommutative probability, Lecture Notes in Mathematics,
+volume 1110, Springer-Verlag, Berlin, 1985.
+[20] R. Jajte, Strong limit theorems in noncommutative L2-spaces, Lecture Notes in Mathematics,
+volume 1477, Springer-Verlag, Berlin, 1991.
+[21] Y. Jiao, N. Randrianantoanina, L. Wu, D. Zhou, Square Functions for Noncommutative Differen-
+tially Subordinate Martingales, Commun. Math. Phys. 374 (2020), no. 2, 975-1019.
+[22] R. Jones, I. Ostrovskii, J. Rosenblatt, Square functions in ergodic theory, Ergod. Th. & Dynam.
+Sys. 16 (1996), no. 2, 267-305.
+[23] R. Jones, J. Rosenblatt, M. Wierdl, Oscillation in ergodic theory, Ergod. Th. & Dynam. Sys. 18
+(1998), no. 4, 889-935.
+[24] M. Junge, C. Le Merdy, Q. Xu, H∞ functional calculus and square functions on noncommutative
+Lp-spaces, Ast´erisque. 305 (2006) vi+138 pp.
+[25] M. Junge, Z. Ruan, D. Sherman, A classification for 2-isometries of noncommutative Lp-spaces,
+Israel J. Math. 150 (2005) 285-314.
+[26] M. Junge, Q. Xu, Noncommutative maximal ergodic theorems, J. Amer. Math. Soc. 20 (2007),
+no. 2, 385-439.
+[27] I. Kov´acs, J. Sz¨ucs, Ergodic type theorems in von Neumann algebras, Acta Sci. Math. (Szeged)
+27 (1966), 233-246.
+[28] U. Krengel, On the speed of convergence in the ergodic theorem, Monatsh. Math. 86 (1978/79),
+no. 1, 3-6.
+[29] B. Kummerer, A non-commutative individual ergodic theorem, Invent. Math., 46 (1978), 139-145.
+[30] E. C. Lance, Ergodic theorems for convex sets and operator algebras, Invent. Math. 37 (1976)
+201–214.
+[31] S. Litvinov, A non-commutative Wiener-Wintner theorem, Illinois J. Math. 58 (2014), no. 3,
+697-708.
+[32] F. Lust-Piquard, In´egalit´es de Khintchine dans Cp (1 < p < ∞), C. R. Acad. Sci. Paris S´er. I
+Math. 303 (1986), no. 7, 289-292.
+[33] F. Lust-Piquard, G. Pisier, Noncommutative Khintchine and Paley inequalities, Ark. Mat. 29
+(1991), no. 2, 241-260.
+[34] T. Mei, Operator valued Hardy spaces, Mem. Amer. Math. Soc. 188 (2007), no. 881, vi+64 pp.
+[35] T. Mei, J. Parcet, Pseudo-localization of singular integrals and noncommutative Littlewood-Paley
+inequalities, Int. Math. Res. Not. 8 (2009) 1433-1487.
+[36] M. Musat, Interpolation between non-commutative BMO and non-commutative Lp-spaces, J.
+Funct. Anal. 202 (2003), no. 1, 195-225.
+[37] J. Parcet, Pseudo-localization of singular integrals and noncommutative Calder´on-Zygmund the-
+ory, J. Funct. Anal. 256 (2009), no. 2, 509-593.
+[38] G. Pisier, Non-commutative vector valued Lp-spaces and completely p-summing maps, Ast´erisque
+247 (1998), vi+131.
+[39] G. Pisier, Q. Xu, Non-commutative martingale inequalities, Comm. Math. Phys. 189 (1997), no.
+3, 667-698.
+[40] G. Pisier, Q. Xu, Noncommutative Lp spaces, Handbook of geometry of Banach spaces, Vol. 2,
+1459-1517, North-Holland, 2003.
+[41] N. Randrianantoanina, Square function inequalities for non-commutative martingales, Israel J.
+Math. 140 (2004), 333-365.
+[42] N. Randrianantoanina, A weak type inequality for non-commutative martingales and applications,
+Proc. London Math. Soc. 91 (2005), no. 2, 509-542.
+[43] F. Riesz, Some mean ergodic theorems, J. Lond. Math. Soc. 13 (1938), no. 4, 274-278.
+[44] F. Riesz, Another proof of the mean ergodic theorem, Acta Univ. Szeged. Sect. Sci. Math. 10
+(1941), 75-76.
+[45] E. Størmer, On the Jordan structure of C∗-algebras, Tran. Amer. Math. Soc. 120 (1965) 438-447.
+
+38
+G. HONG, W. LIU, AND B. XU
+[46] B. Sz.-Nagy, C. Foias, Harmonic Analysis of Operators on Hilbert Space, North-Holland, 1970.
+[47] J. von Neumann, Proof of the quasi-ergodic hypothesis, Proc. Natl. Acad. Sci. USA 18 (1932),
+70-82.
+[48] F. J. Yeadon, Ergodic theorems for semifinite von Neumann algebras. I, J. London Math. Soc. 16
+(1977) 326-332.
+[49] F. J. Yeadon, Ergodic theorems for semifinite von Neumann algebras. II, Math. Proc. Cambridge
+Philos. Soc. 88 (1980), no. 1, 135-147.
+[50] F. J. Yeadon, Isometric of noncommutative Lp-spaces, Math. Proc. Cambridge Philos. Soc 90
+(1981), no. 1, 41-50.
+School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
+Email address: guixiang.hong@whu.edu.cn
+School of Mathematical Sciences, Fudan University, Shanghai 200433, China
+Email address: wliu math@fudan.edu.cn
+Department of Mathematical Sciences, Seoul National University, 08826 Seoul, Re-
+public of Korea
+Email address: bangxu@snu.ac.kr
+
diff --git a/hNAyT4oBgHgl3EQfXffW/content/tmp_files/load_file.txt b/hNAyT4oBgHgl3EQfXffW/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9f16839409d1126d7ba690816f70805886f5dd19
--- /dev/null
+++ b/hNAyT4oBgHgl3EQfXffW/content/tmp_files/load_file.txt
@@ -0,0 +1,1535 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf,len=1534
+page_content='QUANTITATIVE MEAN ERGODIC INEQUALITIES: POWER  BOUNDED OPERATORS ACTING ON ONE SINGLE  NONCOMMUTATIVE Lp SPACE  GUIXIANG HONG, WEI LIU, AND BANG XU  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' In this paper, we establish the quantitative mean ergodic theorems for  two subclasses of power bounded operators on a fixed noncommutative Lp-space  with 1 < p < ∞, which mainly concerns power bounded invertible operators and  Lamperti contractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Our approach to the quantitative ergodic theorems is the  noncommutative square function inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The establishment of the latter involves  several new ingredients such as the almost orthogonality and Calder´on-Zygmund  arguments for non-smooth kernels from semi-commutative harmonic analysis, the  extension properties of the operators under consideration from operator theory, and  a noncommutative version of the classical transference method due to Coifman and  Weiss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Introduction  In classical ergodic theory, there are many papers related to the convergence prop-  erties of certain averages along the orbits with respect to the transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let  (X, F, µ) be a σ-finite measure space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The celebrated von Neumann’s mean ergodic  theorem [47] stated that when T is a unitary operator on L2(X, µ) induced by a µ-  preserving measurable transformation on X, the ergodic averages Mnf defined by  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1)  Mnf(x) =  1  n + 1  n  �  k=0  T kf(x) n ∈ N,  converges in L2(X) for any f ∈ L2(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Later on, Riesz [43] greatly generalized the von  Neumann’s mean ergodic theorem;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' he proved that the convergence of ergodic averages  is also valid for contractive operators defined simultaneously on all Lp(X, µ) (1 ≤  p ≤ ∞) spaces, where (X, µ) is a probability space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Also, Riesz gave a simple proof  when T is a contraction operator on some Hilbert space [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Furthermore, the mean  ergodic theorem for Lp (1 ≤ p ≤ ∞)-contractions acting on general Banach spaces was  established by Dunford and Schwartz [11, VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  It is then natural to ask for the speed of the convergence of the ergodic averages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Unfortunately, Krengel [28] proved that the speed of the ergodic convergence can be  arbitrarily slow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' On the other hand, one can not capture any information on the rate  of the convergence from the classical proofs of aforementioned works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' With the aid of  Date: January 3, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Primary 46L52;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Secondary 46L53, 46L51, 46L55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Mean ergodic theorems, Noncommutative square functions, Noncommuta-  tive Lp spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This work was partially supported by Natural Science Foundation of China (Grant: 12071355).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='00186v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='FA]  31 Dec 2022  2  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  the spectral theorem and the dilation theorem developed in [46], Jones, Ostrovskii and  Rosenblatt [22] established the square function inequalities for ergodic averages (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1)  associated with a contraction on L2(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' More precisely, they proved that for a L2-  contraction T and any sequence of finite positive integers n0 < n1 < · · · < nm  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2)  � m  �  i=1  ��Mni(T)f − Mni−1(T)f  ��2  L2(X)  �1/2  ≤ 25∥f∥L2(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This result can be viewed as a quantitative and finer version of the mean ergodic the-  orem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Indeed, (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) implies that for any ε > 0, the sequence (Mn(f))∞  n=1 admits at  most 625(ε−2∥f∥2  2) jumps of size at least ε in L2 norm, and as a consequence the se-  quence converges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Moreover, many variants of the inequality (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) have been obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Avigad and Rute [3] extended (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) with the power 2 of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) replaced by q (q ≥ 2) to  q-uniformly convex Banach spaces and specific power bounded operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Bourgain [5]  (see also Jones et al [23]) considered the variational inequalities, which may deduce the  inequality (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) and the pointwise convergence of ergodic averages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' We remark that  Calder´on’s transference principle plays an important role in the above papers which  reduces (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) to the study of the related operators in harmonic analysis where more  tools are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Motivated by quantum physics, the convergence of the ergodic averages in von Neu-  mann algebras has attracted much attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  For instance, Kov´acs and Sz¨ucs [27]  considered the mean ergodic theorem for an automorphism T on von Neumann alge-  bras equipped with a faithful T-invariant semifinite normal state, and Lance [30] gave a  complete discussion of this subject.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Later on, Yeadon [48, 49] established the mean er-  godic theorem for positive Dunford-Schwartz operators on noncommutative Lp spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  For more results about the mean ergodic theorem in von Neumann algebras we refer  the reader to [19, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' On the other hand, on the study of pointwise ergodic theorems  in noncommutative Lp, after the work in the case p = ∞ [30, 29, 9] and in the case  p = 1 [48], a breakthrough was made by Junge and Xu [26], where they established  the noncommutative maximal ergodic inequalities for positive Dunford-Schwartz op-  erators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' This celebrated work motivated further research on noncommutative ergodic  theory, such as [2, 4, 16, 18, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' In particular, the first author and his collaborators  broke the framework of Junge and Xu by establishing the maximal and pointwise er-  godic theorems for a large subclass of positive operators on one single noncommutative  Lp space, see [13, 15] for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  However, to the best of the authors’ knowledge, there is no quantitative estimate of  noncommutative ergodic theorems in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' This paper is devoted to the first  study of quantitative mean ergodic theorem (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) under the noncommutative framwork.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  To better state our results, we need to introduce some notions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let M be a semifinite  von Neumann algebra equipped with a normal semifinite faithful (abbrieviated as n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='f )  trace τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let Lp(M) be the associated noncommutative Lp space and Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) be  one noncommutative analogue of Hilbert-valued Lp space (see Section 2 for the precise  definition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Throughout the paper, T stands for a bounded linear operator on Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The one-sided ergodic averages Mn(T) is defined as  Mn(T) =  1  n + 1  n  �  k=0  T k,  ∀ n ∈ N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  3  and if T is invertible, one defines the two-sided ergodic averages Bn(T) by  Bn(T) =  1  2n + 1  n  �  k=−n  T k,  ∀ n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Suppose that T satisfy  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3)  sup  k∈Z  ∥T k : Lp(M) → Lp(M)∥ < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then there exists a positive constant Cp such that  sup  ���  Bni(T)x − Bni+1(T)x  �  i∈N  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ Cp∥x∥Lp(M), ∀x ∈ Lp(M)  where the supremum is taken over all the increasing subsequence (ni)i∈N of positive  integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Similar inequality holds for one-sided ergodic averages (Mn(T))n∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1 is a noncommutative version of [22, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Note  also that Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1 can be viewed as an ergodic theorem with respect to a bounded  Lp(M)-representation of the group Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  And for the bounded noncommuative Lp-  representations of other groups such as the ones of polynomial growth that appeard in  [13], similar quantitative mean ergodic theorems still hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' These results will appear  in a forthcoming paper [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The second main result concerns the quantitative mean theorem for Lamperti oper-  ators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' An operator T is called a Lamperti operator (or supports separating)  if for any two τ-finite projections e, f ∈ M satisfies ef = 0, we have  (Te)∗Tf = Te(Tf)∗ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In [15], the authors derived the maximal inequalities for the convex combinations  of positive Lamperti contraction on one single noncommutative Lp spaces, which can  be viewed as the first Akcoglu’s maximal ergodic inequalities in the noncommutative  setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In this paper, we establish the quantitative mean ergodic theorem for Lamperti  operators where the positivity assumption can be relaxed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Suppose that T belong to the family  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4)  S = convsot{S : Lp(M) → Lp(M) Lamperti contractions},  that is, the closed convex hull of all Lamperti contractions on Lp(M) with respect to  strong operator topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For 2 ≤ p < ∞, there exists a positive constant Cp such that  for any increasing subsequence of positive integers (ni)i∈N,  ���  Mni(T)x − Mni+1(T)x  �  i∈N  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ Cp∥x∥Lp(M) ∀x ∈ Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  For 1 < p < 2, if T ∈ S is positive, then the above conclusion holds too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1 and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4 seem new even in the commutative case since the  quantitative mean ergodic inequalities are deduced for a large class of operators acting  on a fixed Lp spaces with 1 < p ̸= 2 < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  It should be pointed out that when  M is commutative, the class of operators in the two theorems should be able to be  4  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  enlarged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' We left this to the interested reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' With a moment’s thought, there are  many difficulties to apply the classical methods exploited in [1, 3, 22, 23] to our setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Our approach is mainly motivated by the study of maximal ergodic inequalities and  semi-commutative harmonic analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1 and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4 rely on several auxiliary results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Our first  key ingredient is the operator-valued square function inequalities related to the Hardy-  Littlewood averages on Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (ni)i∈N be an increasing sequence in N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' A sequence of  intervals (Ani)i∈N ⊂ Z is called nested if it satisfies one of the following two cases:  (a) each Ani can be written as [−ni, ni];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (b) each Ani can be written as [0, ni].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Let A ⊂ Z be an interval and f : Z → SM be a bounded operator-valued function,  where SM is the subset of M with τ-finite support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The averaging operator over A is  defined by  MAf(v) = 1  |A|  �  y∈A  f(v + y),  v ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (ni)i∈N be an increasing sequence of positive integers and (Ani)i be  the associated nested sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let Ti = MAni − MAni+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then for 1 ≤ p ≤ ∞ the  following assertions are true with a positive constant Cp depending only on p:  (i) for p = 1,  ∥(Tif)i∈N∥L1,∞(N,ℓrc  2 ) ≤ Cp∥f∥1, ∀f ∈ L1(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (ii) for p = ∞,  ���  �  i:i∈N  Tif ⊗ e1i  ���  BMOd(R) +  ���  �  i:i∈N  Tif ⊗ ei1  ���  BMOd(R) ≤ Cp ∥f∥∞, ∀f ∈ L∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (iii) for 1 < p < ∞,  ∥(Tif)i∈N∥Lp(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ Cp∥f∥p, ∀f ∈ Lp(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Here N = L∞(Z)⊗M is equipped with the tensor trace ϕ = �  Z ⊗τ and R = N⊗B(ℓ2)  with the tensor trace ϕ ⊗ tr, where tr is the canonical trace on B(ℓ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We refer to Section 5 for the definition of the dyadic BMO space BMOd(R) intro-  duced by Mei [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Our second key ingredient is to explore the following noncommutative version of the  classical transference principle due to Coifman and Weiss [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (Ani)i be a nested sequence and set Ti = MAni − MAni+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' As-  sume that the operator T satisfies (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3) with 1 < p < ∞ in Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Under the  assumption Ani = [−ni, ni]: if there exists a positive constant Cp such that  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5)  ∥(Tif)i∈N∥Lp(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ Cp∥f∥Lp(N) ∀f ∈ Lp(N),  then there exists a positive constant C such that  ���  Bni(T)x − Bni+1(T)x  �  i∈N  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ CCp∥x∥Lp(M) ∀ x ∈ Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Under the assumption (Ani)i = [0, ni], we have the similar transference result for one-  sided ergodic averages (Mn(T))n∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  5  This noncommutative transference technique is partly motivated by the noncommu-  tative Calder´on’s transference principle developed in [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' In the course of establishing  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6, we need the following extension property of the bounded linear oper-  ators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 ≤ p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Assume that T is a bounded linear operator on Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then T extends to a bounded operator on Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7 follows from the noncommutative Khintchine inequalities—Proposition  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2—without surprise, see Section 6 for the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' However, to exploit the transference  technique in showing Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4 is much more complicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' To this end, we start with  a reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' More precisely, we reduce Lamperti operators to isometric operators by  applying the structural characterizations and dilation properties of Lamperti operators  recently developed in [15] (see Section 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' With this reduction, we give our effort to  the strong type (p, p) estimate of the square function for isometric operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' This will  be achieved by using a similar noncommutative Calder´on’s transference principle as  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6 for isometries, once there holds the following property that concerns  the isometric extension of isometries to Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 ≤ p < ∞ and T : Lp(M) → Lp(M) be an isometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then  T extends to an isometry (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' a contraction) on Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) if 2 ≤ p < ∞ (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  1 ≤ p < 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' If T is morevoer positive, then T extends also to an isometry on Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 )  for 1 < p < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  When M is commutative, the above extension is almost plain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The truly noncommu-  tative case is highly non-trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Our argument depends on the structural description  of isometries, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' [25, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Moreover, for 1 < p < 2, some complicated duality argu-  ment are explored, and similar one has appeared in [15] in dealing with noncommutative  maximal inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For more details we refer to Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' What we need to point out here is that the estimates stated in all  the aforementioned theorems for infinite summations should be understood as a con-  sequence of the corresponding uniform boundedness for all finite summations by the  standard approximation arguments (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' [24, Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='A]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For this reason, as in  [17], we are not going to explain the convergence of infinite sums appearing in the whole  paper if there is no ambiguity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We end the introduction by mentioning the organization of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' In Section 2,  we recall the necessary background including noncommutative Lp spaces and Hilbert-  valued Lp spaces, as well as the noncommutative Calder´on-Zygmund decomposition  recently developed in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Section 3-5 is devoted to the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In  Section 6, we prove Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7, Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6 and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Finally, in Section 7,  we prove Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8 and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4, which involves the intermediate square  function inequalities for isometries—Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Notation: In all what follows, we use the same letter C to denote various positive  constants that may change at each occurrence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Also, we write X ≲ Y for non-negative  quantities X and Y to mean that X ≤ CY for some inessential constant C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Similarly, we use the notation X ≈ Y if both X ≲ Y and Y ≲ X hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  6  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Preliminaries  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Noncommutative Lp spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Throughout this paper, M denotes a semifinite von Neumann algebra equipped with  a n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='f trace τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let M+ be the cone of positive elements in M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Given x ∈ M+, the  support projection of x, denoted by suppx, is defined as the least projection e in M  such that ex = xe = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let SM+ be the set of all x ∈ M+ such that τ(suppx) < ∞  and SM be the linear span of SM+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then SM is a w∗-dense ∗-subalgebra of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Given  0 < p < ∞ and x ∈ SM, if we set  ∥x∥p =  �  τ(|x|p)  �1/p,  where |x| = (x∗x)  1  2 is the modulus of x, then it turns out that ∥ · ∥p is a norm in SM  for 1 ≤ p < ∞, and a p-norm for 0 < p < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The completion of (SM, ∥ · ∥p) is the  noncommutative Lp space associated to the pair (M, τ), which is simply denoted by  Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' As usual, we set L∞(M) = M equipped with the operator norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We also work with noncommutative weak Lp spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let M′ be the commutant of  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' A closed densely defined operator on H (H being the Hilbert space on which M  acts) is said to be affiliated with M if it commutes with any unitary in M′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Given a  densely defined selfadjoint operator x, its spectral projection  �  I dγx(λ) will be simply  denoted by χI(x), where I is a measurable subset of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' A closed and densely defined  operator x affiliated with M is said to be τ-measurable if there is λ ∈ R+ such that  τ  �  χ(λ,∞)(|x|)  �  < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Let L0(M) be the set of the ∗-algebra of τ-measurable operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For 0 < p < ∞, the  weak Lp space Lp,∞(M) is defined as the set of all x in L0(M) with the following finite  quasi-norm  ∥x∥p,∞ = sup  λ>0  λτ  �  χ(λ,∞)(|x|)  � 1  p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The following property has already been proved in [21, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1] that for any x1, x2 ∈  L1,∞(M) and any λ ∈ R+  τ  �  (χ(λ,∞)(|x1 + x2|)  �  ≤ τ  �  χ(λ/2,∞)(|x1|)  �  + τ  �  χ(λ/2,∞)(|x2|)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1)  The reader is referred to e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' [12, 40] for a comprehensive study of noncommutative  Lp spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Noncommutative Hilbert-valued Lp spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In this subsection, we recall the noncommutative Hilbert-valued Lp spaces [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let  (xn) be a finite sequence in Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Define  ∥(xn)∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) = ∥(  �  n  |x∗  n|2)  1  2 ∥p, ∥(xn)∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) = ∥(  �  n  |xn|2)  1  2 ∥p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓr  2) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓc  2)) is defined as the completion of all finite sequences  in Lp(M) with respect to ∥ · ∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ∥ · ∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The space Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) is  defined as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  7  If 2 ≤ p ≤ ∞,  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) = Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓc  2) ∩ Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓr  2)  equipped with the intersection norm:  ∥(xn)∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) =  �  ∥(xn)∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) + ∥(xn)∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2)  � 1  p .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  If 1 ≤ p < 2,  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) = Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓc  2) + Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓr  2)  equipped with the sum norm:  ∥(xn)∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) = inf  �  ∥(yn)∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) + ∥(zn)∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2)  � 1  p ,  where the infimum runs over all possible decompositions xn = yn + zn with yn  and zn in Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This procedure is also used to define the spaces L1,∞(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓr  2) (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' L1,∞(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓc  2)) and  L1,∞(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) with the sum norm,  ∥(xn)∥L1,∞(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) =  inf  xn=yn+zn  �  ∥(yn)∥L1,∞(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) + ∥(zn)∥L1,∞(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We remark that the definition of space Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) equals the classical one [40], and  one can easily see that the following basic properties related to space Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) are  also valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 ≤ p < ∞ and p′ be its conjugate index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then  (Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓc  2))∗ = Lp′(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓc  2),  (Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓr  2))∗ = Lp′(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓr  2)  and  (Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ))∗ = Lp′(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The duality bracket is given by  ⟨(xn), (yn)⟩ =  �  n  τ(xny∗  n),  (xn) ⊂ Lp(M), (yn) ⊂ Lp′(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The following noncommutative Khintchine inequalities will be frequently used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' See  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' [32, 33, 38, 6] for the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (εn) be a sequence of independent Rademarcher random variables  on a probability space (Ω, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 ≤ p < ∞ and (xn) be a sequence in Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  For 1 ≤ p < ∞, there exist two positive constants cp and Cp such that  cp∥(xn)∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤  ����  �  n  εnxn  ����  Lp(L∞(Ω)⊗M)  ≤ Cp∥(xn)∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The above estimate is still true if one replaces the Lp spaces by the weak Lp spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  8  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Noncommutative Calder´on-Zygmund decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In this subsection, we introduce the noncommutative Calder´on-Zygmund decompo-  sition developed in [7], whose construction is based on the noncommutative martingale  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' To this end, we first introduce the related notions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For each n ∈ N, let Fn be  the set of dyadic intervals with length of 2n in Z, that is each interval in Fn can be  written as [s2n, (s + 1)2n), where s is an integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let σn be the n-th σ-algebra gener-  ated by Fn and Nn = L∞(Z, σn)⊗M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Recall that N = L∞(Z)⊗M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then (Nn)n∈N  is a sequence of decreasing von Neumann subalgebras of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hence, (Nn)n∈N forms a  filtration and the resulting conditional expectations (En)n∈N satisfy  ∀ m, n ∈ N,  EmEn = EnEm = Emax(m,n)  and for f ∈ Lp(N) with 1 ≤ p < ∞,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2)  fn := En(f) =  �  I∈Fn  fIχI,  where χI is the characteristic function of I and  fI = 1  |I|  �  y∈I  f(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  It is easy to check that (fn)n∈N is a Lp-reverse martingale, namely supn∈N ∥fn∥Lp(N) <  ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The resulting martingale difference sequence df = (dfn)n∈N is defined by dfn =  fn−1 − fn for n ≥ 1 and df0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  To give the content of noncommutative Calder´on-Zygmund decomposition, consider  Nc,+ =  �  f : Z → M ∩ L1(M)  �� f ≥ 0, −−→  suppf is compact  �  ,  which is dense in L1(N)+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Here −−→  suppf = supp∥f∥L1(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Observe that for any given  f ∈ Nc,+ and λ > 0, there exists mλ(f) ∈ N such that fn ≤ λ1N for all n ≥ mλ(f)  (see [37, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1]), where 1N denotes the unit element in N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The following modified Cuculescu’s theorem [10] was obtained in [37, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let f ∈ Nc,+ and consider its related dyadic martingale (fn)n∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Given  λ > 0, there exists an increasing sequence of projections (qn)n∈N defined by qn = 1N  for n ≥ mλ(f) and recursively for n < mλ(f)  qn = qn(f, λ) = χ(0,λ](qn+1fnqn+1)  such that the following conclusions hold:  (i) qn commutes with qn+1fnqn+1 for each n;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (ii) qn belongs to Nn and qnfnqn ≤ λqn for each n;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (iii) set q0 := q = �mλ(f)  n=0  qn, then λϕ(1N − q) ≤ ∥f∥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In fact, for each n, qn admits the following expression (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' [37])  qn =  �  I∈Fn  qIχI,  QUANTITATIVE MEAN ERGODIC INEQUALITIES  9  with qI projections in M defined by  qI =  �  �  �  �  �  1M  if n > mλ(f),  χ(0,λ](fI)  if n = mλ(f),  χ(0,λ]  �  q�IfIq�I  �  if 0 ≤ n < mλ(f),  where �I is the dyadic father of I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Accordingly, these projections satisfy  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3)  qI ≤ q�I,  qI commutes with q�IfIq�I,  qIfIqI ≤ λqI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  If we define the sequence (pn)n of pairwise disjoint projections by  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4)  pn = qn+1 − qn =  �  I∈Fn  (q�I − qI)χI ≜  �  I∈Fn  pIχI  for each n, then  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5)  �  n  pn = 1N − q = q⊥  and for each n  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6)  ∥pnfnpn∥∞ ≤ 2λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Based on the previous notation, the noncommutative analogue for the Calder´on-  Zygmund decomposition was recently found by Caldilhac et al [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Fix f ∈ Nc,+ and λ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (qn)n and (pn)n be the two sequences  of projections appeared in the above Cuculescu’s construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then there exist a pro-  jection ζ ∈ N defined by  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7)  ζ =  � �  I∈F  pIχ5I  �⊥,  where 5I denotes the interval with the same center as I with length |5I| = 5|I|, and a  decomposition of f,  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8)  f = g + b  such that the following assertions hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (i) λϕ(1N − ζ) ≤ 5∥f∥1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (ii) g = qfq + �  n pnfnpn satisfies ∥g∥1 ≤ ∥f∥1  and  ∥g∥∞ ≤ 2λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (iii) b = �  n bn, where  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9)  bn = pn(f − fn)qn + qn+1(f − fn)pn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Each bn satisfies two cancellation conditions: Enbn = 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' and for all x, y ∈ Z with  y ∈ 5Ix,n, ζ(x)bn(y)ζ(x) = 0, where Ix,n is the unique interval in Fn containing x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5: one reduction  To prove Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5, we give a reduction in the present section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Motivated by  the study of the variational inequalities [5], we split the square function into the ‘long  one’ and the ‘short one’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' To be more precise, fix an increasing sequence (ni)i∈N and let  (Ani)i∈N be the associated nested sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For an interval Ii = [ni, ni+1), one can see  that there are two cases:  Case 1: Ii contains no dyadic point, that is, for any k ∈ N, 2k /∈ Ii;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  10  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  Case 2: Ii contains at least one dyadic point 2k for k ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  According to the above classification, for each interval Ii = [ni, ni+1), we split it into  at most three disjoint parts  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1)  Ii := [ni, ˜ni) ∪ [˜ni, ˜˜ni) ∪ [˜˜ni, ni+1)  by the law: if Ii belongs to Case 1, then set ˜ni = ˜˜ni = ni+1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' if Ii belongs to Case 2,  we set ˜ni = 2ki := min{2k : 2k ∈ Ii} and ˜˜ni = 2li := max{2k : 2k ∈ ¯Ii} where ¯Ii is the  closure of Ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By above decomposition of intervals and using the quasi-triangle inequality for weak  L1 norm ∥ · ∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ), we have  ∥(MAnif − MAni+1f)i∈N∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤ 3∥(MAnif − MA˜nif)i∈N∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + 3∥(MA˜nif − MA˜˜nif)i∈N∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  + 3∥(MA˜˜nif − MAni+1f)i∈N∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2)  On the other hand, by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1), we introduce two collections of intervals with respect  to {[ni, ni+1)}i:  S consists of all intervals Ii belonging to Case 1, or [ni, ˜ni), [˜˜ni, ni+1) in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  L consists of all intervals [˜ni, ˜˜ni) in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  It is not difficult to check that L ∪ S is a disjoint family of intervals and forms a finer  partition of  �  [ni, ni+1)  �  i∈N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2), we have  ∥(MAnif − MAni+1f)i∈N∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤ 3∥(MA˜nif − MA˜˜ni:f)i:[˜ni,˜˜ni)∈L∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  + 6∥(MAmif − MA �  mif)i:[mi, �mi)∈S∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3)  We now focus on the first term on the right hand side of the above inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Fix an  interval [˜ni, ˜˜ni).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1), we write [˜ni, ˜˜ni) = [2ki, 2li).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Decompose  (MA2ki f − MA2li f) = (MA2ki f − Ekif) + (Ekif − Elif) + (Elif − MA2li f),  where (Ek)k is the dyadic conditional expectations defined in the preliminary section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  As a consequence, there exists a sequence of positive integers k0 < l0 ≤ k1 < l1 < · · · ≤  ki < li ≤ · · · such that  ∥(MA˜nif − MA˜˜nif)i:[˜ni,˜˜ni)∈L∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ 3∥(MA2ki f − Ekif)i∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  + 3∥(Ekif − Elif)i∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + 3∥(MA2li f − Elif)i∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Using the fact that n �→ (�n  k=1 |xk|2)  1  2 is increasing, one easily checks that  ∥(MA˜nif − MA˜˜nif)i:[˜ni,˜˜ni)∈L∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤ 3∥(Ekif − Elif)i∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + 6∥(MA2kf − Ekf)k∈Z∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4)  Together with (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4), we obtain  ∥(MAnif − MAni+1f)i∈N∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤ 6∥(MAmif − MA �  mif)i:[mi, �mi)∈S∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  + 9∥(Ekif − Elif)i∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + 18∥(MA2kf − Ekf)k∈Z∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5)  QUANTITATIVE MEAN ERGODIC INEQUALITIES  11  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By applying the same arguments as above, it is clear that there exist  similar dominations as (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5) for ∥·∥Lp(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) and ∥·∥BMOd(R) via the triangle inequalities  with possibly different constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Concerning the sequence (MA2kf − Ekf)k∈Z, the first and third authors [17] estab-  lished the following results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2 ([17]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 ≤ p ≤ ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Set Lkf = MA2kf − Ekf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then the following  assertions are true with a positive constant Cp depending only on p:  (i) for p = 1,  ∥(Lkf)k∈Z∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ Cp∥f∥1, ∀f ∈ L1(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (ii) for p = ∞,  ���  �  k∈Z  Lkf ⊗ e1k  ���  BMOd(R) +  ���  �  k∈Z  Lkf ⊗ ek1  ���  BMOd(R) ≤ Cp ∥f∥∞, ∀f ∈ L∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (iii) for 1 < p < ∞,  ∥(Lkf)k∈Z∥Lp(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ Cp∥f∥p, ∀f ∈ Lp(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  On the other hand, (Ekif − Elif)i forms a new sequence of martingale differences,  and the dyadic martingale analogue of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2 have been established in [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' See  also [39, 41, 42] for more on noncommutative Burkholder-Gundy inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Hence, we give our main efforts to the first term on the right hand side of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5),  namely the sequence (MAmif − MA �  mif)i:[mi, �mi)∈S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' We denote, by abuse of notation,  the sequence {m0, �m0, m1, · · · , mi, �mi, · · · } as {m0, m1, m2 · · · , mi, mi+1, · · · }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then if  [mi, mi+1) ∈ S, we denote it as i ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Setting Tif = MAmif − MAmi+1f, and thus we  get (Tif)i∈S standing for (MAmif − MA �  mif)i:[mi, �mi)∈S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Combining (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5), Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1,  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2 with the fact that n �→ (�n  k=1 |xk|2)  1  2 is increasing, to establish Theorem  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5, it suffices to show the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let S and (Tif)i∈S be defined as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 ≤ p ≤ ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then the  following assertions are true with a positive constant Cp depending only on p:  (i) for p = 1,  ∥(Tif)i∈S∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ Cp∥f∥1, ∀f ∈ L1(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (ii) for p = ∞,  ���  �  i∈S  Tif ⊗ e1i  ���  BMOd(R) +  ���  �  i∈S  Tif ⊗ ei1  ���  BMOd(R) ≤ Cp ∥f∥∞, ∀f ∈ L∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (iii) for 1 < p < ∞,  ∥(Tif)i∈S∥Lp(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ Cp∥f∥p, ∀f ∈ Lp(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3: Weak type (1, 1) estimate  In this section, we show the weak type (1, 1) estimate stated in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  12  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Some technical lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Recall that (εi) is a Rademacher sequence on a fixed probability space (Ω, P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Define  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1)  Tf(x) =  �  i∈S  εiTif(x) =  �  i∈S  εi(MAni − MAni+1)f(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2(ii) immediately implies the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let h ∈ Nc,+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then  ∥(Tih)i∈S∥L1,∞(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≈ ∥Th∥L1,∞(L∞(Ω)⊗N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (Sk,i)k,i∈Z be a sequence of bounded linear operators on L2(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let  h ∈ L2(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' If (un)n∈Z and (vn)n∈Z are two sequences of operators in L2(N) such that  h = �  n∈Z un and �  n∈Z ∥vn∥2  2 < ∞, then  �  k∈Z  ∥(Sk,ih)i∥2  L2(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ w2 �  n∈Z  ∥vn∥2  2  provided that there exists a sequence (σ(j))j∈Z of positive numbers with w = �  j∈Z σ(j) <  ∞ such that  ∥(Sk,iun)i∥L2(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ σ(n − k)∥vn∥2  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2)  for every n, k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By the triangle inequality in L2(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) and the Young inequality in ℓ2,  we deduce that  �  k∈Z  ∥(Sk,ih)i∥2  L2(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤  �  k∈Z  � �  n∈Z  ∥(Sk,iun)i∥L2(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  �2  ≤  �  k∈Z  � �  n∈Z  σ(n − k)∥vn∥2  �2  ≤  � �  n∈Z  σ(n)  �2� �  k∈Z  ∥vk∥2  2  �  ,  which finishes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  Let A be a subset of Z, define  I(A, n) =  �  I∈Fn  ∂A∩I̸=∅  A ∩ I  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3)  and  I1(A, n) =  �  I∈Fn  ∂A∩I̸=∅  I,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4)  where ∂A means the boundary of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  13  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let h ∈ L2(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then for any x ∈ Z, n ∈ N and subset B ⊆ Z,  ���  �  y∈I(x+B,n)  h(y)  ���  2  L2(M) ≤ |I1(x + B, n)|  �  y∈I1(x+B,n)  ∥En(h1x+B)(y)∥2  L2(M);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  ���  �  y∈I(x+B,n)  h(y)  ���  2  L2(M) ≤ |I(x + B, n)|  �  y∈I(x+B,n)  ∥h(y)∥2  L2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' We first prove the first inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' It is easy to check that  �  y∈I(x+B,n)  h(y) =  �  I∈Fn  I∩∂(x+B)̸=∅  �  y∈I  En(h1x+B)(y) =  �  y∈I1(x+B,n)  En(h1x+B)(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By the Minkowski and the Cauchy-Schwarz inequalities, we obtain  ���  �  y∈I(x+B,n)  h(y)  ���  2  L2(M) ≤  �  �  y∈I1(x+B,n)  ∥En(h1x+B)(y)∥L2(M)  �2  ≤ |I1(x + B, n)|  �  y∈I1(x+B,n)  ∥En(h1x+B)(y)∥2  L2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The same argument gives  ���  �  y∈I(x+B,n)  h(y)  ���  2  L2(M) ≤  �  �  y∈I(x+B,n)  ∥h(y)∥L2(M)  �2  ≤ |I(x + B, n)|  �  y∈I(x+B,n)  ∥h(y)∥2  L2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  Now we are ready to prove the weak type (1, 1) estimate in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Note that  we just consider the case that each Ani is written as [0, ni], since another case Ani of  the form [−ni, ni] can be handled in the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By decomposing f = f1 − f2 + i(f3 − f4) with fj ≥ 0 such that ∥fj∥1 ≤ ∥f∥1  for j = 1, 2, 3, 4, we may assume that f is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Moreover, since Nc,+ is dense in  L1(N)+, by the standard approximation argument, it suffices to consider f ∈ Nc,+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Now fix one f ∈ Nc,+ and a λ ∈ (0, +∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Using Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4, we can decompose f as  f = g + b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then the distribution inequality gives (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1),  �ϕ  �  χ(λ,∞)(|Tf|)  �  ≤ �ϕ  �  χ(λ/2,∞)(|Tg|)  �  + �ϕ  �  χ(λ/2,∞)(|Tb|)  �  ,  where �ϕ =  �  Ω ⊗ϕ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Therefore, by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1, it suffices to show  �ϕ(χ(λ/2,∞)(|Tb|)) ≲ ∥f∥1  λ  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5)  �ϕ(χ(λ/2,∞)(|Tg|)) ≲ ∥f∥1  λ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6)  14  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Weak type estimate for the bad function: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Using the projection ζ introduced in Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4, we decompose Tb as  Tb = (1N − ζ)Tb(1N − ζ) + ζ Tb(1N − ζ) + (1N − ζ)Tbζ + ζ Tbζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In particular, by Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4(i), we find  �ϕ  �  χ(λ/2,∞)(|Tb|)  �  ≲ ϕ(1N − ζ) + �ϕ  �  χ(λ/8,∞)(|ζTbζ|)  �  ≲ ∥f∥1  λ  + �ϕ  �  χ(λ/8,∞)(|ζTbζ|)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Hence, we are reduced to showing  �ϕ  �  χ(λ/8,∞)(|ζTbζ|)  �  ≲ ∥f∥1  λ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Note that the Chebychev inequality gives  λ2 �ϕ  �  χ(λ/8,∞)(|ζTbζ|)  �  ≲ ∥ζTbζ∥2  L2(L∞(Ω)⊗N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Hence, it is enough to prove  ∥ζTbζ∥2  L2(L∞(Ω)⊗N) ≲ λ2 �  n  ∥pn∥2  2,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7)  due to Cuculescu’s construction and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5),  �  n  ∥pn∥2  2 =  �  n  ∥pn∥1 ≲ ∥f∥1  λ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  To estimate (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7), we first use the orthogonality of εi to get  ∥ζTbζ∥2  L2(L∞(Ω)⊗N) =  �  i∈S  ∥ζ Tib ζ∥2  2 =  �  i∈S  ∥ζ (MAni − MAni+1)b ζ∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  For each k ∈ Z, let Sk be the set of i such that [ni, ni+1) ⊆ [2k, 2k+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then clearly  S = ∪k∈ZSk since for k < 0, Sk is empty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' With this convention, we deduce that  �  i∈S  ∥ζ (MAni − MAni+1)b ζ∥2  2 =  �  k  �  i∈Sk  ∥ζ (MAni − MAni+1)b ζ∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Hence, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7) is reduced to showing  �  k  �  i∈Sk  ∥ζ (MAni − MAni+1)b ζ∥2  2 ≲ λ2 �  n  ∥pn∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8)  To show (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8), by noting the definition of mλ(f), we can express b as b = �  n≤mλ(f) bn,  where bn = pn(f − fn)qn + qn+1(f − fn)pn as in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  On the other hand, let  (Sk,ih)i∈Sk = (ζ(MAni − MAni+1)bζ)i∈Sk, un = bn and vn = pn in Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then it  suffices to show �  i∈Sk  ∥ζ(MAni − MAni+1)bnζ∥2  2 ≲ 2−|k−n|λ2∥pn∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9)  In the following, we divide the proof of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9) into several steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Fix i ∈ Sk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then for k ≤ n,  ζ(x)(MAni − MAni+1)bn(x)ζ(x) = 0, ∀x ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  15  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' This follows from the observation ζ(x)MAnibn(x)ζ(x) = ζ(x)MAni+1bn(x)ζ(x) =  0, ∀x ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  To see this, fix one x ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The cancellation property announced in  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4(iii) implies  ζ(x)MAni+1bn(x)ζ(x) = ζ(x)  1  |Ani+1|  �  y∈x+Ani+1  bn(y)1y /∈5Ix,nζ(x) = 0  since x+Ani+1 ⊂ 5Ix,n and k ≤ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The same reasoning implies ζ(x)MAnibn(x)ζ(x) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This finishes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  With Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4, since ζ is a projection, it suffices to show for n < k  �  i∈Sk  ∥(MAni − MAni+1)bn∥2  2 ≲ 2n−kλ2∥pn∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='10)  To show (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='10), by applying the Minkowski inequality, we have  �  i∈Sk  ∥(MAni − MAni+1)bn∥2  2 ≲  �  i∈Sk  �  x∈Z  ���  1  |Ani+1|  �  y∈x+Ani+1\\Ani  bn(y)  ���  2  L2(M)  +  �  i∈Sk  �  1  |Ani| −  1  |Ani+1|  �2 �  x∈Z  ���  �  y∈x+Ani  bn(y)  ���  2  L2(M)  ≜ I1  k,n + I2  k,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Estimate of I1  k,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For n < k, we have  I1  k,n ≲ 2n−kλ2∥pn∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' First, the cancellation property-Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4(iii) of bn gives  I1  k,n =  �  i∈Sk  �  x∈Z  ���  1  |Ani+1|  �  y∈I(x+Ani+1\\Ani,n)  bn(y)  ���  2  L2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  On the other hand, observe that  bn = pnfqn + qn+1fpn − qn+1fnpn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='11)  Indeed, by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4), pn = qn+1−qn ≤ qn+1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' moreover, by Cuculescu’s construction-Lemma  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3(i), we obtain  pnfnqn = pnqn+1fnqn+1qn = pnqnqn+1fnqn+1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This gives the desired expression (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  With the observation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='11) and the Minkowski inequality, we see that to obtain the  desired inequality for the term I1  k,n, it suffices to estimate the following three terms  I1  k,n,1  ≜  �  i∈Sk  �  x∈Z  ���  1  |Ani+1|  �  y∈I(x+Ani+1\\Ani,n)  (pnfqn)(y)  ���  2  L2(M)  I1  k,n,2  ≜  �  i∈Sk  �  x∈Z  ���  1  |Ani+1|  �  y∈I(x+Ani+1\\Ani,n)  (qn+1fpn)(y)  ���  2  L2(M)  16  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  I1  k,n,3  ≜  �  i∈Sk  �  x∈Z  ���  1  |Ani+1|  �  y∈I(x+Ani+1\\Ani,n)  (qn+1fnpn)(y)  ���  2  L2(M),  We first deal with the term I1  k,n,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3, we have  ���  1  |Ani+1|  �  y∈I(x+Ani+1\\Ani,n)  (pnfqn)(y)  ���  2  L2(M)  ≲ 2n−2k  �  y∈I1(x+Ani+1\\Ani,n)  τ(|En(pnfqn1x+Ani+1\\Ani)(y)|2),  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='12)  where we used the fact that for all i ∈ Sk, 2k ≤ |Ani| ≤ 2k+1 and |I1(x + Ani+1 \\  Ani, n)| ≲ 2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Note that f1x+Ani+1\\Ani is positive in N and f1x+Ani+1\\Ani ≤ f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Since En is a posi-  tive map, we obtain En(f1x+Ani+1\\Ani) ≤ fn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Moreover, applying the H¨older inequality,  we find  τ(|pn(y)En(f1x+Ani+1\\Ani)(y)qn(y)|2)  = τ  �  pn(y)En(f1x+Ani+1\\Ani)(y)qn(y)En(f1x+Ani+1\\Ani)(y)pn(y)  �  ≤ τ  �  pn(y)En(f1x+Ani+1\\Ani)(y)pn(y)  �  ∥qn(y)En(f1x+Ani+1\\Ani)(y)qn(y)∥M  ≤ τ  �  pn(y)En(f1x+Ani+1\\Ani)(y)pn(y)  �  ∥qn(y)fn(y)qn(y)∥M  ≤ λτ  �  pn(y)En(f1x+Ani+1\\Ani)(y)pn(y)  �  ,  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='13)  where the last inequality follows from Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3(ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Combining above estimate  with (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='12), we get  I1  k,n,1 ≲ λ2n−2k �  x∈Z  �  i∈Sk  �  y∈I1(x+Ani+1\\Ani,n)  τ(pn(y)En(f1x+Ani+1\\Ani)(y)pn(y)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Note that for any fixed x ∈ Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ∪i∈SkI(x + Ani+1 \\ Ani,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' n) ⊆ x + A2k+1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' which implies  �  i∈Sk  �  y∈I1(x+Ani+1\\Ani,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='n)  τ(pn(y)En(f1x+Ani+1\\Ani)(y)pn(y))  =  �  i∈Sk  �  I∈Fn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  I∩∂(x+Ani+1\\Ani)̸=∅  �  y∈I  τ(En(pnf1x+Ani+1\\Anipn)(y))  =  �  i∈Sk  �  I∈Fn,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  I∩∂(x+Ani+1\\Ani)̸=∅  �  y∈I∩(x+Ani+1\\Ani)  τ(pn(y)f(y)pn(y))  =  �  i∈Sk  �  y∈I(x+Ani+1\\Ani,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='n)  τ(pn(y)f(y)pn(y))  ≤  �  y∈x+A2k+1  τ(pn(y)f(y)pn(y)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  17  where in the second equality we used the fact that the conditional expectation is trace-  preserving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Therefore, putting these observations together, we finally get  I1  k,n,1 ≲ λ2n−2k �  x∈Z  �  y∈x+A2k+1  τ(pn(y)f(y)pn(y)) ≲ λ2n−k �  x∈Z  τ(pn(x)f(x)pn(x))  ≲ λ22n−k �  x∈Z  τ(pn(x)) = λ22n−k∥pn∥2  2,  where the second inequality followed from the Fubini theorem and the last inequality  from (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' This finishes the proof of I1  k,n,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We now turn to the terms I1  k,n,2 and I1  k,n,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Note that qn+1 ∈ Nn and  qn+1fnqn+1 ≲ qn+1fn+1qn+1 ≤ λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='14)  Then the argument (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='13) also works for the terms I1  k,n,2 and I1  k,n,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' As a consequence,  we can estimate these two terms in the similar way as in the proof of I1  k,n,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hence, we  omit the details and the proof is complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Estimate of I2  k,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For n < k, we have  I2  k,n ≲ 2n−kλ2∥pn∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By the same arguments of I1  k,n, that is using the cancellation property and the  definition of bn, we are reduced to estimating the following three terms:  I2  k,n,1  ≜  �  i∈Sk  �  1  |Ani| −  1  |Ani+1|  �2 �  x∈Z  ���  �  y∈I(x+Ani,n)  (pnfqn)(y)  ���  2  L2(M)  I2  k,n,2  ≜  �  i∈Sk  �  1  |Ani| −  1  |Ani+1|  �2 �  x∈Z  ���  �  y∈I(x+Ani,n)  (qn+1fpn)(y)  ���  2  L2(M)  I2  k,n,3  ≜  �  i∈Sk  �  1  |Ani| −  1  |Ani+1|  �2 �  x∈Z  ���  �  y∈I(x+Ani,n)  (qn+1fnpn)(y)  ���  2  L2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We begin with the term I2  k,n,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Using Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3, the fact that I1(x + Ani, n) ⊆  x + A2k+2 and |I1(x + Ani, n)| ≲ 2n for all i ∈ Sk, we deduce that  ���  �  y∈I(x+Ani,n)  (pnfqn)(y)  ���  2  L2(M) ≲ 2n  �  y∈I1(x+Ani,n)  τ(|En(pnfqn1x+Ani)(y)|2)  ≤ 2n  �  y∈I1(x+Ani,n)  τ(|En(pnfqn1x+Ani)(y)|2)  ≤ 2n  �  y∈x+A2k+2  τ(|En(pnfqn1x+Ani)(y)|2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Since En is a positive map, by applying (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6) and the H¨older inequality, we obtain  τ(|En(pnfqn1x+Ani)(y)|2) ≤ τ  �  pn(y)fn(y)pn(y)  �  ∥qn(y)fn(y)qn(y)∥M ≲ λ2τ(pn(y)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  18  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  Combining the above observations with the fact that for i ∈ Sk, A2k ⊂ Ani ⊂ A2k+1,  we have  I2  k,n,1 ≲ 2nλ2 �  i∈Sk  �  1  |Ani| −  1  |Ani+1|  �2 �  x∈Z  �  y∈x+A2k+2  τ(pn(y))  ≤ 2nλ2�  1  |A2k| −  1  |A2k+1|  �2 �  x∈Z  �  z∈x+An2k+2  τ(pn(z))  ≲ 2n−kλ2∥pn∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The same arguments also work for the terms I2  k,n,2 and I2  k,n,3 just by noticing the  relation (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='14) and qn+1 ∈ Nn, we omit the proofs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The lemma is proved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  Proof of estimate (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6, we conclude the desired estimate  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9) and complete the argument for Tb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Weak type estimate for the good function: (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In order to estimate the good part, we need the following proposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let h ∈ L2(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then  ∥Th∥L2(L∞(Ω)⊗N) ≲ ∥h∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  With this proposition at hand, we prove easily the estimate (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof of estimate (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' We clearly have  �ϕ(χ(λ/2,∞)(|Tg|)) ≤  ∥Tg∥2  L2(L∞(Ω)⊗N)  λ2  ≲ ∥g∥2  2  λ2  ≤ ∥g∥1∥g∥∞  λ2  ≲ ∥f∥1  λ  ,  as a consequence of the Chebychev inequality, Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7, the H¨older inequality  and conclusion (ii) in Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' This completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  We now prove Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The key idea is the almost orthogonality argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof of Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let h ∈ L2(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Without loss of generality, we can assume  that h is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let h = �  n∈Z  dhn, where dhn = hn−1 − hn for n > 1 and dhn = 0 for  n ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' The property of martingale difference implies  �  n∈N  ∥dhn∥2  2 = ∥h∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then by the orthogonality of εi and the definition of Sk, one has  ∥Th∥2  L2(L∞(Ω)⊗N) =  �  i∈S  ∥(MAni − MAni+1)  �  n  dhn∥2  2  =  �  k  �  i∈Sk  ���  �  MAni − MAni+1  � �  n  dhn  ���  2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  19  Hence, from Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2, it is enough to prove  �  i∈Sk  ∥(MAni − MAni+1)dhn∥2  2 ≲ 2−|n−k|∥dhn∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='15)  To prove (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='15), let us first assume n > k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Recalling that Fn−1 is the set of all atoms  of n − 1-th dyadic σ-algebra, we may write  �  i∈Sk  ∥(MAni − MAni+1)dhn∥2  2 =  �  I∈Fn−1  �  x∈I  �  i∈Sk  ∥(MAni − MAni+1)dhn(x)∥2  L2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Fix one x ∈ I ∈ Fn−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Since dhn is a constant operator on I, �  i∈Sk ∥(MAni −  MAni+1)dhn(x)∥2  L2(M) may be nonzero only if for some i ∈ Sk, at least one of intervals  x + Ani or x + Ani+1 intersects the boundary of I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let Sk(dhn)(x) = �  i∈Sk ∥(MAni −  MAni+1)dhn(x)∥2  L2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' It can be easily seen that  {x ∈ I : Sk(dhn)(x) ̸= 0} ⊆ {x ∈ I : x + A2k+1 ∩ ∂I ̸= ∅},  and by a simple geometric argument  |{x ∈ I : x + A2k+1 ∩ ∂I ̸= ∅}| ≲ 2k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  On the other hand, we have the following crude estimate for x ∈ I  � �  i∈Sk  ∥(MAni − MAni+1)dhn(x)∥2  L2(M)  � 1  2 ≤  �  i∈Sk  ∥(MAni − MAni+1)dhn(x)∥L2(M)  ≤  �  i∈Sk  1  |Ani+1|  �  y∈x+Ani+1\\Ani  ∥dhn(y)∥L2(M)  +  �  i∈Sk  �  1  |Ani| −  1  |Ani+1|  �  �  y∈x+Ani  ∥dhn(y)∥L2(M)  ≲  1  |A2k|  �  y∈x+A2k+1  ∥dhn(y)∥L2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Set JI = ∪x∈I{J : J ∈ Fn−1&J ∩ x + A2k+1 ̸= ∅} and mI = maxJ∈JI ∥dhn(cJ)∥L2(M),  where cJ stands for the left endpoint of the dyadic interval J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' With these definitions,  one can see at once that  1  |A2k|  �  y∈x+A2k+1 ∥dhn(y)∥L2(M) ≲ mI for every x ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' It  follows from the above observations that  �  I∈Fn−1  �  x∈I  �  i∈Sk  ∥(MAni − MAni+1)dhn(x)∥2  L2(M)  =  �  I∈Fn−1  �  x∈I  x+A2k+1∩∂I̸=∅  �  i∈Sk  ∥(MAni − MAni+1)dhn(x)∥2  L2(M)  ≲ 2k  �  I∈Fn−1  m2  I  ≲ 2k−n  �  I∈Fn−1  �  J∈JI  �  x∈J  ∥dhn(x)∥2  L2(M)  20  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  ≲ 2k−n∥dhn∥2  2,  where we used the fact that the number #{J : J ∈ JI} ≤ 4 for every I ∈ Fn−1 in the  last inequality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' So we finish the argument of (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='15) in the case n > k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Let us now estimate (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='15) for the case n ≤ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By the Minkowski inequality,  �  i∈Sk  ∥(MAni − MAni+1)dhn∥2  2 ≲  �  i∈Sk  �  x∈Z  ���  1  |Ani+1|  �  y∈x+Ani+1\\Ani  dhn(y)  ���  2  L2(M)  +  �  i∈Sk  �  x∈Z  �  1  |Ani| −  1  |Ani+1|  �2���  �  y∈x+Ani  dhn(y)  ���  2  L2(M)  ≜ C1  k,n + C2  k,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The cancellation property of dhn over atoms in Fn implies  C1  k,n =  �  i∈Sk  �  x∈Z  ���  1  |Ani+1|  �  y∈I(x+Ani+1\\Ani,n)  dhn(y)  ���  2  L2(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Since 2k ≤ supi∈Sk |Ani| ≤ 2k+1, ∪i∈SkI(x+Ani+1\\Ani, n) ⊆ x+A2k+1 and supi∈Sk |I(x+  Ani+1 \\ Ani, n)| ≲ 2n, we use Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3 to get  C1  k,n ≤ 2n−2k �  i∈Sk  �  x∈Z  �  y∈I(x+Ani+1\\Ani,n)  ∥dhn(y)∥2  L2(M)  ≤ 2n−2k �  x∈Z  �  y∈x+A2k+1  ∥dhn(y)∥2  L2(M) ≤ 2n−k∥dhn∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  It remains to estimate C2  k,n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Using the cancellation property of dhn over atoms in Fn,  I(x + Ani, n) ⊆ x + A2k+1, supi∈Sk |I(x + Ani, n)| ≲ 2n and Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3 again, we find  C2  k,n ≲ sup  i∈Sk  �  x∈Z  ���  �  y∈I(x+Ani,n)  dhn(y)  ���  2  L2(M)  � �  i∈Sk  1  |Ani| −  1  |Ani+1|  �2  ≲ 2n+k �  x∈Z  ∥dhn(x)∥2  L2(M) sup  i∈Sk  1  |Ani|2  ≲2n−k∥dhn∥2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This finishes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3: (L∞, BMO) and strong type (p, p) estimates  In this section, we examine the (L∞, BMO) and strong type (p, p) estimates stated  in Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' (L∞, BMO) estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We first recall the definition of BMO spaces associated to the von Neumann algebra  R = N⊗B(ℓ2) equipped with the tensor trace ψ = ϕ ⊗ tr where tr is the canonical  trace on B(ℓ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' According to [35], the dyadic BMO space BMOd(R) is defined as a  subspace of L∞(M⊗B(ℓ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Lrc  2 (Z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' dx/(1 + |x|)2)) with  ∥f∥BMOd(R) = max  �  ∥f∥BMOr  d (R), ∥f∥BMOc  d (R)  �  < ∞,  QUANTITATIVE MEAN ERGODIC INEQUALITIES  21  where the row and column dyadic BMOd norms are given by  ∥f∥BMOr  d (R)  =  sup  I∈F  ���  � 1  |I|  �  x∈I  ���  �  f(x) − 1  |I|  �  y∈I  f(y)  �∗���  2� 1  2 ���  M⊗B(ℓ2),  ∥f∥BMOc  d (R)  =  sup  I∈F  ���  � 1  |I|  �  x∈I  ���f(x) − 1  |I|  �  y∈I  f(y)  ���  2� 1  2 ���  M⊗B(ℓ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By the definition of BMO spaces, we are reduced to showing  ���  �  i∈S  Tif ⊗ ei1  ���  BMOd(R) ≲ ∥f∥∞,  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1)  and  ���  �  i∈S  Tif ⊗ e1i  ���  BMOd(R) ≲ ∥f∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2)  However, it suffices to estimate (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Indeed, we assume (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Notice that (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1) is  equivalent to  ���  �  i∈S  Tif ⊗ ei1  ���  BMOc  d(R) ≲ ∥f∥∞  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3)  and  ���  �  i∈S  Tif ⊗ ei1  ���  BMOr  d(R) ≲ ∥f∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4)  Using the fact ∥g∥BMOc  d(R) = ∥g∗∥BMOr  d(R) and taking the adjoint of both sides of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3),  we obtain���  �  i∈S  Tif ⊗ e1i  ��  BMOr  d(R) =  ���  � �  i∈S  Tif ⊗ e1i  �∗���  BMOc  d(R)  =  ���  �  i∈S  Tif∗ ⊗ ei1  ���  BMOc  d(R) ≲ ∥f∗∥∞ = ∥f∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Similarly, we use (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4) to get  ���  �  i∈S  Tif ⊗ e1i  ���  BMOc  d(R) ≲ ∥f∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  These two inequalities imply  ���  �  i∈S  Tif ⊗ e1i  ���  BMOd(R) ≲ ∥f∥∞,  which is the desired estimate (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Now let us prove (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let f ∈ L∞(N) and I be a dyadic cube in Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Decompose f as f =  fχ3I + fχZ\\3I ≜ f1 + f2, where 3I denotes the interval with the same center as I  such that |3I| = 3|I|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' If we set αI,i = Tif2(cI) where cI is the center of I or the left  22  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  neighborhood in Z of the center if the center does not belong to Z, and αI = �  i  αI,i⊗ei1,  then  Tif(x) − αI,i = Tif1(x) + (Tif2(x) − αI,i) ≜ Bi1f + Bi2f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We first prove (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By the operator convexity of square function x �→ |x|2, we obtain  �� �  i∈S  (Tif − αI,i) ⊗ ei1  ��2 ≤ 2  �� �  i∈S  Bi1f ⊗ ei1  ��2 + 2  �� �  i∈S  Bi2f ⊗ ei1  ��2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The first term B1f = �  i  Bi1f ⊗ ei1 is easy to estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Indeed,  ���  � 1  |I|  �  x∈I  (B1f(x))∗(B1f(x))  � 1  2 ���  2  M⊗B(ℓ2)  =  ���  � 1  |I|  �  x∈I  �  i∈S  |Tif1(x)|2� 1  2 ���  2  M  = 1  |I|  ���  �  x∈I  �  i∈S  |Tif1(x)|2���  M  = 1  |I|  sup  ∥a∥L2(M)≤1  τ  �  x∈I  �  i∈S  |Tif1(x)a|2  ≤ 1  |I|  sup  ∥a∥L2(M)≤1  τ  �  x∈Z  �  i∈S  |Tif1(x)a|2  = 1  |I|  sup  ∥a∥L2(M)≤1  ∥(Ti(fχ3Ia))i∈S∥2  L2(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲ 1  |I|  sup  ∥a∥L2(M)≤1  ∥fχ3Ia∥2  2 ≲ ∥f∥2  ∞,  where in the third equality, we considered elements in M as bounded linear oper-  ators on L2(M) via the left multiplication and the last inequality follows from the  L2-boundedness of T, namely Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Now we turn to the second term B2f = �  i∈S  Bi2f ⊗ ei1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Note that  B2f(x)∗B2f(x)  =  �  i∈S  |Tif2(x) − Tif2(cI)|2  =  �  i∈S  |(MAnif2(x) − MAni+1f2(x)) − (MAnif2(cI) − MAni+1f2(cI))|2  =  �  k  �  i∈Sk  |(MAnif2(x) − MAni+1f2(x)) − (MAnif2(cI) − MAni+1f2(cI))|2  ≜  �  k  �  i∈Sk  |Fk,i(x)|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We claim that for any k satisfying 2k+1 < |I|, Fk,i(x) = 0 for any i ∈ Sk and x ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Indeed, fix i ∈ Sk and x ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Since 2k+1 < |I| and f2 is supported in Z \\ 3I, a simple  QUANTITATIVE MEAN ERGODIC INEQUALITIES  23  geometric observation implies that both MAni+1f2 and MAnif2 are supported in Z \\ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This is precisely the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hence,  B2f(x)∗B2f(x) =  �  k:2k+1≥|I|  �  i∈Sk  |Fk,i(x)|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In the following, we further spilt the summation over Sk to two parts by comparing  ni+1 − ni and |I|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' More precisely, we decompose B2f(x)∗B2f(x) as  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni<|I|  |Fk,i(x)|2 +  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni≥|I|  |Fk,i(x)|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Let us estimate term of the case ni+1 −ni < |I|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By the operator-convexity of square  function x �→ |x|2,  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni<|I|  |Fk,i(x)|2 ≲  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni<|I|  |MAnif2(x) − MAni+1f2(x)|2  +  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni<|I|  |MAnif2(cI) − MAni+1f2(cI)|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Now we claim that to complete the argument of the case ni+1 − ni < |I|, it is enough  to show for any z ∈ I  ∥MAnif2(z) − MAni+1f2(z)∥M ≲ ∥f∥∞|I|  1  2  � � |Ani+1|  |Ani|  1  u2 du  � 1  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5)  Indeed, by (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5) and the Minkowski inequality, we have  ���  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni<|I|  |Fk,I(x)|2���  M  ≤  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni<|I|  ∥Fk,I(x)∥2  M  ≲  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni<|I|  ∥f∥2  ∞|I|  � |Ani+1|  |Ani|  1  u2 du  ≤ ∥f∥2  ∞|I|  �  k:2k+1≥|I|  �  i∈Sk  � |Ani+1|  |Ani|  1  u2 du  ≤ ∥f∥2  ∞|I|  �  k:2k+1≥|I|  � 2k+1  2k  1  u2 du  ≲ ∥f∥2  ∞|I|  �  k:2k+1≥|I|  2−k−1 ≲ ∥f∥2  ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  24  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  Thus we deduce that  ���  � 1  |I|  �  x∈I  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni<|I|  |Fk,i(x)|2� 1  2 ���  2  M  ≤ 1  |I|  �  x∈I  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni<|I|  ∥Fk,i(x)∥2  M  ≲ ∥f∥2  ∞,  which is the desired estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' It remains to show (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' To this end, fix z ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  ∥MAnif2(z) − MAni+1f2(z)∥M  =  ���  �  1  |Ani| −  1  |Ani+1|  �  �  y∈z+Ani  f2(y) +  1  |Ani+1|  �  y∈z+Ani+1\\Ani  f2(y)  ���  M  ≤  �  1  |Ani| −  1  |Ani+1|  �  �  y∈z+Ani  ∥f2(y)∥M +  1  |Ani+1|  �  y∈z+Ani+1\\Ani  ∥f2(y)∥M  ≤  �  1  |Ani| −  1  |Ani+1|  �  |Ani|∥f2∥∞ +  1  |Ani+1|(|Ani+1| − |Ani|)∥f2∥∞  = 2(|Ani+1| − |Ani|)  1  |Ani+1|∥f∥∞  ≲ ∥f∥∞  � |Ani+1|  |Ani|  1  udu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Furthermore, by the H¨older inequality and the fact that ni+1 − ni < |I|, we see that  ∥MAnif2(z) − MAni+1f2(z)∥M ≲ ∥f∥∞(|Ani+1| − |Ani|)  1  2  � � |Ani+1|  |Ani|  1  u2 du  � 1  2  ≲ ∥f∥∞|I|  1  2  � � |Ani+1|  |Ani|  1  u2 du  � 1  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Let us now turn to the case ni+1 − ni ≥ |I|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Likewise, we use the operator-convexity  of square function x �→ |x|2 to obtain  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni≥|I|  |Fk,i(x)|2 ≲  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni≥|I|  |MAnif2(x) − MAnif2(cI)|2  +  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni≥|I|  |MAni+1f2(x) − MAni+1f2(cI)|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In this case, observe that for any Ani,  ∥MAnif2(x) − MAnif2(cI)∥M =  1  |Ani|∥  �  y∈x+Ani  f2(y) −  �  y∈cI+Ani  f2(y)∥∞  QUANTITATIVE MEAN ERGODIC INEQUALITIES  25  =  1  |Ani|  �  y∈Z  ∥f2(y)(χx+Ani(y) − χcI+Ani(y))∥∞  ≤  1  |Ani|∥f∥∞|(cI + Ani)∆(x + Ani)|,  where ∆ denotes the usual symmetric difference of two sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Note that |(cI +Ani)∆(x+  Ani)| ≲ |x − cI|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then  ∥MAnif2(x) − MAnif2(cI)∥∞ ≲  1  |Ani||x − cI|∥f∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Moreover, it is not difficult to verify that the number of i ∈ Sk such that ni+1 −ni ≥ |I|  is smaller than 2k  |I|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Therefore,  ���  � 1  |I|  �  x∈I  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni≥|I|  |Fk,i(x)|2� 1  2 ���  2  ∞  ≤ 1  |I|  �  x∈I  �  k:2k+1≥|I|  �  i∈Sk  ni+1−ni≥|I|  ∥Fk,i(x)∥2  ∞  ≲ ∥f∥2  ∞  1  |I|  �  x∈I  �  k:2k+1≥|I|  2k  |I|  1  |Ani|2 |x − cI|2  ≤ ∥f∥2  ∞  �  k:2k+1≥|I|  2k  |I|  1  |Ani|2 |I|2  ≤ ∥f∥2  ∞|I|  �  k:2k+1≥|I|  2−k−1 ≲ ∥f∥2  ∞,  where we used the relations |x − cI| ≤ |I| and |Ani| ≈ 2k+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' So we complete the proof  of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We now consider (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' However, we just deal with the term B1f = �  i∈S  Bi1f ⊗ ei1,  since B2f can be treated as before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' We note that  ���  � 1  |I|  �  x∈I  (B1f(x))(B1f(x))∗� 1  2 ���  2  M⊗B(ℓ2)  = 1  |I|  ���  �  x∈I  (B1f(x))(B1f(x))∗���  M⊗B(ℓ2)  = 1  |I|  ���  �  i1,i2∈S  � �  x∈I  Ti1f1(x)Ti2f∗  1 (x)  �  ⊗ ei1,i2  ���  M⊗B(ℓ2)  ≜ 1  |I|∥Λ∥M⊗B(ℓ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  26  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  Note that Λ is a positive operator acting on ℓ2(L2(M)) (= L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hence,  1  |I|  ���  �  x∈I  (B1f(x))(B1f(x))∗���  M⊗B(ℓ2)  = 1  |I|  sup  ∥a∥L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )≤1  �  Λa, a  �  = 1  |I|  sup  ∥a∥L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )≤1  τ  �� �  i1∈S  a∗  i1 ⊗ e1i1  �  Λ  � �  i2∈S  ai2 ⊗ ei21  ��  = 1  |I|  sup  ∥a∥L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )≤1  τ  �  x∈I  ���  �  i∈S  Tif∗  1 (x)ai  ���  2  ≤ 1  |I|  sup  ∥a∥L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )≤1  τ  �  x∈Z  ���  �  i∈S  Ti(f∗  1 ai)(x)  ���  2  ≲ 1  |I|  sup  ∥a∥L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )≤1  τ  �  x∈Z  �  i∈S  |f∗  1 (x)ai|2  ≤ 1  |I|  sup  ∥a∥L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )≤1  τ(  �  i:i∈S  |ai|2)|3I| ∥f∥2  ∞ ≲ ∥f∥2  ∞,  where in the second inequality we applied Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' This proves (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Finally,  putting all the estimates obtained so far together with their row analogues, we get  max  ����  �  i∈S  Tif ⊗ ei1  ���  BMOd(R),  ���  �  i∈S  Tif ⊗ e1i  ���  BMOd(R)  �  ≲ ∥f∥∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This completes the proof of the (L∞, BMO) estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Strong type (p, p) estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In this subsection, we complete the proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3 by showing the strong type  (p, p) estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then (Ti)i∈S is bounded from Lp(N) to Lp(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7 gives the result for p = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For the case 1 < p < 2, by applying  the weak type (1, 1) estimate of T and Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7, we conclude that T is bounded  from Lp(N) to Lp(L∞(Ω)⊗N) by real interpolation [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Thus (Ti)i∈S is bounded  from Lp(N) to Lp(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) according to noncommutative Khintchine’s inequalities—  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Consider the case 2 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' If we set Tcf = �  i∈S Tif ⊗ ei1 and Trf = �  i∈S Tif ⊗  e1i, then Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7 and (L∞, BMO) estimates yield that Tc and Tr are bounded  from Lp(N) to Lp(N⊗B(ℓ2)) via complex interpolation [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Therefore, (Ti) is bounded  from Lp(N) to Lp(N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) for all 2 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1  In this section we prove the extension property—Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7, the transference principle—  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6 and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1 immediately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  27  Proof of Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (xn)n>0 be a sequence in Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By the noncommutative  Khintchine inequalities Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2, there exist two positive constants C1, C2 such  that  ∥(Txn)n∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ C−1  1  ����  �  n  εnTxn  ����  Lp(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='Lp(M))  ≤ C−1  1 ∥id ⊗ T∥Lp(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='Lp(M))→Lp(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='Lp(M))  ����  �  n  εnxn  ����  Lp(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='Lp(M))  ≤ C−1  1 C2∥T∥Lp(M)→Lp(M)∥(xn)n∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ),  which completes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  We now establish the following noncommutative variant of Coifman-Weiss’s trans-  ference principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof of Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' In the following we only consider the two-sided ergodic av-  erages while the one-sided ones can be handled quite similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By the standard ap-  proximation argument stated in Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9, it suffices to show for any fixed integer  i0 ≥ 1  ���  Bni(T)x − Bni+1(T)x  �  0≤i≤i0  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≲ ∥x∥Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1)  For each n ∈ N, define  B′  n : Lp(Z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Lp(M)) → Lp(Z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Lp(M)), B′  nf(k) =  1  2n + 1  n  �  l=−n  f(l + k), ∀k ∈ Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Let m be a large integer bigger than N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Fix x ∈ Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Define a Lp(M)-valued  function fm on Z as  fm(l) = T lx,  if |l| ≤ m + N;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  fm(l) = 0 otherwise,  where N = ni0+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then for all −m ≤ k ≤ m and 1 ≤ n ≤ N,  T kBn(T)x =  1  2n + 1  n  �  l=−n  T k+lx =  1  2n + 1  n  �  l=−n  fm(l + k) = B′  nfm(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Therefore, for −m ≤ k ≤ m and 0 ≤ i ≤ i0,  T k(Bni(T)x − Bni+1(T)x) = B′  nifm(k) − B′  ni+1fm(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Note that T is a power bounded operator, namely supk∈Z ∥T k∥Lp(M)→Lp(M) < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then for each k ∈ Z, Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7 implies  ���  Bni(T)x − Bni+1(T)x  �  0≤i≤i0  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲  ���  T k(Bni(T)x − Bni+1(T)x)  �  0≤i≤i0  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  =  ���  B′  nifm(k) − B′  ni+1fm(k)  �  0≤i≤i0  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2)  Now we prove (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Consider the case 2 < p < ∞ firstly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In this case, by the  assumption (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5), we have  ���  B′  nifm − B′  ni+1fm  �  0≤i≤i0  ��  Lp(M⊗ℓ∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≲ ∥fm∥Lp(M⊗ℓ∞(N)),  28  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  which is equivalent to  m  �  k=−m  ���  B′  nifm(k) − B′  ni+1fm(k)  �  0≤i≤i0  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≲ ∥fm∥p  Lp(M⊗ℓ∞(N)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Hence, we use (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) to obtain that for any m ≥ 1,  ���  Bni(T)x − Bni+1(T)x  �  0≤i≤i0  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲  1  2m + 1  m  �  k=−m  ���  B′  nifm(k) − B′  ni+1fm(k)  �  0≤i≤i0  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲  1  2m + 1∥fm∥p  Lp(M⊗ℓ∞(N)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then by the definition of fm, we see that  ���  Bni(T)x − Bni+1(T)x  �  0≤i≤i0  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≲  1  2m + 1  m+N  �  l=−m−N  ∥fm(l)∥p  Lp(M)  =  1  2m + 1  m+N  �  l=−m−N  ∥T lx∥p  Lp(M)  ≲ 2m + 2N + 1  2m + 1  ∥x∥p  Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Since m is arbitrarily chosen, we get  ���  Bni(T)x − Bni+1(T)x  �  0≤i≤i0  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≲ ∥x∥Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  This gives the desired estimate for the case 2 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  It remains to show the case 1 < p ≤ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' In this case, for any ε > 0, there exists a  factorization B′  nifm − B′  ni+1fm = gi + hi such that  ∥(gi)0≤i≤i0∥p  Lp(M⊗ℓ∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) + ∥(hi)0≤i≤i0∥p  Lp(M⊗ℓ∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2)  ≤  ���  B′  nifm − B′  ni+1fm  �  0≤i≤i0  ��p  Lp(M⊗ℓ∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then we have  m  �  k=−m  ���  B′  nifm(k) − B′  ni+1fm(k)  �  0≤i≤i0  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤  m  �  k=−m  ∥(gi(k))0≤i≤i0∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) +  m  �  k=−m  ∥(hi(k))0≤i≤i0∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2)  ≲  ���  B′  nifm − B′  ni+1fm  �  0≤i≤i0  ��p  Lp(M⊗ℓ∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Since ε is arbitrarily chosen, we obtain  m  �  k=−m  ���  B′  nifm(k) − B′  ni+1fm(k)  �  0≤i≤i0  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲  ���  B′  nifm − B′  ni+1fm  �  0≤i≤i0  ��p  Lp(M⊗ℓ∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3)  QUANTITATIVE MEAN ERGODIC INEQUALITIES  29  Finally, by (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) and the assumption (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5), we deduce that for any m ≥ 1,  ���  Bni(T)x − Bni+1(T)x  �  0≤i≤i0  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲  1  2m + 1  m  �  k=−m  ���  B′  nifm(k) − B′  ni+1fm(k)  �  0≤i≤i0  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲  1  2m + 1  ���  B′  nifm − B′  ni+1fm  �  0≤i≤i0  ��p  Lp(M⊗ℓ∞(N);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲  1  2m + 1∥fm∥p  Lp(M⊗ℓ∞(N)) ≲ 2m + 2N + 1  2m + 1  ∥x∥p  Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By the arbitrariness of m, we find  ���  Bni(T)x − Bni+1(T)x  �  0≤i≤i0  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≲ ∥x∥Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  So we finish the proof of (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  Now, we are able to conclude Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Actually, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1 follows immediately from Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6  and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4  In this section, we prove Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8 and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Before that, we give some  notations and lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' We first recall the definitions of dilations and N-dilation in the  noncommutative setting (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' [15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Definition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 ≤ p ≤ ∞ and T : Lp(M, τM) → Lp(M, τM) be a contrac-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We call the operator T has a dilation if there exist a von Neumann algebra  A equipped with a normal faithful semifinite trace τA, two contraction linear opera-  tors Q : Lp(A, τA) → Lp(M, τM), J : Lp(M, τM) → Lp(A, τA) and an isometry  U : Lp(A, τA) → Lp(A, τA) such that  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1)  T n = QUnJ, ∀n ∈ N ∪ {0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We can use the following diagrams to represent the above decomposition  Lp(M, τM)  T n �  J  �  Lp(M, τM)  Lp(A, τA)  Un  � Lp(A, τA)  Q  �  for all n ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We call the operator T has an N-dilation if (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1) holds for all n ∈ {0, 1, · · · , N}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Let 1 ≤ p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let SS(Lp(M)) denote the set of all Lamperti contractions on  Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Moreover, for a given set A consisting of operators on Lp(M), we denote by  conv{A} the convex hull of A, namely  conv{A} =  �  n  �  i=1  λiTi : Ti ∈ A,  n  �  i=1  λi = 1, λi ≥ 0, n ∈ N  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  30  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  The following result which can be seen as a N-dilation theorem for conv(SS(Lp(M)))  was established in [15, Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Each operator T ∈ conv(SS(Lp(M))) has an N-dilation  for all N ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Now we present a characterization theorem for isometric operators established in  [50, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let M and A be two von Neumann algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' A complex linear map J : M →  A is called a Jordan ∗-homomorphism if J(x)∗ = J(x∗) and J(x2) = J(x)2 for all  x ∈ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Moreover, J is called the Jordan ∗-monomorphism if J is an injective Jordan  ∗-homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The following lemma was obtained by Størmer [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let J : M → A be a normal (completely additive, ultraweakly continuous)  Jordan ∗-homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Let  �  A denote the von Neumann subalgebra generated by  J(M) in A, and Z �  A be the center of �  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then there are two projections e, f ∈ Z �  A  satisfying e + f = 1 �  A, such that the map x → J(x)e is a ∗-homomorphism and x →  J(x)f is a ∗-anti-homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The following characterization of isometric operators will be frequently used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' [50, 25] Let 1 ≤ p ̸= 2 < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Assume that T : Lp(M, τM) →  Lp(A, τA) is a bounded linear operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then T is an isometry if and only if there exist  uniquely a partial isometry w ∈ A, a normal Jordan ∗-monomorphism J : M → A,  and a positive self-adjoint operator b affiliated with A, such that  (i) w∗w = suppb = J(1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (ii) For all x ∈ M, J(x) commutes with every spectral projection of b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (iii) T(x) = wbJ(x) for all x ∈ SM;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (iv) τA(bpJ(x)) = τM(x) for all x ∈ M+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Now we are ready to prove Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof of Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (xn)1≤n≤N be a finite sequence in Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By an  approximation argument, without loss of generality, we may assume that xn ∈ SM for  all 1 ≤ n ≤ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' For p = 2, the conclusion is trivially right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Indeed, in this case  ���  T(xn)  �  n  ��2  L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) =  �  n  ∥Txn∥2  L2(M) = ∥(xn)n∥L2(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We now focus on the case 2 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Since T is an isometric operator, there exist  w, b, J such that T = wbJ satisfying properties (i)-(iii) in Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Moreover,  by Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3, we may find projections e, f such that  �  T(xn)  �∗�  T(xn)  �  =  ���  bJ(xn)e + bJ(xn)f  ���2  =  �  bJ(xn)e + bJ(xn)f  �∗�  bJ(xn)e + bJ(xn)f  �  =  �  bJ(x∗  n)e + bJ(x∗  n)f  ��  bJ(xn)e + bJ(xn)f  �  = b2J(x∗  nxn)e + b2J(xnx∗  n)f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2)  As a consequence,  �  n  �  T(xn)  �∗�  T(xn)  �  = b2J  � �  n  x∗  nxn  �  e + b2J  � �  n  xnx∗  n  �  f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  31  Set y1 =  � �  n x∗  nxn  �1/2 and y2 =  � �  n xnx∗  n  �1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then  �  n  �  T(xn)  �∗�  T(xn)  �  = b2J(y2  1)e + b2J(y2  2)f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Hence, we have  ���  T(xn)  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) = τ  ��  b2J(y2  1)e + b2J(y2  2)f  � p  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  According to Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3 and Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4(ii), we further have  τ  ��  b2J(y2  1)e + b2J(y2  2)f  � p  2  �  = τ(bpJ(yp  1)e) + τ(bpJ(yp  2)f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  So, we obtain  ���  T(xn)  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) = τ(bpJ(yp  1)e) + τ(bpJ(yp  2)f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3)  On the other hand, applying the fact T = wbJ, we get  �  T(xn)  ��  T(xn)  �∗ = (wbJ(xn))(wbJ(xn))∗  = wb2J(xn)J(xn)∗w∗ = wb2J(xnx∗  n)ew∗ + wb2J(x∗  nxn)fw∗,  which gives rise to  �  n  �  T(xn)  ��  T(xn)  �∗ = wb2J(y2  2)ew∗ + wb2J(y2  1)fw∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then by the above observations and Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4(i), we find  ���  T(xn)  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) = ∥w(b2J(y2  2)e + b2J(y2  1)f)w∗∥  p  2  L p  2 (M)  = ∥(b2J(y2  2)e + b2J(y2  1)f)  1  2 w∗w(b2J(y2  2)e + b2J(y2  1)f)  1  2 ∥  p  2  L p  2 (M)  = ∥b2J(y2  2)e + b2J(y2  1)f∥  p  2  L p  2 (M)  = τ(bpJ(yp  2)e) + τ(bpJ(yp  1)f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4)  Therefore, combining (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3) with (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4), we arrive at  ���  T(xn)  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) +  ���  T(xn)  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2)  = τ(bpJ(yp  1)e) + τ(bpJ(yp  2)f) + τ(bpJ(yp  2)e) + τ(bpJ(yp  1)f)  = τ(bpJ(yp  1)) + τ(bpJ(yp  2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Moreover, by Proposition 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4(iv), we have  ���  T(xn)  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) +  ���  T(xn)  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) = τ(yp  1) + τ(yp  2)  = ∥(xn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) + ∥(xn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2),  which yields ∥  �  T(xn)  �  n∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) = ∥(xn)n∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' So T is an isometry on Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 )  and we finish the proof of the case 2 < p < ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  We then turn to the case 1 ≤ p < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Since (xn)n ∈ Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ), for any given ε > 0,  there are two finite sequences (gn)n and (hn)n such that xn = gn + hn and  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5)  ∥(gn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) + ∥(hn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) ≤ ∥(xn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  32  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  Then by Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3, we may decompose T(xn) as  T(xn) = T(gn)e + T(hn)f + (T(gn)f + T(hn)e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By the definition of the norm ∥ · ∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ), we have  ���  T(xn)  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤  ���  T(gn)e + T(hn)f  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) +  ���  T(gn)f + T(hn)e  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6)  On one hand, similar to (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2), we have  �  n  |T(gn)e + T(hn)f|2 =  �  n  (wbJ(gn)e + wbJ(hn)f)∗(wbJ(gn)e + wbJ(hn)f)  = b2J  � �  n  g∗  ngn  �  e + b2J  � �  n  hnh∗  n  �  f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7)  Set y3 =  � �  n g∗  ngn  �1/2 and y4 =  � �  n hnh∗  n  �1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8)  ���  T(gn)e + T(hn)f  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) = τ(bpJ(yp  3)e) + τ(bpJ(yp  4)f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  On the other hand, for the term  ���  T(gn)f + T(hn)e  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2), similar to (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7), we  deduce that  �  n  |(T(gn)f + T(hn)e)∗|2 =  �  n  (wbJ(gn)f + wbJ(hn)e)(wbJ(gn)f + wbJ(hn)e)∗  = wb2J  � �  n  g∗  ngn  �  fw∗ + wb2J  � �  n  hnh∗  n  �  ew∗  = wb2J(y2  3)fw∗ + wb2J(y2  4)ew∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Using the same argument as in (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4), we have  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9)  ���  T(gn)f + T(hn)e  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) = τ(bpJ(yp  3)f) + τ(bpJ(yp  4)e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Together (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8), (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9) and (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6) with Proposition (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4)(iv) and (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5), we get  ���  T(xn)  �  n  ��p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ ∥(xn)n∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By the arbitrariness of ε, we proved that T extends to a contraction on Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Finally, we assume that T is positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' It is sufficient to consider the case 1 < p < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  The following facts are taken from [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Note that T is a positive isometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then T is  Lamperti and T = bJ, where b, J are defined in Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3 (see [15, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3 and  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let A be the von Neumann algebra generated by J(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3,  we may decompose A = A1 ⊕ A2, where A1 and A2 are two von Neumann subalgebras  of A, and write J = J1 + J2 such that J1 : M → A1 is a normal ∗-homomorphism  and J2 : M → A2 is a normal ∗-anti-homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let σ : A2 → Aop  2 be the usual  opposite map and define  Σ : A → A1 ⊕ Aop  2 ,  Σ = IdA1 ⊕ σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then Σ ◦ J is a normal ∗-homomorphism and Σ(J(M)) is a von Neumann subalgebra  of A1 ⊕ Aop  2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Define  ϕ : Σ(J(M))+ → [0, ∞],  x �→ τ(bpΣ−1x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  33  Then ϕ becomes a normal semifinite trace on Σ(J(M)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let Lp(Σ(J(M)), ϕ) be the  associated noncommutative Lp space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then Σ ◦ J extends to a positive surjective  isometry  ˜J : Lp(M, τ) → Lp(Σ(J(M)), ϕ),  x �→ Σ(J(x)),  whence ˜J−1 is well defined, positive and isometric on Lp(Σ(J(M)), ϕ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' We refer to [15,  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3] for the detailed description of above facts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In the following, we claim that ˜J extends to an isometry from Lp(M, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) onto  Lp(Σ(J(M)), ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' To see this, we divide the proof of the claim into three steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In the first step, we prove that for any finite sequence (xn) in Lp(M, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) and each  xn ∈ SM,  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='10)  ∥( ˜J(xn))n∥p  Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) = ∥(xn)n∥p  Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2)  and  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='11)  ∥( ˜J(xn))n∥p  Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) = ∥(xn)n∥p  Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  To prove (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='10), note that for x ∈ M, ˜J(x)∗ = (Σ(J(x)))∗ = J1(x∗)⊕σ(J2(x∗)) = ˜J(x∗)  which implies ˜J(x)∗ ˜J(x) = ˜J(x∗) ˜J(x) = ˜J(x∗x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then  ∥( ˜J(xn))n∥p  Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) =  ���  � �  n  | ˜J(xn)|2�1/2���  p  Lp(Σ(J(M)),ϕ)  = ϕ  �� �  n  ˜J(xn)∗ ˜J(xn)  �p/2�  = τ  �  bpΣ−1�  ˜J  � �  n  x∗  nxn  ��p/2�  = τ  �  bpΣ−1�  Σ ◦ J  � �  n  x∗  nxn  ��p/2�  = τ  �  bp�  J  �� �  n  |xn|2�1/2��p�  = τ  ��  bJ  �� �  n  |xn|2�1/2��p�  =  ���T  �� �  n  |xn|2�1/2����  p  Lp(M,τ) = ∥(xn)n∥p  Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2),  which gives (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Replacing ˜J(xn) by ˜J(xn)∗ in the above argument, we obtain (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  In the second step, we show  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='12)  ��� ˜J(xn)  �  n  ��  Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ ∥(xn)n∥Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  To see this, since (xn) ∈ Lp(M, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ), for any given ε > 0, there exist sequences (gn)n  and (hn)n such that xn = gn + hn and  ∥(gn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) + ∥(hn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) ≤ ∥(xn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then by (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='10) and (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='11), we have  ��� ˜J(xn)  �  n  ��p  Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤  ��� ˜J(gn)  �  n  ��p  Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) +  ��� ˜J(hn)  �  n  ��p  Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2)  = ∥(gn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) + ∥(hn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2)  ≤ ∥(xn)n∥p  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By the arbitrariness of ε, we obtain (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  34  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  In the last step, we prove  (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='13)  ��� ˜J−1(xn)  �  n  ��  Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ ∥(xn)n∥Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Indeed, notice that ˜J−1 is positive and isometric from Lp(Σ(J(M)), ϕ) to Lp(M, τ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Then  ∥( ˜J−1(xn))n∥p  Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) = τ  ��  ˜J−1� �  n  x∗  nxn  ��p/2�  =  ��� ˜J−1�� �  n  |xn|2�1/2����  p  Lp(M,τ) = ∥(xn)n∥p  Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Replacing ˜J−1(xn) by ˜J−1(xn)∗, we also have  ∥( ˜J−1(xn))n∥Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) = ∥(xn)n∥Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Therefore, repeating argument as in (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='12), we get (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  From (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='12) and (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='13), we deduce the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  To complete the argument, there remains to verify that the embedding  Lp(Σ(J(M)), ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) → Lp(M, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ),  (xn)n �→ (bΣ−1xn)n  is an isometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let p′ be the conjugate index of p, that is 1  p + 1  p′ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then 2 < p′ <  ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (xn) be a finite sequence in Lp′(Σ(J(M)), ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Write xn = (xn,1, xn,2) ∈  Lp′(A1) ⊕ Lp′(Aop  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then  ∥(bp/p′Σ−1xn)n∥p′  Lp′(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) =  ���  � �  n  |bp/p′Σ−1xn|2�1/2���  p′  Lp′(M,τ)  = τ  �  bp� �  n  Σ−1(x∗  n)Σ−1(xn)  �p′/2�  = τ  �  bp� �  n  �  x∗  n,1xn,1 + σ−1(xn,2x∗  n,2)  ��p′/2�  = τ  �  bp� �  n  x∗  n,1xn,1 + σ−1� �  n  xn,2x∗  n,2  ��p′/2�  = τ  �  bp� �  n  x∗  n,1xn,1  �p′/2�  + τ  �  bp�  σ−1� �  n  xn,2x∗  n,2  ��p′/2�  = ∥(xn,1)n∥p′  Lp′(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) + ∥(xn,2)n∥p′  Lp′(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Note that (bp/p′Σ−1xn)∗ = bp/p′Σ−1x∗  n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then replacing bp/p′Σ−1xn by (bp/p′Σ−1xn)∗ in  the above identities, we deduce that  ∥(bp/p′Σ−1xn)n∥p′  Lp′(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) = ∥(xn,1)n∥p′  Lp′(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) + ∥(xn,2)n∥p′  Lp′(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Combining the above two identities, we have  ∥(bp/p′Σ−1xn)n∥p′  Lp′(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) + ∥(bp/p′Σ−1xn)n∥p′  Lp′(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2)  = ∥(xn,1)n∥p′  Lp′(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2) + ∥(xn,2)n∥p′  Lp′(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓr  2)  + ∥(xn,1)n∥p′  Lp′(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2) + ∥(xn,2)n∥p′  Lp′(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓc  2)  = ∥(xn)n∥p′  Lp′(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  35  Hence the map  φ : Lp′(Σ(J(M)), ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) → Lp′(M, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ),  (xn)n �→ (bp/p′Σ−1xn)n  is an isometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='1, we know that (Lp(Σ(J(M)), ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ))∗ = Lp′(Σ(J(M)), ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Let φ∗ be the conjugate of φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then we can check that φ∗((bΣ−1xn)n) = (xn)n (see the  proof of Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='3 in [15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Therefore, recalling that T is a contraction on Lp(M, τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ) with T = bJ and together  with above observations, we finally get  ∥(xn)n∥Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) = ∥φ∗((bΣ−1xn)n)∥Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤ ∥(bΣ−1xn)n∥Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) = ∥(T ˜J−1xn)n∥Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤ ∥( ˜J−1xn)n∥Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) = ∥(xn)n∥Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ),  which gives ∥(xn)n∥Lp(Σ(J(M)),ϕ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) = ∥(bΣ−1xn)n∥Lp(M,τ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' So the proof of Proposi-  tion 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8 is complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  Based on Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8, a similar Coifman-Weiss’s transference principle as Propo-  sition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6 holds also for isometries and we thus get the following quantitative mean  ergodic theorem for isometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 ≤ p < ∞ and T : Lp(M) → Lp(M) be an isometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (ni)i∈N be  any increasing sequence of positive integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then for 2 ≤ p < ∞,  ���  Mni(T)x − Mni+1(T)x  �  i∈N  ��  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≲ ∥x∥Lp(M), forallx ∈ Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  If T is moreover positive, then the above inequality holds also for 1 < p < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5 can be proved in a similar way as Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6 by observing that the  “≲” in (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2) can be strengthened to “=” due to Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' We omit the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  By Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5, we now can conclude the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Recall that Mn(T) =  1  n+1  �n  k=0 T k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' By the density argument,  it is enough to prove the theorem for any finite positive sequence (ni)0≤i≤N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Fix an arbitrary N ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Note that T ∈ S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then by definition, we can find (Tj) ⊆  conv(SS(Lp(M))) such that Tj converges to T in the sense of strong operator topology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Moreover, according to Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2, for each Tj, there exist two contractions Qj,N, Jj,N  and one isometry Uj,N such that T ni  j  = Qj,NU ni  j,NJj,N for every 0 ≤ ni ≤ nN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' As a  consequence, by Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='7, Qj,N and Jj,N extend to two bounded operators on  Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Therefore, for any fixed x ∈ Lp(M), together with Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='5, we get  ∥  �  Mni(Tj)x − Mni+1(Tj)x  �  0≤i≤N∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  = ∥(Qj,N(Mni − Mni+1)(Uj,N)Jj,Nx)0≤i≤N∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≤ ∥((Mni − Mni+1)(Uj,N)Jj,Nx)0≤i≤N∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲ ∥Jj,Nx∥Lp(M) ≲ ∥x∥Lp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Consequently, combined with the noncommutative Khintchine inequality in Lp space-  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='2, we finally deduce that  ∥  �  Mni(T)x − Mni+1(T)x  �  0≤i≤N∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  36  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  ≤ ∥  ��  Mni − Mni+1  �  Tjx)0≤i≤N∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) + ∥  ��  Mni − Mni+1  �  (T − Tj)x  �  )0≤i≤N∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≲ ∥x∥Lp(M) + ∥  ��  Mni − Mni+1  �  (T − Tj)x  �  )0≤i≤N∥Lp(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 )  ≈ ∥x∥Lp(M) +  ����  N  �  i=0  εi  �  Mni − Mni+1  �  (T − Tj)x  ����  Lp(Ω;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='Lp(M))  ≲ ∥x∥Lp(M) +  N  �  i=0  ∥  �  Mni − Mni+1  �  (T − Tj)x∥Lp(M),  By letting j → ∞, we obtain the desired conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  □  By the argument of Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4 in [15] and Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='4, we immediately obtain  the quantitative mean ergodic theorem for operator-valued positive contractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Corollary 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let 1 < p < ∞ and let (Ω, µ) be a σ-finite measure space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Suppose  that T : Lp(Ω) → Lp(Ω) is a positive contraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Define �T = T ⊗ ILp(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Let (ni)i∈N  be any increasing sequence of positive integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Then there exists a positive constant  Cp such that  ���  Mni( �T)x − Mni+1( �T)x  �  i∈N  ��  Lp(L∞(Ω)⊗M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ℓrc  2 ) ≤ Cp∥x∥p ∀ x ∈ Lp(L∞(Ω)⊗M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' ℓrc  2 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  References  [1] M .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Akcoglu, A pointwise ergodic theorem in Lp-spaces, Canad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 27 (1975), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 5,  1075-1082.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Anantharaman-Delaroche, On ergodic theorems for free group actions on noncommutative  spaces, Probab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Theory Related Fields 135 (2006), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 4, 520-546.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [3] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Avigad, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Rute, Oscillation and the mean ergodic theorem for uniformly convex Banach spaces,  Ergod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' & Dynam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 35 (2015), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 4, 1009-1027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Bekjan, Noncommutative maximal ergodic theorems for positive contractions, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  254 (2008), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 9, 2401-2418.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [5] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Bourgain, Pointwise ergodic theorems for arithmetic sets, Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' IHES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 69 (1989), 5-41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [6] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Cadilhac, Noncommutative Khintchine inequalities in interpolation spaces of Lp-spaces, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 352 (2019) 265-296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [7] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Cadilhac, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Conde-Alonso, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Parcet, Spectral multipliers in group algebras and noncommu-  tative Calder´on-Zygmund theory, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Pures Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' (9) 163 (2022) 450-472.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Coifman, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Weiss, Transference methods in Analysis, CBMS No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 31, Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=',  Providence, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=', 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Conze, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Dang-Ngoc, Ergodic theorems for noncommutative dynamical systems, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=', 46 (1978), 1-15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [10] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Cuculescu, Martingales on von Neumann algebras, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Multivariate Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 1 (1971), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 1, 17-27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [11] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Dunford, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Schwartz, Linear Operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' General Theory, Applied Mathematics, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Interscience Publishers, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=', New York, 1958.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Fack, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Kosaki, Generalized s-numbers of τ-measurable operators, Pacific J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 123 (1986),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 2, 269-300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [13] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hong, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Liao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Wang, Noncommutative maximal ergodic inequalities associated with dou-  bling conditions, Duke Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 170 (2021), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 2, 205-246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [14] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hong, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Liu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Xu, Quantitative mean ergodic inequalities II: power bounded operators  acting on one noncommutative Lp space, prepare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [15] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Ray, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Wang, Maximal ergodic inequalities for some positive operators on noncom-  mutative Lp-spaces, arXiv:1907,12967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [16] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sun, Noncommutative multi-parameter Wiener-Wintner type ergodic theorem, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 275 (2018), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 5, 1100-1137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  QUANTITATIVE MEAN ERGODIC INEQUALITIES  37  [17] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hong, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Xu, A noncommutative weak (1, 1) type estimate for a square function from ergodic  theory, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 280 (2021), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='9, 108959.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Hu, Maximal ergodic theorems for some group actions, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 254 (2008), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 5,  1282-1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Jajte, Strong limit theorems in noncommutative probability, Lecture Notes in Mathematics,  volume 1110, Springer-Verlag, Berlin, 1985.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [20] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Jajte, Strong limit theorems in noncommutative L2-spaces, Lecture Notes in Mathematics,  volume 1477, Springer-Verlag, Berlin, 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [21] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Jiao, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Randrianantoanina, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Wu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Zhou, Square Functions for Noncommutative Differen-  tially Subordinate Martingales, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 374 (2020), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 2, 975-1019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [22] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Jones, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Ostrovskii, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Rosenblatt, Square functions in ergodic theory, Ergod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' & Dynam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Sys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 16 (1996), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 2, 267-305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [23] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Jones, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Rosenblatt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Wierdl, Oscillation in ergodic theory, Ergod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' & Dynam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 18  (1998), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 4, 889-935.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Junge, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Le Merdy, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Xu, H∞ functional calculus and square functions on noncommutative  Lp-spaces, Ast´erisque.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 305 (2006) vi+138 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Junge, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Ruan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sherman, A classification for 2-isometries of noncommutative Lp-spaces,  Israel J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 150 (2005) 285-314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Junge, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Xu, Noncommutative maximal ergodic theorems, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 20 (2007),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 2, 385-439.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [27] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Kov´acs, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sz¨ucs, Ergodic type theorems in von Neumann algebras, Acta Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' (Szeged)  27 (1966), 233-246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [28] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Krengel, On the speed of convergence in the ergodic theorem, Monatsh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 86 (1978/79),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 1, 3-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [29] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Kummerer, A non-commutative individual ergodic theorem, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=', 46 (1978), 139-145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [30] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Lance, Ergodic theorems for convex sets and operator algebras, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 37 (1976)  201–214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [31] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Litvinov, A non-commutative Wiener-Wintner theorem, Illinois J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 58 (2014), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 3,  697-708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [32] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Lust-Piquard, In´egalit´es de Khintchine dans Cp (1 < p < ∞), C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Paris S´er.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' I  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 303 (1986), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 7, 289-292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [33] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Lust-Piquard, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Pisier, Noncommutative Khintchine and Paley inequalities, Ark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 29  (1991), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 2, 241-260.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [34] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Mei, Operator valued Hardy spaces, Mem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 188 (2007), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 881, vi+64 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [35] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Mei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Parcet, Pseudo-localization of singular integrals and noncommutative Littlewood-Paley  inequalities, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 8 (2009) 1433-1487.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [36] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Musat, Interpolation between non-commutative BMO and non-commutative Lp-spaces, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 202 (2003), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 1, 195-225.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [37] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Parcet, Pseudo-localization of singular integrals and noncommutative Calder´on-Zygmund the-  ory, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Funct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 256 (2009), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 2, 509-593.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [38] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Pisier, Non-commutative vector valued Lp-spaces and completely p-summing maps, Ast´erisque  247 (1998), vi+131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [39] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Pisier, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Xu, Non-commutative martingale inequalities, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 189 (1997), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  3, 667-698.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [40] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Pisier, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Xu, Noncommutative Lp spaces, Handbook of geometry of Banach spaces, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 2,  1459-1517, North-Holland, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [41] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Randrianantoanina, Square function inequalities for non-commutative martingales, Israel J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 140 (2004), 333-365.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [42] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Randrianantoanina, A weak type inequality for non-commutative martingales and applications,  Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 91 (2005), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 2, 509-542.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [43] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Riesz, Some mean ergodic theorems, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Lond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 13 (1938), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 4, 274-278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [44] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Riesz, Another proof of the mean ergodic theorem, Acta Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Szeged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 10  (1941), 75-76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [45] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Størmer, On the Jordan structure of C∗-algebras, Tran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 120 (1965) 438-447.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  38  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' HONG, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' LIU, AND B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' XU  [46] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='-Nagy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Foias, Harmonic Analysis of Operators on Hilbert Space, North-Holland, 1970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [47] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' von Neumann, Proof of the quasi-ergodic hypothesis, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' USA 18 (1932),  70-82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [48] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Yeadon, Ergodic theorems for semifinite von Neumann algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' I, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 16  (1977) 326-332.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [49] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Yeadon, Ergodic theorems for semifinite von Neumann algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' II, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Cambridge  Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 88 (1980), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 1, 135-147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  [50] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Yeadon, Isometric of noncommutative Lp-spaces, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Cambridge Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' Soc 90  (1981), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content=' 1, 41-50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='  School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China  Email address: guixiang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='hong@whu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='cn  School of Mathematical Sciences, Fudan University, Shanghai 200433, China  Email address: wliu math@fudan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='cn  Department of Mathematical Sciences, Seoul National University, 08826 Seoul, Re-  public of Korea  Email address: bangxu@snu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
+page_content='kr' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/hNAyT4oBgHgl3EQfXffW/content/2301.00186v1.pdf'}
diff --git a/i9AyT4oBgHgl3EQfkfhZ/content/tmp_files/2301.00434v1.pdf.txt b/i9AyT4oBgHgl3EQfkfhZ/content/tmp_files/2301.00434v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..78897dcf254432ca0ffc719d4056333feec7a82d
--- /dev/null
+++ b/i9AyT4oBgHgl3EQfkfhZ/content/tmp_files/2301.00434v1.pdf.txt
@@ -0,0 +1,555 @@
+arXiv:2301.00434v1  [math.CO]  1 Jan 2023
+Cops and Robbers Pebbling in Graphs
+Joshua Forkin∗
+Glenn Hurlbert∗
+Dedicated to Oleksandr Stanzhytsky, and others like him
+who are doing less mathematics than usual at this time.
+Abstract
+Here we merge the two fields of Cops and Robbers and Graph Pebbling to introduce the new topic
+of Cops and Robbers Pebbling. Both paradigms can be described by moving tokens (the cops) along the
+edges of a graph to capture a special token (the robber). In Cops and Robbers, all tokens move freely,
+whereas, in Graph Pebbling, some of the chasing tokens disappear with movement while the robber is
+stationary. In Cops and Robbers Pebbling, some of the chasing tokens (cops) disappear with movement,
+while the robber moves freely. We define the cop pebbling number of a graph to be the minimum number
+of cops necessary to capture the robber in this context, and present upper and lower bounds and exact
+values, some involving various domination parameters, for an array of graph classes. We also offer several
+interesting problems and conjectures.
+∗Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, USA
+1
+
+1
+Introduction
+There are numerous versions of moving tokens in a graph for various purposes. Two popular versions are
+called Cops and Robbers and Graph Pebbling. In both cases we have tokens of one type (C) attempting to
+capture a token of another type (R), and all token movements occur on the edges of a graph. In the former
+instance, all tokens move freely, whereas in the latter instance, type R tokens are stationary and type C
+movements come at a cost. In this paper we merge these two subjects to create Cops and Robbers Pebbling,
+wherein type R tokens move freely and type C tokens move at a cost.
+We define these three paradigms more specifically in Subsection 1.1 below. The new graph invariant we
+define to study in this paper is the cop pebbling number of a graph, denoted πc(G); roughly, this equals
+the minimum number of cops necessary to capture the robber in the cops and robbers pebbling paradigm.
+In Subsections 1.2–1.4 we present known results about cops and robbers, dominating sets, and optimal
+pebbling, respectively, that will be used in the sequel.
+We record in Subsections 2.1–2.3 new theorems
+on lower bounds, upper bounds, and exact answers for πc(G), respectively, for a range of graph families,
+including paths, cycles, trees, chordal graphs, high girth graphs, and cop-win graphs, as well as, in some
+cases, for all graphs. Section 3 contains theorems for Cartesian products of graphs, and we finish in Section
+4 with some natural questions left open from this work, including a version of Meyniel’s Cops and Robbers
+Conjecture that may hold in the Cops and Robbers Pebbling world.
+1.1
+Definitions
+We use several standard notations in graph theory, including V (G)for the set of vertices of a graph G (with
+n(G) = |V (G)|), E(G) for its edge set, rad(G) for its radius, diam(G) for its diameter, and gir(G) for its
+girth, as well as deg(v) for the degree of a vertex, and dist(u, v) for the distance between vertices u and v. For
+a vertex v in a graph G, we use the notations Nd(v) = {u | dist(u, v) < d} and Nd[v] = {u | dist(u, v) ≤ d}.
+If d = 1 we drop the subscript. We often use T to denote a generic tree, and set Pn, Cn, and Kn to be the
+path, cycle, and complete graph on n vertices, respectively.
+1.1.1
+Graph Pebbling
+A configuration C of pebbles on a graph G is a function from the vertices of G to the non-negative integers.
+Its size equals |C| = �
+v∈G C(v). For adjacent vertices u and v with C(u) ≥ 2, a pebbling step from u to v
+removes two pebbles from u and adds one pebble to v, while, when C(u) ≥ 1, a free step from u to v removes
+one pebble from u and adds one pebble to v. In the context of moving pebbles, we use the word move to
+mean move via pebbling steps.
+2
+
+The pebbling number of a graph G, denoted π(G), is the minimum number m so that, from any config-
+uration of size m, one can move a pebble to any specified target vertex. The optimal pebbling number of a
+graph G, denoted π∗(G), is the minimum number m so that, from some configuration of size m, one can
+move a pebble to any specified target vertex.
+1.1.2
+Cops and Robbers
+In cops and robbers, the cops are the pebbles, the robber is the target, and the robber is allowed to move.
+The cops and robbers alternate making moves in turns. At each turn, any positive number of cops make
+one free step, then the robber chooses to make a free step or not. In graph pebbling literature, the activity
+of moving a pebble to a target is called solving or reaching the target; here we use the analogous cops and
+robbers terminology of capturing the robber.
+The cop number c(G) is defined as the minimum number m so that, from some configuration of m cops,
+it is possible to capture any robber via free steps. If the cops catch the robber on their tth turn, then we
+say that the length of the game is t; if the robber wins then the length is infinite. When c(G) = m, the
+m-capture time of G, denoted captm(G), is defined to be the length of the game on G when both cops and
+robbers play optimally. That is, it equals the minimum (over all cop strategies) of the maximum (over all
+robber strategies) of the length of the game on G. For graphs of cop number 1, we simply say capture time
+and write capt(G) without the subscript.
+When necessary or convenient to use pronouns, we follow the literature by having female cops and a male
+robber.
+1.1.3
+Cop Pebbling
+The cop pebbling number πc(G) is defined as the minimum number m so that, from some configuration of m
+cops, it is possible to capture any robber via pebbling steps. We call an instance of a graph G, configuration
+C, and robber vertex v a game, and say that the cops win the game if they can capture the robber; else
+the robber wins. Note that in standard cops and robbers, the robber must elude capture forever to win the
+game, since there is no cost to cop movements. However, since we lose a cop with each pebbling step, the
+cops and robbers pebbling game is finite — the robber wins if not captured within |C| − 1 turns.
+We may assume that all graphs are simple. Because games on K1 are trivial, we will assume that all
+graph components have at least two vertices. Additionally, because of the following fact, we will restrict our
+attention in this paper to connected graphs.
+Fact. If G has connected components G1, . . . , Gk then πc(G) = �k
+i=1 πc(Gi).
+3
+
+A set S ⊆ V (G) is a distance-d dominating set if ∪v∈SNd[v] = V (S). We denote by γd(G) the size of the
+smallest distance-d dominating set.
+1.2
+Cop Results
+A graph G is cop-win if c(G) = 1. A vertex u in G is called a corner if there is a vertex v ̸= u such that
+N[u] ⊆ N[v]. We say that G is dismantlable if either G is a single vertex or there is a corner u such that
+G − u is dismantlable. Note that chordal graphs are dismantlable.
+Result 1. [19] A graph is cop-win if and only if it is dismantlable.
+Result 2. [1] Let t be a positive integer, and let G be a graph with gir(G) ≥ 8t − 3 and δ(G) > d. Then
+c(G) ≥ dt.
+Result 3. [4] If G is a chordal graph with radius r, then capt(G) ≤ r.
+This bound is tight. For example, P5 has both radius 2 and capt(G) = 2.
+1.3
+Dominating Set Results
+Result 4. [17] If G is a graph on n vertices then γd(G) ≤
+n
+d+1.
+Define the spider S(k, d) to be the tree having a unique vertex x of degree greater than 2, all k of whose
+leaves have distance d from x. The bound in Result 4 can be tight, as witnessed by S(k, d + 1) for any k.
+Result 5. [6] If |Nd[v]| ≥ c for all v ∈ G then γ2d(G) ≤ n/c.
+Result 6. [5] Almost all cop-win graphs G have γ(G) = 1.
+Result 7. [12] If G is an n × m grid such that 16 ≤ n ≤ m, then γ(G) ≤
+�
+(n+2)(m+2)
+5
+�
+− 4.
+1.4
+Optimal Pebbling Results
+Result 8. [6] For every graph G, π∗(G) ≤ ⌈2n/3⌉. Equality holds when G is a path or cycle.
+Fractional pebbling allows for rational values of pebbles. A fractional pebbling step from vertex u to one
+of its neighbors v removes x pebbles from u and adds x/2 pebbles to v, where x is an rational number such
+that 0 < x ≤ C(u). The optimal fractional pebbling number of a graph G, denoted ˆπ∗(G), is the minimum
+number m so that, from some configuration of size m, one can move, via fractional pebbling moves, a sum
+of one pebble to any specified target vertex.
+Result 9. [13, 18] For every graph G we have π∗(G) ≥ ⌈ˆπ∗(G)⌉.
+4
+
+The authors of [13] prove that ˆπ∗(G) can be calculated by a linear program. Furthermore, they use this
+result to show that there is uniform configuration that witnesses the optimal fractional pebbling number of
+any vertex-transitive graph; that is, the configuration C defined by C(v) = ˆπ∗(G)/n(G) for all v fractionally
+solves any specified vertex. From this they prove the following.
+Result 10. [13] Let G be a vertex-transitive graph and, for any fixed vertex v, define m = �
+u∈V (G) 2−dist(u,v).
+Then ˆπ∗(G) = n(G)/m.
+Result 11. [6] If G is an n-vertex graph with gir(G) ≥ 2s + 1 and δ(G) = k then π∗(G) ≤
+22sn
+σk(s), where
+σk(s) = 1 + k �s
+i=1(k − 1)i−1.
+2
+Main Theorems
+2.1
+Lower Bounds
+Theorem 1. For any graph G, πc(G) ≥ c(G), with equality if and only if G = K1.
+Proof. Any configuration of cops that can capture the robber via pebbling steps can also capture the robber
+via free steps.
+If G = K1 then πc(G) = 1 = c(G).
+If πc(G) = c(G) then capturing the robber requires no steps. That means that a successful pebbling
+configuration has no vertex without a pebble; i.e. πc(G) = n(G). However, if n(G) ≥ 3 then πc(G) < n by
+Corollary 5, below, a contradiction. If n(G) = 2 then G = K2 and πc(K2) = 2 > 1 = c(K2), a contradiction.
+Hence G = K1.
+Theorem 2. For any graph G, πc(G) ≥ π∗(G). Equality holds if G is a tree or cycle.
+Proof. Any configuration of k cops, where k < π∗(G), will contain a vertex v which is unreachable. The
+robber can then choose to start and stay on v and thus not be captured.
+If G is a cycle then Theorems 8 and 17 yield the equality.
+If G is a tree then place π∗(G) cops according to an optimal pebbling configuration C. The robber
+beginning at some vertex v defines a subtree T containing v for which every cop in T is on a leaf of T , and
+any leaf of T with no cop is a leaf of G. Thus the robber can never escape T . Because C can reach every
+vertex of T , they can capture the robber, regardless of where he moves. Hence πc(G) ≤ π∗(G), and the
+equality follows.
+Typically, Theorem 2 gives a sharper lower bound on πc(G) than Theorem 1. However, this may not be
+true for all graphs.
+5
+
+Theorem 3. If G is a graph with δ(G) = k for some k ≥ 4097, and with gir(G) ≥ 8t − 2 and n(G) ≤ k4t−1
+for some t ≥ 3, then c(G) > π∗(G).
+Proof. Given G as above, set d = k − 1. Then we have gir(G) ≥ 8t − 3, and so c(G) ≥ dt by Result 2. Also,
+with s = 4t − 2, we have gir(G) > 2s + 1, and so π∗(G) ≤ 22sn/σδ(s) by Result 11. Note that 22sn/σδ(s) <
+4sn/ds ≤ (4/d)4t−2(d + 1)4t−1. Thus the result will be proved by showing that (4/d)4t−2(d + 1)4t−1 ≤ dt.
+Since k ≥ 4097 we have d ≥ 212, so that [4(1 + 1/d)]4 < [4(2)]4 = 212 ≤ d. It is easy to calculate that
+[4(1 + 1/d)]4t < dt(16/d)(1 + 1/d) when d = 212 and t = 3, and to observe that the gap in the inequality
+grows if either d or t increases. From this it follows that (4/d)4t−2(d + 1)4t−1 ≤ dt.
+At issue here is that it is not known if there exists a graph that satisfies the hypothesis of Theorem 3.
+Indeed, Biggs [3] defines a sequence of k-regular graphs {Gi} with increasing n(Gi) to have large girth if
+gir(Gi) ≥ α logk−1(n(Gi)) for some constant α. It is known that α ≤ 2, and the greatest known constant
+is a construction of [16] that yields α = 4/3. However, a graph satisfying the hypothesis of Theorem 3
+necessarilty has α = 2.
+2.2
+Upper Bounds
+Theorem 4. Let G be a graph with dominating set S. Suppose that S′ ⊆ S is a dominating set of V (G)−S.
+Then πc(G) ≤ |S| + |S′|. In particular, πc(G) ≤ 2γ(G).
+Proof. Place two cops on each vertex of S′ and one cop on each vertex of S − S′.
+In order to not be
+immediately captured, the robber must start in V (G) − S, but then is captured in one step by some pair
+of cops from S′. The second statement follows from choosing S′ = S to be a minimum dominating set of
+G.
+To illustrate the improvement of |S| + |S′| compared to 2γ(G), consider the following example.
+Example 1. For positive integers m ≥ 2k ≥ 2, let Y = {y1, . . . , ym} and let Q = {Q1, . . . , Qk} be a partition
+of Y with each part size |Qi| ≥ 2. Define a bipartite graph G with vertices Y , Z = {z1, . . . , zk}, and x as
+follows. For each 1 ≤ j ≤ k set zj ∼ yi if and only if yi ∈ Qj. Also set x ∼ yi for every 1 ≤ i ≤ m.
+Then γ(G) = k + 1. Indeed, since the neighborhoods of each zj are pairwise disjoint, at least k vertices in
+Y ∪ Z are required to dominate Z, one from each N[zj]. Suppose that S is a dominating set of size k. By
+the above, |S ∩ N[zj]| = 1 for all j. But to dominate x, some yi must be in S. Let yi ∈ N(zj); then yi does
+not dominate any other yi′ ∈ N(zj). Hence γ(G) ≥ k + 1. It is easy to see that S = Z ∪ {x} is a dominating
+set, so that γ(G) = k + 1. With this choice of S we have S′ = {x}, so that πc(G) ≤ k + 2, much better than
+2γ(G) = 2k + 2.
+6
+
+An obvious corollary of Theorem 4 (recorded as Corollary 15, below) is that any graph G with a domi-
+nating vertex has πc(G) = 2. A more interesting corollary is the following.
+Corollary 5. Every graph G satisfies πc(G) ≤ n − ∆(G) + 1. In particular, if n(G) ≤ 2 then πc(G) = n, if
+n(G) ≥ 3 then πc(G) ≤ n − 1, and if n(G) ≥ 6 then πc(G) ≤ n − 2.
+Proof. Let v be a vertex with deg(v) = ∆(G) and set S = V (G)−N[v], with S′ = {v}. Then apply Theorem
+4. Next, it is easy to see that πc(Kn) = n for n ≤ 2. Then, a graph with at least three vertices has a vertex
+of degree at least two, so that n − ∆(G) + 1 ≤ n − 1. Finally, if ∆(G) ≥ 3 then n − ∆(G) + 1 ≤ n − 2, while
+if ∆(G) ≤ 2 then G is a path or cycle, for which Theorem 17 yields πc(G) = ⌈ 2n
+3 ⌉, which is at most n − 2
+when n ≥ 6.
+All three conditional bounds in Corollary 5 are tight: for example, π∗(P2) = 2, π∗(P5) = 4, and π∗(P7) =
+5. Furthermore, its more general bound of n − ∆(G) + 1 is tight for a graph with a dominating vertex (see
+Corollary 15).
+A set A of edges of a graph G is called an induced k-star packing of G if every component of the subgraph
+G[A] induced by A is a star with at most k edges and is an induced subgraph of G. Kelmans [14] showed that
+there is a polynomial algorithm for finding a k-star packing that covers the maximum number of vertices
+in a graph. Of course, this problem is NP-hard if k is not fixed. Perfect star packings cover all vertices in
+a graph, and have been studied in [20]. Suppose that X = {X1, . . . , Xm} is a packing of stars in G, with
+corresponding centers U = {u1, . . . , um}. If X covers all but the vertices W, then Theorem 4 implies that
+πc(G) ≤ |W| + 2m = n − �
+i deg(ui) + m; this follows from setting S = W ∪ U and S′ = U. In fact, the
+resulting placement of cops is a roman dominating set of G, defined in [9] as a {0, 1, 2}-labeling of V (G) so
+that every vertex labeled 0 is adjacent to some vertex labeled 2. They define the roman domination number
+γR(G) to be the minimum sum of labels of a roman dominating set. Hence we obtain the following bound.
+Theorem 6. Every graph G satisfies πc(G) ≤ γR(G).
+Theorem 7. Let H be an induced subgraph of a graph G. Then, for any s, if πc(H) ≤ n(H) − s then
+πc(G) ≤ n(G) − s.
+Proof. Suppose that πc(H) ≤ n(H) − s. Then there is a configuration CH of n(H) − s cops on H that
+captures any robber on H. Define the configuration CG of n(G) − s cops on G by placing one cop on each
+vertex of G − H and CH(v) cops on each vertex v ∈ H. Then CH captures any robber on G.
+Corollary 8. For all s ≥ 2 there is an N = N(s) such that every graph G with n = n(G) ≥ N has
+πc(G) ≤ n − s.
+7
+
+Proof. Suppose that πc(G) ≥ n − s + 1. Then Corollary 5 implies that ∆(G) ≤ s. Consider if diam(G) ≥ 3s.
+Then there exists an induced path P of length 3s in G. By Theorem 17 we have πc(P3s) = 2s ≤ 2s + 1 =
+n(P) − s. By Theorem 7, we must have that πc(G) ≤ n − s, contradicting our assumption that πc(G) ≥
+n − s + 1. Thus, we conclude that diam(G) < 3s. Since there are finitely many (at most ∆(G)diam(G)) such
+graphs, there must be some N such that πc(G) ≤ n − s for all s ≥ N.
+Define the cop deficiency of a graph G to be ¨Ic(G) := n(G) − πc(G). Then Theorem 7 and Corollary 8
+can be restated as follows.
+Theorem 9. Let H be an induced subgraph of a graph G. Then ¨Ic(G) ≥ ¨Ic(H).
+Corollary 10. For all s ≥ 2 there is an N = N(s) such that every graph G with n = n(G) ≥ N has
+¨Ic(G) ≥ s.
+Theorem 11. If G is a cop-win graph with capt(G) = t, then πc(G) ≤ 2t. More generally, if c(G) = k and
+captk(G) = t then πc(G) ≤ k2t.
+Proof. If G is a cop-win graph with capt(G) = t, then there is some vertex v at which the cop begins and
+the robber can be caught with free steps in at most t moves. If 2t cops are placed on v, the cops can use
+the same capture strategy, and there will be sufficiently many cops for up to t pebbling steps. Similarly, by
+placing 2t on each of c(G) cops, there will be sufficiently many cops for up to t rounds of pebbling steps.
+For example, let T be a complete k-ary tree of depth t. Then capt(T ) = t by Result 3, and so πc(T ) ≤ 2t.
+Theorem 11 is tight for some graphs, as witnessed by any graph G with a dominating vertex (see Corollary
+15, below). It is also tight for any complete k-ary tree of depth two, when k ≥ 3 (see Corollary 19, below).
+Corollary 12. If G is a chordal graph with radius r, then πc(G) ≤ 2r.
+Proof. Follows from Result 3 and Theorem 11.
+Theorem 13. If T is an n-vertex tree, then πc(T ) ≤ ⌈ 2n
+3 ⌉.
+Proof. Consider a maximum length path P in T . Let z be an endpoint of P (necessarily a leaf), let y be the
+neighbor of z, and let x be the other neighbor of y on P.
+Base case: For n = 3, the only tree is P3. Place two cops on the central vertex, and the robber will be
+caught on the cops’ first move.
+Inductive Step: Assume that for trees with n < k vertices, πc(T ) ≤ ⌈ 2n
+3 ⌉. If d(y) > 2, form a new tree
+T ′ = T − {z} − {y} − ({N[y] − {x})}. By our inductive hypothesis, we can distribute the cops in such a way
+8
+
+that the robber is caught if the robber starts on T ′. By placing two cops on y, we can also ensure that the
+robber is caught on the first move if the robber starts on T − T ′.
+On the other hand, if d(x) = d(y) = 2, form a new tree T ′ = T − {x, y, z}. By our inductive hypothesis,
+we can distribute the cops in such a way that the robber is caught if the robber starts on T ′. By placing
+two cops on y, we can also ensure that the robber is caught if the robber starts on T − T ′.
+If d(y) = 2 and d(x) > 2, and x has a leaf neighbor u, form a new tree T ′ = T − {u, y, z}. By our
+inductive hypothesis, we can distribute the cops in some distribution D′ so that the robber is caught if the
+robber starts on T ′. By placing two cops on y, we can also ensure that the robber is caught if the robber
+starts on vertices y or z. To capture a robber on u, one cop can reach x from D′, and another cop can reach
+x from y. We then can reach x from u.
+Finally, suppose d(y) = 2 and d(x) > 2, and x has no leaf neighbor u. Denote the neighborhood of x
+which is not on P as N[x ∩ P c] = N2[x] ∩ T [V (T ) \ V (P)], and let u ∈ N[x] ∩ T [V (T ) \ V (P)]. Since P has
+maximum length, N[u] − {x} consists only of leaves. Let v ∈ N[u] − {x}, and let T ′ = T − {v, y, z}. By
+our inductive hypothesis, we can distribute the cops in some distribution D′ that the robber is caught if the
+robber starts on T ′. If two cops can reach x in T ′, we can add 2 more cops to x to catch the robber on the
+vertices {v, y, z}. If two cops can reach u in T ′, then v and x are reachable, so we can add 2 more cops to y
+to catch the robber on the vertices {x, z}. Last, if two cops cannot reach x or u, then no sequences of cop
+moves in T ′ will use the edge uv (otherwise, we would be able to get two cops on at least one of the two
+vertices). Thus, we can simultaneously get one cop on x and one cop on u. By adding two cops onto y, the
+cops can reach the vertices {v, y, z}.
+Note that, on a tree, cops move greedily toward the robber, so if a cop p can reach a vertex v then the
+robber cannot ever occupy v, as the robber has no access to v except through p. Hence if G is a tree then
+πc(G) = π∗(G). We note that Theorems 11 and 13 can each be stronger then each other, as the following
+two examples show.
+Example 2. For integers k and d, the spider S = S(k, d) has c(S) = 1 and capt(S) = d, with n = kd + 1.
+Thus Theorem 11 yields πc(S) ≤ 2d, while Theorem 13 yields πc(S) ≤ ⌈(2kd + 2)/3⌉. Hence one bound is
+stronger than the other depending on how k compares, roughly, to 3 · 2d−1/d.
+Example 3. For integers k, t ≥ 1, let T be a complete k-ary tree of depth t. Then n(T ) = �t
+i=0 ki =
+(kt+1 − 1)/(k − 1). Thus Theorem 11 is stronger than Theorem 13 for k ≥ 3 and for k = 2 with t ≥ 2, while
+Theorem 13 is stronger than Theorem 11 when k = 1 and t ≥ 5 (because capt(Pt) = ⌈t/2⌉).
+Theorem 14. For any positive integer d, if G is a graph with gir(G) ≥ 4d − 1, then πc(G) ≤ 2dγd(G).
+9
+
+Proof. Let S = {v1, v2, ...} be a minimum d-distance dominating set of G, and place 2d cops on each vi.
+Suppose the robber starts at vertex v. Since gir(G) ≥ 4d − 1, we know that T = Nd[u] is a tree for all u. We
+write Ti = Nd[vi] and, for each v ∈ T , denote the unique vu-path in T by Pv.
+Let J be such that T ∩ Tj ̸= ∅ if and only if j ∈ J, and set Qj = T ∩ Tj. Note that gir(G) ≥ 4d − 1
+implies that, for each j ∈ J, there is some v ∈ T such that Qj ⊆ Pv. Moreover, by the definition of S, we
+have ∪j∈JQj = T . In addition, gir(G) ≥ 4d − 1 implies that, for each j ∈ J, the shortest viv-path P ∗
+i is
+unique.
+For each j ∈ J, each cop at vj adopts the strategy to move at each turn toward v along P ∗
+i until reaching
+T , at which time then moving toward the robber along the unique path in T . This strategy ensures the
+property that, at any point in the game, if some cop is on vertex x while the robber is on vertex z, then
+the robber can never move to a vertex y for which the unique yz-path in T contains x — which includes x
+itself. It also implies that the game will last at most d turns. Hence, if we suppose that the robber wins
+the game, then the game lasted exactly d turns and the robber now sits on some vertex z. However, by the
+definition of S, some cop reached z within d turns, which implies by the property just mentioned that the
+robber cannot move to z, a contradiction. Hence the cops win the game, capturing the robber.
+An obvious corollary (recorded as Corollary 15, below) is that any graph G with a dominating vertex has
+πc(G) = 2.
+We remark that Theorem 14 applies to trees. P5 is an example for which this bound is tight. In the case
+of the spider S(k, 2), this bound is significantly better than Corollary 5 when k is large. The case d = 1
+yields the same upper bound of 2γ(T ) from Theorem 4, which is better than the bound of Theorem 13 if
+and only if γ(T ) < ⌈(n− 1)/3⌉. Since γ(T ) can be as high as n/2, both theorems are relevant. The following
+example shows that Theorem 14 can be stronger than Theorem 13 for any d.
+Example 4. For 1 ≤ i ≤ 3, define the tree Ti to be the complete binary tree of depth d − 1, rooted at vertex
+vi, and define the tree T to be the union of the three Ti with an additional root vertex adjacent to each vi.
+Then γd(T ) = d, and n = 3(2d − 1) + 1, so that the bound from Theorem 14 is stronger than the bound from
+Theorem 13.
+Theorem 14 can be stronger than other prior bounds as well, as shown by the following example.
+Example 5. For integers k and d, define the theta graph Θ(k, d) as the union of k internally disjoint xy-
+paths, each of length d. Then Θ = Θ(k, 2d) has n = k(d − 1) + 2, c(Θ) = 2, capt2(Θ) = d, gir(Θ) = 4d,
+γ(Θ) = k⌈(2d−3)/3⌉, and γd = 2. Thus Theorem 4 yields an upper bound of roughly 4kd/3, while Theorems
+11 and 14 both yield the upper bound of 2d+1, which is better or worse than Theorem 4 when k is bigger or
+less than, roughly, 3 · 2d−1/d.
+10
+
+The following example illustrates the need for stronger bounds than given by Theorem 14.
+Example 6. Consider the (3, 7)-cage McGee graph M, defined by V = {vi | i ∈ Z24}, with vi ∼ vi+1
+for all i, vi ∼ vi+12 for all i ≡ 0 (mod 3), and vi ∼ vi+7 for all i ≡ 1 (mod 3). We have γ2(M) ≤ 4
+(e.g. {v0, v6, v9, v15}), and so π∗(M) ≤ πc(M) ≤ 16 by Theorem 14. However, this bound is not tight, as
+πc(M) ≤ 12: the vertex set {vi | i ≡ 0 (mod 3)} induces a matching of size 4 — for each edge, place 2 cops
+on one of its vertices and 1 cop on the other. Incidentally, this yields π∗(M) ≤ 12; the best known lower
+bound on π∗ comes from Result 10: π∗(M) ≥ ⌈ˆπ∗(M)⌉ = ⌈64/7⌉ = 10. Hence we are left with a gap in the
+bounds for M: 10 ≤ π∗(M) ≤ πc(M) ≤ 12.
+2.3
+Exact Results
+The following is a corollary of Theorem 4, as well as of Theorem 14.
+Corollary 15. If G is a graph with a dominating vertex then πc(G) = 2.
+The following is a corollary of Results 6 and Theorem 7.
+Corollary 16. Almost all cop-win graphs G have πc(G) = 2.
+Theorem 17. For all n ≥ 1 we have πc(Pn) = πc(Cn) = ⌈ 2n
+3 ⌉.
+Proof. We have from Theorem 2 that πc(Pn) ≥ π∗(Pn) = ⌈ 2n
+3 ⌉ and πc(Cn) ≥ π∗(Cn) = ⌈ 2n
+3 ⌉.
+We have from Theorem 13 that πc(Pn) ≤ ⌈ 2n
+3 ⌉. For Cn, partition Cn into ⌊ n
+3 ⌋ copies of P3 and, possibly,
+an extra P1 or P2. Place two cops on the center vertex of each P3, and one cop on each vertex of the
+remaining one or two vertices. The robber can only choose to start on one of the copies of P3, where he is
+next to a pair of cops, and so will be captured on the first move. Thus πc(Cn) ≤ ⌈ 2n
+3 ⌉.
+Theorem 18. If T is a tree with rad(T ) = 2 and diam(T ) = 4 then πc(T ) = 4.
+Proof. The upper bound follows from Result 3 and Theorem 11. The lower bound follows from Theorem 17
+since T contains P5.)
+Corollary 19. If T is a complete k-ary tree of depth 2 with k ≥ 3, then πc(T ) = 4.
+3
+Cartesian Products
+For graphs G and H we define the Cartesian product G�H by having vertices V (G) × V (H) and edges
+(u, v)(w, x) with either uw ∈ E(G) and v = x or u = w and vx ∈ E(H).
+11
+
+Theorem 20. For every graph G we have πc(G�Kt) ≤ tπc(G).
+Proof. Let C be a configuration of πc(G) cops on G that can capture any robber. Define the configuration
+C′ on G�Kt by C′(u, v) = C(u) for all u ∈ V (G) and v ∈ V (Kt); then |C′| = t|C|. Let C′
+v be the restriction
+of C′ to the vertices Vv = {(u, v) | u ∈ V (G)}. Then each C′
+v is a copy of C on Vv. Now imagine, for
+any robber on some vertex (u, v), placing a copy of the robber on each vertex (u′, v) and maintaining that
+property with every robber movement. Then the cops on each Vv will move in unison to catch their copy of
+the robber in Vv, one of which is the real robber.
+When G = Pm and t = 2, Theorems 17 and 20 yields πc(Pm�K2) ≤ 2⌈ 2m
+3 ⌉. However, it is not difficult to
+see that πc(Pm�K2) ≤ m + 1. Indeed, label the vertices {vi,j | i ∈ Zm, j ∈ Z2} and define the configuration
+C by C(v0,0) = 1, C(Vi,1) = 2 for all i ≡ 1 (mod 4), and C(vi,0) = 2 for all i ≡ 3 (mod 4). If m is odd then
+also define C(vi,m−1) = 1 for i = (m + 1)/2 mod 2. Then |C| = m + 1 and, since the set of vertices with
+pebbles on them is a dominating set, C can catch any robber.
+A famous conjecture of Graham [7] postulates that every pair of graphs G and H satisfy π(G�H) ≤
+π(G)π(H). This relationship was shown by Shiue to hold for optimal pebbling.
+Theorem 21. [21] Every pair of graphs G and H satisfy π∗(G�H) ≤ π∗(G)π∗(H).
+One might ask whether or not the analogous relationship holds between πc(G�H) and πc(G)πc(H).
+Theorem 20 shows that this is true for H = K2. However, the inequality is false in general, as the following
+theorem shows. For any graph G define G1 = G and Gd = G�Gd−1 for d > 1.
+Theorem 22. There exist graphs G and H such that πc(G�H) > πc(G)πc(H).
+Proof. Suppose that πc(G�H) ≤ πc(G)πc(H) for all G and H. For fixed k ≥ 2, let d ≥ 25k2, v ∈ V (Cd
+k),
+and m = �
+u∈V (Cd
+k) 2−dist(u,v). Then
+√
+d > ln d, so that d/ ln d >
+√
+d ≥ 5k >
+2
+ln(3/2)k, which implies that
+12
+
+d2k < (3/2)d. Also d ≥
+�
+k/8 + 2, so that
+�
+k/8 ≥ d − 2. Thus
+�2
+3
+�d
+�
+u∈V (Cd
+k)
+2−dist(u,v) ≤
+�2
+3
+�d kd/2
+�
+i=0
+�i + k − 1
+k − 1
+�
+2−i
+≤
+�2
+3
+�d kd/2
+�
+i=0
+�i + k − 1
+k − 1
+�
+≤
+�2
+3
+�d �kd/2 + k
+k
+�
+≤
+�2
+3
+�d
+(kd/2 + k)k/k!
+≤
+�2
+3
+�d
+(d + 2)k�
+k/2
+k2−k
+≤
+�2
+3
+�d
+(d + 2)k(d − 2)k
+≤
+�2
+3
+�d
+d2k
+< 1.
+Therefore we would have
+πc(P d
+k ) ≤ πc(Pk)d ≤
+�2
+3k
+�d
+=
+�2
+3
+�d
+n(P d
+k ) < n(Cd
+k)/m = ˆπ∗(Cd
+k) ≤ ˆπ∗(P d
+k ) ≤ π∗(P d
+k ),
+by Fact 9 and Theorem 10. This, however, contradicts Theorem 2.
+4
+Open Questions
+Theorem 3 shows one potential way to find a graph with larger cop number than optimal pebbling number.
+But can such a graph be found by a different method?
+Question 23. Is there a graph G that satisfies c(G) > π∗(G)?
+Question 24. Is it true that πc(Pm�P2) = m + 1 for all m ≥ 1?
+Question 25. Result 7 and Theorem 4 yield πc(Pm�Pn) ≤ 2
+�
+(n+2)(m+2)
+5
+�
+− 8 for all 16 ≤ n ≤ m. Can
+this bound be improved?
+The argument in the proof of Theorem 22 shows that, for any constant a < 3/2, there exists a large
+enough d = d(a) so that P d
+k is a counterexample to the statement that πc(G�H) ≤ aπc(G)πc(H). This begs
+two questions.
+13
+
+Question 26. Is there an infinite family of graphs G for which πc(G�H) ≤ πc(G)πc(H) for all G, H ∈ G?
+Question 27. Is there some constant a ≥ 3/2 such that πc(G�H) ≤ aπc(G)πc(H) for all G and H?
+In addition to chordal graphs and cartesian products discussed above, it would be interesting to study
+other graph classes. It was proved in [8] that c(G) ≤ 2 for outerplanar G, and in [1] that c(G) ≤ 3 for planar
+G.
+Problem 28. Are there constant upper bounds on πc(G) when G is planar or outerplanar?
+Finally, Meyniel [10] conjectured in 1985 that every graph G on n vertices satisfies c(G) = O(√n). Along
+these lines, we make the following conjecture.
+Conjecture 29. Every graph G on n vertices satisfies πc(G) = O(√n2
+√n).
+References
+[1] M. Aigner and M. Fromme, A game of cops and robbers, Discrete Appl. Math. 8 (1984), 1–11.
+[2] C. Berge, The theory of graphs. (Translated from the 1958 French edition by Alison Doig. Second
+printing of the 1962 first English edition.) Dover Publications, Inc., Mineola, NY, 2001.
+[3] N. Biggs, Graphs with large girth. Eleventh British Combinatorial Conference (London, 1987). Ars
+Combin. 25-C (1988), 73–80.
+[4] A. Bonato, P. Golovach, G. Hahn, and J. Kratochvil, The capture time of a graph, Discrete Math. 309
+(2009), no. 18, 1–666.
+[5] A. Bonato, G. Kemkes, and P. Pra�lat, Almost all cop-win graphs contain a universal vertex, Discrete
+Math. 312 (2012), no. 10, 1652–1657.
+[6] D. Bunde, E. Chambers, D. Cranston, K. Milans, and D. West, Pebbling and optimal pebbling in graphs,
+J. Graph Theory 57 (2008), no. 3, 215–238.
+[7] F.R.K. Chung, Pebbling in hypercubes, SIAM J. Discrete Math. 2 (1989), no. 4, 467–472.
+[8] N.E. Clarke, Constrained cops and robber, Ph. D. Thesis, Dalhousie Univ., 2002.
+[9] E. Cockayne, P. Dreyer, S.M. Hedetniemi, S.T. Hedetniemi, Roman domination in graphs, Discrete
+Math. 278 (2004), no. 1–3, 11–22.
+14
+
+[10] P. Frankl, Cops and robbers in graphs with large girth and Cayley graphs, Discrete Appl. Math 17 (1987),
+no. 3, 301–305.
+[11] T. Gavenˇciak, Cop-win graphs with maximum capture-time, Discrete Math. 310 (2010), no. 10–11,
+1557–1563.
+[12] D. Gon¸calves, A. Pinlou, M. Rao, and S. Thomass´e, The domination number of grids. SIAM J. Discrete
+Math. 25 (2011), no. 3, 1443–1453.
+[13] D. Herscovici, B. Hester, and G. Hurlbert, t-Pebbling and extensions, Graphs Combin. 29 (2013), no.
+4, 955–975.
+[14] A. Kelmans, Optimal packing of induced stars in a graph, Discrete Math. 173 (1997), no. 1–3, 97–127.
+[15] A. Kosowski, B. Li, N. Nisse, and K. Suchan, k-chordal graphs: from cops and robber to compact routing
+via treewidth, Algorithmica 72 (2015), no. 3, 758–777.
+[16] F. Lazebnik, V. Ustimenko, A. Woldar, A new series of dense graphs of high girth, Bull. Amer. Math.
+Soc. (N.S.) 32 (1995), no. 1, 73–79.
+[17] A. Meir and J. W. Moon, Relations between packing and covering numbers of a tree, Pacific J. Math.
+61 (1975), no. 1, 225–233.
+[18] D. Moews, Optimally pebbling hypercubes and powers, Discrete Math. 190 (1998), no. 1–3, 271–276.
+[19] R.J. Nowakowski and P. Winkler, Vertex-to-vertex pursuit in a graph, Discrete Math. 43 (1983) 235–239.
+[20] M.A. Shalu, S. Vijayakumar, T.P. Sandhya, J. Mondal, Induced star partition of graphs, Discrete Appl.
+Math. 319 (2022), 81–91.
+[21] C. L. Shiue, Optimally pebbling graphs, Ph.D. dissertation, Department of Applied Mathematics, Na-
+tional Chiao Tung University (1999), Hsin chu, Taiwan.
+[22] P. Slater, Locating dominating sets and locating-dominating sets, Graph theory, combinatorics, and
+algorithms, Vol. 1, 2 (Kalamazoo, MI, 1992), 1073–1079, Wiley-Intersci. Publ., Wiley, New York, 1995.
+15
+
diff --git a/i9AyT4oBgHgl3EQfkfhZ/content/tmp_files/load_file.txt b/i9AyT4oBgHgl3EQfkfhZ/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e8c7564bf8bf7638d450a3afefcec58132bf67fb
--- /dev/null
+++ b/i9AyT4oBgHgl3EQfkfhZ/content/tmp_files/load_file.txt
@@ -0,0 +1,567 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf,len=566
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='00434v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='CO]  1 Jan 2023  Cops and Robbers Pebbling in Graphs  Joshua Forkin∗  Glenn Hurlbert∗  Dedicated to Oleksandr Stanzhytsky, and others like him  who are doing less mathematics than usual at this time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Abstract  Here we merge the two fields of Cops and Robbers and Graph Pebbling to introduce the new topic  of Cops and Robbers Pebbling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Both paradigms can be described by moving tokens (the cops) along the  edges of a graph to capture a special token (the robber).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In Cops and Robbers, all tokens move freely,  whereas, in Graph Pebbling, some of the chasing tokens disappear with movement while the robber is  stationary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In Cops and Robbers Pebbling, some of the chasing tokens (cops) disappear with movement,  while the robber moves freely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We define the cop pebbling number of a graph to be the minimum number  of cops necessary to capture the robber in this context, and present upper and lower bounds and exact  values, some involving various domination parameters, for an array of graph classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We also offer several  interesting problems and conjectures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  ∗Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, USA  1  1  Introduction  There are numerous versions of moving tokens in a graph for various purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Two popular versions are  called Cops and Robbers and Graph Pebbling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In both cases we have tokens of one type (C) attempting to  capture a token of another type (R), and all token movements occur on the edges of a graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In the former  instance, all tokens move freely, whereas in the latter instance, type R tokens are stationary and type C  movements come at a cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In this paper we merge these two subjects to create Cops and Robbers Pebbling,  wherein type R tokens move freely and type C tokens move at a cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  We define these three paradigms more specifically in Subsection 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='1 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The new graph invariant we  define to study in this paper is the cop pebbling number of a graph, denoted πc(G);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' roughly, this equals  the minimum number of cops necessary to capture the robber in the cops and robbers pebbling paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  In Subsections 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='2–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='4 we present known results about cops and robbers, dominating sets, and optimal  pebbling, respectively, that will be used in the sequel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  We record in Subsections 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='1–2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='3 new theorems  on lower bounds, upper bounds, and exact answers for πc(G), respectively, for a range of graph families,  including paths, cycles, trees, chordal graphs, high girth graphs, and cop-win graphs, as well as, in some  cases, for all graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Section 3 contains theorems for Cartesian products of graphs, and we finish in Section  4 with some natural questions left open from this work, including a version of Meyniel’s Cops and Robbers  Conjecture that may hold in the Cops and Robbers Pebbling world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='1  Definitions  We use several standard notations in graph theory, including V (G)for the set of vertices of a graph G (with  n(G) = |V (G)|), E(G) for its edge set, rad(G) for its radius, diam(G) for its diameter, and gir(G) for its  girth, as well as deg(v) for the degree of a vertex, and dist(u, v) for the distance between vertices u and v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For  a vertex v in a graph G, we use the notations Nd(v) = {u | dist(u, v) < d} and Nd[v] = {u | dist(u, v) ≤ d}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  If d = 1 we drop the subscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We often use T to denote a generic tree, and set Pn, Cn, and Kn to be the  path, cycle, and complete graph on n vertices, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='1  Graph Pebbling  A configuration C of pebbles on a graph G is a function from the vertices of G to the non-negative integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Its size equals |C| = �  v∈G C(v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For adjacent vertices u and v with C(u) ≥ 2, a pebbling step from u to v  removes two pebbles from u and adds one pebble to v, while, when C(u) ≥ 1, a free step from u to v removes  one pebble from u and adds one pebble to v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In the context of moving pebbles, we use the word move to  mean move via pebbling steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  2  The pebbling number of a graph G, denoted π(G), is the minimum number m so that, from any config-  uration of size m, one can move a pebble to any specified target vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The optimal pebbling number of a  graph G, denoted π∗(G), is the minimum number m so that, from some configuration of size m, one can  move a pebble to any specified target vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='2  Cops and Robbers  In cops and robbers, the cops are the pebbles, the robber is the target, and the robber is allowed to move.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  The cops and robbers alternate making moves in turns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' At each turn, any positive number of cops make  one free step, then the robber chooses to make a free step or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In graph pebbling literature, the activity  of moving a pebble to a target is called solving or reaching the target;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' here we use the analogous cops and  robbers terminology of capturing the robber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  The cop number c(G) is defined as the minimum number m so that, from some configuration of m cops,  it is possible to capture any robber via free steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If the cops catch the robber on their tth turn, then we  say that the length of the game is t;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' if the robber wins then the length is infinite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' When c(G) = m, the  m-capture time of G, denoted captm(G), is defined to be the length of the game on G when both cops and  robbers play optimally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' That is, it equals the minimum (over all cop strategies) of the maximum (over all  robber strategies) of the length of the game on G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For graphs of cop number 1, we simply say capture time  and write capt(G) without the subscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  When necessary or convenient to use pronouns, we follow the literature by having female cops and a male  robber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='3  Cop Pebbling  The cop pebbling number πc(G) is defined as the minimum number m so that, from some configuration of m  cops, it is possible to capture any robber via pebbling steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We call an instance of a graph G, configuration  C, and robber vertex v a game, and say that the cops win the game if they can capture the robber;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' else  the robber wins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Note that in standard cops and robbers, the robber must elude capture forever to win the  game, since there is no cost to cop movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' However, since we lose a cop with each pebbling step, the  cops and robbers pebbling game is finite — the robber wins if not captured within |C| − 1 turns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  We may assume that all graphs are simple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Because games on K1 are trivial, we will assume that all  graph components have at least two vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Additionally, because of the following fact, we will restrict our  attention in this paper to connected graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Fact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If G has connected components G1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' , Gk then πc(G) = �k  i=1 πc(Gi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  3  A set S ⊆ V (G) is a distance-d dominating set if ∪v∈SNd[v] = V (S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We denote by γd(G) the size of the  smallest distance-d dominating set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='2  Cop Results  A graph G is cop-win if c(G) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' A vertex u in G is called a corner if there is a vertex v ̸= u such that  N[u] ⊆ N[v].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We say that G is dismantlable if either G is a single vertex or there is a corner u such that  G − u is dismantlable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Note that chordal graphs are dismantlable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Result 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [19] A graph is cop-win if and only if it is dismantlable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Result 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [1] Let t be a positive integer, and let G be a graph with gir(G) ≥ 8t − 3 and δ(G) > d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then  c(G) ≥ dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Result 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [4] If G is a chordal graph with radius r, then capt(G) ≤ r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  This bound is tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For example, P5 has both radius 2 and capt(G) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='3  Dominating Set Results  Result 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [17] If G is a graph on n vertices then γd(G) ≤  n  d+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Define the spider S(k, d) to be the tree having a unique vertex x of degree greater than 2, all k of whose  leaves have distance d from x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The bound in Result 4 can be tight, as witnessed by S(k, d + 1) for any k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Result 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [6] If |Nd[v]| ≥ c for all v ∈ G then γ2d(G) ≤ n/c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Result 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [5] Almost all cop-win graphs G have γ(G) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Result 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [12] If G is an n × m grid such that 16 ≤ n ≤ m, then γ(G) ≤  �  (n+2)(m+2)  5  �  − 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='4  Optimal Pebbling Results  Result 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [6] For every graph G, π∗(G) ≤ ⌈2n/3⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Equality holds when G is a path or cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Fractional pebbling allows for rational values of pebbles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' A fractional pebbling step from vertex u to one  of its neighbors v removes x pebbles from u and adds x/2 pebbles to v, where x is an rational number such  that 0 < x ≤ C(u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The optimal fractional pebbling number of a graph G, denoted ˆπ∗(G), is the minimum  number m so that, from some configuration of size m, one can move, via fractional pebbling moves, a sum  of one pebble to any specified target vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Result 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [13, 18] For every graph G we have π∗(G) ≥ ⌈ˆπ∗(G)⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  4  The authors of [13] prove that ˆπ∗(G) can be calculated by a linear program.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Furthermore, they use this  result to show that there is uniform configuration that witnesses the optimal fractional pebbling number of  any vertex-transitive graph;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' that is, the configuration C defined by C(v) = ˆπ∗(G)/n(G) for all v fractionally  solves any specified vertex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' From this they prove the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Result 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [13] Let G be a vertex-transitive graph and, for any fixed vertex v, define m = �  u∈V (G) 2−dist(u,v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Then ˆπ∗(G) = n(G)/m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Result 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [6] If G is an n-vertex graph with gir(G) ≥ 2s + 1 and δ(G) = k then π∗(G) ≤  22sn  σk(s), where  σk(s) = 1 + k �s  i=1(k − 1)i−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  2  Main Theorems  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='1  Lower Bounds  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For any graph G, πc(G) ≥ c(G), with equality if and only if G = K1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Any configuration of cops that can capture the robber via pebbling steps can also capture the robber  via free steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  If G = K1 then πc(G) = 1 = c(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  If πc(G) = c(G) then capturing the robber requires no steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' That means that a successful pebbling  configuration has no vertex without a pebble;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' πc(G) = n(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' However, if n(G) ≥ 3 then πc(G) < n by  Corollary 5, below, a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If n(G) = 2 then G = K2 and πc(K2) = 2 > 1 = c(K2), a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Hence G = K1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For any graph G, πc(G) ≥ π∗(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Equality holds if G is a tree or cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Any configuration of k cops, where k < π∗(G), will contain a vertex v which is unreachable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The  robber can then choose to start and stay on v and thus not be captured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  If G is a cycle then Theorems 8 and 17 yield the equality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  If G is a tree then place π∗(G) cops according to an optimal pebbling configuration C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The robber  beginning at some vertex v defines a subtree T containing v for which every cop in T is on a leaf of T , and  any leaf of T with no cop is a leaf of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thus the robber can never escape T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Because C can reach every  vertex of T , they can capture the robber, regardless of where he moves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hence πc(G) ≤ π∗(G), and the  equality follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Typically, Theorem 2 gives a sharper lower bound on πc(G) than Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' However, this may not be  true for all graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  5  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If G is a graph with δ(G) = k for some k ≥ 4097, and with gir(G) ≥ 8t − 2 and n(G) ≤ k4t−1  for some t ≥ 3, then c(G) > π∗(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Given G as above, set d = k − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then we have gir(G) ≥ 8t − 3, and so c(G) ≥ dt by Result 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Also,  with s = 4t − 2, we have gir(G) > 2s + 1, and so π∗(G) ≤ 22sn/σδ(s) by Result 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Note that 22sn/σδ(s) <  4sn/ds ≤ (4/d)4t−2(d + 1)4t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thus the result will be proved by showing that (4/d)4t−2(d + 1)4t−1 ≤ dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Since k ≥ 4097 we have d ≥ 212, so that [4(1 + 1/d)]4 < [4(2)]4 = 212 ≤ d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' It is easy to calculate that  [4(1 + 1/d)]4t < dt(16/d)(1 + 1/d) when d = 212 and t = 3, and to observe that the gap in the inequality  grows if either d or t increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' From this it follows that (4/d)4t−2(d + 1)4t−1 ≤ dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  At issue here is that it is not known if there exists a graph that satisfies the hypothesis of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Indeed, Biggs [3] defines a sequence of k-regular graphs {Gi} with increasing n(Gi) to have large girth if  gir(Gi) ≥ α logk−1(n(Gi)) for some constant α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' It is known that α ≤ 2, and the greatest known constant  is a construction of [16] that yields α = 4/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' However, a graph satisfying the hypothesis of Theorem 3  necessarilty has α = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='2  Upper Bounds  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let G be a graph with dominating set S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Suppose that S′ ⊆ S is a dominating set of V (G)−S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Then πc(G) ≤ |S| + |S′|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In particular, πc(G) ≤ 2γ(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Place two cops on each vertex of S′ and one cop on each vertex of S − S′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  In order to not be  immediately captured, the robber must start in V (G) − S, but then is captured in one step by some pair  of cops from S′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The second statement follows from choosing S′ = S to be a minimum dominating set of  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  To illustrate the improvement of |S| + |S′| compared to 2γ(G), consider the following example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Example 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For positive integers m ≥ 2k ≥ 2, let Y = {y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' , ym} and let Q = {Q1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' , Qk} be a partition  of Y with each part size |Qi| ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Define a bipartite graph G with vertices Y , Z = {z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' , zk}, and x as  follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For each 1 ≤ j ≤ k set zj ∼ yi if and only if yi ∈ Qj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Also set x ∼ yi for every 1 ≤ i ≤ m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Then γ(G) = k + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Indeed, since the neighborhoods of each zj are pairwise disjoint, at least k vertices in  Y ∪ Z are required to dominate Z, one from each N[zj].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Suppose that S is a dominating set of size k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By  the above, |S ∩ N[zj]| = 1 for all j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' But to dominate x, some yi must be in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let yi ∈ N(zj);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' then yi does  not dominate any other yi′ ∈ N(zj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hence γ(G) ≥ k + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' It is easy to see that S = Z ∪ {x} is a dominating  set, so that γ(G) = k + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' With this choice of S we have S′ = {x}, so that πc(G) ≤ k + 2, much better than  2γ(G) = 2k + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  6  An obvious corollary of Theorem 4 (recorded as Corollary 15, below) is that any graph G with a domi-  nating vertex has πc(G) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' A more interesting corollary is the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Corollary 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Every graph G satisfies πc(G) ≤ n − ∆(G) + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In particular, if n(G) ≤ 2 then πc(G) = n, if  n(G) ≥ 3 then πc(G) ≤ n − 1, and if n(G) ≥ 6 then πc(G) ≤ n − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let v be a vertex with deg(v) = ∆(G) and set S = V (G)−N[v], with S′ = {v}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then apply Theorem  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Next, it is easy to see that πc(Kn) = n for n ≤ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then, a graph with at least three vertices has a vertex  of degree at least two, so that n − ∆(G) + 1 ≤ n − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Finally, if ∆(G) ≥ 3 then n − ∆(G) + 1 ≤ n − 2, while  if ∆(G) ≤ 2 then G is a path or cycle, for which Theorem 17 yields πc(G) = ⌈ 2n  3 ⌉, which is at most n − 2  when n ≥ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  All three conditional bounds in Corollary 5 are tight: for example, π∗(P2) = 2, π∗(P5) = 4, and π∗(P7) =  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Furthermore, its more general bound of n − ∆(G) + 1 is tight for a graph with a dominating vertex (see  Corollary 15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  A set A of edges of a graph G is called an induced k-star packing of G if every component of the subgraph  G[A] induced by A is a star with at most k edges and is an induced subgraph of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Kelmans [14] showed that  there is a polynomial algorithm for finding a k-star packing that covers the maximum number of vertices  in a graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Of course, this problem is NP-hard if k is not fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Perfect star packings cover all vertices in  a graph, and have been studied in [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Suppose that X = {X1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' , Xm} is a packing of stars in G, with  corresponding centers U = {u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' , um}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If X covers all but the vertices W, then Theorem 4 implies that  πc(G) ≤ |W| + 2m = n − �  i deg(ui) + m;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' this follows from setting S = W ∪ U and S′ = U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In fact, the  resulting placement of cops is a roman dominating set of G, defined in [9] as a {0, 1, 2}-labeling of V (G) so  that every vertex labeled 0 is adjacent to some vertex labeled 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' They define the roman domination number  γR(G) to be the minimum sum of labels of a roman dominating set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hence we obtain the following bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Every graph G satisfies πc(G) ≤ γR(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let H be an induced subgraph of a graph G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then, for any s, if πc(H) ≤ n(H) − s then  πc(G) ≤ n(G) − s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Suppose that πc(H) ≤ n(H) − s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then there is a configuration CH of n(H) − s cops on H that  captures any robber on H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Define the configuration CG of n(G) − s cops on G by placing one cop on each  vertex of G − H and CH(v) cops on each vertex v ∈ H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then CH captures any robber on G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Corollary 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For all s ≥ 2 there is an N = N(s) such that every graph G with n = n(G) ≥ N has  πc(G) ≤ n − s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  7  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Suppose that πc(G) ≥ n − s + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then Corollary 5 implies that ∆(G) ≤ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Consider if diam(G) ≥ 3s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Then there exists an induced path P of length 3s in G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By Theorem 17 we have πc(P3s) = 2s ≤ 2s + 1 =  n(P) − s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By Theorem 7, we must have that πc(G) ≤ n − s, contradicting our assumption that πc(G) ≥  n − s + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thus, we conclude that diam(G) < 3s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Since there are finitely many (at most ∆(G)diam(G)) such  graphs, there must be some N such that πc(G) ≤ n − s for all s ≥ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Define the cop deficiency of a graph G to be ¨Ic(G) := n(G) − πc(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then Theorem 7 and Corollary 8  can be restated as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let H be an induced subgraph of a graph G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then ¨Ic(G) ≥ ¨Ic(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Corollary 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For all s ≥ 2 there is an N = N(s) such that every graph G with n = n(G) ≥ N has  ¨Ic(G) ≥ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If G is a cop-win graph with capt(G) = t, then πc(G) ≤ 2t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' More generally, if c(G) = k and  captk(G) = t then πc(G) ≤ k2t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If G is a cop-win graph with capt(G) = t, then there is some vertex v at which the cop begins and  the robber can be caught with free steps in at most t moves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If 2t cops are placed on v, the cops can use  the same capture strategy, and there will be sufficiently many cops for up to t pebbling steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Similarly, by  placing 2t on each of c(G) cops, there will be sufficiently many cops for up to t rounds of pebbling steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  For example, let T be a complete k-ary tree of depth t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then capt(T ) = t by Result 3, and so πc(T ) ≤ 2t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 11 is tight for some graphs, as witnessed by any graph G with a dominating vertex (see Corollary  15, below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' It is also tight for any complete k-ary tree of depth two, when k ≥ 3 (see Corollary 19, below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Corollary 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If G is a chordal graph with radius r, then πc(G) ≤ 2r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Follows from Result 3 and Theorem 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If T is an n-vertex tree, then πc(T ) ≤ ⌈ 2n  3 ⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Consider a maximum length path P in T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let z be an endpoint of P (necessarily a leaf), let y be the  neighbor of z, and let x be the other neighbor of y on P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Base case: For n = 3, the only tree is P3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Place two cops on the central vertex, and the robber will be  caught on the cops’ first move.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Inductive Step: Assume that for trees with n < k vertices, πc(T ) ≤ ⌈ 2n  3 ⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If d(y) > 2, form a new tree  T ′ = T − {z} − {y} − ({N[y] − {x})}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By our inductive hypothesis, we can distribute the cops in such a way  8  that the robber is caught if the robber starts on T ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By placing two cops on y, we can also ensure that the  robber is caught on the first move if the robber starts on T − T ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  On the other hand, if d(x) = d(y) = 2, form a new tree T ′ = T − {x, y, z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By our inductive hypothesis,  we can distribute the cops in such a way that the robber is caught if the robber starts on T ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By placing  two cops on y, we can also ensure that the robber is caught if the robber starts on T − T ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  If d(y) = 2 and d(x) > 2, and x has a leaf neighbor u, form a new tree T ′ = T − {u, y, z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By our  inductive hypothesis, we can distribute the cops in some distribution D′ so that the robber is caught if the  robber starts on T ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By placing two cops on y, we can also ensure that the robber is caught if the robber  starts on vertices y or z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' To capture a robber on u, one cop can reach x from D′, and another cop can reach  x from y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We then can reach x from u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Finally, suppose d(y) = 2 and d(x) > 2, and x has no leaf neighbor u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Denote the neighborhood of x  which is not on P as N[x ∩ P c] = N2[x] ∩ T [V (T ) \\ V (P)], and let u ∈ N[x] ∩ T [V (T ) \\ V (P)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Since P has  maximum length, N[u] − {x} consists only of leaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let v ∈ N[u] − {x}, and let T ′ = T − {v, y, z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By  our inductive hypothesis, we can distribute the cops in some distribution D′ that the robber is caught if the  robber starts on T ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If two cops can reach x in T ′, we can add 2 more cops to x to catch the robber on the  vertices {v, y, z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If two cops can reach u in T ′, then v and x are reachable, so we can add 2 more cops to y  to catch the robber on the vertices {x, z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Last, if two cops cannot reach x or u, then no sequences of cop  moves in T ′ will use the edge uv (otherwise, we would be able to get two cops on at least one of the two  vertices).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thus, we can simultaneously get one cop on x and one cop on u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' By adding two cops onto y, the  cops can reach the vertices {v, y, z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Note that, on a tree, cops move greedily toward the robber, so if a cop p can reach a vertex v then the  robber cannot ever occupy v, as the robber has no access to v except through p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hence if G is a tree then  πc(G) = π∗(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We note that Theorems 11 and 13 can each be stronger then each other, as the following  two examples show.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For integers k and d, the spider S = S(k, d) has c(S) = 1 and capt(S) = d, with n = kd + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Thus Theorem 11 yields πc(S) ≤ 2d, while Theorem 13 yields πc(S) ≤ ⌈(2kd + 2)/3⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hence one bound is  stronger than the other depending on how k compares, roughly, to 3 · 2d−1/d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For integers k, t ≥ 1, let T be a complete k-ary tree of depth t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then n(T ) = �t  i=0 ki =  (kt+1 − 1)/(k − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thus Theorem 11 is stronger than Theorem 13 for k ≥ 3 and for k = 2 with t ≥ 2, while  Theorem 13 is stronger than Theorem 11 when k = 1 and t ≥ 5 (because capt(Pt) = ⌈t/2⌉).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For any positive integer d, if G is a graph with gir(G) ≥ 4d − 1, then πc(G) ≤ 2dγd(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  9  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let S = {v1, v2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='} be a minimum d-distance dominating set of G, and place 2d cops on each vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Suppose the robber starts at vertex v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Since gir(G) ≥ 4d − 1, we know that T = Nd[u] is a tree for all u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We  write Ti = Nd[vi] and, for each v ∈ T , denote the unique vu-path in T by Pv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Let J be such that T ∩ Tj ̸= ∅ if and only if j ∈ J, and set Qj = T ∩ Tj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Note that gir(G) ≥ 4d − 1  implies that, for each j ∈ J, there is some v ∈ T such that Qj ⊆ Pv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Moreover, by the definition of S, we  have ∪j∈JQj = T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In addition, gir(G) ≥ 4d − 1 implies that, for each j ∈ J, the shortest viv-path P ∗  i is  unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  For each j ∈ J, each cop at vj adopts the strategy to move at each turn toward v along P ∗  i until reaching  T , at which time then moving toward the robber along the unique path in T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' This strategy ensures the  property that, at any point in the game, if some cop is on vertex x while the robber is on vertex z, then  the robber can never move to a vertex y for which the unique yz-path in T contains x — which includes x  itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' It also implies that the game will last at most d turns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hence, if we suppose that the robber wins  the game, then the game lasted exactly d turns and the robber now sits on some vertex z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' However, by the  definition of S, some cop reached z within d turns, which implies by the property just mentioned that the  robber cannot move to z, a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hence the cops win the game, capturing the robber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  An obvious corollary (recorded as Corollary 15, below) is that any graph G with a dominating vertex has  πc(G) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  We remark that Theorem 14 applies to trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' P5 is an example for which this bound is tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' In the case  of the spider S(k, 2), this bound is significantly better than Corollary 5 when k is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The case d = 1  yields the same upper bound of 2γ(T ) from Theorem 4, which is better than the bound of Theorem 13 if  and only if γ(T ) < ⌈(n− 1)/3⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Since γ(T ) can be as high as n/2, both theorems are relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The following  example shows that Theorem 14 can be stronger than Theorem 13 for any d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For 1 ≤ i ≤ 3, define the tree Ti to be the complete binary tree of depth d − 1, rooted at vertex  vi, and define the tree T to be the union of the three Ti with an additional root vertex adjacent to each vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Then γd(T ) = d, and n = 3(2d − 1) + 1, so that the bound from Theorem 14 is stronger than the bound from  Theorem 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 14 can be stronger than other prior bounds as well, as shown by the following example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For integers k and d, define the theta graph Θ(k, d) as the union of k internally disjoint xy-  paths, each of length d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then Θ = Θ(k, 2d) has n = k(d − 1) + 2, c(Θ) = 2, capt2(Θ) = d, gir(Θ) = 4d,  γ(Θ) = k⌈(2d−3)/3⌉, and γd = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thus Theorem 4 yields an upper bound of roughly 4kd/3, while Theorems  11 and 14 both yield the upper bound of 2d+1, which is better or worse than Theorem 4 when k is bigger or  less than, roughly, 3 · 2d−1/d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  10  The following example illustrates the need for stronger bounds than given by Theorem 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Example 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Consider the (3, 7)-cage McGee graph M, defined by V = {vi | i ∈ Z24}, with vi ∼ vi+1  for all i, vi ∼ vi+12 for all i ≡ 0 (mod 3), and vi ∼ vi+7 for all i ≡ 1 (mod 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We have γ2(M) ≤ 4  (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' {v0, v6, v9, v15}), and so π∗(M) ≤ πc(M) ≤ 16 by Theorem 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' However, this bound is not tight, as  πc(M) ≤ 12: the vertex set {vi | i ≡ 0 (mod 3)} induces a matching of size 4 — for each edge, place 2 cops  on one of its vertices and 1 cop on the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Incidentally, this yields π∗(M) ≤ 12;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' the best known lower  bound on π∗ comes from Result 10: π∗(M) ≥ ⌈ˆπ∗(M)⌉ = ⌈64/7⌉ = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hence we are left with a gap in the  bounds for M: 10 ≤ π∗(M) ≤ πc(M) ≤ 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='3  Exact Results  The following is a corollary of Theorem 4, as well as of Theorem 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Corollary 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If G is a graph with a dominating vertex then πc(G) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  The following is a corollary of Results 6 and Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Corollary 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Almost all cop-win graphs G have πc(G) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For all n ≥ 1 we have πc(Pn) = πc(Cn) = ⌈ 2n  3 ⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' We have from Theorem 2 that πc(Pn) ≥ π∗(Pn) = ⌈ 2n  3 ⌉ and πc(Cn) ≥ π∗(Cn) = ⌈ 2n  3 ⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  We have from Theorem 13 that πc(Pn) ≤ ⌈ 2n  3 ⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For Cn, partition Cn into ⌊ n  3 ⌋ copies of P3 and, possibly,  an extra P1 or P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Place two cops on the center vertex of each P3, and one cop on each vertex of the  remaining one or two vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The robber can only choose to start on one of the copies of P3, where he is  next to a pair of cops, and so will be captured on the first move.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thus πc(Cn) ≤ ⌈ 2n  3 ⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If T is a tree with rad(T ) = 2 and diam(T ) = 4 then πc(T ) = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The upper bound follows from Result 3 and Theorem 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' The lower bound follows from Theorem 17  since T contains P5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=')  Corollary 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If T is a complete k-ary tree of depth 2 with k ≥ 3, then πc(T ) = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  3  Cartesian Products  For graphs G and H we define the Cartesian product G�H by having vertices V (G) × V (H) and edges  (u, v)(w, x) with either uw ∈ E(G) and v = x or u = w and vx ∈ E(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  11  Theorem 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For every graph G we have πc(G�Kt) ≤ tπc(G).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let C be a configuration of πc(G) cops on G that can capture any robber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Define the configuration  C′ on G�Kt by C′(u, v) = C(u) for all u ∈ V (G) and v ∈ V (Kt);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' then |C′| = t|C|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Let C′  v be the restriction  of C′ to the vertices Vv = {(u, v) | u ∈ V (G)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then each C′  v is a copy of C on Vv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Now imagine, for  any robber on some vertex (u, v), placing a copy of the robber on each vertex (u′, v) and maintaining that  property with every robber movement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then the cops on each Vv will move in unison to catch their copy of  the robber in Vv, one of which is the real robber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  When G = Pm and t = 2, Theorems 17 and 20 yields πc(Pm�K2) ≤ 2⌈ 2m  3 ⌉.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' However, it is not difficult to  see that πc(Pm�K2) ≤ m + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Indeed, label the vertices {vi,j | i ∈ Zm, j ∈ Z2} and define the configuration  C by C(v0,0) = 1, C(Vi,1) = 2 for all i ≡ 1 (mod 4), and C(vi,0) = 2 for all i ≡ 3 (mod 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' If m is odd then  also define C(vi,m−1) = 1 for i = (m + 1)/2 mod 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then |C| = m + 1 and, since the set of vertices with  pebbles on them is a dominating set, C can catch any robber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  A famous conjecture of Graham [7] postulates that every pair of graphs G and H satisfy π(G�H) ≤  π(G)π(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' This relationship was shown by Shiue to hold for optimal pebbling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' [21] Every pair of graphs G and H satisfy π∗(G�H) ≤ π∗(G)π∗(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  One might ask whether or not the analogous relationship holds between πc(G�H) and πc(G)πc(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 20 shows that this is true for H = K2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' However, the inequality is false in general, as the following  theorem shows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For any graph G define G1 = G and Gd = G�Gd−1 for d > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Theorem 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' There exist graphs G and H such that πc(G�H) > πc(G)πc(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Suppose that πc(G�H) ≤ πc(G)πc(H) for all G and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' For fixed k ≥ 2, let d ≥ 25k2, v ∈ V (Cd  k),  and m = �  u∈V (Cd  k) 2−dist(u,v).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Then  √  d > ln d, so that d/ ln d >  √  d ≥ 5k >  2  ln(3/2)k, which implies that  12  d2k < (3/2)d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Also d ≥  �  k/8 + 2, so that  �  k/8 ≥ d − 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thus  �2  3  �d  �  u∈V (Cd  k)  2−dist(u,v) ≤  �2  3  �d kd/2  �  i=0  �i + k − 1  k − 1  �  2−i  ≤  �2  3  �d kd/2  �  i=0  �i + k − 1  k − 1  �  ≤  �2  3  �d �kd/2 + k  k  �  ≤  �2  3  �d  (kd/2 + k)k/k!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  ≤  �2  3  �d  (d + 2)k�  k/2  k2−k  ≤  �2  3  �d  (d + 2)k(d − 2)k  ≤  �2  3  �d  d2k  < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Therefore we would have  πc(P d  k ) ≤ πc(Pk)d ≤  �2  3k  �d  =  �2  3  �d  n(P d  k ) < n(Cd  k)/m = ˆπ∗(Cd  k) ≤ ˆπ∗(P d  k ) ≤ π∗(P d  k ),  by Fact 9 and Theorem 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' This, however, contradicts Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  4  Open Questions  Theorem 3 shows one potential way to find a graph with larger cop number than optimal pebbling number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  But can such a graph be found by a different method?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Question 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Is there a graph G that satisfies c(G) > π∗(G)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Question 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Is it true that πc(Pm�P2) = m + 1 for all m ≥ 1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Question 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Result 7 and Theorem 4 yield πc(Pm�Pn) ≤ 2  �  (n+2)(m+2)  5  �  − 8 for all 16 ≤ n ≤ m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Can  this bound be improved?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  The argument in the proof of Theorem 22 shows that, for any constant a < 3/2, there exists a large  enough d = d(a) so that P d  k is a counterexample to the statement that πc(G�H) ≤ aπc(G)πc(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' This begs  two questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  13  Question 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Is there an infinite family of graphs G for which πc(G�H) ≤ πc(G)πc(H) for all G, H ∈ G?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Question 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Is there some constant a ≥ 3/2 such that πc(G�H) ≤ aπc(G)πc(H) for all G and H?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  In addition to chordal graphs and cartesian products discussed above, it would be interesting to study  other graph classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' It was proved in [8] that c(G) ≤ 2 for outerplanar G, and in [1] that c(G) ≤ 3 for planar  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Problem 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Are there constant upper bounds on πc(G) when G is planar or outerplanar?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Finally, Meyniel [10] conjectured in 1985 that every graph G on n vertices satisfies c(G) = O(√n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Along  these lines, we make the following conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Conjecture 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Every graph G on n vertices satisfies πc(G) = O(√n2  √n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  References  [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Aigner and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Fromme, A game of cops and robbers, Discrete Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 8 (1984), 1–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Berge, The theory of graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' (Translated from the 1958 French edition by Alison Doig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Second  printing of the 1962 first English edition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=') Dover Publications, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=', Mineola, NY, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [3] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Biggs, Graphs with large girth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Eleventh British Combinatorial Conference (London, 1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Ars  Combin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 25-C (1988), 73–80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Bonato, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Golovach, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hahn, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Kratochvil, The capture time of a graph, Discrete Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 309  (2009), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 18, 1–666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Bonato, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Kemkes, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Pra�lat, Almost all cop-win graphs contain a universal vertex, Discrete  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 312 (2012), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 10, 1652–1657.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [6] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Bunde, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Chambers, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Cranston, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Milans, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' West, Pebbling and optimal pebbling in graphs,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Graph Theory 57 (2008), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 3, 215–238.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [7] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Chung, Pebbling in hypercubes, SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Discrete Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 2 (1989), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 4, 467–472.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [8] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Clarke, Constrained cops and robber, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thesis, Dalhousie Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=', 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [9] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Cockayne, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Dreyer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hedetniemi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hedetniemi, Roman domination in graphs, Discrete  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 278 (2004), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 1–3, 11–22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  14  [10] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Frankl, Cops and robbers in graphs with large girth and Cayley graphs, Discrete Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Math 17 (1987),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 3, 301–305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [11] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Gavenˇciak, Cop-win graphs with maximum capture-time, Discrete Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 310 (2010), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 10–11,  1557–1563.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [12] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Gon¸calves, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Pinlou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Rao, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Thomass´e, The domination number of grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Discrete  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 25 (2011), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 3, 1443–1453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Herscovici, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hester, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Hurlbert, t-Pebbling and extensions, Graphs Combin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 29 (2013), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  4, 955–975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Kelmans, Optimal packing of induced stars in a graph, Discrete Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 173 (1997), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 1–3, 97–127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Kosowski, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Li, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Nisse, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Suchan, k-chordal graphs: from cops and robber to compact routing  via treewidth, Algorithmica 72 (2015), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 3, 758–777.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [16] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Lazebnik, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Ustimenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Woldar, A new series of dense graphs of high girth, Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' (N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=') 32 (1995), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 1, 73–79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Meir and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Moon, Relations between packing and covering numbers of a tree, Pacific J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  61 (1975), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 1, 225–233.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [18] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Moews, Optimally pebbling hypercubes and powers, Discrete Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 190 (1998), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 1–3, 271–276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Nowakowski and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Winkler, Vertex-to-vertex pursuit in a graph, Discrete Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 43 (1983) 235–239.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Shalu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Vijayakumar, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Sandhya, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Mondal, Induced star partition of graphs, Discrete Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 319 (2022), 81–91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [21] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Shiue, Optimally pebbling graphs, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' dissertation, Department of Applied Mathematics, Na-  tional Chiao Tung University (1999), Hsin chu, Taiwan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  [22] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Slater, Locating dominating sets and locating-dominating sets, Graph theory, combinatorics, and  algorithms, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' 1, 2 (Kalamazoo, MI, 1992), 1073–1079, Wiley-Intersci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content=', Wiley, New York, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
+page_content='  15' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/i9AyT4oBgHgl3EQfkfhZ/content/2301.00434v1.pdf'}
diff --git a/iNFMT4oBgHgl3EQf4jES/content/tmp_files/2301.12452v1.pdf.txt b/iNFMT4oBgHgl3EQf4jES/content/tmp_files/2301.12452v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2f85d221488fcf5db45248956426c234a2215571
--- /dev/null
+++ b/iNFMT4oBgHgl3EQf4jES/content/tmp_files/2301.12452v1.pdf.txt
@@ -0,0 +1,4381 @@
+arXiv:2301.12452v1  [math.AG]  29 Jan 2023
+COX RINGS OF MORPHISMS AND RESOLUTION OF
+SINGULARITIES
+JAROS�LAW W�LODARCZYK
+Abstract. We extend the Cox-Hu-Keel construction of the Cox rings to any
+proper birational morphisms of normal schemes. It allows the representation
+of any proper birational morphism by a map of schemes with mild singularities
+with torus actions.
+In a particular case, the notion generalizes the combinatorial construction
+of Satriano [Sat13] and the recent construction of multiple weighted blow-ups
+on Artin-stacks by Abramovich-Quek [AQ21].
+The latter can be viewed as an extension of stack theoretic blow-ups by
+Abramovich, Temkin and W�lodarczyk [ATW19], a similar construction of Mc-
+Quillan [McQ19] and and the author’s recent cobordant recent cobordant blow-
+ups [W�lo22] at weighted centers to a more general situation of arbitrary locally
+monomial centers.
+We show some applications of this operation to the resolution of singulari-
+ties over a field of any characteristic.
+1. Introduction
+The importance of Gm-actions in birational geometry and their connection with
+the Mori theory was already discovered by Reid, Thaddeus, and many others (see
+[Tha94a], [Tha94b], [Tha96], [Rei], [DH98]). This was also reflected in the proof of
+the Weak Factorization theorem, which relied on the notion of birational cobordism
+and a critical role of Gm-action [W�lo00], [W�lo03], [AKMW02].
+The idea of the birational cobordism from [W�lo00] is to construct a smooth
+scheme with Gm-action which represents a proper birational morphism and parametrizes
+possible birational elementary modifications such as blow-ups, blow-downs, and
+flips. This allows decomposing the proper birational maps of smooth varieties into
+a sequence of blow-ups and blow-downs with smooth centers.
+A similar idea was considered shortly after by Hu-Keel [HK00], who constructed
+their Mori dream space, parametrizing possible birational modifications in the Mori
+program via torus actions. The Mori dream space plays a vital role in the Mori
+theory. One of the key ingredients in constructing the Mori dream space is the Cox
+rings.
+Recall that the Cox rings for toric varieties were considered first by Cox in
+[Cox95].
+The main idea of the construction comes from the convex geometry:
+Any polyhedral complex can be realized as the image of the simplicial complex.
+Similarly, any fan in toric geometry can be represented as the image of the subfan of
+a regular cone. This simple observation leads to the fundamental formula describing
+Date: January 31, 2023.
+This research is supported by BSF grant 2014365.
+1
+
+2
+J. W�LODARCZYK
+the Cox coordinate ring of tor the toric variety X as
+C(X) :=
+�
+D∈Cl(X)
+H0(X, OX(D)),
+where Cl(X) is the Weil divisor class group. The action of torus T = Spec Z[Cl(X)]
+naturally occurs in the construction, and is determined by the Cl(X)-gradation.
+The Cox formula generalizes the construction of the coordinate ring of the pro-
+jective scheme X = Pn
+Z, namely
+Z[x0, . . . , xn] =
+�
+n∈Z
+H0(X, OX(n))
+The projective space X = Pn can be seen as the geometric quotient of the
+characteristic space
+ˆX = SpecX(
+�
+D∈Cl(X)
+OX(D) → X,
+introduced in [ADHL15]. The characteristic space ˆX comes with the natural em-
+bedding ˆX ֒→ X into the coordinate space:
+X := Spec(
+�
+D∈Cl(X)
+H0(X, OX(D))
+In particular, for X = Pn we obtain
+ˆX = An+1
+Z
+∖ {0} ֒→ X = An+1
+Z
+This leads to the standard Proj -construction:
+Proj(Z[x0, . . . , xn])
+=
+(Spec(Z[x0, . . . , xn] ∖ V (x0, . . . , xn))/Gm
+∥
+∥
+X
+=
+ˆX/T,
+.
+In this paper, we introduce the idea of the Cox rings of the proper birational
+morphisms and propose a more general approach to embedded resolution prob-
+lems in the language of torus actions, extending the ideas of McQuillan [McQ19]
+and Abramovich-Temkin-W�lodarczyk [ATW19] of the weighted resolution, and
+Abramovich-Quek [AQ21] of the multiple weighted resolutions.
+The idea of utilizing group actions to resolve singularities is ancient and should be
+traced back to Newton. In the method that he developed, known later as Newton-
+Puiseau theorem, he shows that any polynomial function f(x, y) on X = C2 with
+expansion containing the term yr can be, in fact, upon a coordinate change, resolved
+by a Newton-Puiseau series y = g(x1/k). In other words one considers the space
+X′ = C2 with the group action of µk = ⟨ξ⟩, ξ(x, y) = (ξ · x, y), giving the quotient
+X′ → X, (x, y) �→ (xk, y), and a smooth holomorphic branch V (y − g(x1/k)) on X′
+parametrizing subspace V (f) on X.
+Originally in the Hironaka embedded resolution, only smooth centers were used
+(see [Hir64],[Vil89],[BM97],[W�lo05],[EH02], [EV03], [Kol07]). In the recent papers
+[ATW17], [ATW20] in the resolution process of logarithmic schemes and morphisms,
+we considered the stack-theoretic blow-ups of the centers of the form
+J = (u1, . . . , uk, m1/w1
+1
+, . . . , m1/wr
+r
+),
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+3
+in the context of Kummer ´etale topology on the logarithmic stacks. The functorial
+properties of the algorithm of logarithmic resolution of morphisms dictated such
+general centers.
+Then in [ATW19], we developed the formalism of the stack-theoretic blow-ups
+of the weighted centers of the form (u1/w1
+1
+, . . . , u1/wk
+k
+). This approach allows to
+simplify the resolution procedure in characteristic zero.
+The algorithm is more
+efficient and avoids many unnecessary blow-ups reducing technicalities. It uses a
+very simple geometric invariant, which improves after each step and is indepen-
+dent of the logarithmic structure. A similar result was obtained by McQuillan in
+[McQ19]. More general centers were considered in the paper[Que20] of Quek in the
+logarithmic context.
+In work [AQ21] of Abramovich-Quek, the authors introduce multi-weighted blow-
+ups, further extending the results in [Que20]. The multiple weighted blow-ups gen-
+eralize the weighted blow-ups and are used to obtain a smooth and toroidal resolu-
+tion version of Artin stacks (see Section 5.5). The Abramovich-Quek weighted blow-
+up generalizes the Satriano toroidal construction on Artin logarithmically smooth
+stacks in [Sat13] to locally monomial ideals.
+Subsequently in the paper [W�lo22] the operation of cobordant blow-up B+ → X
+with weighted centers J = (u1/w1
+1
+, . . . , u1/wk
+k
+) was introduced, where u1, . . . , uk is
+a partial system of local parameters
+B = SpecX(OX[t−1, tw1x1, . . . , twkxk]),
+B+ = B ∖ V (x1tw1, . . . , xktwk),
+(1)
+where t is an introduced unknown. A similar formula was discovered by Rydh in
+the paper of [QR19] and studied in the context of the stack-theoretic blow-ups.
+Moreover, a certain relation between toric Cox construction and toric weighted
+cobordant blow-ups was already observed in [QR19] and [W�lo22].
+The operation of cobordant blow-up allows representing stack-theoretic weighted
+blow-ups and more general Kummer blow-ups in the language of smooth varieties
+with torus action without stack theoretic language.
+Moreover, apart from fast
+functorial resolution with SNC divisors in characteristic zero, the approach leads to
+the resolution of some classes of singularities in positive and mixed characteristic
+(see [W�lo22]).
+In the present paper, we associate the Cox coordinate ring to arbitrary proper
+birational morphisms π : Y → X of normal schemes as follows:
+AY/X := π∗(
+�
+E∈Cl(Y/X)
+OY (E)),
+where Cl(Y/X) ⊂ Cl(Y ) is a free group generated by the exceptional divisors. It
+comes with the coaction of the associated torus T = Spec(Z[Cl(Y/X)]).
+Per analogy with the standard Cox construction, we call the space
+B := SpecX(π∗(
+�
+E∈Cl(Y/X)
+OY (E))
+(2)
+the relative Cox coordinate space. The scheme
+B+ := SpecY (
+�
+E∈Cl(Y/X)
+OY (E)
+(3)
+will be called the relative Cox characteristic space.
+
+4
+J. W�LODARCZYK
+In this language, any proper birational morphism π : Y → X can be represented
+by a T -equivariant morphism B+ → B such that the induced morphism of the good
+quotient coincides with π : Y → X:
+B+ � T
+→
+B � T
+∥
+∥
+Y
+π→
+X,
+.
+As in the standard construction, the morphism B+ ⊂ B is an open immersion
+upon some reasonable assumptions.
+If Y → X is the the blow-up of the ideal J on X the associated presentation
+B+ � T → X can be thought as the normalized extended Proj introduced by
+Swanson-Huneke [HS06]:
+B+ � T = ProjX(OX[J t, t−1])nor.
+(See Section 5.2.)
+Note that the morphism B → X is affine and is locally described by a single chart.
+The spaces B+ and B usually have nicer singularities and simpler descriptions, and
+the morphism B+ ⊂ B is way simpler than the original π : Y → X.
+As in
+the standard Cox construction, the semiinvariant functions on B+ and B can be
+interpreted as forms on Y and are convenient for the computations.
+For instance, the construction can be applied to normalized blow-ups of locally
+monomial centers, leading to general classes of modifications of singularities of
+subschemes and ideals that preserve regular ambient schemes.
+Given a locally toric or simply regular scheme X over a field and any locally
+toric proper birational morphism π : Y → X, one associates with π a morphism of
+Cox regular spaces B+ ⊂ B, where
+B = Spec(OX[t−1
+1 , . . . , t−1
+k , u1tα1, . . . , uktαk])
+In particular, one represents the normalized blow-up of any locally monomial
+J by a smooth cobordant blow-up B+ → X of J equipped with torus action.
+The formula generalizes the weighted cobordant blow-up introduced in [W�lo22]
+with B+ = B ∖ V (J tα), for the corresponding multi-indexes α, α1, . . . , αk. It also
+leads to a version of the multi-weighted blow-up of [AQ21, Definition 2.1.6] when
+considering the stack theoretic quotient [B+ � T ].
+One can think of this approach as an extension of the resolution by cobordant
+blow-ups with weighted centers to more general locally monomial ideals or Q-ideals.
+When replacing the group Cl(Y/X) with a subgroup Γ ⊂ Cl(Y/X) ⊗ Q in the
+formulas (2) and (3), one further generalizes the construction. We obtain
+BΓ := SpecX(π∗(
+�
+E∈Γ
+OY (E)),
+BΓ
++ := SpecY (
+�
+E∈Γ
+OY (E).
+This generalized construction can be linked to the weighted cobordant blow-ups
+as in [W�lo22] (See Section 5.4). In particular let π : Y → X be the weighted blow-
+up of schemes with the Q-ideal center J = (u1/w1
+1
+, . . . , u1/wk
+k
+). This is simply the
+normalized blow-up of the ideal J (a) := (ua/w1
+1
+, . . . , ua/wk
+k
+), with the exceptional
+irreducible Q-Cartier divisor (1/a)Ea with OY (−Ea) = OX · J (a), where a is any
+positive integer such that wi|a,. The cobordant blow-up of J (a) with respect to the
+group Γ = Z· 1
+aEa ⊂ Cl(Y/X)⊗Q gives the formula (1) for the cobordant weighted
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+5
+blow-up of J = (u1/w1
+1
+, . . . , u1/wk
+k
+). Note that the above definition does not depend
+upon the choice of a, and the Q-Cartier divisor (1/a)Ea can be interpreted as the
+divisor corresponding to the Q-ideal OY · J = OY (−Ea)1/a.
+More generally, let J be a locally monomial center, and π : Y → X be the
+normalized blow-up of J . Denote by E1, . . . , Ek the exceptional divisors of π. The
+cobordant blow-up of J with respect to the subgroup
+Γ = Z 1
+b1
+E1 ⊕ . . . ⊕ Z 1
+bk
+Ek ⊂ Cl(Y/X) ⊗ Q,
+generated by 1
+b1 E1, . . . , 1
+bk Ek, where b1, . . . , bk are any positive integers, leads to the
+multiple weighted blow-up, considered by Abramovich-Quek in [AQ21]. It can be
+understood as the fantastack associated with the stack-theoretic quotient [B+ � T ]
+(See Section 5.5). Since the stabilizers of the action are not finite, in general, one
+obtains an Artin stack as the stack-theoretic quotient.
+Note that in the resolution process of hypersurfaces, one often considers locally
+the corresponding Newton polytope. It is naturally associated with a certain co-
+ordinate system and rises to a locally monomial center. In a more general setting,
+the Newton polytope is replaced with the dual valuation complex of the locally
+monomial center. We show some conditions for singularities when the cobordant
+blow-up of such a center immediately resolves singularities. (see Theorems 4.4.5,
+4.5.9, 4.5.11, 4.6.5, 4.6.9, 4.8.1, 4.8.2). The particular resolution methods and the-
+orems extend the relevant results for the weighted cobordant blow-ups in [W�lo22].
+As a Corollary 4.6.1, we obtain Abramovich-Quek’s [AQ21, Theorem 5.1.2].
+The resolution algorithm outputs a smooth scheme with a torus action which
+admits a good quotient having locally toric singularities and birational to the orig-
+inal scheme. It can be directly resolved by the canonical combinatorial methods
+in any characteristic as in [W�lo20, Theorem 7.17.1]. Alternatively, by Proposition
+3.5.2, one can always replace in the resolution process each B+ with an open sta-
+ble subset Bs admitting a geometric quotient, and then apply the destackification
+method of Bergh-Rydh in [BR19]. It is also possible to use the canonical reduction
+of stabilizers due to Edidin- Rydh [ER21], and then the destackification method of
+Bergh-Rydh in [BR19].
+1.0.1. Aknowledgements. The author would like to thank Dan Abramovich, J¨urgen
+Hausen, Antonio Laface, Michael Temkin, Ilya Tyomkin, and Jaros�law Wi´sniewski
+for helpful discussions and suggestions.
+1.1. Preliminaries. The definition of Cox spaces of morphisms is similar, with
+some important differences, to the notion of Cox spaces of varieties, as presented
+in [ADHL15].
+1.1.1. Construction of Cox sheaves. Given a proper birational morphism π : Y →
+X of normal integral schemes, consider the the free group Cl(Y/X) ⊂ Div(Y ) gen-
+erated by the images of the exceptional irreducible divisors Ei. It can be identified
+with the kernel of the surjective morphism π∗ : Cl(Y ) → Cl(X).
+Definition 1.1.2. By the relative Cox ring w mean the sheaf of graded OY -algebras
+CY/X =
+�
+E∈Cl(Y/X)
+CE =
+�
+E∈Cl(Y/X)
+OY (E),
+
+6
+J. W�LODARCZYK
+graded by Cl(Y/X), where CE := OY (E) for
+OY (E)(U) = {f ∈ κ(Y ) | (divY (f) + E)|U ≥ 0} ⊂ κ(Y ) = κ(X).
+Note the C0 = OY . One can introduce the dummy variables t = (t1, . . . , tk)
+so that Ei corresponds to t−1
+i
+and E �→ tE. This defines the isomorphism of the
+gradings:
+Cl(Y/X) ≃ {t−α | α ∈ Zk} ≃ Zk
+Using this notation, we can write
+CY/X =
+�
+E∈Cl(Y/X)
+CEtE =
+�
+α∈Zk
+Cα · ta1
+1 · . . . · tak
+k ⊆
+�
+E∈Cl(Y/X)
+κ(Y )tE
+1.1.3. Forms. As mentioned, the Cox relative ring construction, similarly to the
+absolute case, is analogous to the coordinate ring Z[x0, . . . , xn] on projective space
+X = Pn
+Z. One can choose a very ample divisor, for instance D = V (x0), and identify
+the functions f = F(x0, . . . , xn)/xn
+0 ∈ OX(nD) with the forms F(x1, . . . , xn) so
+that the vanishing locus V (F) equals to
+V (F) = VX(F) = div(f) + nD.
+Per this analogy, and as in [ADHL15], the elements in CE will be called forms
+of degree E on Y and can be written formally as F = ftE , where f ∈ OY (E),
+with the natural componentwise operation of addition and multiplication. We also
+define the divisor of the form F = ftE on Y as divY (F) = divY (f) + E, and its
+vanishing locus on Y to be
+VY (F) := supp(divY (f) + E).
+1.1.4. Exceptional valuations. By the exceptional valuations of π : Y → X we shall
+mean the valuations ν1, . . . , νk of κ(X) = κ(Y ) associated with the generic points
+of the exceptional divisors E1, . . . , Ek of π.
+These valuations define ideals Iν,a,X ⊂ OX on X for a ∈ Z, generated by the
+functions f ∈ OX, with ν(f) ≥ a. In particular Iν,a = OX if a ≤ 0.
+Lemma 1.1.5. Let E = � niEi correspond to t−n1
+1
+· . . . · t−n1
+k
+. Then
+(1) π∗(OY (Ei)) = OX.
+(2) If all ni ≥ 0 then π∗(OY (E)) = OX.
+(3) If there is ni < 0, then
+π∗(OY (E)) =
+�
+ni<0
+Iνi,−ni,X =
+k�
+i=1
+Iνi,−ni,X.
+Proof. First, since π : Y → X is proper, birational and X is normal, we have
+π∗(OY ) = OX.
+We can reduce the situation to the case when X is affine since the problem is
+local on X. Then
+g ∈ OY (E)(π−1(X)) ⊂ κ(X) = κ(Y )
+if and only if
+divY (g) + E ≥ 0.
+This implies that divU(g) ≥ 0, where U := Y ∖(� Ei), and U ⊂ X, where X ∖U is
+of codimension ≥ 2. Thus divX(g) ≥ 0. So, since X is normal, w get g ∈ π∗(OY ) =
+OX, whence π∗(OY (E)) ⊆ OX.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+7
+(1) and (2) If E = � niEi with ni ≥ 0 then
+OX = π∗(OY ) ⊆ π∗(OY (E)) ⊆ OX.
+(3) In general, g ∈ π∗(OY (E)) ⊆ OX iff divY (g) + E ≥ 0. This translates into
+divY (g) + �
+ni<0 niEi ≥ 0 by part (2). Thus νi(g) ≥ −ni for all ni < 0, which
+yields
+g ∈
+�
+ni<0
+Iνi,−ni,X =
+k�
+i=1
+Iνi,−ni,X.
+We use here the fact that by definition Iνi,−ni = OX if ni ≥ 0.
+♣
+1.2. Cox coordinate space.
+1.2.1. Cox algebra. As a corollary from Lemma 1.1.5, we obtain
+Proposition 1.2.2. Let π : Y → X be a proper birational morphism of normal
+irreducible schemes. Assume that Ek, . . . , Ek are the irreducible exceptional divisors
+of π, and νi are the associated valuations. Then the direct image π∗(CY/X) of the
+relative Cox ring is a Cl(Y/X) = Zk-graded OX-algebra:
+AY/X := π∗(CY/X) =
+�
+ai∈Z
+k�
+i=1
+Iνi,ai · ta1
+1 · . . . · tak
+k ⊂ OX[t1, t−1
+1 , . . . , tk, t−1
+k ],
+where Ei correspond to t−1
+i .
+♣
+1.2.3. Cox coordinate space.
+Definition 1.2.4. Given a proper birational morphism π : Y → X of normal
+integral schemes. The Cox relative coordinate space is the scheme
+B = Cox(Y/X) := SpecX(AY/X),
+over X with the natural action of TB = Spec Z[Cl(Y/X)]. The Cox relative char-
+acteristic space is the space
+B+ = Cox(Y/X)+ := SpecY (CY/X).
+over Y . The Cox trivial space is given by
+B− := B ∖ VB(t−1
+1
+· . . . · t−1
+k ).
+1.2.5. Good and geometric quotient. We consider here a relatively affine action of
+T = Spec(Z[t1, t−1
+1 , . . . , tk, t−1
+k ])
+on a scheme X over Z. By the good quotient (or GIT-quotient) of X by T we mean
+an affine T -invariant morphism
+π : X → Y = X � T
+such that the induced morphism of the sheaves OY → π∗(OX) defines the isomor-
+phism onto the subsheaf of invariants OY ≃ π∗(OX)T ⊂ π∗(OX).
+Then π : X → Y = X/T will be called the geometric quotient if additionally
+every fiber Xy of π over s geometric point y : Spec(κ) → Y defines a single orbit of
+the action of Tκ = T ×κ Spec(κ) = Spec(κ[t1, t−1
+1 , . . . , tk, t−1
+k ]) on Xy.
+
+8
+J. W�LODARCZYK
+Lemma 1.2.6. Let π : X → Y = X �T be a good quotient of integral schemes of a
+relatively affine action of the torus T . Then π is surjective. Moreover, the inverse
+image π−1(Z) ⊂ Xof a closed connected subscheme Z ⊂ Y is connected.
+Proof. The problem reduces to the affine situation π : X = Spec(A) → Spec AT .
+Then the coaction of T on A determines the gradation
+A =
+�
+α∈Zn
+Aαtα,
+where B = A0. Then for any prime ideal p ⊂ AT = A0, the extended ideal pA in A
+is proper, and p = pA ∩ A0 is a contracted ideal. This implies that π is surjective.
+Let I ⊂ A0 be an ideal such that the scheme Spec(A0/I) is connected. Suppose
+that for the ideal
+IA =
+�
+α∈Zn
+IAαtα
+of A the space Spec(A/IA) is disconnected. Then there is a nontrivial ring decom-
+position A/IA = A′ ⊕ A′′, and (A/IA)0 = A′
+0 ⊕ A′′
+0. Hence either the ring A′
+0 = 0
+or A′′
+0 = 0. Consequently, either A′ = 0 or A′′ = 0, and the decomposition is trivial.
+♣
+Lemma 1.2.7. The natural morphisms
+πB : B → B � TB ≃ X,
+πB+,Y : B+ → B+ � TB ≃ Y
+are good quotients.
+Proof.
+Spec(OB�TB) = Spec(OTB
+B ) = SpecX(AY/X)TB = SpecX(OX) = X
+Spec(OB+�TB) = Spec(OTB
+B+) = SpecY (CY/X)TB = SpecY (OY ) = Y
+♣
+1.2.8. Exceptional divisors on B = Cox(Y/X). Let π : X → Y be a proper bi-
+rational morphism of normal schemes.
+Using the natural birational morphism
+iB : B+ → B, one can interpret the notion of the exceptional divisors of B.
+Any exceptional divisor Ei on Y defines a canonical form
+Fi = t−1
+i
+= tEi ∈ OY (E)t−1 ⊂ OB
+on Y of degree Ei which vanishes on VY (F) = Ei. The form t−1
+i
+also defines a
+regular homogenous function t−1
+i
+on B of degree Ei. Its divisor Di := divB(t−1
+i )
+on B determines the divisor Di+ := Di|B+ = divB+(t−1
+i
+) on B+ which maps to Ei.
+Lemma 1.2.9. The natural quotient morphism πB+,Y : B+ → Y , (respectively
+πB : B → X) takes the exceptional divisors Di+ = VB+(t−1
+i ) (respectively Di =
+VB(t−1
+i
+)) surjectively onto Ei (respectively surjectively to the center of ZX(νi) =
+VX(Iνi,1,X) of the valuation νi). Moreover the induced morphism Di+ → Ei (resp.
+D → ZX(νi)) is defined by the good quotient.
+♣
+Proof.
+Di+ = VB+(t−1
+i
+) = SpecY CY/X/t−1
+i CY/X =
+= SpecY (
+�
+(OY (E)/OY (E − Ei))tE)
+→
+→
+SpecY ((CY/X/(t−1
+i CY/X)0 = Spec(OY /OY (−Ei)) = Ei
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+9
+Thus the morphism Di+ → Y is defined by the good quotient and is surjective by
+Lemma 1.2.6. The proof for the divisors Di is similar.
+♣
+Definition 1.2.10. The divisors Di = VB(t−1
+i ), respectively Di+ = VB+(t−1
+i
+) will
+be called the exceptional divisors of B = Cox(Y/X) → X, respectively of B+ → Y .
+Lemma 1.2.11. The divisors Di = VB(t−1
+i ) on B and Di+ = VB+(t−1
+i ) on B+ are
+irreducible.
+Proof. By Lemma 1.2.6, the divisors Di are connected, so it suffices to show that
+they are locally irreducible. We can assume that X is affine. It suffices to show
+that
+t−1
+i
+= tEi ∈ O(B) = AY/X(X)
+is a prime element. The latter can be verified for the homogenous elements. Let νi
+be the valuation on X associated with Ei ⊂ Y .
+Let
+t−1
+i
+= tEi|(tE · f)(tE′ · g) = tE+E′fg
+where f ∈ OX(E), and g ∈ OX(E′), and suppose t−1
+i
+does not divide both (tE · f),
+and (tE′ · g). The first assumption implies that tE+E′−Eifg ∈ O(B). So fg ∈
+π∗(OY (E + E′ − Ei)).
+Write the presentations E = � njEj and E′ = � n′
+jEj. Then, by the assump-
+tion νi(f) = ni and νi(g) = n′
+i. Thus, by Proposition 1.2.2, and the assumptions
+on f and g, we have
+νi(fg) > ni + n′
+i = νi(f) + νi(g),
+which is a contradiction since νi is a valuation.
+The same reasoning works for
+Di+.
+♣
+1.2.12. Morphisms of Cox spaces. The following result is analogous to
+[ADHL15][Construction 1.6.3.1] for the Cox spaces of varieties.
+Proposition 1.2.13. Let π : Y → X is a proper birational morphism of normal
+schemes, and TB := Spec(Z[Cl(Y/X)]). Let E be the exceptional divisor with the
+components Ei. Denote by Uπ := Y ∖ E ⊂ Y the open subset of Y , which can
+be identified with the open subset of X, where Y → X is an isomorphism.
+Let
+πB : B → X, and πB+,Y : B+ → Y be the natural projections.
+There is a natural TB-equivariant birational morphism
+iB : B+ = Cox(Y/X)+ → B = Cox(Y/X).
+over X, which is an isomorphism over Uπ, with
+π−1
+B (Uπ) = π−1
+B+,Y (Uπ) = Uπ × TB,
+and such that π−1
+B (Di) = Di+.
+Moreover, the morphism iB induces the morphism of the good quotients:
+π : B+ � TB = Y
+→ B � TB = X.
+Proof. For any open affine U ⊂ X, we have the natural identifications
+Γ(U, π∗(CY/X)) = Γ(π−1
+B (U), OB)
+and
+Γ(U, π∗(CY/X)) = Γ(π−1(U), CY/X) = Γ(π−1
+B+,Y (π−1(U)), OB+)
+
+10
+J. W�LODARCZYK
+Combining both equalities gives us:
+Γ(π−1
+B (U), OB) = Γ(π−1
+B+,Y (π−1(U)), OB+).
+Since π−1
+B (U) ⊂ Cox(Y/X) is affine we obtain a natural morphism
+φU : π−1
+B+,Y (π−1(U)) → π−1
+B (U)
+over U induced by the isomorphisms on global sections. The constructed morphisms
+are functorial for open embeddings U ⊂ V of affine subsets on X and glue to a global
+morphism B+ → B.
+The morphism B+ → B is birational as it is an isomorphism over Uπ ⊂ X.
+Moreover iB is an isomorphism over Uπ:
+π−1
+B (Uπ) = π−1
+B+,Y (Uπ) = SpecUπ(
+�
+E∈Cl(Y/X)
+OUπtE) = Uπ × TB.
+By the construction,
+π−1
+B (Di) = π−1
+B (VB(t−1
+i )) = VB+(t−1
+i ) = Di+.
+Locally for any open affine V ⊂ π−1(U) the induced homomorphisms
+OB(π−1
+B (U)) = Γ(U, π∗(CY/X)) = Γ(π−1(U), CY/X) → Γ(V, CY/X) = OB+(π−1
+B+,Y (V ))
+determine the homomorphisms
+(OB(π−1
+B (U)))T = Γ(U, π∗(CY/X)T ) → Γ(V, CT
+Y/X) = OB+((π−1
+B+,Y (V )))T ,
+and define the global morphism B+ � TB = Y → B � TB = X.
+♣
+1.2.14. Cobordization.
+Definition 1.2.15. Let π : Y → X be a proper birational morphism. Then the
+morphism πB : B = Cox(Y/X) → X, (respectively πB+,Y : B+ = Cox(Y/X)+ →
+X) will be called the full cobordization of π (respectively the cobordization of π).
+If I is an ideal on X, then by the full cobordant blow-up σ : B → X at I
+(respectively cobordant blow-up σ+ : B+ → X at I we mean the full cobordization
+(respectively cobordization) of the normalized blow-up blJ (X) → X.
+1.2.16. The Cox trivial space.
+Lemma 1.2.17. Let π : Y → X be a proper birational morphism of normal
+schemes, and E = � Ei be its exceptional divisor.
+Let Uπ = Y ∖ E ⊂ X be
+the maximal open subset of X and of Y where π is an isomorphism exactly. Then
+the Cox trivial space is B− = X × TB. Moreover we have
+i−1
+B (B−) = B+ ×B B− = Uπ × TB.
+Proof. By Proposition 1.2.2 we have
+B− := B ∖
+k�
+i=1
+Di = B ∖ V (t−1
+1
+· . . . · t−1
+k ) = Spec(OX[t1, t−1
+1 , . . . , tk, t−1
+k ]) = X × TB
+B+ ×B B− := B+ ∖
+k�
+i=1
+Di = B+ ∖ VB+(t−1
+1
+· . . . · t−1
+k ) =
+= Spec(
+�
+E∈Cl(Y/X)
+OY (E)tE)[t1, t−1
+1 , . . . , tk, t−1
+k ]) = Spec(OUπ[t1, t−1
+1 , . . . , tk, t−1
+k ])
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+11
+♣
+1.3. Open immersion of Cox spaces.
+1.3.1. Generating forms.
+Lemma 1.3.2. Let X be an affine scheme and π : Y → X be a proper birational
+morphism of normal integral schemes.
+Assume that YF is affine, for a certain
+form F = ft−E on Y , with f ∈ H0(Y, OY (−E)) = H0(X, π∗(OY (−E)). Then
+(B+)F = BF is affine and π−1
+B+,Y (YF ) = (B+)F . Moreover
+CY/X(YF ) = (CY/X(Y ))F = (H0(B, OB))F .
+Proof. If y ∈ YF then F = ft−E is invertible in the stalk (CY/X)y.
+Indeed
+div(ft−E) = 0 at y so E = div(f) is principal at y, and thus (ft−E)−1 = f −1tE
+is the inverse of ft−E.
+This shows that the form F is invertible in CY/X(YF ),
+and the function F is invertible on the scheme π−1
+B+,Y (YF ) ⊂ B+. Thus we have
+an open immersion π−1
+B+,Y (YF ) ֒→ B+F .
+Since F is invertible on π−1
+B+,Y (YF )
+the natural homorphism CY/X(Y ) → CY/X(YF ) factors through the localization
+(CY/X(Y ))F → CY/X(YF ).
+On the other hand if
+G = gt−E′ ∈ CY/X(YF )
+is a form on YF then, by definition,
+divY (G · F n) = divY (G) + n · divY (F) ≥ 0
+on Y for sufficiently large n. Hence G·F n ∈ CY/X. This shows that (CY/X(Y ))F →
+CY/X(YF ) is surjective. But this morphism is defined by the restrictions of forms,
+so functions on open subsets of B+, and thus it is also injective. Hence it is an
+isomorphism.
+This defines an isomorphism of the global sections
+(CY/X(Y ))F = H0(B+, OB+)F = H0((B+)F , OB+)
+→ H0(π−1
+B+,Y (YF ), OB+) = CY/X(YF )
+If YF is affine then we obtain then π−1
+B+,Y (YF ) is also affine, and the open im-
+mersion π−1
+B+,Y (YF ) ֒→ (B+)F has the left inverse (B+)F → π−1
+B+,Y (YF ) determined
+by the global sections. Since the schemes are separated, it is an isomorphism.
+Finally we observe that H0(X, π∗(OY (E)) = H0(Y, OY (E). Hence
+H0(Y, CY/X) = H0(X, π∗(CY/X)) = H0(X, AY/X) = H0(B, OB),
+and
+H0(BF , OB) = AY/X(X))F = CY/X(Y ))F = CY/X(YF ).
+♣
+1.3.3. Irrelevant ideal and open immersion of Cox spaces. The notion of irrelevant
+ideals was used in [ADHL15] in the context of Cox rings. Here we consider the
+analogous definition and results for morphisms.
+
+12
+J. W�LODARCZYK
+Proposition 1.3.4. Let π : Y → X be a proper birational morphism of normal
+schemes. Assume that X can be covered by open subsets Xi such Yi := π−1(Xi)
+admits an open affine cover (Yi)Fj, where Fij = fijt−Eij is a form on Yi for
+fij ∈ OYi(−Eij). Then there is a natural open TB-equivariant embedding
+B+ = Cox(Y/X)+ ֒→ B = Cox(Y/X),
+It induces the morphism of the good quotients:
+B+ � TB = Y
+→ B � TB = X.
+Moreover B ∖ B+ is of codimension ≥ 2 in B.
+Proof. The problem is local on X, so we can replace X with Xi, and drop the
+subscripts i.
+By Lemma 1.3.2, the open affine cover YFj of Y where Fj ∈ Iirr
+defines the open affine cover B+Fi = SpecY ((CY/X)Fi) = π−1
+B+,Y (Yi) of B+ mapping
+it isomorphically onto open subsets BFi = SpecX((AY/X)Fi) ⊂ X. This induces
+the open immersion
+B+ ֒→ B.
+For “moreover part” let Uπ = Y ∖ E ⊂ Y be the maximal open subset, where
+π : Y → X is an isomorphism. Then Uπ can be identified with an open subset of
+X, and the complement X ∖ Uπ of the open set is of codimension ≥ 2, and
+B+ ∖ D = Uπ × TB ⊂ B− = B ∖ D = X × TB.
+if of codimension ≥ 2 in B− = B ∖ D.
+On the other hand, by Lemma 1.2.11, the divisors Di = VB(t−1
+i
+) are irreducible
+on B.
+Consequently the difference Di ∖ B+ = Di ∖ Di+ is of codimension ≥ 2. Thus
+B ∖ B+ = (B− ∖ B+) ∪ (D ∖ D+)
+is of codimension ≥ 2 in B.
+♣
+The notion of irrelevant ideal on Cox coordinate spces was originally introduced
+in [ADHL15] (Definition 1.6.3.2 and Proposition 1.6.3.3(iii))
+Definition 1.3.5. By the the irrelevant ideal Iirr ⊂ AY/X we mean the ideal
+radically generated by the forms F in AY/X, such that YF is open affine over X.
+Corollary 1.3.6. Under the conditions from Proposition 1.3.4, Iirr is the radical
+coherent ideal determined by the reduced closed subscheme B ∖ B+. Thus we can
+write B+ = B ∖ V (Iirr).
+Proof. The problem is local on X, and we can assume that X is affine. It follows
+from the construction that B+ = B ∖ V (I), where I is generated by all F ∈ AY/X,
+such that YF is affine. Thus rad(I) = Iirr.
+♣
+1.3.7. Cox construction for regular schemes X. Recall a well-known fact:
+Lemma 1.3.8. Let Y be a normal scheme. Then the complement of any open
+affine subset V ⊂ Y is the support of a Weil divisor.
+Thus there is a finite open cover of Y by open affine subsets Vi = Y ∖ Di, where
+Di are Weil divisors on Y .
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+13
+Proof. By definition, V is the set of points of Y where all the functions f ∈
+Γ(V, OY ) ⊂ κ(Y ) are regular. Since Y is normal, this means that the supports
+of the divisors div−(f) of the negative components of div(f) cover Y ∖ V . Conse-
+quently, Y ∖ V is the union of the Weil divisors contained in it. Thus this union is
+finite, and Y ∖ V is the support of the Weil divisor.
+This defines an open cover Vi = Y ∖ Di which can be assumed to be finite.
+♣
+Lemma 1.3.9. Let π : Y → X be a proper birational morphism of normal schemes.
+Let p ∈ X be a regular point on X. There is an open affine neighborhood U of p
+in X, and an open cover of YU = π−1(U) by open affine subsets YF = YU ∖ VY (F),
+where F is a form over U ⊂ X and on YU ⊂ Y .
+Proof. We can assume that X is affine. By the previous lemma, we can find an
+open affine cover
+Vj := Y ∖ (Dj ∪ Ej)
+of Y defined by the divisors Dj ∪ Ej, where Ej are some possibly reducible ex-
+ceptional divisors. Taking the images of Dj in X, we obtain a finite collection of
+divisors D′
+j = π(Dj) on X. Consider an open affine neighborhood
+U := Xg = X ∖ V (g)
+of p ∈ X, for g ∈ H0(X, OX), such that all the divisors D′
+j are principal on U.
+Thus we can write D′
+j = divU(fj), where fj ∈ O(X).
+The pullbacks of the principal divisor D′
+j = divU(fj) on U are of the form
+π∗(D′
+j) = Dj +Ej on YU = π−1(U), where Ej = � nijEi is an exceptional divisor,
+with nij ≥ 0. They define the forms
+Fj := fjt−Ej+Ej
+on YU such that
+divY (Fj) = divY (fj) − Ej + Ej = Dj + Ej.
+and thus VY (Fj) = Dj ∪ Ej on YU. Then
+YU ∖ V (Fj) = YU ∖ (Dj ∪ Ej) = (Vj)g = Vj ∖ VY (g)
+is an open affine cover of YU = π−1(U) = π−1(Xg).
+♣
+Remark 1.3.10. The lemma is valid under the assumption that p ∈ X is a Q-
+factorial point, so any Weil divisor at p is Q-Cartier.
+As a corollary from the above, we obtain the following:
+Proposition 1.3.11. Assume that X is regular, and π : Y → X is a proper
+birational morphism of normal schemes. There is a natural open TB-equivariant
+embedding
+B+ = B ∖ V (Iirr) ֒→ B
+It induces the morphism of the good quotients:
+B+ � TB = Y
+→ B � TB = X.
+1.4. Cobordant blow-ups of ideals.
+
+14
+J. W�LODARCZYK
+1.4.1. The strict and the weak transform under cobordant morphism.
+Definition 1.4.2. Let I be any ideal on a normal scheme X. Let π : Y → X be a
+proper birational morphism from a normal scheme Y , and σ = πB : B → X be the
+full cobordization of π. Then by the strict transform of the ideal I we mean the
+ideal
+σs(I) := (f ∈ OB | t−αf ∈ OB · I, for some α ∈ Zk
+≥0) ⊂ OB.
+The weak transform of the ideal I is given by
+σ◦(I) := tα0I,
+where
+α0 := max{α | I ⊂ t−αOX},
+is defined for the partial componentwise order on the set of components.
+1.4.3. Cobordant blow-ups.
+Lemma 1.4.4. Let J be an ideal on a normal scheme X, such that codim(V (J ) ≥
+2.
+Let π : Y → X be the normalized blow-up of J .
+Let E = � aiEi be the
+exceptional divisor of π, such that OY (−E) = OY · J .
+Set α = (a1, . . . , ak).
+Denote by σ : B → X be the corresponding full cobordant blow-up of J . Then
+(1) σ−1(X ∖ V (J )) = (X ∖ V (J )) × TB is trivial.
+(2) B+ = B ∖ VB(σ◦(J )) = B ∖ VB(tαJ ), where
+σ◦(J ) = OB · t−EJ = OB · tαJ
+is the weak transform of J .
+(3) J · OB+ = t−αOB+ is a locally principal monomial ideal on B+.
+Proof. Let U ⊂ X be an open affine subset. The ideal of sections J (U) is gener-
+ated by some f1 . . . , fk ∈ J (U) ⊂ OX(U) = OY (π−1(U)). The pullbacks of the
+functions f1 . . . , fk ∈ J (U) generate the ideal
+IE = OY (−E) = OY · J
+on YU := π−1(U). Moreover on each YU ∖ VY (Fi), where Fi := fit−E we have
+exactly divYU (fi) = E|YU .
+On the other hand consider the open cover of
+YU = π−1(U) = Proj
+∞
+�
+i=0
+J i(U)ti,
+where t is a dummy unknown by the open subsets
+(YU)fit = π−1(U)fit = (Proj
+∞
+�
+i=0
+J i(U)ti)fit = (Spec(
+∞
+�
+i=0
+J i(U))fit)0,
+where fit ∈ J 1(U)t. Since fjt is invertible on (YU)fjt and fit/fjt = fi/fj are
+regular we wee that O(YU )fj t · J is generated by fj. So E = divY (fj) on (YU)fit,
+and consequently the form Fj = fjt−E is invertible on (YU)fjt.
+Computing div(fit) on the cover (YU)fjt of YU gives us
+div(fit) = div(fit/fjt) = div(fi/fj) = div(fi) − E = div(Fi) = div(fit−E).
+Consequently we conclude that (YU)fit = (YU)Fi is affine and cover YU. Thus, by
+Proposition 1.3.4, there is an open immersion B+ ⊂ B, where B+ is covered by
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+15
+B+Fi. Moreover, by the above, the ideal J tα on B+Fi is generated by fit−E, and
+thus equal to
+J tα
+|B+Fi = OB+Fi · OYFi (−E)t−E = OB+Fi · fit−E = OB+Fi · Fi.
+But Fi = fit−E is invertible on B+Fi of degree −E, whence
+OB+Fi · J = OB+Fi · J tα · t−α = OB+Fit−α,
+which implies that
+OB+ · J = OB+t−α.
+(4)
+On the other hand J tα ⊂ OB, since any element ftα ∈ J (U)tα is in
+Oπ−1(U)(−E)tα which is the −E gradation of OB over U. This also shows that
+J tα = σ◦(J ), as by equality (4) for B+, the form t−α = tE is the maximal factor
+which divides OB · J .
+Finally, by the above
+V (σ◦(J )) = V (f1t−E, . . . , fkt−E) = V (F1, . . . , Fk) = B ∖ B+ = V (Iirr).
+♣
+Remark 1.4.5. It follows from the above that the inverse image OB+ ·J of ideal J
+under the cobordant blow-up is the ideal of the exceptional divisor tE, analogously
+to the standard blow-up of J . However, this is no longer true for the full cobordant
+blow-up J .
+1.5. Cobordant flips.
+Lemma 1.5.1. Let φ1 : X1 → Z, and φ2 : X2 → Z be proper birational morphisms
+from normal schemes X1, X2 to Z. Assume that the induced proper birational map
+X1 ��� X2 over Z is an isomorphism in codimension one. Then
+B := B(X1/Z) = B(X2/Z),
+is equipped with the action of torus TB = Cl(X1/Z) = Cl(X2/Z), and there is
+a natural birational map B(X1/Z)+ ��� B(X2/Z)+ over B. Moreover if φ1, φ2
+satisfy the condition of Proposition 1.3.4, then B(X1/Z)+ and B(X2/Z)+ are open
+subschemes of B which coincide in codimension 1.
+1.6. Functoriality of Cox spaces for open immersions. The construction of
+the full cobordization is functorial for open immersions up to torus factors:
+Lemma 1.6.1. Let π : Y → X be a proper birational morphism of normal integral
+schemes. Let U ⊂ Y be an open subset, and YU := π−1(U). Let E1, . . . , Ek be the
+irreducible exceptional divisors of π : Y → X. Let πB : B = Cox(Y/X) → X be the
+full cobordization of a proper birational morphism π : Y → X, and πB+ : B+ → X
+is its cobordization. Let
+TB∖BU := Spec( Z[ti, t−1
+i
+| Ei ⊂ Y ∖ YU ] ),
+Then
+BU := π−1
+B (U) = B(YU/U) × TB∖BU ,
+BU+ := π−1
+B+(U) = B(YU/U)+ × TB∖BU .
+
+16
+J. W�LODARCZYK
+Proof. For any open subset U ⊂ X, and YU = π−1(U), we can construct a subgroup
+Cl(YU/U) ⊆ Cl(Y/X), with the canonical splitting Cl(Y/X) → Cl(YU/U). Write
+Cl(Y/X) = Cl(YU/U)⊕Cl0(YU/U), where Cl0(YU/U) is generated by Ei ⊂ Y ∖YU.
+π−1
+B (U) = SpecU(
+�
+E∈Cl(Y/X)
+π∗(OY (E)|U)tE =
+SpecU(
+�
+E∈Cl(YU/U)
+π∗(OY (E))|UtE) ⊗OU (
+�
+E∈Cl0(YU /U)
+π∗(OY (E))|UtE)
+SpecU(
+�
+E∈Cl(YU/U)
+π∗(OY (E))|UtE) ⊗OU (
+�
+E∈Cl0(YU /U)
+OUtE) = B(YU/U) × TB∖BU
+Similarly
+π−1
+B+(U) = SpecYU (
+�
+E∈Cl(Y/X)
+OYU (E)tE) =
+SpecYU (
+�
+E∈Cl(YU /U)
+OYU (E)tE) ⊗OYU (
+�
+E∈Cl0(YU /U)
+OYU (E)tE)
+SpecYU (
+�
+E∈Cl(YU /U)
+OYU (E)tE) ⊗OYU (
+�
+E∈Cl0(YU /U)
+OYU tE)
+= B(YU/U)+ ×YU (YU × TB∖BU ) = B(YU/U)+ × TB∖BU
+♣
+2. Relative Cox construction for toric morphisms
+2.1. Toric varieties. Recall some basic properties of toric varieties over a field.
+(See [KKMSD73], [Oda88], [Dan78], [Ful98]).
+2.1.1. Fans. Let κ be a field, and let
+T = Spec(κ[x1, x−1
+1 , . . . , xk, x−1
+k ] = Spec(κ[M])
+be the torus, where M = Hom(T, Gm) ≃ Zk. The elements of M can be described
+by the Laurent monomials xα ∈ M, where α ∈ Zk.
+Denote by N := Hom(Gm, T ) the group of algebraic homomorphisms t → tβ =
+(tb1, . . . , tbk).
+This determines a nondegenerate pairing (·, ·) N × M → Z defined by the com-
+position:
+Hom(Gm, T ) × Hom(T, Gm) → Hom(Gm, Gm)
+, xα ◦ tβ = t(β,α).
+Thus N = M ∗ ≃ Hom(M, Z) is dual to M.
+By a fan ∆ in NQ, we mean a collection of strictly convex cones, which is closed
+under the face relation, and such that two cones intersect along the common face.
+If τ is a face of σ, written as τ ≤ σ then Xτ ⊂ Xσ is an open immersion.
+2.1.2. Toric varieties from fans. With any rational strictly convex cone σ in NQ =
+N ⊗ Q we associate its dual
+σ∨ := {y ∈ MQ | (x, y) ≥ 0
+for all
+x ∈ σ}.
+The cone σ∨ determnies the monoid Pσ := σ∨ ∩ M, and the relevant affine toric
+variety Xσ = Spec(κ[Pσ]).
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+17
+We say that a cone σ in NQ is regular or nonsingular if it is generated by a part
+of a basis of the lattice e1, . . . , ek ∈ N, written
+σ = ⟨e1, . . . , ek⟩ := Q≥0e1 + . . . + Q≥0ek.
+Similarly a cone σ = ⟨v1, . . . , vk⟩ in NQ is simplicial it if it generated by a linearly
+independent set {v1, . . . , vk} ∈ N.
+With a fan Σ we associate the toric variety XΣ obtained by glueing Xσ, where
+σ ∈ Σ, along Xτ, where τ ≤ σ. The torus T = Spec(κ(M)) acts on toric variety
+XΣ with an open dense orbit T = Spec(κ(M)) corresponding to {0} ∈ Σ.
+The fan Σ will be called regular (respectively simplicial) if all its cones are regular
+(respectively simplicial).
+The regular (resp. simplicial) fans Σ are in the bijective correspondence with
+the smooth (resp. Q-factorial) toric varieties XΣ.
+For any r ∈ Z≥0 by Σ(r) denote the set of cones σ of dimension r in Σ. The
+cones in Σ(r) correspond to the orbits Oσ and thus to the irreducible T -stable
+closed subvarieties Oσ. In particular, the irreducible T -stable divisors correspond
+to the one-dimensional faces in Σ(1).
+2.1.3. Toric valuations. Any integral vector v ∈ N determines a monomial valuation
+val(v), which can be defined for f = � cm · m ∈ κ[M], as
+val(v)(f) = val(v)(
+�
+cm · m) = min
+cm̸=0(v, m).
+The center Zval(v) of the valuation val(v) is the union of orbits Oτ, which corre-
+spond to the cones τ in
+Star(τ, Σ) = {τ | σ ≤ τ}.
+The associated ideals on XΣ are given locally on Xσ as
+Ival(v),a,Xσ = (m ∈ Pσ | (v, m) ≥ a).
+By a vertex of Σ, we mean the primitive vector, so the integral vector with
+relatively coprime coordinates, which lies in a one-dimensional face of Σ. The set
+of vertices of Σ will be denoted by Vert(Σ). Each vector v ∈ Vert(Σ) defines the
+one-dimensional face ⟨v⟩, and the valuation val(v), which is precisely the valuation
+of the associated T -stable irreducible divisor D.
+2.1.4. Decomposition of fans. By the support of a fan Σ we mean the union of its
+cones |Σ| = �
+σ∈Σ σ.
+The decomposition of the fan Σ is a fan Σ′ such that any cone σ′ ∈ Σ′ is contained
+in σ ∈ Σ, and |Σ′| = |Σ|.
+For any subset Σ0 of the fan Σ, denote by Σ0 the set of all faces of the cones in
+Σ0. The typical examples of the decompositions are given by the star subdivisions.
+Definition 2.1.5. Let Σ be a fan and v be a primitive vector in the relative interior
+of τ ∈ Σ. Then the star subdivision v · Σ of Σ at v is defined to be
+v · Σ = (Σ ∖ Star(τ, Σ)) ∪ {⟨v⟩ + σ | σ ∈ Star(τ, Σ) ∖ Star(τ, Σ)}.
+The vector v will be called the center of the star subdivision.
+Lemma 2.1.6. The decompositions ∆ of a fan Σ are in bijective correspondence
+with the proper birational T -equivariant morphisms X∆ → XΣ.
+The star subdivision v · Σ corresponds to the blow-up of the valuation, which is
+the normalized blow-up of Ival(v),a,XΣ for a sufficiently divisible a.
+
+18
+J. W�LODARCZYK
+2.1.7. Maps of fans. By a map of fans (Σ′, N′) → (Σ, N) we mean a linear map
+φ : N′ ⊗ Q → N ⊗ Q of vector spaces, such that
+(1) φ(N′) ⊂ N.
+(2) For any σ′ ∈ Σ′ there is is σ ∈ Σ such that φ(σ′) ⊂ σ.
+The map of fans corresponds to a TN′-equivariant morphism of toric varieties
+(XΣ′, TN′) → (XΣ, TN), where the action of TN′ = Spec κ[M′] on XΣ is defined by
+the homomorphism of tori
+TN′ = Spec κ[M′] → TN = Spec κ[M],
+induced by N′ → N. The decomposition Σ′ of a fan Σ corresponds to the proper
+birational morphism.
+2.1.8. Good quotients. Let φ : (σ′, N′) → (σ, N) be a surjective map of cones, such
+that φ(σ′) = σ, and φ(N′) = N. Let N′′ := ker(N′ → N). Then the exact sequence
+0 → N′′ → N′ → N → 0,
+has its dual
+0 → M → M′ → M′′ → 0.
+Thus M can be identified with the sublattice of M ′′ defined as
+M = {m ∈ M ′′ | (n, m) = 0
+for
+all n ∈ N′′}
+Consequently, κ[M] = κ[M′′]TN′′ . Moreover the dual map determine the inclusion
+σ∨ ֒→ (σ′)∨ for which (σ′)∨ ∩ MQ = σ∨, and
+(Pσ′)TN′′ = Pσ′ ∩ M = Pσ.
+Hence
+O(Xσ′)TN′′ = κ[Pσ′]TN′′ = κ[Pσ] = O(Xσ).
+Thus
+Xσ′ → Xσ ≃ Xσ′ � TN′′
+is a good quotient.
+If additionally φ : σ′ → σ is injective, so it is an isomorphism of cones, then the
+inverse image of any orbit is a single orbit, and thus the corresponding morphism
+Xσ′ → Xσ ≃ Xσ′/TN′′ is a geometric quotient.
+If the map of fans φ : (Σ′, N′) → (Σ, N) is surjective, i.e. φ(|Σ′|) = |Σ| and
+φ(N′) = N, and for any cone δ ∈ Σ, the inverse image φ−1(δ)∩|Σ′| is a unique cone
+δ′ ∈ Σ′, then the corresponding morphism XΣ′ → XΣ is affine. Consequently, by
+the previous argument, it is a good quotient with respect to TN ′′ = ker(TN′ → TN),
+where N′′ = ker(N′ → N).
+If additionally, the map |Σ′| → |Σ| is bijective then XΣ′ → XΣ is a geometric
+quotient.
+2.2. Cox construction for toric varieties. We recall here the standard Cox
+construction for toric varieties from the convex geometry point of view. This pre-
+sentation relies greatly on [Cox95], [ADHL15], and will be then adapted to the
+relative situation.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+19
+2.2.1. Cox construction. Given a toric variety X with associated fan Σ in the space
+NQ ≃ Qn containing the standard lattice N ≃ Zn. We shall assume that the fan Σ
+is nondegenerate that is the set Vert(Σ) generate the vector space NQ.
+Let Vert(Σ) = {v1, . . . , vk} denote the set of vertices of Σ. Let e1, . . . , ek denote
+the standard basis of Zk ⊂ Qk, and let
+σB := ⟨e1, . . . , ek⟩ = {
+k
+�
+i=1
+aivi | ai ∈ Q≥0}.
+The cone σB defines a regular fan ΣB in NQ
+B = Qk, consisting of all the faces of σB.
+It corresponds to the affine space
+XσB = Spec(κ[x1, . . . , xk]) = Ak
+κ
+Consider the linear map πB : NQ
+B = Qk → NQ = Qn defined on the basis e1, . . . , ek,
+such that πB(ei) = vi. We construct the subfan ΣB+ of σB to be the set of all
+the faces σ of σB such that πB(σ) is contained in a face of Σ ([ADHL15]). This
+determines a morphism πB : ΣB+ → Σ. Note that it follows from the definition
+that for any face δ = ⟨vi1, . . . vik⟩ of Σ, there is a unique face
+δ0 = π−1
+B (δ) = ⟨ei1, . . . eik⟩ ∈ Cox(Σ).
+2.2.2. Cox coordinate ring. Let Div(X) be the group of Weil divisors on X = XΣ,
+and Div(X)+ be the monoid of the effective Weil divisors and zero on X.
+Let
+Vert(Σ) = {v1, . . . , vk} denote the set of vertices of Σ. The corresponding Weil
+divisors D1, . . . , Dk ∈ Div(X) freely generate Div(X).
+Definition 2.2.3. [Cox95] The Cox coordinate ring is defined to be
+C(X) := κ[x1, . . . , xk] = κ[Div(X)+] =
+�
+D∈Div(X)+
+κxD,
+with the natural identification xi = xDi, and xD = xα and the induced multiplica-
+tion xD1 · xD2 = xD1+D2.
+Denote by Prin(X) the subgroup of Div(X) of the principal divisors on X, which
+is generated by div(m), where m ∈ M, giving an isomorphism
+M ≃ Prin(X),
+m �→
+�
+(vi, m)Di.
+We use here the assumption that Σ is nondegenerate.
+Let Cl(X) = Div(X)/Prin(X) be the Weil divisor class group. Although the Cox
+coordinate ring, as defined, comes with the natural Div(X)-gradation, one can also
+consider its Cl(X) = Div(X)/Prin(X)-gradation. Then for any class [E] ∈ Cl(X)
+of the divisor E ∈ Div(X) the space of effective Weil divisors in [E] on X is T -
+stable and thus generated by all T - invariant effective divisors
+E + div(m) ≥ 0.
+Thus one can describe the [E]- gradation to be
+C(X)[E] =
+�
+D∈[E]
+κ · xD =
+�
+m∈M,div(m)+E≥0
+κxE · xdiv(m) ≃ H0(X, OX(E)) · xE,
+
+20
+J. W�LODARCZYK
+Thus choosing any set E1, . . . Ek of Div(X) which determines a basis of the lattice
+Cl(X), one identifies Cl(X), with the subgroup of Div(X). Under this noncanonical
+identification we can write as in [Cox95] and [ADHL15]:
+C(X) =
+�
+E∈Cl(X)
+H0(X, OX(E)) · xE
+On the other hand the canonical Cl(X)-gradation on C(X) determines the nat-
+ural action of the torus
+TX := Spec(κ[Cl(X)]) ≃ Spec(κ[t1, t−1
+1 , . . . , tr, t−1
+r ],
+where Cl(X) ≃ Zr.
+2.2.4. Cox coordinate space. The Cox coordinate ring defines the Cox coordinate
+space (as in [Cox95] and [ADHL15]) to be
+B = Cox(X) := Spec(C(X)) = Spec(
+�
+E∈Cl(X)
+H0(X, OX(E)) · xE) ≃ Ak,
+It is the toric variety associated with the fan ΣB of all the faces of σB.
+2.2.5. Good and geometric quotients. Let
+B+ = Cox(X)+ := XΣB+ ⊂ B
+be the open toric subscheme of B associated with ΣB+. The subscheme B+ is called
+the Cox characteristic space. The morphism B+ → X corresponding to ΣB+ → Σ
+is toric and affine. It defines the homomorphism of the relevant tori
+φ : TB := Spec(κ[Div(X)]) → T := Spec(κ[M]),
+corresponding to the inclusion M ֒→ Div(X) and defining the exact sequence
+0 → M → Div(X) → Cl(X) → 0.
+Consequently, the kernel of φ can be identified canonically with TX := Spec(κ[Cl(X)]).
+Since TX acts trivially on T ⊂ X, the morphism B+ → X is TX-invariant and
+affine. Moreover for any δ ∈ Σ, and δ0 = π−1(δ), we have that π(δ0) = δ, and
+Xδ0 � TX = Xδ.
+Thus, the affine TX-invariant morphism B+ → X is a good
+quotient.
+2.2.6. Forms. By the form F on X we mean a Cl(X)-homogenous function of
+gradation [E] in
+H0(X, OX(E))xE = H0(B, OB)[E] = C(X)[E] = (OB)[E].
+Each such TB-semiinvariant form can be described as
+F = xD = xα = xm · xE,
+where D ∈ Div(X), D = E + div(xm), and xm ∈ H0(X, OX(E)), for E being a
+linear combination of Ei.
+With any form F = fxE ∈ H0(X, OX(E))xE we can associate its divisor
+divX(F) = E + div(f), and its vanishing locus V (F) = supp(div(F)). This ex-
+tends to a homomorphism
+Div(X) → Div(X),
+D → div(xD),
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+21
+which is identical on generators Ei of Cl(X) ⊂ Div(X), and thus on their linear
+combinations. On the other hand, any class [D] ∈ Cl(X) can be written as the
+difference
+[D] = [E′] ∖ [E′′]
+of effective linear combinations E′ and E′′ of the generators Ei.
+Then E′ + div(xm) = D + E′′ is effective, for a certain m ∈ M, and we have the
+equality for the form F := xmxE′:
+div(F) = div(xmxE′) = div(xD) + div(E′′),
+whence
+D + E′′ = E′ + div(xm) = div(xD) + E′′
+and thus
+divX(xD) = D,
+for any D ∈ Div(X). Consequently V (xD) = supp(D) for any form xD, where
+D ∈ Div(X)+.
+In particular, the vanishing locus div(xi) = div(xDi) = Di corresponds to the
+vertex vi ∈ Vert(Σ).
+2.2.7. Cox characteristic space. The subscheme B+ can be described using the TB-
+semiinvariant forms on X as in [ADHL15]. By the construction, B+ can be covered
+by the open affine subsets Bδ := π−1(Xδ), where δ ∈ ΣB+. For each δ ∈ ΣB+ con-
+sider the form ˇxδ := �
+vi̸∈δ xi on X. Its vanishing locus is equal to the complement
+X ∖ Xδ =
+�
+vi̸∈δ
+Di.
+So we can write Xδ = X ∖ VX(ˇxδ). Similarly Bδ = B ∖ VB(ˇxδ) = Bˇxδ, where ˇxδ is
+considered as a function on B.
+Consequently
+B+ = B ∖ V (Iirr),
+where
+Iirr := (ˇxδ | δ ∈ Σ) ⊂ O(B) = C(X)
+is the irrelevant ideal (see [Cox95],[ADHL15]).
+Moreover the morphism Bδ → Xδ, can be described as
+Bδ = Bˇxδ = Spec(κ[x1, . . . , xk]ˇxδ) → Xδ = Xˇxδ = X ∖ VX(ˇxδ)
+Note however then that the condition f ∈ H0(Xˇxδ, OX(E)) is equivalent to
+div(f) + E + div(ˇxn
+δ ) ≥ 0
+for n ≫ 0. The latter condition can be written as
+fxE · ˇxn
+δ ∈ H0(X, OX(E + n[div(ˇxδ)]) · xE+n[div(ˇxδ)]
+Consequently
+κ[x1, . . . , xk]ˇxδ = (
+�
+E∈Cl(X)
+H0(X, OX(E)) · xE)ˇxδ =
+�
+E∈Cl(X)
+H0(Xδ, OX(E)) · xE
+The latter leads to the formula for the Cox characteristic space to be
+B+ = Cox(X) = SpecX(
+�
+E∈Cl(X)
+OX(E) · xE)
+as in [ADHL15].
+
+22
+J. W�LODARCZYK
+2.3. Cox relative spaces over affine toric schemes. In this section, we shall
+study the general relative Cox construction developed in Chapter 1 in the context
+of birational toric morphisms. To a great extent, it is analogous to the original Cox
+construction for toric varieties (as in [Cox95]) presented in the previous section.
+On the other hand, one can link it to the original construction of Satriano, who
+developed a similar notion in the context of the toric Artin stacks in [Sat13].
+The following result shows the relation between the toric Cox construction for
+toric varieties and the general Cox construction for proper morphisms.
+Lemma 2.3.1. Let σ be a regular cone, and ∆ be its subdivision. Let π : X∆ → Xσ
+be the induced proper birational morphism. Then the toric Cox coordinate space
+Cox(X∆) and the toric Cox characteristic space Cox(X∆)+ for toric variety X∆
+coincide with the relative Cox coordinate space B = Cox(X∆/Xσ) and relative
+Cox characteristic space B+ = Cox(X∆/Xσ)+ for the proper birational morphism
+X∆ → Xσ.
+Proof. The construction of the spaces is formally identical.
+The reason is that
+the gradation in both cases is the group Cl(X∆) = Cl(X∆/Xσ), which is freely
+generated by the exceptional toric divisors Ei with no relations.
+♣
+2.3.2. System of local parameters on affine toric schemes. Let Pσ = σ∨ ∩ M be
+the monoid associated with the affine toric variety Xσ = Spec(κ[Pσ]). Denote by
+P ∗
+σ ≃ Zr the subgroup of the invertible elements in Pσ, and let P σ := Pσ/P ∗
+σ. The
+natural homomorphism of monoids Pσ → P σ = Pσ/P ∗
+σ splits, and one can write
+noncanonically
+Pσ = P σ × P ∗
+σ,
+Let u1 = m1, . . . , us = ms ∈ Pσ be the minimal set of generators of the monoid
+P σ. This set is determined uniquely and consists of the elements m ∈ P σ, which
+cannot be written as m = m′ · m′′ for the nontrivial elements m′, m′′ ∈ P σ.
+Definition 2.3.3. The set of generators of u1, . . . , us ∈ P σ ⊂ Pσ will be called a
+system of local toric parameters on Xσ.
+2.3.4. Cox relative spaces over affine toric schemes.
+Lemma 2.3.5. Let σ0 be any cone in NQ, and ∆ be its subdivision. Consider the
+induced toric morphism π : X∆ → Xσ0 = Spec(κ[Pσ0]).
+Let E1, . . . , Ek be the
+toric exceptional divisors of π corresponding to the vertices v1, . . . , vk ∈ Vert(∆) ∖
+Vert(σ0), and the exceptional valuations νi = val(vi).
+Let B and B+ denote the full cobordization and, respectively, the cobordization
+of the morphism X∆ → Xσ0
+Then
+(1) B = Spec OXσ[t−1
+1 , . . . , t−1
+k , u1tα1, . . . , ustαk], where and u1, . . . , uk ∈ Pσ
+is a system of local toric parameters and αi = (ai1, . . . , aik), with aij :=
+νj(ui).
+(2) B is a toric variety B ≃ Xσ0 × Ak, and the corresponding cone is
+σB = σ0 × ⟨e1, . . . , ek⟩.
+(3) The natural morphism
+B = Spec OXσ0 [t−1
+1 , . . . , t−1
+k , u1tα1, . . . , uktαk] → Xσ0
+is given by the projection πΣ : σB → σ0, mapping ei �→ vi.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+23
+(4) B+ ⊂ XσB can be described as the set ΣB+ of the faces σ of σB such that
+πΣ(σ) ⊆ δ, where δ ∈ ∆. In particular, B+ ⊂ B is an open inclusion.
+Proof. First we will show that X∆ can be covered by the open affine subsets (X∆)F ,
+where F is a form on X∆. The problem translates into a toric situation. For any
+cone δ ∈ ∆ let ω be a maximal common face of δ and σ0. Consider a character
+χδ ∈ σ∨
+0 which is zero on ω and strictly positive on σ0 ∖ω. The character χδ defines
+a regular function on Xσ0, for which
+ni := χδ(vi) = νi(χδ) > 0,
+for any vertex
+vi ∈ Vert(δ) ∖ Vert(ω) = Vert(δ) ∖ Vert(σ0).
+In particular div(χδ) − Eδ ≥ 0, where Eδ := �
+Ei∩Xδ̸=∅ niEi. Then, for the form
+Fδ := χδx−Eδ, its support
+supp(div(Fδ)) = supp(div(χδ)) − Eδ)
+on X∆ is the union of all the toric divisors which are in X∆ ∖ Xδ and which
+correspond to the vertices in Vert(∆) ∖ Vert(δ). Consequently supp(div(Fδ)) =
+X∆ ∖ Xδ, and XFδ = Xδ. This implies, by Proposition 1.3.4, that the natural
+morphism
+B+ =
+�
+δ∈∆
+Bδ ֒→ B
+is an open immersion, where Bδ := BFδ is open affine.
+(1) For any i = 1, . . . , k let ti be the coordinate corresponding to −Ei. Set
+ˇti := (t1, . . . , ˇti, . . . , tk)
+ˇt−1
+i
+:= (t−1
+1 , . . . , ˇt−1
+i , . . . , t−1
+k )
+By Proposition 1.1.5 one can write:
+AY/X =
+�
+ai∈Z
+k�
+i=1
+Iνi,ai · ta1
+1 · . . . · tak
+k =
+k�
+i=1
+�
+ai∈Z
+Iνi,ai · tai
+i [ˇti,ˇt−1
+i ],
+Let u1, . . . , uk ∈ P σ = Pσ/P ∗
+σ ⊂ Pσ be the generators of P σ, and let νi(uj) = aij ∈
+Z≥0 for i = 1, . . . , k, and j = 1, . . . , n. Then
+Iνi,a = (ub1
+1 · . . . · ubn
+n ) |
+k
+�
+j=1
+bjaij ≥ a).
+Comparing gradations we easily see that for each i,
+�
+ai∈Z
+Iνi,atai
+i
+= OX[t−1
+i , ujtaij
+i
+].
+So
+AY/X =
+k�
+i=1
+OX[t−1
+i
+, ujtaij
+i
+][ˇti,ˇt−1
+i ] = OX[t−1
+1 , . . . , t−1
+k , u1tα1, . . . , uktαk],
+where αi = (ai1, . . . , aik).
+
+24
+J. W�LODARCZYK
+(2)
+B = Spec OXσ[t−1
+1 , . . . , t−1
+k , u1tα1, . . . , uktαk] =
+= Spec(κ[u1, . . . , uk, v1, . . . , vr][t−1
+1 , . . . , t−1
+k , u1tα1, . . . , uktαk] =
+= Spec(κ[t−1
+1 , . . . , t−1
+k , u1tα1, . . . , uktαk, v1, . . . , vr] ≃
+≃ Spec(κ[t−1
+1 , . . . , t−1
+k , u1, . . . , uk, v1, . . . , vr]) ≃ Xσ0 × Ak.
+(3) The toric map
+B = Spec(κ[t−1
+1 , . . . , t−1
+k , u1tα1, . . . , uktαk, v1, . . . , vr] →
+Xσ0 = Spec(κ[u1, . . . , us, v1, . . . , vr]),
+corresponds to the map of cones
+πB : σB ≃ σ0 × ⟨e1, . . . , ek⟩ → σ0.
+Under this correspondence
+val(ei)(t−1
+j ) = δij,
+val(ei)(ujtαj) = 0.
+On the other hand val(v)(t−1
+i
+) = 0 for any integral vector v ∈ σ0.
+By the above we can write
+B = Spec(κ[t−1
+1 , . . . , t−1
+k ] × Spec(κ[u1tα1, . . . , uktαk, v1, . . . , vr])
+The toric valuation µi on B associated to the divisor Di = VB(t−1
+i ) satisfies
+µi(ujtαj) = 0, and µi(t−1
+i′ ) = 0 for i ̸= i′. It corresponds to the vector ei, as val(ei)
+fulfills precisely the same relations.
+The quotient morphism πB : B → Xσ0 takes a toric valuation val(v) on B, for
+any integral v ∈ σB to the restriction to O(Xσ0) corresponding to val(πΣ(v)). It
+maps the vertices of the face σ0 ⊂ σB to the very same vertices of σ0. The image
+of the vector ei is the vertex πΣ(ei) = vi ∈ Vert(∆) ∖ Vert(σ0). This follows from
+Lemma 1.2.9 or can be seen by direct computation. By the previous considerations,
+vi corresponds to νi on X∆, and ei to the valuation µi of t−1
+i
+on B+. The restriction
+of the toric valuation µi to κ[u1, . . . , uk], gives
+µi(uj) = µi(ujtαj · t−αj) = µi(tαj) = aij = νi(uj).
+(4) By the considerations at the beginning of the proof, and Lemma 1.3.2, we
+can write B+ as the union of open affine subsets Bδ = BFδ = π−1
+B+(Xδ):
+B+ =
+�
+δ∈∆
+Bδ ⊂ B.
+The induced map of fans ΣB+ → ∆ corresponds to the good quotient B+ → B+�T ,
+and is defined by the linear map:
+πΣ : NQ
+B = NQ
+B+ → NQ = NQ
+Y = NQ
+Y .
+Thus any cone δ ∈ ∆ can be written as the image δ = πΣ(δ′), where δ′ ∈ ΣB+.
+In particular any vertex vi ∈ Vert(∆) ∖ Vert(σ0) is the image vi = π(ei) of ei ∈
+Vert(ΣB) = Vert(ΣB+). Consequently, the fan ΣB+ is determined by the faces τ of
+ΣB such that πΣ(τ) ∈ ∆.
+♣
+2.4. Cox relative spaces for toric morphisms. General case.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+25
+2.4.1. Coborization of proper toric morphisms. Let ∆ be a subdivision of a fan Σ.
+We can further generalize the characterization of the cobordization of any proper
+birational toric morphism π : X∆ → XΣ.
+Proposition 2.4.2. Let ∆ be a fan subdivision of a fan Σ. Let π : Y = X∆ → X =
+XΣ be the associated proper toric morphism of toric varieties. Let v1, . . . , vk be the
+vertices of Vert(∆) ∖ Vert(Σ) corresponding to the toric valuations νi = val(vi),
+associated with the exceptional divisors E1, . . . , Ek. Let σ0 = ⟨e1, . . . , ek⟩ be the
+regular cone defined by the free basis e1, . . . , ek.
+Let πΣ : |Σ| × σ0 → |Σ| be the linear map of the supports of fans such that
+πΣ(ei) = vi, and identical on |Σ|. Consider the subfan ΣB of Σ × σ0 consisting of
+the faces of Σ × σ0 mapping to faces of Σ, under the projection πΣ. Then the full
+cobordization B → X of π can be described as the toric morphism associated with
+the projection πΣ|ΣB : ΣB → Σ.
+The morphism B+ ⊂ B is an open inclusion which corresponds to the subfan
+ΣB+ of ΣB of all the faces of Σ × σ0 mapping to the faces of ∆.
+Proof. By Lemma 2.3.5, and reducing to the affine case, we see that B+ ⊂ B is an
+open immersion.
+Let T0 := Spec(κ[M]) ⊂ XΣ be the torus acting on XΣ, and on X∆.
+Let
+TB := Spec(κ[t1, t−1
+1 , . . . , tk, t−1
+k ]), where the coordinates t−1
+1 , . . . , t−1
+k , correspond
+to e1, . . . , ek on Xσ0 = κ[t−1
+1 , . . . , t−1
+k ]) . By Proposition 1.2.2, we can write B as
+B = Spec(AY/X), where
+AY/X =
+�
+ai∈Z
+k�
+i=1
+Iνi,ai · ta1
+1 · . . . · tak
+k ⊂ OX[t1, t−1
+1 , . . . , tk, t−1
+k ]
+Consequently, B contains a toric variety
+B = SpecX(AY/X) ⊃ B− = SpecX(OX[t1, t−1
+1 , . . . , tk, t−1
+k ]) = XΣ × TB,
+and hence contains a torus T0 × TB. Moreover the torus T0 × TB acts on B.
+On the other hand, by Lemmas 1.6.1, and 2.3.5 the scheme B is the union of
+toric varieties Bσ containing T0 × TB, associated with σ ∈ Σ, such that
+Bσ := π−1
+B (Xσ) = B(X∆|σ/Xσ) × T (Xσ) =
+SpecXσ(OXσ[t−1
+1 , . . . , t−1
+k , u1tα1, . . . , ustαk].
+Thus B is a toric variety, let ΣB its corresponding fan. The affine toric morphism
+B → X determines the homomorphism of tori T0 × TB → T0. It corresponds to the
+map of fans (ΣB, N0 × NB) → (Σ, N0), defined by the natural projection N0 × NB
+Consider the toric variety XΣ × Spec(κ[t−1
+1 , . . . , t−1
+k ]), associated with the fan
+Σ × σ0, with the lattice N0 × NB. The linear map
+πΣ : (|Σ| × σ0, N0 × NB) → (|Σ|, N0),
+satisfies πΣ(ei) = vi, and πΣ|N0 = idN0.
+The full cobordization morphism B → XΣ takes the divisor Di = VB(t−1
+i ) to
+Ei by Lemma 1.2.9. Thus it defines the same map on the lattices πΣ : NB → N.
+Moreover, by Lemmas 1.6.1, and 2.3.5, each toric variety
+Bσ = B(X∆|σ/Xσ) × TB∖Bσ ⊂ B
+corresponds to the subfan determined by the cone σ ×τ(σ) of Σ×σ0, where τ(σ) ≤
+σ0 is generated by all ei with vi ∈ σ.
+
+26
+J. W�LODARCZYK
+Thus, by Lemma 2.3.5(4), ΣB consists exactly of the faces of Σ × σ0 mapping
+into faces of Σ, under the projection πΣ : ei �→ vi. Consequently, B+ corresponds
+to the subfan ΣB+ of ΣB of all the faces mapping to the faces of ∆.
+♣
+2.5. The dual complex of the exceptional divisor.
+2.5.1. The dual complex of toric morphisms. Let π : Y = X∆ → XΣ be a proper
+toric morphism, where ∆ is a subdivision of Σ. Assume that X = XΣ is smooth.
+Then the full cobordization B of π is a smooth toric variety with the toric morphism
+πB : B → X. Consequently the exceptional divisors D = VB(t−1
+1 , . . . , t−1
+k ) of πB
+and D+ = D ∩ B+ of πB+ are SNC. On the other hand the components Di+ map
+to the components Ei of the exceptional toric divisor E of π : Y → X.
+One can define the divisorial stratifications SD, and SD+ on B, and B+ with the
+strata determined by the nonempty sets
+sI :=
+�
+i∈I
+Di ∖
+�
+j∈J
+Dj,
+where I ∪ J = {1, . . . , k}, I ∩ J = ∅. Note that the closure sI can be written in the
+form
+sI =
+�
+i∈I
+Di.
+Likewise the stratification SE od E on Y is determined by the nonempty closed
+sets sIE := �
+i∈I Ei, which determine the strata sE
+I obtained by removing from sIE
+all the proper subsets sJ E ⊂ sIE, with J ⊃ I.
+These three stratifications are coarser than the orbit stratifications; thus, each
+stratum is the union of orbits. The divisorial stratifications SD and SD+ define the
+dual complexes ∆D and ∆D+ ⊂ ∆D. The vertices ei of ∆D and ∆D+ correspond
+to the divisors Di or, respectively Di+. We associate with a stratum s = �
+i∈I Di ∖
+�
+j∈J Dj, the simplex σs := ∆(ei | i ∈ I).
+Similarly, we can define the dual complex ∆E associated with the toric excep-
+tional divisor E on Y (which is usually not SNC). Again the vertices ei of ∆E
+correspond to the divisors Ei. We associate with any set of divisors {Ei | i ∈ I}
+such that �
+i∈I Ei ̸= ∅ the simplex σI := ∆(ei | i ∈ I). Summarizing we obtain the
+following characterization of the complexes:
+Lemma 2.5.2. A simplex σ in ∆D( respectively in ∆D+ or ∆E) corresponds bi-
+jectively to a set of divisors Di ( respectively Di+ or Ei) having a nonempty inter-
+section.
+♣
+Lemma 2.5.3. Let B → X be the full cobordization of π : Y = X∆ → X = XΣ.
+Let D be the exceptional divisor on B, and SD be the induced stratification. Then
+for any stratum s ∈ SD, the image πB(s) is closed in X.
+Proof. The problem is local on X so we can assume that X = Xσ. Let B = Xσ×Xδ,
+where δ = ⟨e1, . . . , ek⟩ the regular cone generated by a free basis {e1, . . . , ek}.
+The morphism B → X corresponds to the projection πΣ : σB = σ × δ → σ,
+mapping ei to vi ∈ Vert(∆) ∖ Vert(σ).
+Any stratum s = �
+i∈I Di ∖ �
+j∈J Dj in SD is closed on the open affine subset
+B′ = B ∖ �
+j∈J Dj of B. By replacing B with the open affine subset B′ = Bt−1
+J ,
+where tJ = �
+j∈J tj, we assume that s = �
+i∈I Di and all the exceptional vertices ei
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+27
+of σ × δ , where i ∈ I, span the cone δ. Then s is the union of orbits corresponding
+to the cones in Star(δ, σB).
+Let δ0 := πΣ(δ) be the image of δ, which is a subcone in σ generated by πΣ(ei).
+Denote by σ0 ≤ σ the unique face such that int(δ0) ⊂ σ0 ≤ σ.
+Thus, since σ is regular, and the map πΣ is surjective, the image πB(s) of s is
+defined by the orbits corresponding to the cones in Star(σ0, σ), and thus it is closed.
+♣
+2.5.4. The center of valuation. Recall that for any valuation ν of the quotient field
+κ(X), we denote its center on X by ZX(ν).
+Corollary 2.5.5. Consider any stratum s ∈ SD such that s = �
+i∈I Di ∖ �
+j∈J Dj.
+Then
+πB(s) =
+�
+i∈I
+ZX(νi),
+Proof. Note that, by Lemma 1.2.9, the image πB(Di) = ZX(νi). Then πB(s) ⊆
+�
+i∈I ZX(νi). The problem is local on X, and we use the notation and the description
+from the proof of the previous Lemma. The stratum s contains a generic toric orbit
+corresponding to the cone δ = ⟨ei | i ∈ I⟩. Its image πB(s) is closed and corresponds
+to the Star(σ0, σ), where σ0 is the smallest face containing the images {vi | i ∈ I},
+where val(vi) = νi.
+On the other hand, �
+i∈I ZX(νi) corresponds to the faces of σ containing all vi.
+Both sets are identical and πB(s) = �
+i∈I ZX(νi).
+♣
+Lemma 2.5.6. The morphism πB+,Y : B+ → Y determines a bijective correspon-
+dence between the sets of divisors {Di+ | i ∈ I} such that � Di+ ̸= 0, and the sets
+{Ei | i ∈ I} for which � Ei ̸= 0.
+Proof. We need to show that �
+i∈I Di+ ̸= ∅ iff �
+i∈I Ei ̸= ∅. By Lemma 2.5.6,
+πB+,Y (Di+) = Ei. Thus if �
+i∈I Di+ is nonempty then
+�
+i∈I
+πB+,Y (Di+) =
+�
+i∈I
+Ei ⊇ πB+,Y (
+�
+i∈I
+Di+) ̸= ∅.
+Conversely, if �
+i∈I Ei is nonempty then the vertices vi corresponding to Ei form
+the subcone τ = ⟨vi | i ∈ I⟩ of a face δ ∈ ∆, with Vert(τ) ⊆ Vert(δ) ∖ Vert(σ).
+Consequently, by Lemma 2.3.5(4), τ is the image of the face δ′ = ⟨ei | i ∈ I⟩ ∈ ∆B+,
+whence �
+i∈I Di+ is nonempty.
+♣
+Corollary 2.5.7. The natural surjective map SD+ → SE determines an isomor-
+phism of the dual complexes ∆D+ ≃ ∆E.
+♣
+Also, we have
+Corollary 2.5.8. The natural morphism SD+ → SD determines the inclusion of
+the dual complexes ∆D+ ≃ ∆D, so that ∆D+ is a subcomplex of ∆D.
+Proof. By the construction, the faces of ∆D (and ∆D+) correspond to the sets of
+divisors {Di | i ∈ I} such that �
+i∈I Di ̸= ∅. Now, if �
+i∈I Di+ ̸= ∅ then obviously
+�
+i∈I Di ̸= ∅.
+♣
+2.6. Newton polytopes of monomial ideals.
+
+28
+J. W�LODARCZYK
+2.6.1. Newton polytopes.
+Definition 2.6.2. Consider the lattice of monomials
+M = {xα | α ∈ Zk} ≃ Zk,
+and let N = Hom(M, Z) be its dual. Let I = (xα1, . . . , xαk) ⊂ κ[x1, . . . , xn] be a
+toric ideal generated by the monomials corresponding to the elements of
+αi ∈ Zn
+≥0 ⊂ σ∨
+0 = ⟨e∗
+1, . . . , e∗
+n⟩ = Qn
+≥0.
+By the associated Newton polytope of I we mean
+P = PI := conv(α1 + Qn
+≥0, . . . , αk + Qn
+≥0) ⊆ Qn
+≥0 ⊆ MQ = M ⊗ Q = Qn
+Conversely any polytope (or polyhedron) P = P + Qn
+≥0 determines the ideal
+I = IP := (xα | α ∈ P).
+Lemma 2.6.3. There is a bijective correspondence I �→ PI, P �→ IP , between
+integrally closed toric ideals I ⊂ κ[x1, . . . , xn], and polytopes P = P + Qn
+≥0 with
+integral vertices.
+♣
+2.6.4. The orbit stratification. One can identify e∗
+i with xi, so we can write σ∨
+0 =
+⟨x1, . . . , xn⟩. Denote by NQ the dual space of MQ, and σ0 ⊂ NQ the dual of σ∨
+0 as
+in Sections 2.1.1, 2.1.2. For any τ ⊂ NQ set
+τ ⊥ := {y ∈ MQ | (x, y) = 0
+for all x ∈ τ},
+Lemma 2.6.5. There is a natural bijective correspondence between
+• the faces τ of σ0
+• the faces τ∗ := τ ⊥ ∩ σ∨
+0 of σ∨
+0 .
+• the open affine subsets Xτ ⊂ Xσ0
+• the minimal closed orbits Oτ ⊂ Xτ which are in Xσ0.
+Moreover under the above identification the closure Oτ of the orbit Oτ is defined
+by the ideal (xi | xi ̸∈ τ ∗).
+Proof. The face τ of σ0 determines the open subset
+Xτ = Spec(κ[τ∨ ∩ M]) = Spec(κ[Pτ]) = Spec(κ[P ∗
+τ ]) × Spec(κ[P τ])
+of Xσ0, where
+Pτ = τ∨ ∩ M = Pσ0 + P ∗
+τ = Pσ0 − (τ ∗ ∩ M).
+Thus τ ∗ ∩ M = P ∗
+τ ∩ Pσ0 consists of the elements of Pσ0 = σ∨
+0 ∩ M, which are
+invertible in Pτ. The closed orbit Oτ ⊂ Xτ is described by the ideal generated by
+the set of noninvertible elements
+Pτ ∖ P ∗
+τ := (τ ∨ ∖ τ ∗ ∖ (−τ ∗)) ∩ M ⊂ Pτ.
+Thus its closure Oτ in Xσ0 is defined by the ideal (xi | xi ̸∈ τ ∗) corresponding to the
+monoid ideal Pσ0 ∖ P ∗
+τ = (σ∨
+0 ∖ τ ∗) ∩ M. Conversely, any face τ ∗ of σ∨
+0 determines
+the closure Oτ ⊂ Xσ0 of the orbit Oτ with the monoid ideal (σ∨
+0 ∖ τ ∗) ∩ M, and
+the face τ = (τ ∗)⊥ ∩ σ0 of σ0 ⊂ NQ.
+♣
+By the construction, Oτ is the smallest T -stable closed subset of Xτ. If τ ⊂ τ′ is
+the inclusion of the faces then Xτ ⊂ Xτ ′ is an open immersion, and Oτ contains Oτ ′.
+Consequently the orbits Oτ form the stratification of Xσ0 = Spec(κ[x1, . . . , xn]).
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+29
+Corollary 2.6.6. Let I ⊂ κ[x1, . . . , xk] be a monomial ideal and PI ⊂ σ∨
+0 be its
+Newton polytope. Then the toric subset V (I) is exactly the union of the orbits Oτ
+such that τ ∗ is disjoint from PI.
+Proof. The orbit Oτ is contained in V (I) if and only if the ideal of Oτ contains I.
+Thus the corresponding monoid ideal (σ∨
+0 ∖ τ∗) ∩ M contains P ∩ M. The latter is
+equivalent to the condition τ∗ ∩ P = ∅.
+♣
+2.6.7. Supporting faces. The monomial ideal I = (xα1, . . . , xαk) defines a piecewise
+linear convex function FI := min(αi, v) on σ0 := ⟨e1, . . . , en⟩ which is dual to σ∨
+0 .
+Likewise any polytope P ⊂ σ∨
+0 determines a piecewise linear convex function
+FP := min((w, v) | w ∈ P)
+on σ0.
+If P = P(I) then both functions coincide:
+FP = FI = min(v, αi) = min((v, w) | w ∈ P))
+By the dual fan or normal fan of P, we mean the fan ∆P = ∆I is determined by
+the maximal cones τ ⊂ σ0, where FP is linear. By definition, ∆P is a decomposition
+of σ0.
+Conversely, the function FP on σ0, determines the polytope
+P = {w ∈ σ∨
+0 | (·, w)|σ0 ≥ FP |σ0}.
+Recall the standard fact from the convex geometry:
+Lemma 2.6.8. There is a bijective correspondence between the faces P of the
+polytope P0, and the faces τP of the fan ∆P0.
+P �→ τP := (P0 − P)∨ = {v ∈ σ0 | (v, w) ≥ 0, w ∈ P0 − P} ∈ ∆P0
+τ �→ Pτ = {w ∈ P | FP |σ = (·, w)|σ}.
+Moreover dim(P) = n − dim(σP ).
+♣
+Remark 2.6.9. For any i = 1, . . . , n, let
+ai := min{xi(p) | p ∈ P}.
+Then
+Pi := {p ∈ P | (xi − ai)(p) = 0}
+is the face of P corresponding to the one-dimensional face ⟨ei⟩ determine by the
+vertex ei of σ.
+Definition 2.6.10. By the supporting facets of P0 we mean the faces corresponding
+to the vertices of Vert(∆P0) ∖ Vert(σ). The affine hull of a supporting face will be
+called a supporting hyperplane. By the supporting faces, we mean the faces, which
+are the intersections of some supporting facets.
+As a corollary from Lemma 2.6.8, we obtain
+Lemma 2.6.11. Let ∆ be the subdivision of regular cone σ0 associated with the
+normalized blow-up π : Y = X∆ → X = Xσ0 of the monomial ideal I ⊂ κ[Pσ] =
+κ[x1, . . . , xn]. Let B → X = Xσ0 = An be the full cobordant blow-up of I. Then
+the following sets are in the bijective correspondence
+(1) The supporting hyperplanes Hi of P(I).
+
+30
+J. W�LODARCZYK
+(2) The vertices vi of Vert(∆) ∖ Vert(σ0).
+(3) The exceptional divisors Di of B → X.
+(4) The exceptional divisors Ei of Y → X.
+(5) The toric exceptional valuations νi = val(vi) on X associated with Ei on
+Y .
+(6) The vertices of the dual complexes ∆E ≃ ∆D+ and ∆D.
+♣
+Remark 2.6.12. The supporting faces exist if codim(V (I)) ≥ 2. On the other
+hand, if I is principal, then ∆ = σ0, and thus P admits no supporting faces.
+Corollary 2.6.13. With the above notation and assumptions:
+(1) Any exceptional valuation ν determines the supporting hyperplane Hν.
+(2) With a face σ of ∆E one can associate the set ωσ of the exceptional valua-
+tions corresponding to the vertices Vert(σ).
+(3) Any face σ of the dual complex ∆E determines the supporting face Pσ of
+P, where
+Pσ =
+�
+ν∈ωσ
+Hν ∩ P.
+(4)
+inv◦
+ωσ(I) := (uα ∈ I | ν(I) = ν(xα), ν ∈ ωσ) =
+= invPσ(I) := (xα ∈ I | α ∈ Pσ).
+♣
+Here
+ν(I) := min{ν(f) | f ∈ I}.
+One can see the above relations in the following example:
+Example 2.6.14. Let I = (xk, xy, yl) ⊂ κ[x, y].
+The Newton polytope P of I is generated by the vertices P1 = (k, 0), P2 =
+(1, 1), P3 = (0, l) of P. The supporting planes H1, and H2 are determined, respec-
+tively, by the supporting facets P12 = conv({(k, 0), (1, 1)}), and P23 = conv({(1, 1), (0, l)}).
+They correspond to the vectors v1 = (v11, v12), v2 = (v21, v22) such that
+kv11 = v11 + v12,
+v21 + v22 = lv21
+Thus v1 = (1, k − 1), v2 = (l − 1, 1). The decomposition ∆P consists of three 2-
+dimesional cones σ1 = ⟨e1, v1⟩, σ2 = ⟨v1, v2⟩, σ3 = ⟨v2, e2⟩, and their 1-dimesional
+faces. These 2-dimesional faces in ∆P correspond to the vertices (k, 0), (1, 1), (0, l)
+of P, and the associated monomials xk, xy, yl. The vectors v1, v2 ∈ Vert(∆p) cor-
+respond to the exceptional valuations ν1 = val(v1), ν2 = val(v2). In particular
+inv◦
+ν1(I) = invP12(I) = (xk, xy),
+inv◦
+ν2(I) = invP23(I) = (xy, yl),
+inv◦
+ν1,ν2(I) = invP2(I) = (xy).
+Note that the vertices in Vert(P), which are, in our case, defined by xk, xy, yl,
+label the maximal faces in ∆P .
+We see that the monomials in inv◦
+ω(I) = invP (I) correspond to the maximal
+cones in the star of the relevant face in ∆P . This face is described as the dual
+to P.
+Equivalently, it is defined as the smallest face containing the set of the
+vertices of ∆P determined by ω. In particular, the generators xk, xy occurring in
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+31
+inv◦
+ν1(I) = inv◦
+P12(I) = (xk, xy) correspond to the maximal cones in the star of the
+face ⟨v1⟩ ∈ ∆P .
+The full cobordant blow-up of I = (xk, xy, yl) is given by
+B = Spec(κ[t−1
+1 , t−1
+2 , xt1tl−1
+2
+, ytk−1
+1
+t2]),
+and using Lemma 1.4.4,
+B+ = Spec(κ[t−1
+1 , t−1
+2 , xt1tl−1
+2
+, ytk−1
+1
+t2]) ∖ V (tk
+1tl
+2(xk, xy, yl)).
+2.7. Geometric quotients for toric morphisms.
+Lemma 2.7.1. Let π : Y = X∆ → XΣ be a toric morphism, associated with the
+decomposition ∆ of Σ. Assume that Σ is simplicial.
+Then its cobordization B+ → Y = B+/TB is a geometric quotient iff ∆ is
+simplicial.
+Proof. The problem is local on X, and can be reduced to the affine toric morphism
+X∆ → Xσ corresponding to the subdivision ∆ of a simplicial cone σ. Then, by
+Proposition 2.4.2, ΣB is simplicial, and so is ΣB+.
+The natural projection ΣB+ → ∆ is defined bijectively on the vertices. Moreover,
+the faces of ∆ are the images of cones in ΣB+. Thus ΣB+ → ∆ is bijective on faces
+if and only if ∆ is simplicial. On the other hand, the condition that ΣB+ → ∆ is
+bijective on faces is equivalent to B+ → Y being a geometric quotient.
+♣
+Lemma 2.7.2. Let π : Y = X∆ → X = XΣ be a proper birational toric morphism
+of toric varieties, with X regular. Then B+ ⊂ B contains open maximal subsets
+Bs ⊂ B+ admitting geometric quotient Bs/TB which is projective birational over
+Y .
+Proof. The morphism Y → X corresponds to the subdivision ∆ of Σ. Consider
+the sequence of the star subdivisions centered at Vert(∆) of ∆. By the definition
+of the star subdivision, the process transforms ∆ into a simplicial fan ∆′ with
+Vert(∆′) = Vert(∆), as all the vertices in the faces form linearly independent sets
+being the centers of the star subdivisions.
+So the valuations of the exceptional
+divisors corresponding to Vert(∆) = Vert(∆′) remain unchanged. Then, by Propo-
+sition 2.4.2 we obtain that B(Y/X) = B(Y ′/X). On the other hand, by the second
+part of Proposition 2.4.2, we have the open inclusions of toric subsets:
+Bs := B(Y ′/X)+ ⊂ B(Y/X)+ ⊂ B(Y/X).
+By the previous Lemma, Bs → Bs/TB = X∆′ is a geometric quotient.
+♣
+3. Cobordization of locally toric morphisms
+3.1. Locally toric morphisms of locally toric schemes.
+3.1.1. Locally toric schemes.
+Definition 3.1.2. A normal scheme X over a field κ is locally toric if any point
+p ∈ X admits an open neighborhood U, and a regular morphism φ : U → Xσ =
+Spec(κ[Pσ]), called a toric chart.
+An ideal I on a locally toric X is called locally monomial if for any point p ∈ X,
+there exists a toric chart U → Xσ = Spec(κ[Pσ]), and a monomial ideal Iσ ⊆ κ[Pσ],
+defined by a subset of Pσ, such that I|U = Iσ · OX|U.
+
+32
+J. W�LODARCZYK
+Remark 3.1.3. The primary reason we consider locally toric schemes over a field
+κ, and not just over Z, is that the morphisms to Spec(Z) are, in general, not flat.
+Thus the toric charts over Z into Spec(Z[Pσ]) which are defined by the monomials
+in Pσ = σ∨ ∩N are not regular (not flat), and some proofs would require a different
+formalism.
+3.1.4. Locally monomial valuations.
+Definition 3.1.5. Let X be a locally toric scheme. A valuation of κ(X) with values
+in Z will be called locally monomial if for any point p in the center Z(ν) ⊂ X, there
+exists a toric chart U → Xσ, and a vector v ∈ σ ∩N, such that Iν,a = OX ·Ival(v),a,
+for any a ∈ Z≥0.
+3.1.6. Locally toric morphisms.
+Definition 3.1.7. A proper birational morphism π : Y → X of normal schemes
+over a field κ is called locally toric if for any point p ∈ X there is an open neigh-
+borhood U, a toric chart φ : U → Xσ, and the fiber square:
+π−1(U)
+ψ→
+X∆
+πU ↓
+πA ↓
+U
+ψ→
+Xσ
+.
+where πU := π|π−1(U) : π−1(U) → U is the restriction of π.
+Proposition 3.1.8. Let J be a locally monomial ideal on a locally monomial
+scheme X. The normalized blow-up of J is a locally toric morphism.
+♣
+3.2. Functoriality of cobordization of locally toric morphisms.
+3.2.1. Local toric presentation of cobordization of locally toric morphisms.
+Lemma 3.2.2. Let π : Y → X be a locally toric proper birational morphism. Then
+for any point p ∈ X there exists an open neighborhood U of p ∈ X, a toric chart
+φU : U → Xσ and a fiber square
+YU := π−1U
+φ→
+X∆
+πU ↓
+πA ↓
+U
+φU
+→
+Xσ,
+.
+such that
+(1) There is a bijective correspondence between the irreducible exceptional di-
+visors of πU and πA. That is, any irreducible exceptional divisor of πU is
+the inverse image of an irreducible exceptional divisor of πA.
+(2) There is a bijective correspondence between the strata of the divisorial strat-
+ifications of the exceptional divisors EU of YU → U and E∆ of X∆ → Xσ,
+which defines the isomorphism Cl(YU/U) → Cl(X∆/Xσ). Moreover, any
+stratum of the stratification SE is the inverse image of a stratum in SE∆.
+(3) For any E′
+U = � ni(EU)i and the corresponding (E∆)′ = � niE∆
+i
+we have
+OYU ((E∆)′) = OY · (OX∆((E∆)′).
+(4) B(πU) = B(πA) ×Xσ U
+B+(πU) = B+(πA)+ ×Xσ U.
+(5) Any irreducible exceptional Weil divisor Ei of π defines a locally monomial
+valuation νi with respect to any given toric chart U → Xσ associated with
+the morphism π.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+33
+Proof. (1) Since φU is regular, the inverse images φ−1
+U (sτ) of the toric strata sτ,
+where τ ≤ σ, define a stratification on U. Moreover, the induced morphisms on the
+strata φ−1
+U (sτ) → sτ are regular.
+We can assume that the given point p ∈ X maps to a point q ∈ Xσ, which is in
+the orbit Oσ ⊂ Xσ. For any τ ≤ σ, the closure sτ := Oτ of the toric orbit Oτ on
+Xσ is normal. Moreover, since φU is regular, the inverse image φ−1
+U (sτ) is normal,
+and thus, it is the disjoint union of the irreducible components of the codimension
+equal to the codimension of sτ.
+Consequently, by shrinking U around p, if necessary, we can assume that the
+inverse image of the closures of the toric strata (i.e., the orbits) on Xσ are irreducible
+subsets of U.
+The inverse image of E∆ is the union of the normal divisorial components. Their
+images under πU are of the codimension ≥ 2. So they are the exceptional divisors
+of πU.
+Moreover all the irreducible exceptional divisors of πU are contained in
+φ−1(E∆).
+The image πA(E∆
+i ) contains the orbit Oσ with φ−1
+U (Oσ) ̸= ∅.
+Then, by the
+assumption, φ−1(E∆
+i ) ̸= ∅.
+We need to show that each φ−1(E∆
+i ) is an irreducible divisor. The image of the
+exceptional divisor E∆
+i
+under πA defines the closure of the toric orbit
+πA(E∆
+i ) = sτ = Oτ
+on Xσ, for some face τ ≤ σ. Denote by q the generic point of E∆
+i , and by q0 the
+generic point of sτ.
+For any divisorial component, Eij in φ−1(E∆
+i ), let pj be its generic point. By
+the assumption π(pj) ∈ U determines a unique point p0 which is the generic point
+of the stratum s on U so that
+s = φ−1
+U (sτ) = p0.
+By definition, the generic point q of the toric divisor E∆
+i
+on X∆ is in the fiber
+Fq0 = π−1
+A (q0). Thus the generic points pj of the components Eij of φ−1(E∆
+i ) are
+in the fiber
+Fp0 = π−1(p0
+i ) = Spec(κ(p0
+i )) ×Spec(κ(q0
+i )) Fq0
+i
+.
+Let ∆τ := ∆|τ be the restriction of ∆ to τ which determines the induced decom-
+position of τ.
+The fiber of
+Fp0 = Spec(κ(p0)) ×Spec(κ(q0)) Fq0 = Y ×X Spec(κ(p0))
+of π : Y = X ×Xσ X∆ → X is isomorphic to the fiber of the induced morphism
+Xκ(p0)
+∆τ
+→ Xκ(p0)
+τ
+over p0 = Spec(κ(p0)). Moreover the natural morphism Fp0 → Fq0 is induced by
+the fiber square
+Xκ(p0)
+∆τ
+φ∆
+→
+Xκ(q0)
+∆τ
+π ↓
+πA ↓
+Xκ(p0)
+τ
+φ→
+Xκ(q0)
+τ
+↓
+↓
+Spec(κ(p0))
+→
+Spec(κ(q0))
+.
+
+34
+J. W�LODARCZYK
+The above morphism is bijective on the toric orbits and their generic points, as
+they correspond to the faces of ∆ or respectively σ. Then the inverse image of the
+point qj ∈ Fq0 ⊂ Xκ(q0)
+∆τ
+corresponds to a unique face in ∆(1) and a unique point p
+in Fp0 ⊂ Xκ(p0)
+∆τ
+.
+Hence the inverse image of the toric divisor E∆
+i
+with the generic point q is the
+unique exceptional divisor Ei with the generic point p = pj over q.
+(2) The same reasoning shows that the inverse image φ−1
+∆ (s∆
+j ) = sj of the closure
+of a toric stratum s∆
+j on Xσ determines a unique stratum sj on YU. We use the
+same relation for the fibers.
+π−1(p0
+j) = Fp0
+j = Spec(κ(p0
+j)) ×Spec(κ(q0
+j )) Fq0
+j
+where pj is the generic point of sj, qj = φ(pj), p0
+j = π(pj) and q0
+j = πA(qj).
+(3) We need to show first that
+OY (nEi) = OY (OX∆(nE∆
+i ))
+By the above, the generic point p of Ei is exactly the generic point of the fiber
+φ−1(q). The induced homomorphism of the completions of the local rings is given
+by
+�
+OX∆,q → �
+OY,p = �
+OX∆,q ⊗κ(q) κ(p)
+Thus we get
+mn
+q · OX∆,p = mn
+q ⊂ OY,p.
+Both points p and q admit a regular neighborhood and its local rings are DVR
+defining the valuation νi of Ei, and ν∆
+i
+of E∆
+i .
+One verifies that Iνi,a,Y = OY · I∆
+νi,a. First observe that the valuation center of
+νi on Y can be described as
+ZY (νi) = VY (Iνi,a,Y ) = Ei = φ−1(E∆
+i ) = V (OY · I∆
+νi,a)
+For any point p′ ∈ Z(νi), and its image q′ = φ(p) ∈ Z(ν∆
+i ) we have
+�
+OY,p = �
+OX∆,p ⊗κ(p) κ(q)[[u1, . . . uk]].
+Consequently the monomial valuation ν∆
+i
+on OX∆,p′ = OXδ,p′ of E∆
+i
+associated
+with a vertex of ∆ extends to a certain unique monomial valuation ν′
+i on �
+OY,p such
+that
+�Iν′
+i,a,p′ = I∆
+νi,a · �
+OY,p′ = I∆
+νi · ( �
+OX∆,p′ ⊗κ(p′) κ(q′)[[u1, . . . uk]])
+which by flatness implies
+Iν′
+i,a,p′ = I∆
+νi,a · OY,p′
+Note that the generic point p of Ei specializes at p′, and the generic point q of E∆
+specializes at q′. Passing to p and q and localizing we obtain that
+Iν′
+i,a,p = I∆
+νi,a,q · OY,p = Iνi,a,p,
+whence both valuations are equal νi = ν′
+i. Thus Iνi,a,p′ = I∆
+νi,a,q′ · OY,p′ and the
+vanishing locus of the ideal
+Iνi,a,YU = OYU · I∆
+νi,a,X∆
+is irreducible by part (1) and defines the center of the valuation νi.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+35
+Now, for any effective divisor (E∆)′ = � aiE∆
+i , and its inverse image (EU)′ =
+� ai(EU)i we have, by flatness
+OYU (−(EU)′) =
+�
+Iνi,ai,YU = OYU · (
+�
+Iνi,ai,X∆) =
+= OYU · OX∆((E∆)′) = OYU ⊗OX∆ OX∆((E∆)′)
+In general, for any (E∆)′ = � aiE∆
+i , we can find a nontrivial monomial m ∈
+Pσ = σ∨ ∩ M such that for n ≫ 0,
+OY ((E∆)′) = m−nOY ((E∆)′ − n · div(m)),
+where −((E∆)′ − n · div(m)) is effective. Consequently
+OYU ((EU)′) = m−nOYU ((EU)′ − n · divY (m)) =
+= OYU · m−n · OX∆((E∆)′ − n · div(m)) = OYU OX∆(E∆) = OYU ⊗OX∆ OX∆(E∆).
+(4) and (5) Since the morphism U → Xσ is affine, and thus YU → X∆ is such
+we have
+BU+ = SpecYU (
+�
+E∈Cl(YU /U)
+OYU (E)) = SpecYU (OYU · (
+�
+E∆∈Cl(X∆/Xσ)
+OX∆(E∆)) =
+= SpecX∆ OYU ⊗OX∆ (
+�
+E∆∈Cl(X∆/Xσ)
+OX∆(E∆)) = YU ×X∆ B+(πA)+ =
+= (U ×Xσ X∆) ×U ×XσB+(πA) = U ×Xσ B+(πA).
+By definition, and since all the schemes are normal
+πA∗(Iν∆
+i ,a,X∆) = πA∗(OX∆(a, E∆
+i )) = Iνσ
+i ,a,Xσ ⊂ πA∗(OX∆(E∆)) = OXσ
+are the toric ideals generated by monomials associated with the toric valuation νσ
+i .
+Similarly
+π∗(Iνi,a,Y )) = π∗(OY (aE)) = Iνi,a,X.
+By the above and since ψ is flat, we have
+Iνi,a,U = π∗(OYU (−Ei)) = π∗(OYU · OX∆(−E∆
+i )) =
+π∗(OYU ⊗ OX∆(−E∆
+i )) = OU ⊗ πA∗(OX∆(−E∆
+i )) = OU · Iνi,a,Xσ
+is a locally monomial valuation.
+Thus for E = � aiEi, we have
+π∗(OYU (E)) =
+�
+Iνi,ai,U =
+�
+OU ·Iνi,a,Xσ = OU ·
+�
+Iνi,ai,Xσ = OU ·π∗(OX∆(E))
+Hence, by the above
+BU = SpecU(
+�
+E∈Cl(YU /U)
+π∗(OYU (E)) = SpecU(OU · (
+�
+E∆∈Cl(X∆/Xσ)
+π∗(OX∆(E∆)) =
+= SpecU(OU ⊗OXσ (
+�
+E∆∈Cl(X∆/Xσ)
+π∗(OX∆(E∆)) = U ×Xσ B(X∆/Xσ).
+♣
+
+36
+J. W�LODARCZYK
+3.2.3. Local description of the exceptional divisor. As a corollary from Lemma 3.2.2
+we obtain:
+Lemma 3.2.4. Let π : Y → X be a locally toric morphism of locally toric schemes.
+Let πB : B → X be its full cobordization.
+For any point p ∈ X, there is a toric chart φU : U → Xσ, such that for the
+induced morphism BU = π−1
+B (U) → X∆, there is a bijective correspondence between
+the strata s = φ−1(sτ) of the divisorial stratifications of the exceptional divisor DBU
+on BU, (respectively DBU+ on BU+) and the strata (sτ) of the exceptional divisor
+DB(X∆/Xσ) on B(X∆/Xσ) (respectively DB(X∆/Xσ)+ on B(X∆/Xσ)+ ) .
+Proof. The reasoning is the same as in the proof of Lemma 3.2.2(2). We can assume,
+as in the proof of Lemma 3.2.2(2), that the inverse image φ−1
+U (si) ⊂ U consists of
+a single stratum.
+By Lemmas 3.2.2 and 3.3.2, we have the following fiber square diagram for the
+cobordizations, with horizontal morphisms being regular:
+BU
+φ→
+B(X∆/Xσ)
+πU ↓
+πB ↓
+U
+φU
+→
+Xσ = An,
+,
+and the analogous fiber square for BU+. Consequently, the inverse image of the
+exceptional divisor on DB(X∆/Xσ) is the exceptional divisor DBU . Its components
+are of the form V B(X∆/Xσ)(t−1
+i
+) and are associated with the components E∆
+i .
+Their inverse images are the irreducible components V BU(t−1
+i )) corresponding to
+the exceptional components Ei = φ−1(E∆
+i ).
+Since φU is regular, the inverse image φ−1(s) of the closure s of any stratum s of
+DB(X∆/Xσ) is normal. Thus it is the disjoint union of the irreducible components.
+To prove that φ−1(s) is irreducible on YU, we need to show that there is a single
+generic point p in the fiber φ−1(q) over the generic point q of s, and such that p
+is of the same codimension in U as s in B(X∆/Xσ) . This can be reduced to the
+problem of the morphism of the fibers
+π−1(p0) = Fp0 → π−1(q0) = Fq0,
+where p0 = πB(p), and q0 = πU(q) are the generic point of the relevent strata.
+But this follows from the relation for the fibers of toric morphisms, as in the
+proof of Lemma 3.2.2(2),
+π−1(p0
+i ) = Fp0
+i = Spec(κ(p0
+i )) ×Spec(κ(q0
+i )) Fq0
+i .
+♣
+3.3. Description of cobordization of locally toric morphisms.
+3.3.1. Local functoriality of relative Cox spaces for smooth morphims.
+Proposition 3.3.2. Let π : Y → X be a proper birational locally toric morphism
+of locally toric varieties over a field κ. Let φ : X′ → X be a regular morphism over
+κ, and π′ : Y ′ → X′ will be the base change. Then for any p′ ∈ Y ′ there are open
+neighborhoods U ′ of p′, and U of p := φ(p′), with the induced smooth morphism
+φ|U′ : U ′ → U such that
+B(YU/U) ×X X′ ≃ B(Y ′
+U′/U ′)
+B(YU/U)+ ×X X′ ≃ B(Y ′
+U′/U ′)+
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+37
+Thus the full cobordization and cobordization of proper birational locally toric
+morphisms are functorial for regular morphisms up to torus factors.
+Proof. This is a direct consequence of Lemma 3.2.2 and definition of locally toric
+morphisms
+♣
+3.3.3. Local description of cobordization of locally toric morphisms.
+Lemma 3.3.4. Let π : Y → X be a proper birational locally toric morphism over
+a field κ, and πB : B → X be its full cobordization. Then
+(1) B+ ⊂ B is the natural open immersion.
+(2) For any point p ∈ X there is an open neighborhood U of p, with a toric
+chart U → Xσ, and the torus
+TB∖BU := Spec( κ[xi, x−1
+i
+| Ei ⊂ B ∖ BU ] ),
+and an induced regular morphism
+BU = σ−1(U) = B(YU/U) × TB∖BU → Xσ × Ak × TB∖BU
+(3) If X is regular then B is regular.
+Proof. By Lemma 3.2.2, the problem reduces locally to a toric situation via toric
+chart U → Xσ.
+(1) By Lemma 2.3.5, B(X∆/Xσ)+ ֒→ B(X∆/Xσ) is an open inclusion. Thus,
+by Lemma 3.2.2, B+ ⊂ B is also such.
+(2) Also locally by Lemma 1.6.1, we can write BU = B(YU/U) × TB∖BU . On
+the other hand, by Lemma 3.2.2(4) B(YU/U) → B(X∆/Xσ) is regular. Finitely by
+Lemma 2.3.5(2), B(X∆/Xσ) = Xσ × Ak.
+(3) Follows from (2).
+♣
+3.4. Local description of cobordization.
+3.4.1. Cobordization of locally monomial maps.
+Definition 3.4.2. Let X be a locally monomial scheme over a field κ. We say
+that u1, . . . , uk is a locally toric system of parameters on X if there is a chart
+φ : U → Xσ, and a local system of toric parameters x1, . . . , xk on Xσ, such that
+ui = φ∗(xi).
+As a Corollary from Proposition 3.3.2, and Lemma 3.3.4 we obtain the following:
+Theorem 3.4.3. Let π : Y → X be a proper birational locally toric morphism of
+locally toric schemes over a field κ . Then locally on X we can write up to torus
+factors
+AY/X = π∗(CY/X) = OX[t−1
+1 , . . . , t−1
+k , u1tα1, . . . , uktαk],
+where
+(1) u1, . . . , uk is a locally toric system of parameters
+on an open U ⊂ X
+defining a toric chart for the morphism π,
+(2) tαi := tai1
+1
+· . . . · taik
+k , with aij := νi(uj) ≥ 0.
+In particular, if X is regular then B and B+ ⊂ B are regular.
+♣
+Proof. We use the fact from Lemma 3.2.2, that the valuations are locally monomial
+with respect to u1, . . . , uk, and Lemma 2.3.5(1).
+♣
+
+38
+J. W�LODARCZYK
+3.4.4. The cobordization of monomial morphisms. Let Y → X be a proper bira-
+tional locally toric morphism over κ.
+Let x1, . . . , xn be a system of local parameters at a point p on a locally toric X
+defining a toric chart for a Y → X. Then the full cobordization of π : Y → X can
+be represented as:
+B = SpecX(OX[t−1
+1 , . . . , t−1
+k , x′
+1, . . . , x′
+n]/(x′
+1t−α1 − x1, . . . , x′
+kt−αk − xk).
+Thus B = V (x′
+1t−α1−x1, . . . , x′
+kt−αk−xk) ⊂ X×An+k is locally a closed subscheme
+of X × An+k defined by a system of local parameters. It is regular for a regular X.
+Consequently, the full cobordization B → X can be described by a single chart up
+to a torus factor with the following coordinates:
+• t−1
+i
+for i = 1, . . . , k is the inverse of the coordinate ti representing the action
+of torus T = Spec(κ[Cl(Y/X)] = Spec(κ[t1, t−1
+1 , . . . , tn, t−1
+n ]).
+• x′
+i = xi · tαi for 1 ≤ i ≤ k, and
+• x′
+j = xj for j > n.
+The open subsets Bx′
+i = B ∖ V (x′
+i), associated with the forms x′
+i = xitαi cover
+the cobordization B+ = B ∖ V (Iirr) producing several ”charts” similarly to the
+standard blow-up.
+These open affine subsets can be conveniently described by
+using toric geometry. They correspond to the maximal faces of the decomposition
+∆ of the cone σ associated with the local toric chart.
+If π : Y
+→ X is the cobordant blow-up of a locally monomial J , where
+codim(V (J ) ≥ 2, then the subset B+, by Lemma 1.4.4, can be described as
+B+ = B ∖ V (J tα), where α = (a1, . . . , ak), and ai are the coefficients of the
+exceptional divisor E = � aiEi of π : Y → X. In this case, the charts of B+
+can also be interpreted by the vertices of the Newton polytope of J .(See Example
+2.6.14)
+Remark 3.4.5. In the particular case, when considering the stack-theoretic quo-
+tients of the blow-up of a locally monomial ideal on a regular scheme, one obtains
+the definition of a multiple weighted blow-up BlJ = [B+ � T ] introduced in [AQ21]
+by Abramovich-Quek via the Satriano construction in [Sat13]. The more general
+definition of BlJ ,b is discussed in Section 5.5.
+3.4.6. Weighted cobordant blow-ups. Recall that the weighted stack-theoretic blow-
+ups were considered in the context of resolution in [McQ19] and [ATW19]. The
+definition of the weighted cobordant blow-up was introduced in [W�lo22]. One can
+view these notions from the more general perspective of Cox cobordant blow-ups
+or the multiple weighted blow-ups of Abramovich-Quek from [AQ21].
+Definition 3.4.7. Let (x1, . . . , xk) be a partial system of local parameters on a
+regular scheme X. Let J be a center of the form (xa1
+1 , . . . , xak
+k ), where a1 ≤ a2 ≤
+. . . ≤ ak are positive integers, and k > 1. Let π : Y → X be the normalized
+blow-up of J . By the weighted cobordant blow-up of J we mean the cobordization
+BJ + → X of π : Y → X.
+The corresponding monomial ideal on the toric chart Ak
+κ defines a piecewise
+linear function G := mini(aie∗
+i ) on the regular coordinate cone σ = ⟨e1, . . . , ek⟩,
+where e∗
+i (ej) = δij. The functions aie∗
+i determine the ray
+ρ := {v ∈ σ | a1e∗
+1(v) = . . . = ake∗
+k(v)}.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+39
+The ray ρ is generated by the primitive vector
+w = (w1, . . . , wk) = w1e1 + . . . + wkek,
+with relatively prime components and such that
+w1a1 = . . . = wkak.
+The normalized blow-up of J is described by the decomposition ∆ of σ into
+maximal subcones where G is linear.
+Thus ∆ is the star subdivision ρ·⟨e1, . . . , ek⟩ at a ray ρ. The vector w determines
+the valuation νE of the unique irreducible exceptional divisor.
+Then, by Lemma 2.3.5(1), the full cobordant blow-up of X at the center J is
+defined by
+BJ = SpecX(OX[t−1, tw1x1, . . . , twkxk]).
+Here we have
+wi = νE(xi) = (w, e∗
+i )
+The cobordant weighted blow-up is simply (BJ )+ = B ∖ V (σ◦(J )), where, by
+Lemma 1.4.4, we have σ◦(J ) = ta · J , where a = ν(J ). Thus
+σ◦(J ) = (xa1
+1 ta1w1, . . . , xak
+k takwk).
+We see that the cobordant weighted blow-up is the cobordization of an ordinary
+toric weighted blow-up corresponding to the star subdivision at the center v ∈ σ.
+We will discuss this construction in the context of the blow-ups of valuative Q-ideals
+in Section 5.4.
+Observe that both notions: the one in Definition 3.4.7, and the one given by the
+formula BJ = SpecX(OX[t−1, tw1x1, . . . , twkxk]), as in [W�lo22], are different in the
+trivial case k = 1 and the blow-up of (xa1
+1 ). Then Y → X is an isomorphism, and
+B = B+ = B− ≃ Y ≃ X. However the formula from [W�lo22] gives us
+B = SpecX(OX[t−1, tw1x1]),
+which defines the isomorphism of the quotients:
+B/Gm ≃ B+/Gm ≃ B−/Gm ≃ Y ≃ X.
+In this case, B+ is a locally trivial Gm-bundle. So both constructions of B+ differ
+locally by the torus factor.
+3.5. Geometric quotients for locally toric morphisms. In general, when con-
+sidering the cobordization B+ of a locally toric morphism π : Y → X, one obtains
+the good quotient B+ � T ≃ Y . Proposition 3.5.2, below shows that if X is regular
+then, by replacing B+ with an open subset Bs ⊆ B+ one obtains the geometric quo-
+tient Bs/T with a proper birational morphism Bs/T → B+�T ≃ Y .xConsequently,
+Bs has a geometric quotient Bs/T with abelian quotient singularities and the trans-
+formation Bs → X can be be used in the resolution instead of B+ → X.
+Lemma 3.5.1. Let π : Y → X be a locally toric morphism, with X regular.
+Then its cobordization B+ determines the geometric quotient B+ → B+/T ≃ Y
+iff Y has abelian quotient singularities.
+Proof. The problem is local and can be reduced to the toric morphism π : X∆ → Xσ
+corresponding to the subdivision ∆ of a regular cone σ. Then, by Lemma 2.3.5,
+the full cobordization B of π is a regular scheme corresponding to the cone ΣB,
+and B+ is its open toric subscheme. The natural projection σB+ → ∆ corresponds
+
+40
+J. W�LODARCZYK
+to the geometric quotient iff ∆ is a simplicial fan, and thus Y has abelian quotient
+singularities.
+♣
+Proposition 3.5.2. Let π : Y → X be a proper birational locally toric morphism of
+locally toric schemes over a field, with X regular. Then B+ = Cox(Y/X)+ ⊂ B =
+Cox(Y/X) contains open maximal subsets Bs ⊂ B+ admitting geometric quotient
+Bs/TB with the projective birational morphism
+Bs/TB → B+/TB = Y.
+Proof. Let E1, . . . , Ek be the irreducible exceptional divisors of π : Y → X, and
+ν1, . . . , νk be the associated exceptional valuations on X. By Lemma 3.2.2(5), the
+valuations are locally toric on X. Consider the sequence of the blow-ups at the
+valuations νi as in [W�lo20, Proposition 8.16.6]. These are precisely the normalized
+blow-ups of Iνi,a,X for a sufficiently divisible a.
+Locally, in the compatible toric charts, U → Xσ the sequence of the blow-ups
+correspond to a sequence of the star subdivisions at the vertices Vert(∆) ∖ Vert(σ)
+(see [W�lo20, Lemma 7.3.9]). As the result we create a new subdivision ∆′ of ∆ with
+Vert(∆′) = Vert(∆). This decomposition is simplicial. Indeed, let δ0 be any cone in
+∆′. By the property of the star subdivisions, for any vertex v0 ∈ Vert(δ) ∖ Vert(σ)
+one can write δ0 = ⟨v0⟩ + δ1, where δ1 is a face of δ0 of codimension one in δ0,
+and v0 is linearly independent of Vert(δ1). We can run this argument inductively
+until we can represent δ0 as δ0 = ⟨v0, . . . , vr⟩ + δr, where v0, . . . , vr ∈ Vert(δ0) are
+linearly independent of Vert(δr) ⊂ Vert(σ). Thus all the vertices of δ0 are linearly
+independent.
+By construction, the valuations of the exceptional divisors corresponding to
+Vert(∆) ∖ Vert(σ) remain unchanged. Then B(Y/X) = B(Y ′/X). On the other
+hand, by the description of the toric case from Lemma 2.3.5(4), we obtain the open
+inclusions
+Bs := B(Y ′/X)+ ⊆ B(Y/X)+ = B+ ⊆ B(Y/X) = B.
+♣
+4. Cobordant resolution of singularities
+4.1. The dual complex of the exceptional divisor. One can extend the con-
+siderations and the results from Section 2.5.1.
+4.1.1. The exceptional divisor. Let π : Y → X be a proper birational locally toric
+morphism, where X is a regular scheme over a field κ, and E1, . . . , Ek be the
+irreducible components of the exceptional divisor E of π. Let πB : B → X be the
+full cobordization of π. By Theorem 4.4.5, B is regular and there is an SNC divisor
+D = VB(t−1
+1
+· . . .· t−1
+k ) with irreducible components Di = VB(t−1
+i ). So is the divisor
+D+ = D|B+ on B+. Moreover, the exceptional divisor E of π : Y → X is locally
+toric.
+We can associate with the SNC divisors D on B, D+ on B+, and with the divisor
+E on Y the divisorial stratifications SD, SD+, and SE, extending the definitions
+from Section 2.5.1. The strata of SD are defined by the irreducible components of
+the locally closed sets :
+�
+i∈I
+Di ∖
+�
+j∈J
+Dj,
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+41
+where I ∪J = {1, . . ., k}. Replacing Di with Di+ we obtain the definition for SD+.
+Consequently, any stratum s ∈ SD+ extends to a stratum in SD.
+The closures of the strata sE ∈ SE are defined by the irreducible components
+of the intersections �
+i∈I Ei.
+The strata sE are obtained by removing from sE
+the proper closed subsets s′E. The stratifications SD, SD+ and SE determine the
+dual simplicial complexes ∆D, ∆D+, and ∆E.
+Since D and D+ are SNC, the
+simplices in ∆D, (respectively ∆D+) are in the bijective correspondence with the
+strata of SD (respectively of SD+). Moreover, by the above, ∆D+ is a subcomplex
+of ∆D corresponding to the strata of SD which intersect B+ ⊂ B. Also, under this
+identification Vert(∆D) = Vert(∆D+).
+The divisor E is usually not SNC, and the strata alone do not determine the
+faces of ∆E.
+The vertices vi of ∆E correspond to the divisors Ei ↔ vi.
+The
+simplices σ = ∆(ei | i ∈ I) in ∆E correspond to the pairs (sE
+σ , Eσ) consisting of
+a stratum sσ ∈ SE and a collection of divisors Eσ = {Ei | i ∈ I), such that sσE
+is an irreducible component of �
+i∈I Ei.
+Thus, in this case, the correspondence
+between the faces of ∆E and the strata of SE is not bijective, and the closures of
+strata could be represented by the intersections of components �
+i∈I Ei defined by
+different subsets I. (See also Section 2.5.1.)
+Summarizing we have
+Lemma 4.1.2. A simplex σ in ∆B (respectively ∆D+, ∆E) is represented by a pair
+({Di | i ∈ I},
+(
+�
+Di)0)
+consisting of a collection of the irreducible divisors Di, (respectively Di+, Ei) which
+have a nonempty intersection and an irreducible component (� Di)0 of � Di (re-
+spectively � Di+,
+� Ei).
+♣
+Corollary 4.1.3. With the previous assumptions and notations:
+(1) There is a bijective correspondence between the divisors Di, Di+, Ei, and
+the valuations νi.
+(2) (a) If s ∈ SD then s is a component of a locally closed set
+�
+Di⊇s
+Di ∖
+�
+Di̸⊇s
+Di
+(b) The image πB(s) is closed. It is an irreducible component of the closed
+set
+πB(
+�
+Di⊇s
+Di ∖
+�
+Di̸⊇s
+Di) =
+�
+Di⊇s
+ZX(νi) =
+�
+Di⊇s
+πB(Di) =
+�
+Di⊇s
+π(Ei)
+where ZX(ν) denotes the center of a valuation ν on X. Moreover, the
+sets �
+Di⊇s Di are locally irreducible over X.
+(c) The morphism πB determines a bijective correspondence between the
+strata defined by the irreducible components of �
+Di⊇s Di ∖ �
+Di̸⊇s Di
+and the irreducible components of �
+Di⊇s ZX(νi).
+(3) The morphism πB+,Y determines a bijective correspondence between the
+components of �
+i∈I Di+ and the components of �
+i∈I Ei. This correspon-
+dence defines the isomorphism of the dual complexes ∆D+ ≃ ∆E.
+
+42
+J. W�LODARCZYK
+(4) The morphism of the stratifications SD+ → SD maps a stratum s+ of SD+
+into an open subset of a stratum s of SD . It determines the inclusion of
+the dual complexes ∆B+ ֒→ ∆B.
+Proof. (1) The correspondence follows from Lemmas 1.2.9, and 1.2.11.
+(2)-(5) By Lemma 3.2.2 and 3.2.4, we can reduce the situation locally to the
+toric case, where we use Lemmas 2.5.3, and 2.5.6, and Corollaries 2.5.5 2.5.7 and
+2.5.8.
+♣
+4.1.4. Dual complex of valuations of a locally toric morphism. Let N = {ν1, . . . , νk}
+be the set of the exceptional valuations of π : Y → X. The vertices of Vert(∆E),
+and thus of Vert(∆B) and Vert(∆B+) are in the bijective correspondence with the
+valuations in N, and the exceptional divisors Ei, Di+, and Di:
+νi ↔ Ei = ZY (νi) ↔ Di+ ↔ Di.
+Consequently, one can associate with the faces of ∆E, ∆B+, and ∆B the subsets
+of N.
+This determines the complexes ∆N
+B , ∆N
+B+, ∆N
+E , called the dual valuation
+complexes, together with natural isomorphisms of the simplicial complexes
+∆B → ∆N
+B ,
+, ∆B+ → ∆N
+B+,
+∆E → ∆N
+E
+Then, by Lemma 4.1.3, ∆N
+E = ∆B+ determine the same subcomplex of ∆N
+B .
+The simplices of the valuation complexes will be called the valuation faces. The
+valuation faces come with natural face inclusions inherited from ∆N
+B , ∆N
+B+, ∆N
+E .
+By Lemma 4.1.3 we get:
+Lemma 4.1.5.
+(1) A valuation face σ in ∆N
+B is represented by a pair (ω, Z0
+X(ω))
+defined by the collection of valuations ω = ωσ in N, such that
+ZX(ω) :=
+�
+ν∈ω
+ZX(ν) ̸= ∅,
+and an irreducible component Z0
+X(ω) of ZX(ω).
+(2) A simplex σ of ∆N
+E = ∆N
+B+ corresponds to a subset ω ⊂ N, such that
+ZY (ω) :=
+�
+ν∈ω
+ZY (ν) ̸= ∅,
+and an irreducible component, denoted as Z0
+Y (ω) of the set
+ZY (ω) :=
+�
+ν∈ω
+ZY (ν).
+The face relations are given by the inclusions of the sets of valuations and the
+associated components.
+♣
+Remark 4.1.6. Thus, the dual valuation complexes could be thought of as ordinary
+dual complexes of the exceptional divisors with the associated valuation structure so
+that the vertices define the relevant exceptional valuations, and the faces determine
+the sets of the valuations.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+43
+4.1.7. Dual complex associated with a locally monomial ideal. If J is locally mono-
+mial ideal on a regular scheme, such that codim(V (I)) ≥ 2, then one can asso-
+ciate with J the normalized blow-up π : Y → X, and the full cobordant blow-up
+πB : B → X of J . The morphism π : Y → X is locally toric, and we shall call the
+dual complexes ∆D, ∆D+ ≃ ∆E and the corresponding dual valuation complexes
+∆N
+D, ∆N
+D+ ≃ ∆N
+E associated with J .
+4.2. Graded rings defined by the valuations.
+4.2.1. Graded rings defined by valuations. In the considerations below, let ω =
+{ν1, . . . , νr} be a set of valuations on a regular scheme X. We associate with each
+valuation νi a dummy variable ti for i = 1, . . . , r. Set
+t := (t1, . . . , tk)
+and
+t−1 := (t−1
+1 , . . . , t−1
+k ).
+Consider the partial componentwise order on Zr
+≥o. For α := (a1, . . . , ar) ∈ Zr
+≥0
+we define the ideals
+J α
+ω :=
+�
+νi∈ω
+Iνi,ai ⊂ OX,
+J >α
+ω
+:=
+�
+β>α
+J β
+ω .
+(5)
+This determines the Zk
+≥0-graded Rees algebra
+Aω :=
+�
+a∈Z≥0
+J α
+ω tα ⊂ OX[t],
+where tα = ta1
+1 · . . . · tar
+r , and the associated gradation
+grω(OX) =
+�
+a∈Z≥0
+(J α
+ω /J >α
+ω
+)tα = Aω/(Aω ∩ t−1Aω]) = Aω[t−1]/(t−1 · Aω[t−1]).
+(6)
+In particular, for α = 0 = (0, . . . , 0) we have locally on X:
+Jω := J >0
+ω
+= IZX(ω),
+where
+ZX(ω) :=
+k�
+i=1
+ZX(νi).
+Then grω(OX) is a sheaf of graded OX/Jω = OV (Jω)-modules.
+Lemma 4.2.2. Assume the valuations in the set ω = {ν1, . . . , νr} are monomial
+for a certain partial system of local parameters u1, . . . , un on a regular scheme X.
+Then
+(1) Jω = �k
+i=1 Iνi,1 = (uj | νi(uj) > 0, for some νi ∈ ω) , and
+(2) grω(OX) = OV (Jω)[u1tα1, . . . , uktαk], where ui ∈ J αi
+ω
+∖ J >αi
+ω
+, and αi =
+(ai1, . . . , ain), with νi(uj) = aij ∈ Z≥0 for i = 1, . . . , r, and j = 1, . . . , n
+Proof. (1) Note that IZX(νi) = (uj | νi(uj) > 0). Thus
+Jω = IZX(ω) =
+�
+ν∈ω
+IZX(νi) = (uj | νi(uj) > 0, for some νi ∈ ω)
+
+44
+J. W�LODARCZYK
+(3) By definition of Aω, the equality (5), and the Proof of Lemma 2.3.5(1).
+Aω[t−1] = (
+�
+ai∈Z≥0
+r�
+i=1
+Iνi,ai · ta1
+1 · . . . · tar
+r )[t−1
+1 , . . . , t−1
+r ] =
+= OX[t−1
+1 , . . . , t−1
+r , u1tα1, . . . , untαn]) = OX[t−1, u1tα1, . . . , untαk],
+where αi = (ai1, . . . , ain), and νi(uj) = aij ∈ Z≥0 for i = 1, . . . , r, and j = 1, . . . , n.
+Thus by the equality (6):
+grω(OX) = Aω[t−1]/(t−1 · Aω[t−1] =
+= (OX[t−1, u1tα1, . . . , untαk])/(t−1) ≃
+= (OX/Jω)[u1tα1, . . . , untαk].
+♣
+We shall call the corresponding scheme
+Nω(X) := SpecV (Jω)(grω(OX)) = SpecZX(ω)(grω(OX))
+the weighted normal bundle of X at the set of valuations ω.
+One can extend this to any valuation face in ∆N
+B , associated with a full cobordant
+blow-up B → X.
+Definition 4.2.3. By the weighted normal bundle of X at the valuation face ω ∈
+∆N
+B we mean the scheme
+Nω(X) := SpecZ0
+X(ω)(grω(OX))
+over the component Z0
+X(ω) of ZX(ω) associated with the face ω.
+As ∆N
+E ⊂ ∆N
+B the above definition is also valid for any valuation face ω ∈ ∆N
+E .
+4.2.4. The ideals of the initial forms. With any function f ∈ OX,p, regular at
+p ∈ V (J ), such that f ∈ J α
+ω ∖ J >α
+ω
+, for a certain a ∈ N one can associate the
+unique homogenous element, called the initial form
+inω(f) = (f + J >α
+ω
+) ∈ (J α
+ω /J >α
+ω
+)tα
+ω ⊂ grω(OX).
+Similarly, we associate with an ideal sheaf I, the filtration Iα
+ω := I ∩ J α
+ω and set
+I>α
+ω
+= I ∩ J >α
+ω
+.
+We define the ideal of the initial forms of I to be the ideal
+inω(I) =
+�
+α∈Z≥0
+Iα
+ω/I>α
+ω
+=
+�
+α∈Z≥0
+(Iα
+ω + J >α
+ω
+)/J >α
+ω
+⊂ grω(OX)
+on NJ (X).
+For the ideal sheaf I, its weak ideal of the initial forms on NJ (X) is given by
+in◦
+ω(I) = grω(OX) · Iα0
+ω /I>α0
+ω
+⊂ grω(OX),
+where I ⊂ J α0
+ω , and I ̸⊂ J >α0
+ω
+.
+Remark 4.2.5. For any function f ∈ OX,
+inω(f) = inω(OX · f) = in◦
+ω(OX · f).
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+45
+4.2.6. Composition of gradations.
+Lemma 4.2.7. Let ω = {ν1, . . . , νr} be a set of valuations which are monomial for
+a common partial system of local parameters u1, . . . , un on a regular X. Consider
+its partition into subsets ω1 = {ν1, . . . , νs}, and ω2 = {νs+1, . . . , νr}. Let t :=
+(t1, . . . , tr) ( respectively tω1 := (t1, . . . , ts)) be the set of the unknowns ti associated
+to the valuations νi ∈ ω, ( respectively and νi ∈ ω1). Let Jω1 = (u1, . . . , uℓ). Then
+(1) The set ω2 = {νs+1, . . . , νr} determines the set of monomial valuations
+ω2 = {νs+1, . . . , νr} on the multi-graded ring
+grω1(OX) = OV (Jω1 )[u1tα1
+ω1, . . . , uℓtαn
+ω1 ] ≃ OV (Jω1 )[u1, . . . , uℓ],
+with the ideals
+Iνi,ai = inω1(Iνi,ai)
+(2) grω2(grω1(OX) ≃ grω(OX).
+(3) If I ⊂ OX then
+(a) inω(I) = inω2(inω1(I)).
+(b) in◦
+ω(I) = in◦
+ω2(in◦
+ω1(I)).
+Proof. (1) For j ≤ ℓ, inωw1(uj) is identified with uj in OV (Jω1 )[u1, . . . , uℓ]. Other-
+wise if j > ℓ, then inωw1 (uj) is a parameter in OV (Jω1) = OX/Jω1 = OX/(u1, . . . , uℓ).
+Consequently νj determine the monomial valuations νj on grω(OX) with inω1(Iνj,a) =
+(Iνj,a).
+(2) and (3) For the multiindex α = (α1, α2), where αi correspond to ωi for
+i = 1, 2, consider a function f ∈ J α
+ω ∖ J >α
+ω
+:
+f ∈ J α
+ω ∖ J >α
+ω
+= J α1
+ω1 ∩ J α2
+ω2 ∖ (J >α1
+ω1
+∩ J α2
+ω2 + J α1
+ω1 ∩ J >α2
+ω2
+)
+The ideal inω1(J α2
+ω2 ) ⊂ grω1(OX) is homogenous and inω1(f) is in α1-gradation
+of inω1(J α2
+ω2 )α1 ⊂ (grω1(OX))α1:
+inω1(J α2
+ω2 )α1 = J α1
+ω1 ∩ J α2
+ω2
+J >α1
+ω1
+∩ J α2
+ω2
+⊆ (grω1(OX))α1 = J α1
+ω1
+J >α1
+ω1
+and
+inω1(J >α2
+ω2
+)α1 = J α1
+ω1 ∩ J >α2
+ω2
++ J >α1
+ω1
+∩ J α2
+ω2
+J >α1
+ω1
+∩ J α2
+ω2
+Consequently, by the above,
+inω2(inω1(f)) ∈ inω2(inω1(J α2
+ω2 )α1) = (inω1(J α2
+ω2 ))α1
+(inω1(J >α2
+ω2
+))α1
+=
+=
+J α1
+ω1 ∩ J α2
+ω2
+J α1
+ω1 ∩ J >α2
+ω2
++ J >α1
+ω1
+∩ J α2
+ω2
+= J α
+ω
+J >α
+ω
+= (grω1(OX))α
+On the other hand the initial form
+inω(f) ∈ J α
+ω
+J >α
+ω
+= (grω1(OX))α,
+determines the same element:
+inω(f) = inω2(inω1(f)) ∈ (grω(OX))α = grω2((grω1(OX))α1)α2,
+which implies (3).
+♣
+
+46
+J. W�LODARCZYK
+4.3. The weighted normal bundles at valuations. The following extends a
+classical result of Huneke-Swanson on extended Rees algebras and smooth blow-ups
+[HS06, Definition 5.1.5], and the recent results of Rydh in [QR19] and W�lodarczyk
+in [W�lo22, Lemma 5.1.4] on the weighted normal cone.
+Lemma 4.3.1. Let π : Y → X be a locally toric proper birational morphism to a
+regular scheme X over a field κ, with the exceptional components Ei, for i = 1, . . . , k
+and let πB : B → X be its full cobordization. Then for any stratum s = sω ∈ SD of
+the exceptional divisor D = V (t−1
+1
+· . . . · t−1
+k ) on B and the corresponding valuation
+face ω in ∆N
+B there is an isomorphism:
+s ≃ Nω(X) × ˇtω.
+where Tˇtω := Spec(κ[ˇtω,ˇt−1
+ω ]), for the set ˇtω of the unknowns corresponding to the
+remaining exceptional valuations which are not in ω.
+Proof. We can replace X with its open subset and assume ZX(ω) is irreducible so
+that πB(s) = Z0
+X(ω) = ZX(ω) .
+By separating variables into tω and ˇtω we can factor any monomial tα = tα
+ω · ˇtα
+ω
+uniquely into the product of the relevant monomials tα
+ω and ˇtα
+ω respectively in tω
+and ˇtω. Then by Corollary 4.1.3(2), we can write s = V (t−1
+ω ) in a neighborhood of
+s, and s = V (t−1
+ω ) ∖ V (ˇt−1
+ω ) as there is only one component of V (t−1
+ω ) mapping to
+πB(s) = Z0
+X(ω) = ZX(ω).
+By definition B = Spec(A[t−1]), where
+A =
+�
+α∈Zk
+≥0
+J αtα,
+J α :=
+k�
+i=1
+Iνi,ai ⊂ OX.
+Let
+Aω =
+�
+α
+J α
+ω tα
+ω,
+J α
+ω :=
+�
+νi∈ω
+Iνi,ai ⊂ OX.
+Thus for the open subset Bω ⊂ B where ˇt−1
+ω
+are invertible we can write:
+Bω := Bˇt−1
+ω
+= SpecX(A[t−1][ˇtω]) = SpecX(Aω[t−1
+ω ])[ˇtω,ˇt−1
+ω ])
+Consequently s = VBω(t−1
+ω ) ⊂ Bω, by Corollary 4.1.3(2), so we can write
+Os = Aω[t−1
+ω ][ˇtω,ˇt−1
+ω ]/(t−1
+ω ) = (Aω[t−1
+ω ]/((t−1
+ω · Aω[t−1
+ω ]))[ˇtω,ˇt−1
+ω ] =
+= (Aω/((t−1
+ω · Aω) ∩ Aω))[ˇtω,ˇt−1
+ω ] = grω(OX)[ˇtω,ˇt−1
+ω ].
+The latter equality follows from Section 4.2.1.
+♣
+4.3.2. The weak and the strict transforms and the ideal of the initial forms. The
+identification from Lemma 4.3.1 can be extended to the strict transforms of the
+ideals.
+The following generalizes the result from [W�lo22, Lemma 5.1.4] for the
+weighted blow-ups.
+Lemma 4.3.3. Let X be a regular scheme over a field Let B → X be the full
+cobordant blow-up of a locally monomial center J . Let I ⊂ OX be an ideal sheaf
+on X. Let σs(I) ⊂ OB be the strict transform of I, and σ◦(I) ⊂ OB be its weak
+transform (see Definition 1.4.2). Then for any s ∈ SD, the natural isomorphism
+Os ≃ OB[ˇtω,ˇt−1
+ω ]/(t−1
+ω ) → grω(OX)[ˇtω,ˇt−1
+ω ]
+takes
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+47
+(1) σs(I)|s onto inω(I)[ˇtω,ˇt−1
+ω ] ⊂ grω(OX)[ˇtω,ˇt−1
+ω ].
+(2) σ◦(I)|s onto in◦
+ω(I)[ˇtω,ˇt−1
+ω ] ⊂ grω(OX)[ˇtω,ˇt−1
+ω ].
+Proof. Let f ∈ I such that f ∈ J α ∖ J >α. By the definition of
+OB = (
+�
+α≥0
+J αtα)[t−1]
+we conclude that σs(f) = tαf.
+Then f ∈ J α
+ω ∖ J >α
+ω
+, and in a neighborhood of s we have that ˇt−1
+ω
+is invertible.
+Then the strict transform
+σs(f) = tαf = tα
+ωˇtα
+ωf ∈ J αtα ⊂ J α
+ω tα
+ω[ˇtω,ˇt−1
+ω ],
+and its reduction modulo (t−1
+ω OB ∩J α
+ω )tα = J >α
+ω
+tα can be written as the homoge-
+nous element
+σs(f) = tαf + tαJ >a
+ω
+= tα
+ωˇtα
+ωf + tα
+ωˇtα
+ω · J >a
+ω
+in
+OB[ˇtω,ˇt−1
+ω ]/(t−1
+ω · OB[ˇtω,ˇt−1
+ω ]) = grω(OX)[ˇtω,ˇt−1
+ω ]
+in the gradation
+J α
+ω tα
+ω[ˇtω,ˇt−1
+ω ]/(t−1
+ω OB[ˇtω,ˇt−1
+ω ] ∩ OB[ˇtω,ˇt−1
+ω ])
+= (J α
+ω /J >a
+ω )tα
+ω[ˇtω,ˇt−1
+ω ] ⊂ grω(OX)[ˇtω,ˇt−1
+ω ]
+On the other hand f determines its initial form
+inω(f) = (f + J >α
+ω
+)tω ∈ (J α
+ω /J >α
+ω
+)tα
+ω,
+and thus, by the above σs(f) naturally and bijectively corresponds to
+ˇtα
+ω inω(f) ∈ (J α
+ω /J >α
+ω
+)tα
+ω[ˇtω,ˇt−1
+ω ] ⊂ grω(OX)[ˇtω,ˇt−1
+ω ].
+The latter differs from inω(f) by the unit ˇtα
+ω:
+ˇtα
+ω inω(f) ∼ inω(f).
+♣
+4.4. Cobordant resolution by locally monomial centers.
+4.4.1. Weighted normal cone.
+Definition 4.4.2. Let X be a regular scheme over a field. Let Y ⊂ X be a closed
+reduced subscheme with the ideal IY . Let ω be a set of monomial valuations for a
+partial system of local parameters. The subscheme Cω(Y ) = V (inω IY ) ⊂ Nω(X)
+will be called the weighted normal cone of Y at ω.
+Lemma 4.4.3. Let X be a regular universal catenary scheme over a field. Let
+Y ⊂ X be a subscheme of pure codimension d. Let ω be a set of monomial valuations
+for a common partial local system of parameters u1, . . . , uk on X. Then Cω(Y ) is
+of pure codimension d in Nω(X).
+Proof. Let ω = {ν1, . . . , νr} and ω1 = {ν1, . . . , νr−1} be its subset.
+Then, by
+Lemma 4.2.7, we can write
+inω(I) = inνr(inω1(I)),
+where νr is monomial on
+Nω1(X) = Spec(grω1(OX)) = Spec(OV (Jω1 )[u1, . . . , uℓ])
+
+48
+J. W�LODARCZYK
+is also universally catenary. Here we assume without loss of generality that Jω1 =
+u1, . . . , uℓ for ℓ ≤ k.
+By the inductive argument for inω1(I) on Nω1(X) we can reduce the situation
+to a single monomial valuation ν = νr.
+Let ν(u1) = w1, . . . , ν(uk) = wk, and find some integers a1, . . . , ak such that
+a1w1 = . . . = akwk,
+Consider the full cobordant blow-up B of I = (ua1
+1 , . . . , uak
+k )
+B = SpecX(OX[t−1, u1tw1, . . . , uktwk].
+We apply the argument from [W�lo22, Theorem 5.2.1]. By the assumption, B is
+catenary. Let d be the codimension of Y in X. Then for the morphism
+πB− : B− = B ∖ V (t−1) = X × Gm → X,
+the inverse image π−1
+B−(Y ) is of pure codimension d in B−. So it is its scheme-
+theoretic closure Y ′ := πB−(Y ), which is the strict transform V (σs(I)) of Y .
+Note that t−1 is not a zero divisor in
+Y ′ = V (σs(I)) = Spec(OB/σs(I)),
+since t−1f ∈ σs(I) implies f ∈ σs(I), by definition of the strict transform.
+Then, by the Krull Hauptidealsatz, we have that each component of Y ′ ∩V (t−1)
+is of codimension 1 in Y ′, and of codimension d + 1 in B. We conclude that each
+component of
+Y ′ ∩ V (t−1) = V (Ot−1 · σs(I)) = Cν(Y ) ⊂ Nν(X)
+is of codimension d in V (t−1) = Nν(X).
+♣
+4.4.4. Cobordant resolution. For any scheme Y , let Sing(Y ) denote its singular
+locus.
+For any ideal I on X by Sing(V (I)) we mean the singular locus of the
+scheme
+V (I) = SpecX(OX/I).
+The following theorem extends [W�lo22, Theorem 5.2.2].
+Theorem 4.4.5. Let X be a regular universally catenary scheme over a field. Let
+Y ⊂ X be an integral, closed subscheme of pure codimension d defined by IY .
+Assume there is a locally monomial ideal J ⊃ IY on X, with the cosupport
+V (J ) of codimension ≥ 2, and with the associated exceptional divisor E on the
+normalized blow-up σ : Y = blJ (X) → X, and the dual valuation complex ∆N
+E such
+that
+(1) Sing(V (IY )) ⊆ V (J ).
+(2) For any valuation face ω ∈ ∆N
+E ⊂ ∆N
+B , and the ideal inω(IY ) ⊂ grJω(OX)1
+we have
+SingNω(X)(V (inω IY )) ⊆ V (in◦
+ω J ).
+1Definition 4.2.3
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+49
+(respectively
+(2’) For any valuation face ω ∈ ∆N
+E ⊂ ∆N
+B , we have
+SingNω(X)(V (in◦
+ω IY )) ⊆ V (in◦
+ω J ).)
+Then the cobordant blow-up B+ → X of J defines a cobordant resolution of Y .
+That is, the strict transform Y ′ = V (σs(IY )) of Y (respectively the weak transform
+Y ′ = V (σ◦(IY )) of Y ) is a regular subscheme of B+ of the codimension equal to
+the codimension of Y in X.
+Proof. The problem is local on X. Thus, up to a torus factor, we can assume that
+the full cobordant blow-up of J is given locally on X by
+σ : B = Spec(OX[t−1, tα1u1, . . . , tαkuk]) → X.
+Then for the restriction morphism πB− : B− = X × T → X, the inverse im-
+age π−1
+B−(Y ) is irreducible of codimension d.
+So is its closure Y ′ := σ−1(Y ) =
+V (σc(IY )), which is the strict transform of Y . Since V (J ) is of codimension ≥ 2,
+the divisor D = VB(t−1) is exceptional for B → X. Observe that
+Sing(Y ′) ∖ D = Sing(Y ′) ∩ B− ⊂ V ◦
+B−(J ) ⊆ VB(σ◦(J ))
+On the other hand, the exceptional divisor D+ = D|B+ is the union of the strata
+s+ ∈ SD+. By Corollary 4.1.3(4),(5), each such a stratum s+ extends to s ∈ SD,
+and corresponds to the valuation face ω ∈ ∆N
+D+ = ∆N
+E ⊂ ∆N
+D.
+Since the singular locus of V (inω IY ) is contained in V (in◦
+ω(J )) and by Lemmas
+4.3.1, 4.3.3, we have
+Sing(Y ′ ∩ s) = SingNω(X)(V (inω IY )) × ˇtω ⊆ V (in◦
+ω J ) × ˇtω = VB(σ◦(J )|s),
+Then using Lemmas 4.4.3 and 4.3.1 we conclude that the subscheme
+Y ′ ∩ s ≃ V (inω IY )) × ˇtω
+is of pure codimension d in s ≃ Nω(X) × ˇtω, and
+(Y ′ ∩ s) ∩ B+ = ((Y ′ ∩ s) ∖ VB(σ◦(J ))
+is regular of codimension d in s.
+Hence for p ∈ ((Y ′ ∩ s) ∖ VB(σ◦(J )), we can find parameters v1, . . . vd ∈ Os,p ·
+IY ′ = (OB,p · IY ′)/(t−1
+ω ) at p which vanish on Y ′ ∩ s. But these parameters come
+from local parameters in IY ′ on B at p. So they define a regular subscheme Y ′′
+of B+ of codimension d, containing locally Y ′. Thus Y ′′ locally coincides with Y ′
+which must be regular at p ∈ s∖VB(σ◦(J )). Consequently Sing(Y ′) is contained in
+VB(σ◦(J )), and, by Lemma 1.4.4, Y ′ is a regular subscheme of B+ = B∖VB(σ◦(J ))
+of codimension d.
+The proof for the weak transform σ◦(I) (with stronger assumptions in condition
+(2’)) is identical.
+♣
+As a corollary, we obtain the following:
+Theorem 4.4.6. Let X be a smooth variety over a field κ of any characteristic.
+Let Y ⊂ X be a closed integral subscheme of X Assume there is a locally monomial
+ideal J ⊃ IY on X , with the cosupport V (J ) of codimension ≥ 2, and with the
+associated exceptional divisor E on the normalized blow-up σ : Y = blJ (X) → X,
+and the dual valuation complex ∆N
+E such that
+
+50
+J. W�LODARCZYK
+(1) Sing(V (IY )) ⊆ V (J ).
+(2) For any valuation face ω ∈ ∆N
+E , the ideal the singular locus
+SingNω(X)(V (inω IY )) ⊆ V (in◦
+ω J ).
+Then there is a resolution of Y at Z, that is, a projective birational morphism
+φ : Y res → Y from a smooth variety Y res with the exceptional locus Z ⊂ Y , such
+that φ−1(Z) is an SNC divisor on Y ′.
+Proof. Take the cobordant resolution B+ → X from Theorem 4.4.5. We use Section
+3.4.4 to embed cobordant blow-up B+ as a smooth subspace of the relative affine
+space An
+X. This implies that B+ � T is locally toric.
+The locally toric singularities of B+ � T can be canonically resolved by the
+combinatorial method of [W�lo20, Theorem 7.17.1]. This produces the projective
+birational resolution Y ′ → Y of Y such that the inverse image of the singular point
+is an SNC divisor.
+♣
+4.5. Resolution of hypersurfaces via the Newton method.
+4.5.1. The Newton polytope of a monomial ideal. Let X = Ak
+Z = Spec(OZ[x1, . . . , xk]),
+where Z is a smooth scheme over κ, and I ⊂ OZ[x1, . . . , xk] is an ideal. One can
+extend the notion of the Newton polytope of monomial ideals I = (xα1, . . . , xαk) ⊂
+κ[x1, . . . , xn] considered previously in Section 2.6.1 in the case Z = Spec(κ), where
+κ is a field.
+As before, by the associated Newton polytope of I we mean
+PI := conv(α1 + Qn
+≥0, . . . , αk + Qn
+≥0) ⊆ Qn
+≥0
+Conversely, with a polytope P ⊂ Qn
+≥0 we associate the monomial ideal
+IP := (xα | α ∈ P ∩ Zn).
+4.5.2. The initial forms defined by faces.
+Definition 4.5.3. (see [AQ21]) If I = (xα)α∈A ⊂ OZ[x1, . . . , xn] is a monomial
+ideal and PI is its Newton polytope and P ≤ PI be its face, we define the initial
+form with respect to a face of the PI to be:
+invP (I) := (xα | α ∈ A ∩ P).
+The definition invP (I) is a particular case of the notion o the initial form inv◦
+ω(I)
+with respect to a valuation face ω ∈ ∆N
+E .
+By Corollary 2.6.13 we obtain
+Lemma 4.5.4. Let ∆N
+E be the valuation dual complex associated with a monomial
+ideal I, and let P = PI be its Newton polytope.
+Any valuation face ω ∈ ∆N
+E of the associated dual valuation complex ∆N
+E defines
+the induced face
+Pω := P ∩
+�
+ν∈ω
+Hν
+of the Newton polytope P, for the supporting hyperplanes Hν associated with ν and
+we have:
+inv◦
+ω(I) = invPω(I).
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+51
+Conversely for any supporting face P ′ of P there is a valuation face ω ∈ ∆N
+E ,
+such that inv◦
+ω(I) = invPω(I).
+♣
+Remark 4.5.5. The above correspondence is not bijective. Several valuation faces
+ω could define the same supporting face of P. The information encoded in the dual
+valuation complex is richer and can be applied to a more general setting.
+4.5.6. The Newton polytopes of polynomials and ideals. By the Newton polytope of
+the function
+f =
+�
+cαxα ∈ O(Z)[x1, . . . , xk],
+where cα ∈ O(Z) we mean the Newton polytope of the monomial ideal
+Jf := (xα | cα ̸= 0),
+generated by the exponents α occurring in the presentation of f with nonzero
+coefficients. Note that Jf is the smallest monomial ideal which contains f.
+This definition can be extended to any ideal I ⊂ OZ[x1, . . . , xk]. We associate
+with I the monomial ideal J = JI generated by If, where f ∈ I. The Newton
+polytope PI of I is simply the Newton polytope of the monomial ideal J .
+If P ≤ PI is a face of the Newton polytope PI, and f = �
+α∈A cαxα ∈ I we put
+invP (f) :=
+�
+α∈A∩P
+cαxα.
+Then invP (I) is the ideal generated by invP (f), where f ∈ I.
+Let ∆N
+E be the dual valuation complex associated with a monomial ideal J ⊂
+OZ[x1, . . . , xk]. Recall that, by Section 4.2.4, and using identification :
+grωOZ[x1, . . . , xk] = OZ[x1, . . . , xk], for any valuation face ω ∈ ∆N
+E we write
+invω(f) :=
+�
+α∈Aω,f
+cαxα ∈ grω(OZ[x1, . . . , xk]) = OZ[x1, . . . , xk].
+where
+Aω,f = {α ∈ A | ν(xα) = ν(f), ν ∈ ω}.
+Similarly for the ideal I ⊂ OZ[x1, . . . , xk] the ideal of the initial forms inv◦
+ω(I)
+is generated by all invω(f), where f ∈ I, and ν(f) = ν(I) for all ν ∈ ω.
+The following is an immediate consequence of Lemma 4.5.4, and the above:
+Lemma 4.5.7. Let Pf (respectively PI) be the Newton polytope of f = � cαxα
+(respectively of an ideal I ⊂ OZ[x1, . . . , xk]), and let Jf (respectively JI) be the
+associated monomial ideal. Then for any valuation face ω ∈ ∆N
+E of the associated
+dual valuation complex ∆N
+E and the corresponding face Pω of P.
+invω(f) = invPω(f).
+(respectively
+inv◦
+ω(I) = invPω(I)).
+♣
+
+52
+J. W�LODARCZYK
+4.5.8. Resolution by the Newton polytopes. The following is a particular case of
+Theorem 4.4.5 for hypersurfaces, written in a more straightforward setup.
+Theorem 4.5.9. X = An
+Z = Spec OZ[x1, . . . , xk], where Z is a regular scheme
+over a field κ. Let
+f =
+�
+α∈Af
+cαxα ∈ OZ[x1, . . . , xk]
+where cα ̸= 0 for α ∈ Af. Let J = (xα | α ∈ Af)sat be the induced monomial ideal,
+and Pf = PJ be its Newton polytope. Assume that
+(1) The cosupport V (J ) is of codimension ≥ 2,
+(2) Sing(V ((f)) ⊆ V (J ).
+(3) For any supporting face P of Pf, Sing(V (inP (f)) ⊂ V (inP (J )).
+Then the cobordant blow-up B+ → X of J resolves the singularity of V (f). That is,
+the strict transform Y ′ = V (σs(f)) of Y (which coincides with the weak transform
+V (σ◦(f)) of Y ) is a regular subscheme of B+.
+Proof. By Lemmas 4.5.7, 4.5.4, and the assumption (3) we get that
+Sing(invω(f)) = Sing(inv◦
+ω(f)) ⊂ V (in◦
+ω(J )),
+for any ω ∈ ∆N
+E and the corollary follows from Theorem 4.4.5.
+♣
+Remark 4.5.10. The theorem shows that in the case of hypersurface V (f) the
+critical combinatorial information is related to the faces P of the Newton polytope
+Pf. Generally, one considers the dual valuation complex ∆N
+E associated with the
+ideal I. In such a case, invP (f) is replaced with more general invω(I), and the
+role of the Newton polytope of a monomial ideal is limited (see Theorems 4.4.5,
+Theorems 4.6.9). However, it still can be used in the context of the order of the
+ideals in OZ[x1, . . . , xk] (see Theorems 4.8.1, 4.8.2).
+One can easily extend these results to the products of schemes:
+Theorem 4.5.11. Let X = �
+Z Xj, where each Xj = Anj
+Z
+= Spec(OZ[xj]) =
+Spec OZ[xj1, . . . , xjkj], where Z is a regular scheme over a field κ for j = 1, . . . , r.
+Let
+fj =
+�
+α∈Afj
+cjαxjα ∈ OZ[xj1, . . . , xjkj ]
+where cjα ̸= 0 for α ∈ Afj. Let
+Jj = (xα
+j | α ∈ Afj)sat ⊂ OZ[xj]
+be the induced monomial ideal, and Pfj := PJj be its Newton polytope in Qkj.
+Assume that for any j = 1, . . . , r
+(1) The cosupport V (Jj) is of codimension ≥ 2,
+(2) Sing(V (fj)) ⊆ V (Jj).
+(3) For any supporting face P of Pfj,Sing(V (inP (f)) ⊆ V (inP (Ji)).
+Then the cobordant blow-up B+ → X of �r
+j=1 OX · Ji resolves the singularity of
+V (f1, . . . , fk).
+That is, the strict transform Y ′ = V (σs((f1, . . . , fk)) of Y is a
+regular subscheme of B+.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+53
+Proof. The cobordant blow-up of �r
+j=1 OX · Ji is equal to the product over Z of
+the cobordant blow-ups Bj+ of Ji on Spec(OZ[xj]), each of which is smooth over
+Z.
+♣
+4.6. The Abramovich-Quek resolution. The following result is due to Abramovich-
+Quek (with some minor modifications):
+Corollary 4.6.1. [AQ21, Theorem 5.1.2] Let X = An
+Z = Spec OZ[x1, . . . , xn],
+where Z is a regular scheme over a field. Consider the induced SNC divisor D :=
+V (x1 · . . . · xn). Let
+f =
+�
+α∈Af
+cαxα ∈ O(Z)[x1, . . . , xk]
+where cα ̸= 0 for α ∈ Af. Let J = Jf := (xα | α ∈ Af) be the associated monomial
+ideal, and Pf := PJ be its Newton polytope. Assume that the cosupport V (J ) is of
+codimension ≥ 2, and for any face P of Pf, the ideal (inP (f)) determines a smooth
+subscheme outside of D.
+Then the cobordant blow-up B+ → X of J resolves the singularity of V (f). That
+is, the strict transform Y ′ = V (σs(f)) = V (σ◦(f)) of Y is a regular subscheme of
+B+.
+Remark 4.6.2. Note that unlike in the original formulation the coefficients cα are
+not necessarily invertible. Theorem 4.6.1 is further generalized for the ideals in the
+context of order. See Remark 4.8.3.
+Proof. Let σ∨
+0 = Qn
+≥0 = ⟨x1, . . . , xn⟩ be the cone corresponding to the ring
+OZ[x1, . . . , xn].
+It suffices to show that conditions (2), (3) of Theorem 4.5.9 are satisfied.
+To prove condition (3) let P ′ be any supporting face of Pf. By Lemma 2.6.5,
+there is a stratification of X with strata sτ, where τ is a face of σ0 . It is determined
+by the pull-back of the orbit stratification on Xσ0, via X = Xσ0 × Z → Xσ0.
+Assume that sτ is not in V (in◦
+P ′(J )). This means, by Corollary 2.6.6, that τ ∗
+intersects P ′ so we consider the face P := P ′ ∩ τ∗. Moreover, by Lemma 2.6.5, we
+can write the closure of the stratum sτ as
+sτ := V (xi | xi ̸∈ τ∗).
+On the other hand, since P ⊂ τ∗, the polynomial inP (f) ∈ OZ[xi ∈ τ ∗] ⊂
+OZ[x1, . . . , xn] can be identified with
+inP (f)|sτ ∈ OZ[x1, . . . , xn]/(xi | xi ̸∈ τ ∗) ≃ OZ[xi ∈ τ ∗].
+Now inP (f) is simply equal to
+inP (f)|sτ = inP ′(f)|sτ ,
+By the assumption inP (f) ∈ OZ[xi ∈ τ∗] is a local parameter on
+Spec(OZ[x1, . . . , xn] ∖ V (
+�
+xi)
+=
+(Spec(OZ[xi ∈ τ ∗]) ∖ V (
+�
+xi∈τ ∗
+xi))
+×
+(Spec(OZ[xi ̸∈ τ ∗]) ∖ V (
+�
+xi̸∈τ ∗
+xi)),
+
+54
+J. W�LODARCZYK
+and on
+(Spec(OZ[xi ∈ τ ∗]) ∖ V (
+�
+xi∈τ ∗
+xi)) ≃
+≃ V (xi | xi ̸∈ τ∗) ∖ V (
+�
+xi∈τ ∗
+xi)) = sτ ∖ V (
+�
+xi∈τ ∗
+xi)) = sτ
+Consequently inP (f)|sτ = inP ′(f)|sτ defines a local parameter on the stratum sτ.
+This implies that inP ′(f) is a local parameter on all strata sτ outside of V (in◦
+P ′(J )).
+The proof of condition (2) is similar. Consider any face τ of σ0. If sτ is not in
+V (J ), then, by Corollary 2.6.6, τ intersects Pf so we consider the face P := Pf ∩τ ∗.
+Consequently, by the assumption
+(inP (f))|sτ = f|sτ ∈ OZ[xi ∈ τ∗]
+defines a local parameter on the stratum
+sτ = sτ ∖ V (
+�
+xi∈τ ∗
+xi),
+This implies that f is a local parameter on all strata sτ outside of V (J ), showing
+condition (2) of Theorem 4.5.9 and completing the proof.
+♣
+Corollary 4.6.3. Let Z be a regular scheme over a field κ, and X = �
+Z Xj, where
+Xj := Anj
+Z = Spec O(Z)[xj1, . . . , xjkj ] for j = 1, . . . , r. Let
+fj =
+�
+α∈Afj
+cjαxjα ∈ OZ[xj1, . . . , xjkj ]
+where cjα ̸= 0 for α ∈ Afj. Let Jj := (xα
+j | α ∈ Afj) be the induced monomial
+ideal, and Pfj := PJj be its Newton polytope in Qkj. Assume that for any j =
+1, . . . , r the cosupport V (Jj) is of codimension ≥ 2, and for any face P of Pfj,
+the ideal (inP (fj)) determines a smooth subscheme outside of V (xj1 · . . . · xjkj ).
+Then the cobordant blow-up B+ → X of �r
+j=1 OX · Ji resolves the singularities
+of V (f1, . . . , fk). That is, the strict transform Y ′ = V (σs((f1, . . . , fk)) of Y is a
+regular subscheme of B+.
+4.6.4. Examples of resolution.
+Theorem 4.6.5. Let X = SpecZ(OZ[x1, . . . , xk]), where Z is a smooth variety
+over a field κ. Consider the closed subscheme Y on X defined by a function f ∈
+H0(X, OX) of the form
+f =
+k
+�
+i=1
+cαi(v)xαi,
+where cαi(v) ∈ O(Z)∗ are invertible.
+Assume that for the presentation of f, one of the following holds:
+• char(κ) = 0, and for any αi except possibly one, there is a variable xji such
+that a power x
+aji
+ji
+of xji, occurs in xαi and xji does not occur in the others
+xαj for j ̸= i.
+• char(κ) = p, and for any αi except possibly one there is a variable xji such
+that a power x
+aji
+ji
+of xji, occurs in xαi, with p ∤ aji and xji does not occur
+in the others xαj for j ̸= i except as some k · p-th power for k ∈ N.
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+55
+Then the cobordant blow-up B+ → X of J = (xα1, . . . , xαk) resolves singularity,
+so that the strict transform πs
+B(f) determines a regular subscheme σs(Y ) of B+.
+Proof. Let D(f) be the ideal generated by f, and all the derivatives D(f). At any
+point p of Sing(f) , we have that ordp(f) ≥ 2 which implies Sing(V (f)) = V (D(f)).
+But the ideal D(f) contains all but possibly one monomials xαi ∼ xj(i)Dxj(i)(f) .
+Since f = �k
+i=1 cαi(v)xαi, and all but at most one monomial xαi are in D(f) we
+conclude that D(f) ⊇ J = (xα1, . . . , xαk). So
+Sing(Y ) = V (D(f)) ⊆ V (J ).
+Similarly
+Sing(inP (f)) = V (D(inP (f)) ⊆ V ((in◦
+P (J )).
+Thus the conditions of Theorem 4.5.9 are satisfied.
+♣
+Example 4.6.6. Let f = xa1
+1 + . . . + xak
+k ∈ κ[x1, . . . , xk], where the characteristic
+p divides at most one ai. Then the cobordant blow-up of (xa1
+1 , . . . , xak
+k ) resolves
+singularity. By Example 3.4.6, it is given by
+B = SpecX(OX[t−1, x1tw1, . . . , xktw
+k ])
+B+ = B ∖ VB(σs(J )) = B ∖ VB(x1tw1, . . . , xktwk).
+The morphism B+ → X is interpreted in Section 5.4 as the cobordant blow-up
+of the weighted center J = (x1/w1
+1
+, . . . , x1/wk
+k
+), such that OB+ · J = OB+ · t−1.
+Example 4.6.7.
+xp
+1 + axp
+2x3 + bx1xp
+4xp2
+5 ∈ κ[x1, x2, x3, x4, x5, ],
+where a, b ∈ κ∗can be resolved by the single cobordant blow-up of
+J = (xp
+1, xp
+2x3, x1xp
+4xp2
+5 )
+over a field κ of characteristic p. Here for xp
+2x3 the variable x3 does not occur in
+the other terms, and for x1xp
+4xp2
+5 the coordinate x1 occurs in the other terms as xp
+1
+-power or does not show at all.
+Example 4.6.8.
+x2
+1x5
+2 + 7x7
+4x5
+3 + 25x1x6
+3 ∈ κ[x1, x2, x3, x4]
+can be resolved by the cobordant blow-up of
+J = (x2
+1x5
+2, x7
+4x5
+3, x1x6
+3)
+over a field κ of char(κ) ̸= 5, 7. We use x2 for x2
+1x5
+2, and x4 for x7
+4x5
+3.
+Theorem 4.6.9. Let Z be a smooth variety over a field κ. Let
+X = SpecZ(OZ[x1, . . . , xn]) = SpecZ(OZ[x1, . . . , xr]),
+where
+xi := (xki−1, . . . , xki−1),
+for k0 = 1 < k1 < . . . < kr = n + 1. Consider the closed subscheme Y of X defined
+by the set of the polynomial functions fj ∈ H0(X, OX), where j = 1, . . . , r of the
+form
+fj =
+rj
+�
+i=1
+cαij(v)xαij
+j
+,
+
+56
+J. W�LODARCZYK
+where cαij(v) ∈ O(Z)∗ are invertible.
+Assume that for any j = 1, . . . , r and for the presentation of fj one of the
+following holds:
+• char(κ) = 0, and for any αij except possibly one, there is a variable xji
+such that a power x
+aji
+ji
+of xji, occurs in xαij and xji does not occur in the
+others xαi′j for i′ ̸= i.
+• char(κ) = p, and for any αij except possibly one there is a variable xji such
+that a power x
+aji
+ji
+of xji occurs in xαij , with p ∤ aji and xji does not occur
+in the others xαi′j for i′ ̸= i except as some k · p-th power for k ∈ N.
+Then the cobordant blow-up B+ → X of
+J =
+r
+�
+j=1
+(xα1
+j , . . . , xαk
+j )
+resolves singularity, so that the strict transform σs(f1, . . . , fr) determines a smooth
+subvariety of B+.
+Proof. The space X can be written as the fiber product
+X =
+�
+Z
+Aki−ki−1
+Z
+=
+�
+Z
+SpecZ(OZ[xj]).
+The cobordant blow-up of J is equal to the product over Z of the cobordant blow-
+ups Bj+ of (xα1
+j , . . . , xαk
+j ) on SpecZ(OZ[xj]), and each of Bj+ is smooth over Z by
+Theorem 4.6.5.
+♣
+Example 4.6.10. The system of equations
+xp
+1 + ax1xp
+2x3 + bx4xp
+5xp2
+6
+= 0
+yp3
+1 + cyp2
+2 y3y6 + dy1yp
+4yp2
+5 y2
+6
+= 0
+in
+κ[x1, . . . , x6, y1, . . . , y5],
+where a, b, c, d ∈ κ∗, can be resolved by the single cobordant blow-up of
+J = (xp
+1, xp
+2x3, x1x4xp
+5xp2
+6 ) · (yp3
+1 , yp2
+2 y3, y4yp
+5yp2
+6 )
+in characteristic p.
+Example 4.6.11. Let fj = xa1
+1j + . . . + xak
+kjj ∈ κ[xij], where j = 1, . . . , k and the
+characteristic p divides at most one aij for any j. Then the cobordant blow-up of
+�
+j(xa1
+1j , . . . , xak
+kjj) resolves singularity of V (fj)j=1,...,k.
+4.7. Partial resolution by the order. The method can be linked to different
+invariants, particularly to the order
+ordp(I) := max{k | Ip ⊂ mk
+p},
+where mp ⊂ OX,p is the maximal ideal of a point p ∈ X.
+Definition 4.7.1. Let I be an ideal on a regular scheme X, and d ∈ N be an
+integer. We define
+supp(I, d) := {p ∈ X | ordp(I) ≥ d}.
+The following theorem extends [W�lo22, Lemma 5.3.1]:
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+57
+Theorem 4.7.2. Let I be an ideal on a regular scheme X over a field, and let
+d ∈ N be any natural number. Assume that there exists a locally monomial center
+J , with codim(V (J ) ≥ 2, with the associated dual valuation complex ∆N
+E , and such
+that
+(1) supp(I, d) ⊆ V (J ) ⊂ X,
+(2) supp(inω(I), d) ⊆ V (in◦
+ω(J )) ⊂ Nω(X), for any ω ∈ ∆N
+E .
+(respectively
+(2’) supp(in◦
+ω(I), d) ⊆ V (in◦
+ω(J )) ⊂ Nω(X), for any ω ∈ ∆N
+E .)
+Then for the cobordant blow-up σ+ : B+ → X of J , the maximal order of the
+strict transform σs(I) (respectively the weak transform σ◦(I)) on B+ is strictly
+smaller than d.
+Proof. Let q ∈ D+ = D ∖ VB(σ◦(J )), where D = V (t−1
+1
+· . . . t−1
+k ) is the exceptional
+divisor of B → X. Then there is ω ∈ ∆N
+E , and the corresponding stratum s in SD
+such that
+q ∈ s ∖ V (σ◦(J )).
+By Lemmas 4.3.1, 4.3.3, there is a natural isomorphism s → Spec(grω(O)[ˇtω,ˇt−1
+ω ]),
+which takes σs(I)|s to inω(I)[ˇtω,ˇt−1
+ω ] (and σ◦(J )|s to in◦
+ω(J )[ˇtω,ˇt−1
+ω ]).
+Conse-
+quently
+ordq(σs(I)) ≤ ordq(σs(I)|s) = ordq(inω(I)[ˇtω,ˇt−1
+ω ]) < d.
+If
+q ∈ B ∖ D ∖ V (σs(J )) = B− ∖ V (σs(J )) = (X ∖ V (J )) × T,
+then since πB(q) ∈ X ∖ V (J ) we conclude that
+ordq(σs(I)) = ordπB(q)(I) < d.
+The proof for σ◦(I) is the same.
+♣
+4.8. The Newton method of decreasing order. As a corollary from Theorem
+4.7.2, and Lemma 4.5.4 we obtain:
+Theorem 4.8.1. X = An
+Z = Spec OX[x1, . . . , xk], where Z is regular over a field
+κ of characteristic p.
+Let I ⊂ OZ[x1, . . . , xk] be an ideal, and J = JI, be its
+associated monomial ideal with the Newton polytope PJ = PI and d ∈ N be any
+natural number such that
+(1) codim(V (J )) ≥ 2.
+(2) supp(I, d) ⊆ V (J ).
+(3) for any supporting face P of PJ , supp(inP (I), d) ⊂ V (invP (J )).
+Then the maximal order of the weak transform σ◦(I) on B+ under cobordant blow-
+up of J is strictly smaller than d.
+♣
+Thus we get
+Theorem 4.8.2. X = An
+Z = Spec OX[x1, . . . , xk], where Z is regular over a field
+κ of characteristic p.
+Let I ⊂ OZ[x1, . . . , xk] be an ideal, and J = JI, be its
+associated monomial ideal with with codim(V (J ) ≥ 2, and let PJ = PI be its
+Newton polytope and d ∈ N be any natural number such that for any face P of PJ ,
+supp(inP (I), d) ⊂ D := V (x1·, . . . · xk).
+Then the maximal order of the weak transform σ◦(I) under cobordant blow-up
+B+ → X of J is strictly smaller than d.
+♣
+
+58
+J. W�LODARCZYK
+Proof. The proof uses similar arguments as the proof of Corollary 4.6.1. We need
+to show that the conditions of Theorem 4.8.1 are satisfied
+For condition (3) of Theorem 4.8.1, let P ′ be any supporting face of PI. Consider
+the closure of the stratum sτ, where τ is a face of σ0.
+If sτ is not in V (in◦
+P ′(J )) consider the face P := P ′ ∩ τ ∗. Then
+supp(inP ′(I))|sτ , d) = supp(inP (f)|sτ , d)
+is contained in sτ ∖ sτ = V (�
+xi∈τ ∗ xi) so it is not in sτ. This implies that
+supp(inP ′(I)), d) is contained V (in◦
+P ′(J ).
+The proof of condition (2) of Theorem 4.8.1 is the same, except we replace P ′
+with PJ , in◦
+P ′(J ) with J = in◦
+PJ (J ) , and P with P = PJ ∩ τ ∗.
+Thus the corollary is a consequence of Theorem 4.8.1.
+♣
+Remark 4.8.3. Theorems 4.8.1, 4.8.2 generalize respectively Theorem 4.5.9, and
+Corollary 4.6.1. We put I = (f), and d = 2. Then Sing(V (f)) = supp((f), 2).
+Example 4.8.4. (See also Example 2.6.14)
+Let Y ⊂ X = Spec κ[x, y, z] be described by the ideal
+I = (xk + xy + yl,
+zkl + xk−2zkl−1 + yk−2zkl−1)
+of order 2, where gcd(k, l) = 1. Consider the corresponding admissible monomial
+ideal
+J = (xk, xy, yl, zkl, xk−2zkl−1, yk−2zkl−1)
+and its associated Newton polytope P generated by the exponents
+(k, 0, 0), (1, 1, 0), (0, l, 0), (0, 0, kl) ⊂ σ∨ = ⟨e∗
+1, e∗
+2, e∗
+3⟩.
+This corresponds to two supporting faces P1, P2 defined, respectively, by
+(k, 0, 0), (1, 1, 0), (0, 0, kl),
+and
+(1, 1, 0), (0, l, 0), (0, 0, kl).
+They intersect at the face P12 = (1, 1, 0), (0, 0, kl).
+The faces P1, P2 corresponds to the primitive vectors v1 = (a1, a2, a3) such that
+a1k = a1 + a2 = a3kl,
+and v2 = (b1, b2, b3), where
+b1 + b2 = lb2 = klb3
+in the dual plane. So
+v1 = (l, l(k − 1), 1),
+v2 = (k(l − 1), k, 1).
+This defines the set of two extremal valuations ν1, ν2.
+Then
+inP1(I) = (xk + xy, zkl),
+inP2(f) = (xy + yl, zkl),
+inP12(f) = (xy, zkl).
+By considering the ideals of the derivatives D(inP (f)) we see that in all cases
+supp(inP (I), 2) = V (x, y, z)
+Similarly supp(I, 2) = V (x, y, z).
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+59
+The cobordant blow-up of J = (xk, x2y, yl) is described as
+B = SpecX(OX[t−1
+1 , t−1
+2 , xtl
+1tk(l−1)
+2
+, ytl(k−1)
+1
+tk
+2, zt1t2] =
+Spec(κ[t−1
+1 , t−1
+2 , xtl
+1tk(l−1)
+2
+, ytl(k−1)
+1
+tk
+2, zt1t2])
+B+ = B ∖ V (σs(J )) = B ∖ tαJ ,
+where σs(J ) = tαJ , and the coefficients are given by the exceptional divisor E =
+α1E1 + α2E2 of the toric normalized blow-up of J .
+α1 = ν1(f) = a1k = a1 + a2 = a3kl = kl,
+and
+α2 = ν2(f) = b1 + b2 = lb2 = klb3 = kl
+Thus
+B+ = B ∖ V ((xk, xy, yl, zkl) · tkl
+1 tkl
+2 ),
+By Lemma 4.6.9, the cobordant blow-up B+ → X of J = (xk, xy, yl, zkl) decreases
+the order of I to 1.
+5. Generalized cobordant blow-ups and Q-ideals
+5.1. Cobordization with respect to subgroups Γ ⊂ Cl(Y/X) ⊗ Q.
+Definition 5.1.1. Let π : Y → X be a proper birational morphism. Let Γ ⊂
+Cl(Y/X) ⊗ Q be a finitely generated subgroup. We define the full cobordization
+(resp. cobordization of π) with respect to Γ to be
+B = BΓ := SpecX(π∗(
+�
+E∈Γ
+OX(E))
+B+ = BΓ
++ = SpecY (
+�
+E∈Γ
+OY (E)).
+Proposition 5.1.2. The natural morphism BΓ
++ → BΓ is an open immersion if
+locally on X there are forms F = fx−E, with E ∈ Γ such that XF are open affine
+and cover X.
+Proof. The proposition follows from the first part of the proof of Proposition 1.3.4.
+♣
+Definition 5.1.3. Let π : Y → X be the normalized blow-up of the an I on a
+normal scheme X. Let Γ ⊂ Cl(Y/X) ⊗ Q be a finitely generated subgroup. Then
+we define the full cobordant blow-up of I with respect to Γ (resp. the cobordant
+blow-up of I with respect to Γ) to be the full cobordization (resp. cobordization
+of) π with respect to Γ.
+Proposition 5.1.4. π : Y → X be the normalized blow-up of an ideal J on a nor-
+mal scheme X, and let E0 be the exceptional Cartier divisor such that OY (−E0) =
+OY · J . If a finitely generated group Γ ⊂ Cl(Y/X) ⊗ Q contains divisor E0, then
+BΓ
++ = BΓ ∖ V (It−E0).
+Proof. The proof is identical to the proof of Lemma 1.4.4.
+♣
+
+60
+J. W�LODARCZYK
+5.2. Simple cobordant blow-up of ideal I.
+Definition 5.2.1. Let π : Y → X be the normalized blow-up of an ideal I on a
+normal scheme X, with the exceptional divisor E0, such that OY (−E0) = OY · I.
+By the simple cobordant blow-up of I on X we mean the cobordization BΓ
++ of
+π : Y → X with respect to the subgroup Γ = Z · E0 ⊂ Cl(Y/X) generated by E0.
+Lemma 5.2.2. The simple cobordant blow-up of I is given by
+B = SpecX(OX[t−1, It])int,
+B+ = B ∖ V (It).
+Proof. It follows that OY (−nE0) = OY · In. Moreover π∗(OY (−nE0)) = (In)int
+is the integral closure of In.
+Consequently
+B = BΓ
+I = SpecX(π∗(
+�
+n∈Z
+OY (nE0)tnE0) = SpecX(OX[t−1, It])int,
+under the identification of tE0 with t−1. By Proposition 5.1.4,
+B+ = B ∖ V (σs(I)) = B ∖ V (It).
+and thus is described by the standard Rees extended algebra.
+♣
+5.3. Cobordant blow-ups of Q-ideals.
+5.3.1. Valuative Q-ideals. The valuative Q-ideals were introduced in [ATW19]. Here
+we consider its particular version considered in [W�lo22].
+Definition 5.3.2. By valuative Q-ideals, or, simply, Q-ideals on a normal scheme
+X we mean the equivalence classes of formal expressions I1/n, where I is the ideal
+on X, and n ∈ N. We say that two Q-ideals I1/n, and J 1/m are equivalent if the
+integral closures of Im, and J n are the same.
+In particular, if D is a Cartier effective divisor on X then any Q-Cartier effective
+divisor
+1
+m · D determines the Q-ideal OX(−D)
+1
+m .
+By the vanishing locus of J = I1/n we mean V (J ) = V (I).
+One can define the operation of addition and multiplication on Q-ideals:
+I1/n + J 1/m := (Im + J n)1/mn,
+I1/n · J 1/m = (Im · J n)1/mn.
+For any valuative Q-ideal J = I1/n on X we define the associated ideal of
+sections on X:
+JX := {f ∈ OX | f n ∈ Iint},
+where Iint is the integral closure of I. In particular, for the effective Cartier divisor
+D, we have the equalities
+(OX(−D)1/m)X = OX(− 1
+mD) = {f ∈ OX | div(f) − 1
+mD ≥ 0}.
+With any valuative Q-ideal J we associate the Rees algebra on X :
+OX[J t]X =
+�
+n∈Z≥0
+(J n)Xtn ⊂ OX[t],
+and the extended Rees algebra on X:
+OX[t−1, J t]X =
+�
+n∈Z≥0
+J n
+Xtn ⊕
+�
+−n∈Z<0
+t−n ⊂ OX[t, t−1].
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+61
+5.3.3. Cobordant blow-up of Q-ideals. Let J = I1/m be a Q-ideal on X. Consider
+the normalized blow-up π : Y → X of I, with the exceptional divisor E0 such that
+OY (−E0) = OY · I.
+Then OY ·I1/m is the Q-ideal OY (−E0)1/m, which corresponds to the Q-Cartier
+exceptional divisor
+1
+mE0 on Y .
+Consequently, by the blow-up of the Q-ideal J = I1/m we mean the the normal-
+ized blow-up π : Y → X of I, with the associated Q-Cartier divisor
+1
+mE0.
+Definition 5.3.4. By the simple cobordant blow-up/full cobordant blow-up of the
+Q-ideal J = I1/m we mean the cobordization/full cobordization of the normalized
+blow-up Y → X of J with respect to the group Γ = Z · 1
+mE0 ⊂ Cl(Y/X) ⊗ Q
+generated by
+1
+mE0.
+Lemma 5.3.5. Let σ : B → X be the simple full cobordant blow-up of the Q-ideal
+J = I1/m on a normal scheme X. Then
+B = SpecX(OX[t−1, J t])X
+(1) B+ = B ∖ V (J t)
+(2) OB+ · J = t−1 · OB+
+Proof. Let π : Y → X be the normalized blow-up of I, E0 is the exceptional divisor
+on Y such OX · I = OY (−E0). Thus, by [W�lo22, Proof of Lemma 2.1.4],
+π∗(OY (− n
+mE0) = (f ∈ π∗(OY ) = OX : f n ∈ π∗(OY (−mE0)) = (Im)int) = J m
+X .
+giving the formula for B:
+B = SpecX(π∗(
+�
+n∈Z
+OY (n · (1/m) · E0)tn)) = SpecX(OX[t−1, J t])X.
+By Proposition 5.1.4,
+B+ = B ∖ V (I · t−E0) = B ∖ V (J t−(1/m)E0) = B ∖ V (J t),
+as (1/m)E0 generates Γ, and t(1/m)E0 corresponds to t−1. Thus the inverse image
+of
+OB+ · I1/m = OB+ · J = t−1OB+ · J t = OB+ · t−1
+is a Cartier exceptional divisor. We use here the fact that the Q-ideal J t|B+ = OB+,
+as J t = (Ita)1/a = (I · t−E0)1/a is trivial on B+ = B ∖ V (It−E0).
+♣
+5.4. Weighted cobordant blow-ups revisited. Let πB : B → X be the simple
+cobordant blow-up of the weighted center J = (u1/w1
+1
+, . . . , u1/wk
+k
+), where u1, . . . , uk
+is a partial system of local parameters on a regular scheme. Assume, first, that the
+weights wi are relatively prime. The center J can be written as J = I1/m, where
+I = (um/w1
+1
+, . . . , um/wk
+k
+),
+is the ideal, and the weights wi|m.
+Let E0 be the exceptional divisor of the blow-up π : Y → X of J . Let νE0 be
+the associated exceptional valuation. Using the toric chart, defined by u1, . . . , uk
+one reduces the situation to the blow-up of the toric Q-ideal J on a toric variety
+Xσ, where σ = ⟨e1, . . . , ek⟩ is regular. The Q-ideal J = I1/m defines a piecewise
+linear convex function
+FJ = min( 1
+w1
+e∗
+1, . . . , 1
+wk
+e∗
+k) = 1/m · min( m
+w1
+e∗
+1, . . . , m
+wk
+e∗
+k).
+
+62
+J. W�LODARCZYK
+The normalized blow-up of J defines a decomposition ∆ of σ into the maximal
+subcones where FJ is linear. Let w := (w1, . . . , wk) , and
+FJ (ei) = 0, . . . , FJ (w) = 1.
+Then ∆ is the star subdivision at ⟨w⟩. Moreover, the vector mw corresponds to
+mFJ = FI in the sense that they define the same Weil divisors , and w and
+corresponds to E0, so the valuation νE0 on Y is associated with w. In particular,
+νE0(ui) = e∗
+i (w) = wi.
+Consequently, OY · (um/w1
+1
+, . . . , um/wk
+k
+) = OY (−mE0) is the ideal of the Cartier
+divisor mE0 on Y , associated with the integral function mFJ , and the Q-ideal
+J = (u1/w1
+1
+, . . . , u1/wk
+k
+) corresponds to the Q-divisor (1/m) · mE0 = E0 which is a
+Weil divisor.
+The cobordant blow-up associated with the group Γ = Z·E0 = Cl(Y/X) is given
+by the standard formula from Theorem 3.4.3:
+B = SpecX(π∗(
+�
+n∈Z
+OY (nE0))tn = SpecX(OX[t−1, J t])X =
+= SpecX(
+�
+ai∈Z
+Iν,ai · ta1
+1 · . . . · tak
+k ) =
+= SpecX(OX[t−1, u1tw1, . . . , uktwk]),
+where wi = νE0(ui).
+In general, for arbitrary weights, the simple cobordant blow-up of (u1/w1
+1
+, . . . , u1/wk
+k
+)
+is associated with the group Γ = Z· 1
+w0 E0 =
+1
+w0 ·Cl(Y/X), where w0 := gcd(w1, . . . , wk),
+and with the valuation w0ν, with
+w0ν(xi) = wi.
+Now
+Iw0ν,a = (ub1
+1 · . . . · ubk
+k ) |
+k
+�
+j=1
+bjwi ≥ a).
+Comparing gradations we see
+�
+a∈Z
+Iw0ν,ata = OX[t−1, uitwi].
+Then
+B = SpecX(π∗(
+�
+n∈Z
+OY (n · (1/w0) · E0)tn =
+= SpecX(
+�
+ai∈Z
+Iw0ν,a · ta) = SpecX(OX[t−1, tw1x1, . . . , twkxk]).
+By the above B+ = B ∖ V (J t) = B ∖ V (tw1x1, . . . , twkxk), and OB+ · J =
+OB+ · t−1.
+These weighted cobordant blow-ups were studied in [W�lo22] and used for the
+resolution of varieties in characteristic zero and some classes of singularities in pos-
+itive and mixed characteristic. To a great extent, they are equivalent to the stack-
+theoretic weighted blow-ups introduced and considered in [McQ19], and [ATW19].
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+63
+5.5. Multiple weighted cobordant blow-ups of Abramovich-Quek. In the
+paper [AQ21], the authors consider the generalization of the weighted blow-ups,
+so-called, multi-weighted blow-ups BlJ ,b, associated with a Q-ideal J and a vec-
+tor b = (b1, . . . , bk). They are constructed locally in toric charts in the language
+of fantastacks and stack-theoretic quotients via Satriano combinatorial approach
+[Sat13]. The multi-weighted blow-ups are used to prove the logarithmic resolution
+on smooth toroidal ambient Artin stacks in characteristic zero.
+We give here a geometric interpretation of this construction in the language of
+cobordizations with respect to a subgroup. In particular, this approach does not
+rely on coordinates or combinatorics.
+Let π : Y → X be the normalized blow-up of a locally monomial center J on
+a regular scheme over a field. Denote by E1, . . . , Ek the irreducible exceptional
+divisors. Let ν1, . . . , νk be the associated exceptional valuations. We consider the
+full cobordant blow-up of J with respect to the subgroup
+Γb := Z 1
+b1
+E1 ⊕ . . . ⊕ Z 1
+bk
+Ek ⊂ Cl(Y/X) ⊗ Q,
+for any positive integers b1, . . . , bk, and b = (b1, . . . , bk). Write
+B = SpecX(π∗(
+�
+E∈Γb
+OX(E)),
+B+ = SpecY (
+�
+E∈Γb
+OY (E)).
+The generators
+1
+b1 E1, . . . , 1
+bk Ek are associated with the monomial valuations
+νb
+1 := b1ν1, . . . , νb
+k := bkνk.
+Then locally on X using the Proposition 1.2.2, and the proof of Lemma 2.3.5(1) we
+can write
+B = SpecX(
+�
+ai∈Z
+k�
+i=1
+Iνb
+i ,ai · ta1
+1 · . . . · tak
+k ) =
+=
+k�
+i=1
+OX[t−1
+i , ujtνb
+i (uj)
+i
+][ˇti,ˇt−1
+i ] =
+= SpecX(OX[t−1
+1 , . . . , t−1
+k , u1tαb
+1, . . . , uktαb
+k]),
+where
+• ˇti := t1, . . . , ˇti, . . . , tk
+• u1, . . . , uk, is a system of coordinates on open U ⊂ X defining monomial
+generators for J , and
+• tαb
+i := tab
+i1
+1
+· . . . · tab
+ik
+k ,
+with
+ab
+ij := νb
+i (uj) = biνi(uj) ≥ 0.
+Note that under this correspondence t−1
+i
+�→ t
+1
+bi Ei.
+Let
+E0 = a1E1 + . . . + akEk
+(7)
+be the exceptional divisor of π : Y → X, for the relevant ai ∈ Z≥0, such that
+OY (−E0) = OY · J . By Proposition 5.1.4,
+B+ = B ∖ V (J t−E0) = B ∖ V (J tαb),
+
+64
+J. W�LODARCZYK
+where tαb corresponds to t−E0, under t−1
+i
+�→ t
+1
+bi Ei. Thus by (7), αb = (b1a1, . . . , bkak),
+and
+B+ = B ∖ V (J t−E0) = B ∖ V (J tb1a1
+1
+· . . . · tbkak
+k
+).
+In particular, if X is regular over a field and J is a locally monomial ideal on
+X, then the full cobordant blow-up B of J with respect to Γb is regular.
+5.5.1. Multiple weighted blow-ups associated with Q-ideals. Consider the normalized
+blow-up π : Y → X of a monomial Q-ideal J , with the associated exceptional
+divisor E0 = a1E1 + . . . + akEk with rational, positive coefficients ai, as in Section
+5.3.3. We choose b = (b1, . . . , bk) with bi ∈ Z>0, such that
+Γb = Z 1
+b1
+E1 ⊕ . . . ⊕ Z 1
+bk
+Ek ⊂ Cl(Y/X) ⊗ Q,
+is the minimal subgroup of Cl(Y/X) ⊗ Q containing E0.
+Thus any monomial Q-ideal I and b = (b1, . . . , bk) ∈ Zk
+>0 determines a unique
+associated cobordant blow-up B+ → X with respect to the group Γb. This way, tak-
+ing the stack-theoretic quotient, we obtain the Abramovich-Quek multiple weighted
+blow-up [B+ � T ] → X from [AQ21], which is necessarily regular for a regular X.
+References
+[ADHL15]
+Ivan Arzhantsev, Ulrich Derenthal, J¨urgen Hausen, and Antonio Laface, Cox rings,
+2015, pp. viii+530. MR 3307753
+[AKMW02]
+Dan Abramovich, Kalle Karu, Kenji Matsuki, and Jaros�law W�lodarczyk, Torification
+and factorization of birational maps, J. Amer. Math. Soc. 15 (2002), no. 3, 531–572
+(electronic). MR 1896232 (2003c:14016)
+[AQ21]
+Dan Abramovich and Ming Hao Quek, Logarithmic resolution via multi-weighted
+blow-ups, 2021.
+[ATW17]
+Dan Abramovich, Michael Temkin, and Jaros�law W�lodarczyk, Principalization of
+ideals on toroidal orbifolds, JEMS, to appear, (2017), arXiv:1709.03185.
+[ATW19]
+, Functorial embedded resolution via weighted blowings up, arXiv e-prints
+(2019), arXiv:1906.07106.
+[ATW20]
+Dan Abramovich, Michael Temkin, and Jaros�law W�lodarczyk, Relative desingular-
+ization and principalization of ideals, arXiv:2003.03659.
+[BM97]
+Edward Bierstone and Pierre D. Milman, Canonical desingularization in character-
+istic zero by blowing up the maximum strata of a local invariant, Invent. Math. 128
+(1997), no. 2, 207–302. MR 1440306 (98e:14010)
+[BR19]
+Daniel Bergh and David Rydh, Functorial destackification and weak factorization
+of orbifolds, arXiv e-prints (2019), arXiv:1905.00872.
+[Cox95]
+David A. Cox, The homogeneous coordinate ring of a toric variety, 1995, pp. 17–50.
+MR 1299003
+[Dan78]
+V. I. Danilov, The geometry of toric varieties, Uspekhi Mat. Nauk 33 (1978),
+no. 2(200), 85–134, 247. MR 495499
+[DH98]
+Igor V Dolgachev and Yi Hu, Variation of geometric invariant theory quotients, Inst.
+Hautes ´Etudes Sci. Publ. Math. (1998), no. 87, 5–56, With an appendix by Nicolas
+Ressayre. MR 1659282
+[EH02]
+Santiago Encinas and Herwig Hauser, Strong resolution of singularities in charac-
+teristic zero, Comment. Math. Helv. 77 (2002), no. 4, 821–845. MR 1949115
+[ER21]
+Dan Edidin and David Rydh, Canonical reduction of stabilizers for Artin stacks
+with good moduli spaces, Duke Math. J. 170 (2021), no. 5, 827–880. MR 4255045
+[EV03]
+Santiago Encinas and Orlando Villamayor, A new proof of desingularization over
+fields of characteristic zero, Proceedings of the International Conference on Algebraic
+Geometry and Singularities (Spanish) (Sevilla, 2001), vol. 19, 2003, pp. 339–353.
+MR 2023188
+
+COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES
+65
+[Ful98]
+William Fulton, Intersection theory, second ed., Ergebnisse der Mathematik und
+ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in
+Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathe-
+matics], vol. 2, Springer-Verlag, Berlin, 1998. MR 1644323
+[Hir64]
+Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of
+characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203; ibid. (2) 79 (1964),
+205–326. MR 0199184
+[HK00]
+Yi Hu and Sean Keel, Mori dream spaces and GIT, vol. 48, 2000, Dedicated to
+William Fulton on the occasion of his 60th birthday, pp. 331–348. MR 1786494
+[HS06]
+Craig Huneke and Irena Swanson, Integral closure of ideals, rings, and modules,
+London Mathematical Society Lecture Note Series, vol. 336, Cambridge University
+Press, Cambridge, 2006. MR 2266432
+[KKMSD73] George Kempf, Finn Faye Knudsen, David Mumford, and Bernard Saint-Donat,
+Toroidal embeddings. I, Lecture Notes in Mathematics, Vol. 339, Springer-Verlag,
+Berlin, 1973. MR 0335518 (49 #299)
+[Kol07]
+J´anos Koll´ar, Lectures on resolution of singularities, Annals of Mathematics Studies,
+vol. 166, Princeton University Press, Princeton, NJ, 2007. MR 2289519 (2008f:14026)
+[McQ19]
+Michael McQuillan, Very fast, very functorial, and very easy resolution of singular-
+ities, 2019, preprint, written with the collaboration of G. Marzo.
+[Oda88]
+Tadao Oda, Convex bodies and algebraic geometry—toric varieties and applications.
+I, 1988, pp. 89–94. MR 966447
+[QR19]
+Ming Hao Quek and David Rydh, Weighted blow-ups, 2019, in preparation.
+[Que20]
+Ming Hao Quek, Logarithmic resolution via weighted toroidal blowings up, arXiv
+e-prints (2020), arXiv:2005.05939.
+[Rei]
+Miles Reid, What is a flip?, Colloquium Talk, Univ. Of Utah, Dec , 1992.
+[Sat13]
+Matthew Satriano, Canonical Artin stacks over log smooth schemes, Math. Z. 274
+(2013), no. 3-4, 779–804. MR 3078247
+[Tha94a]
+Michael Thaddeus, Stable pairs, linear systems and the Verlinde formula, Invent.
+Math. 117 (1994), no. 2, 317–353. MR 1273268
+[Tha94b]
+, Toric quotients and flips, Topology, geometry and field theory, World Sci.
+Publ., River Edge, NJ, 1994, pp. 193–213. MR 1312182
+[Tha96]
+, Geometric invariant theory and flips, J. Amer. Math. Soc. 9 (1996), no. 3,
+691–723. MR 1333296
+[Vil89]
+Orlando Villamayor, Constructiveness of Hironaka’s resolution, Ann. Sci. ´Ecole
+Norm. Sup. (4) 22 (1989), no. 1, 1–32. MR 985852
+[W�lo00]
+Jaros�law W�lodarczyk, Birational cobordisms and factorization of birational maps,
+J. Algebraic Geom. 9 (2000), no. 3, 425–449. MR 1752010 (2002d:14019)
+[W�lo03]
+, Toroidal varieties and the weak factorization theorem, Invent. Math. 154
+(2003), no. 2, 223–331. MR 2013783 (2004m:14113)
+[W�lo05]
+, Simple Hironaka resolution in characteristic zero, J. Amer. Math. Soc. 18
+(2005), no. 4, 779–822 (electronic). MR 2163383
+[W�lo20]
+Jaros�law W�lodarczyk, Functorial resolution except for toroidal locus. Toroidal com-
+pactification, Advances in Mathematics Volume 407, 8, October 2022, 108551.
+[W�lo22]
+Jaros�law W�lodarczyk, Functorial resolution by torus actions, arXiv e-prints (2022)
+arXiv:2007.13846 .
+Department of Mathematics, Purdue University, 150 N. University Street,, West
+Lafayette, IN 47907-2067
+Email address: wlodarcz@purdue.edu
+
diff --git a/iNFMT4oBgHgl3EQf4jES/content/tmp_files/load_file.txt b/iNFMT4oBgHgl3EQf4jES/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ed7f972dfc56df56144c9ae06224d633a000a51e
--- /dev/null
+++ b/iNFMT4oBgHgl3EQf4jES/content/tmp_files/load_file.txt
@@ -0,0 +1,3417 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf,len=3416
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='12452v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='AG]  29 Jan 2023  COX RINGS OF MORPHISMS AND RESOLUTION OF  SINGULARITIES  JAROS�LAW W�LODARCZYK  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We extend the Cox-Hu-Keel construction of the Cox rings to any  proper birational morphisms of normal schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It allows the representation  of any proper birational morphism by a map of schemes with mild singularities  with torus actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In a particular case, the notion generalizes the combinatorial construction  of Satriano [Sat13] and the recent construction of multiple weighted blow-ups  on Artin-stacks by Abramovich-Quek [AQ21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The latter can be viewed as an extension of stack theoretic blow-ups by  Abramovich, Temkin and W�lodarczyk [ATW19], a similar construction of Mc-  Quillan [McQ19] and and the author’s recent cobordant recent cobordant blow-  ups [W�lo22] at weighted centers to a more general situation of arbitrary locally  monomial centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We show some applications of this operation to the resolution of singulari-  ties over a field of any characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Introduction  The importance of Gm-actions in birational geometry and their connection with  the Mori theory was already discovered by Reid, Thaddeus, and many others (see  [Tha94a], [Tha94b], [Tha96], [Rei], [DH98]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This was also reflected in the proof of  the Weak Factorization theorem, which relied on the notion of birational cobordism  and a critical role of Gm-action [W�lo00], [W�lo03], [AKMW02].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The idea of the birational cobordism from [W�lo00] is to construct a smooth  scheme with Gm-action which represents a proper birational morphism and parametrizes  possible birational elementary modifications such as blow-ups, blow-downs, and  flips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This allows decomposing the proper birational maps of smooth varieties into  a sequence of blow-ups and blow-downs with smooth centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  A similar idea was considered shortly after by Hu-Keel [HK00], who constructed  their Mori dream space, parametrizing possible birational modifications in the Mori  program via torus actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Mori dream space plays a vital role in the Mori  theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' One of the key ingredients in constructing the Mori dream space is the Cox  rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Recall that the Cox rings for toric varieties were considered first by Cox in  [Cox95].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The main idea of the construction comes from the convex geometry:  Any polyhedral complex can be realized as the image of the simplicial complex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Similarly, any fan in toric geometry can be represented as the image of the subfan of  a regular cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This simple observation leads to the fundamental formula describing  Date: January 31, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This research is supported by BSF grant 2014365.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1  2  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  the Cox coordinate ring of tor the toric variety X as  C(X) :=  �  D∈Cl(X)  H0(X, OX(D)),  where Cl(X) is the Weil divisor class group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The action of torus T = Spec Z[Cl(X)]  naturally occurs in the construction, and is determined by the Cl(X)-gradation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The Cox formula generalizes the construction of the coordinate ring of the pro-  jective scheme X = Pn  Z, namely  Z[x0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn] =  �  n∈Z  H0(X, OX(n))  The projective space X = Pn can be seen as the geometric quotient of the  characteristic space  ˆX = SpecX(  �  D∈Cl(X)  OX(D) → X,  introduced in [ADHL15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The characteristic space ˆX comes with the natural em-  bedding ˆX ֒→ X into the coordinate space:  X := Spec(  �  D∈Cl(X)  H0(X, OX(D))  In particular, for X = Pn we obtain  ˆX = An+1  Z  ∖ {0} ֒→ X = An+1  Z  This leads to the standard Proj -construction:  Proj(Z[x0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn])  =  (Spec(Z[x0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn] ∖ V (x0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn))/Gm  ∥  ∥  X  =  ˆX/T,  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In this paper, we introduce the idea of the Cox rings of the proper birational  morphisms and propose a more general approach to embedded resolution prob-  lems in the language of torus actions, extending the ideas of McQuillan [McQ19]  and Abramovich-Temkin-W�lodarczyk [ATW19] of the weighted resolution, and  Abramovich-Quek [AQ21] of the multiple weighted resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The idea of utilizing group actions to resolve singularities is ancient and should be  traced back to Newton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In the method that he developed, known later as Newton-  Puiseau theorem, he shows that any polynomial function f(x, y) on X = C2 with  expansion containing the term yr can be, in fact, upon a coordinate change, resolved  by a Newton-Puiseau series y = g(x1/k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In other words one considers the space  X′ = C2 with the group action of µk = ⟨ξ⟩, ξ(x, y) = (ξ · x, y), giving the quotient  X′ → X, (x, y) �→ (xk, y), and a smooth holomorphic branch V (y − g(x1/k)) on X′  parametrizing subspace V (f) on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Originally in the Hironaka embedded resolution, only smooth centers were used  (see [Hir64],[Vil89],[BM97],[W�lo05],[EH02], [EV03], [Kol07]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In the recent papers  [ATW17], [ATW20] in the resolution process of logarithmic schemes and morphisms,  we considered the stack-theoretic blow-ups of the centers of the form  J = (u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk, m1/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , m1/wr  r  ),  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  3  in the context of Kummer ´etale topology on the logarithmic stacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The functorial  properties of the algorithm of logarithmic resolution of morphisms dictated such  general centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then in [ATW19], we developed the formalism of the stack-theoretic blow-ups  of the weighted centers of the form (u1/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , u1/wk  k  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This approach allows to  simplify the resolution procedure in characteristic zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The algorithm is more  efficient and avoids many unnecessary blow-ups reducing technicalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It uses a  very simple geometric invariant, which improves after each step and is indepen-  dent of the logarithmic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' A similar result was obtained by McQuillan in  [McQ19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' More general centers were considered in the paper[Que20] of Quek in the  logarithmic context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In work [AQ21] of Abramovich-Quek, the authors introduce multi-weighted blow-  ups, further extending the results in [Que20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The multiple weighted blow-ups gen-  eralize the weighted blow-ups and are used to obtain a smooth and toroidal resolu-  tion version of Artin stacks (see Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Abramovich-Quek weighted blow-  up generalizes the Satriano toroidal construction on Artin logarithmically smooth  stacks in [Sat13] to locally monomial ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Subsequently in the paper [W�lo22] the operation of cobordant blow-up B+ → X  with weighted centers J = (u1/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , u1/wk  k  ) was introduced, where u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk is  a partial system of local parameters  B = SpecX(OX[t−1, tw1x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , twkxk]),  B+ = B ∖ V (x1tw1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xktwk),  (1)  where t is an introduced unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' A similar formula was discovered by Rydh in  the paper of [QR19] and studied in the context of the stack-theoretic blow-ups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover, a certain relation between toric Cox construction and toric weighted  cobordant blow-ups was already observed in [QR19] and [W�lo22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The operation of cobordant blow-up allows representing stack-theoretic weighted  blow-ups and more general Kummer blow-ups in the language of smooth varieties  with torus action without stack theoretic language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover, apart from fast  functorial resolution with SNC divisors in characteristic zero, the approach leads to  the resolution of some classes of singularities in positive and mixed characteristic  (see [W�lo22]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In the present paper, we associate the Cox coordinate ring to arbitrary proper  birational morphisms π : Y → X of normal schemes as follows:  AY/X := π∗(  �  E∈Cl(Y/X)  OY (E)),  where Cl(Y/X) ⊂ Cl(Y ) is a free group generated by the exceptional divisors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It  comes with the coaction of the associated torus T = Spec(Z[Cl(Y/X)]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Per analogy with the standard Cox construction, we call the space  B := SpecX(π∗(  �  E∈Cl(Y/X)  OY (E))  (2)  the relative Cox coordinate space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The scheme  B+ := SpecY (  �  E∈Cl(Y/X)  OY (E)  (3)  will be called the relative Cox characteristic space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  In this language, any proper birational morphism π : Y → X can be represented  by a T -equivariant morphism B+ → B such that the induced morphism of the good  quotient coincides with π : Y → X:  B+ � T  →  B � T  ∥  ∥  Y  π→  X,  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  As in the standard construction, the morphism B+ ⊂ B is an open immersion  upon some reasonable assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If Y → X is the the blow-up of the ideal J on X the associated presentation  B+ � T → X can be thought as the normalized extended Proj introduced by  Swanson-Huneke [HS06]:  B+ � T = ProjX(OX[J t, t−1])nor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (See Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=')  Note that the morphism B → X is affine and is locally described by a single chart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The spaces B+ and B usually have nicer singularities and simpler descriptions, and  the morphism B+ ⊂ B is way simpler than the original π : Y → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  As in  the standard Cox construction, the semiinvariant functions on B+ and B can be  interpreted as forms on Y and are convenient for the computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  For instance, the construction can be applied to normalized blow-ups of locally  monomial centers, leading to general classes of modifications of singularities of  subschemes and ideals that preserve regular ambient schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Given a locally toric or simply regular scheme X over a field and any locally  toric proper birational morphism π : Y → X, one associates with π a morphism of  Cox regular spaces B+ ⊂ B, where  B = Spec(OX[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk])  In particular, one represents the normalized blow-up of any locally monomial  J by a smooth cobordant blow-up B+ → X of J equipped with torus action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The formula generalizes the weighted cobordant blow-up introduced in [W�lo22]  with B+ = B ∖ V (J tα), for the corresponding multi-indexes α, α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , αk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It also  leads to a version of the multi-weighted blow-up of [AQ21, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6] when  considering the stack theoretic quotient [B+ � T ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  One can think of this approach as an extension of the resolution by cobordant  blow-ups with weighted centers to more general locally monomial ideals or Q-ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  When replacing the group Cl(Y/X) with a subgroup Γ ⊂ Cl(Y/X) ⊗ Q in the  formulas (2) and (3), one further generalizes the construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We obtain  BΓ := SpecX(π∗(  �  E∈Γ  OY (E)),  BΓ  + := SpecY (  �  E∈Γ  OY (E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This generalized construction can be linked to the weighted cobordant blow-ups  as in [W�lo22] (See Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In particular let π : Y → X be the weighted blow-  up of schemes with the Q-ideal center J = (u1/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , u1/wk  k  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This is simply the  normalized blow-up of the ideal J (a) := (ua/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ua/wk  k  ), with the exceptional  irreducible Q-Cartier divisor (1/a)Ea with OY (−Ea) = OX · J (a), where a is any  positive integer such that wi|a,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The cobordant blow-up of J (a) with respect to the  group Γ = Z· 1  aEa ⊂ Cl(Y/X)⊗Q gives the formula (1) for the cobordant weighted  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  5  blow-up of J = (u1/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , u1/wk  k  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Note that the above definition does not depend  upon the choice of a, and the Q-Cartier divisor (1/a)Ea can be interpreted as the  divisor corresponding to the Q-ideal OY · J = OY (−Ea)1/a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  More generally, let J be a locally monomial center, and π : Y → X be the  normalized blow-up of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Denote by E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Ek the exceptional divisors of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The  cobordant blow-up of J with respect to the subgroup  Γ = Z 1  b1  E1 ⊕ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' ⊕ Z 1  bk  Ek ⊂ Cl(Y/X) ⊗ Q,  generated by 1  b1 E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , 1  bk Ek, where b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , bk are any positive integers, leads to the  multiple weighted blow-up, considered by Abramovich-Quek in [AQ21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It can be  understood as the fantastack associated with the stack-theoretic quotient [B+ � T ]  (See Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Since the stabilizers of the action are not finite, in general, one  obtains an Artin stack as the stack-theoretic quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Note that in the resolution process of hypersurfaces, one often considers locally  the corresponding Newton polytope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It is naturally associated with a certain co-  ordinate system and rises to a locally monomial center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In a more general setting,  the Newton polytope is replaced with the dual valuation complex of the locally  monomial center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We show some conditions for singularities when the cobordant  blow-up of such a center immediately resolves singularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (see Theorems 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5,  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='11, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The particular resolution methods and the-  orems extend the relevant results for the weighted cobordant blow-ups in [W�lo22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  As a Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, we obtain Abramovich-Quek’s [AQ21, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The resolution algorithm outputs a smooth scheme with a torus action which  admits a good quotient having locally toric singularities and birational to the orig-  inal scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It can be directly resolved by the canonical combinatorial methods  in any characteristic as in [W�lo20, Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Alternatively, by Proposition  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, one can always replace in the resolution process each B+ with an open sta-  ble subset Bs admitting a geometric quotient, and then apply the destackification  method of Bergh-Rydh in [BR19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It is also possible to use the canonical reduction  of stabilizers due to Edidin- Rydh [ER21], and then the destackification method of  Bergh-Rydh in [BR19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Aknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The author would like to thank Dan Abramovich, J¨urgen  Hausen, Antonio Laface, Michael Temkin, Ilya Tyomkin, and Jaros�law Wi´sniewski  for helpful discussions and suggestions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Preliminaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The definition of Cox spaces of morphisms is similar, with  some important differences, to the notion of Cox spaces of varieties, as presented  in [ADHL15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Construction of Cox sheaves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Given a proper birational morphism π : Y →  X of normal integral schemes, consider the the free group Cl(Y/X) ⊂ Div(Y ) gen-  erated by the images of the exceptional irreducible divisors Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It can be identified  with the kernel of the surjective morphism π∗ : Cl(Y ) → Cl(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the relative Cox ring w mean the sheaf of graded OY -algebras  CY/X =  �  E∈Cl(Y/X)  CE =  �  E∈Cl(Y/X)  OY (E),  6  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  graded by Cl(Y/X), where CE := OY (E) for  OY (E)(U) = {f ∈ κ(Y ) | (divY (f) + E)|U ≥ 0} ⊂ κ(Y ) = κ(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Note the C0 = OY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' One can introduce the dummy variables t = (t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk)  so that Ei corresponds to t−1  i  and E �→ tE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This defines the isomorphism of the  gradings:  Cl(Y/X) ≃ {t−α | α ∈ Zk} ≃ Zk  Using this notation, we can write  CY/X =  �  E∈Cl(Y/X)  CEtE =  �  α∈Zk  Cα · ta1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tak  k ⊆  �  E∈Cl(Y/X)  κ(Y )tE  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' As mentioned, the Cox relative ring construction, similarly to the  absolute case, is analogous to the coordinate ring Z[x0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn] on projective space  X = Pn  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' One can choose a very ample divisor, for instance D = V (x0), and identify  the functions f = F(x0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn)/xn  0 ∈ OX(nD) with the forms F(x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn) so  that the vanishing locus V (F) equals to  V (F) = VX(F) = div(f) + nD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Per this analogy, and as in [ADHL15], the elements in CE will be called forms  of degree E on Y and can be written formally as F = ftE , where f ∈ OY (E),  with the natural componentwise operation of addition and multiplication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We also  define the divisor of the form F = ftE on Y as divY (F) = divY (f) + E, and its  vanishing locus on Y to be  VY (F) := supp(divY (f) + E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Exceptional valuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the exceptional valuations of π : Y → X we shall  mean the valuations ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νk of κ(X) = κ(Y ) associated with the generic points  of the exceptional divisors E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Ek of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  These valuations define ideals Iν,a,X ⊂ OX on X for a ∈ Z, generated by the  functions f ∈ OX, with ν(f) ≥ a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In particular Iν,a = OX if a ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let E = � niEi correspond to t−n1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · t−n1  k  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  (1) π∗(OY (Ei)) = OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) If all ni ≥ 0 then π∗(OY (E)) = OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) If there is ni < 0, then  π∗(OY (E)) =  �  ni<0  Iνi,−ni,X =  k�  i=1  Iνi,−ni,X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' First, since π : Y → X is proper, birational and X is normal, we have  π∗(OY ) = OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We can reduce the situation to the case when X is affine since the problem is  local on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  g ∈ OY (E)(π−1(X)) ⊂ κ(X) = κ(Y )  if and only if  divY (g) + E ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This implies that divU(g) ≥ 0, where U := Y ∖(� Ei), and U ⊂ X, where X ∖U is  of codimension ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus divX(g) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So, since X is normal, w get g ∈ π∗(OY ) =  OX, whence π∗(OY (E)) ⊆ OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  7  (1) and (2) If E = � niEi with ni ≥ 0 then  OX = π∗(OY ) ⊆ π∗(OY (E)) ⊆ OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) In general, g ∈ π∗(OY (E)) ⊆ OX iff divY (g) + E ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This translates into  divY (g) + �  ni<0 niEi ≥ 0 by part (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus νi(g) ≥ −ni for all ni < 0, which  yields  g ∈  �  ni<0  Iνi,−ni,X =  k�  i=1  Iνi,−ni,X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We use here the fact that by definition Iνi,−ni = OX if ni ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox coordinate space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' As a corollary from Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5, we obtain  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational morphism of normal  irreducible schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that Ek, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Ek are the irreducible exceptional divisors  of π, and νi are the associated valuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the direct image π∗(CY/X) of the  relative Cox ring is a Cl(Y/X) = Zk-graded OX-algebra:  AY/X := π∗(CY/X) =  �  ai∈Z  k�  i=1  Iνi,ai · ta1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tak  k ⊂ OX[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk, t−1  k ],  where Ei correspond to t−1  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox coordinate space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Given a proper birational morphism π : Y → X of normal  integral schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Cox relative coordinate space is the scheme  B = Cox(Y/X) := SpecX(AY/X),  over X with the natural action of TB = Spec Z[Cl(Y/X)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Cox relative char-  acteristic space is the space  B+ = Cox(Y/X)+ := SpecY (CY/X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  over Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Cox trivial space is given by  B− := B ∖ VB(t−1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · t−1  k ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Good and geometric quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We consider here a relatively affine action of  T = Spec(Z[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk, t−1  k ])  on a scheme X over Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the good quotient (or GIT-quotient) of X by T we mean  an affine T -invariant morphism  π : X → Y = X � T  such that the induced morphism of the sheaves OY → π∗(OX) defines the isomor-  phism onto the subsheaf of invariants OY ≃ π∗(OX)T ⊂ π∗(OX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then π : X → Y = X/T will be called the geometric quotient if additionally  every fiber Xy of π over s geometric point y : Spec(κ) → Y defines a single orbit of  the action of Tκ = T ×κ Spec(κ) = Spec(κ[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk, t−1  k ]) on Xy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  8  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : X → Y = X �T be a good quotient of integral schemes of a  relatively affine action of the torus T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then π is surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, the inverse  image π−1(Z) ⊂ Xof a closed connected subscheme Z ⊂ Y is connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The problem reduces to the affine situation π : X = Spec(A) → Spec AT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the coaction of T on A determines the gradation  A =  �  α∈Zn  Aαtα,  where B = A0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then for any prime ideal p ⊂ AT = A0, the extended ideal pA in A  is proper, and p = pA ∩ A0 is a contracted ideal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This implies that π is surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let I ⊂ A0 be an ideal such that the scheme Spec(A0/I) is connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Suppose  that for the ideal  IA =  �  α∈Zn  IAαtα  of A the space Spec(A/IA) is disconnected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then there is a nontrivial ring decom-  position A/IA = A′ ⊕ A′′, and (A/IA)0 = A′  0 ⊕ A′′  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Hence either the ring A′  0 = 0  or A′′  0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently, either A′ = 0 or A′′ = 0, and the decomposition is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The natural morphisms  πB : B → B � TB ≃ X,  πB+,Y : B+ → B+ � TB ≃ Y  are good quotients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Spec(OB�TB) = Spec(OTB  B ) = SpecX(AY/X)TB = SpecX(OX) = X  Spec(OB+�TB) = Spec(OTB  B+) = SpecY (CY/X)TB = SpecY (OY ) = Y  ♣  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Exceptional divisors on B = Cox(Y/X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : X → Y be a proper bi-  rational morphism of normal schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Using the natural birational morphism  iB : B+ → B, one can interpret the notion of the exceptional divisors of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Any exceptional divisor Ei on Y defines a canonical form  Fi = t−1  i  = tEi ∈ OY (E)t−1 ⊂ OB  on Y of degree Ei which vanishes on VY (F) = Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The form t−1  i  also defines a  regular homogenous function t−1  i  on B of degree Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Its divisor Di := divB(t−1  i )  on B determines the divisor Di+ := Di|B+ = divB+(t−1  i  ) on B+ which maps to Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The natural quotient morphism πB+,Y : B+ → Y , (respectively  πB : B → X) takes the exceptional divisors Di+ = VB+(t−1  i ) (respectively Di =  VB(t−1  i  )) surjectively onto Ei (respectively surjectively to the center of ZX(νi) =  VX(Iνi,1,X) of the valuation νi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover the induced morphism Di+ → Ei (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  D → ZX(νi)) is defined by the good quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Di+ = VB+(t−1  i  ) = SpecY CY/X/t−1  i CY/X =  = SpecY (  �  (OY (E)/OY (E − Ei))tE)  →  →  SpecY ((CY/X/(t−1  i CY/X)0 = Spec(OY /OY (−Ei)) = Ei  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  9  Thus the morphism Di+ → Y is defined by the good quotient and is surjective by  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The proof for the divisors Di is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The divisors Di = VB(t−1  i ), respectively Di+ = VB+(t−1  i  ) will  be called the exceptional divisors of B = Cox(Y/X) → X, respectively of B+ → Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The divisors Di = VB(t−1  i ) on B and Di+ = VB+(t−1  i ) on B+ are  irreducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6, the divisors Di are connected, so it suffices to show that  they are locally irreducible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We can assume that X is affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It suffices to show  that  t−1  i  = tEi ∈ O(B) = AY/X(X)  is a prime element.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The latter can be verified for the homogenous elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let νi  be the valuation on X associated with Ei ⊂ Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let  t−1  i  = tEi|(tE · f)(tE′ · g) = tE+E′fg  where f ∈ OX(E), and g ∈ OX(E′), and suppose t−1  i  does not divide both (tE · f),  and (tE′ · g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The first assumption implies that tE+E′−Eifg ∈ O(B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So fg ∈  π∗(OY (E + E′ − Ei)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Write the presentations E = � njEj and E′ = � n′  jEj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then, by the assump-  tion νi(f) = ni and νi(g) = n′  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus, by Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, and the assumptions  on f and g, we have  νi(fg) > ni + n′  i = νi(f) + νi(g),  which is a contradiction since νi is a valuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The same reasoning works for  Di+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Morphisms of Cox spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The following result is analogous to  [ADHL15][Construction 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1] for the Cox spaces of varieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X is a proper birational morphism of normal  schemes, and TB := Spec(Z[Cl(Y/X)]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let E be the exceptional divisor with the  components Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Denote by Uπ := Y ∖ E ⊂ Y the open subset of Y , which can  be identified with the open subset of X, where Y → X is an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let  πB : B → X, and πB+,Y : B+ → Y be the natural projections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  There is a natural TB-equivariant birational morphism  iB : B+ = Cox(Y/X)+ → B = Cox(Y/X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  over X, which is an isomorphism over Uπ, with  π−1  B (Uπ) = π−1  B+,Y (Uπ) = Uπ × TB,  and such that π−1  B (Di) = Di+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover, the morphism iB induces the morphism of the good quotients:  π : B+ � TB = Y  → B � TB = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For any open affine U ⊂ X, we have the natural identifications  Γ(U, π∗(CY/X)) = Γ(π−1  B (U), OB)  and  Γ(U, π∗(CY/X)) = Γ(π−1(U), CY/X) = Γ(π−1  B+,Y (π−1(U)), OB+)  10  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  Combining both equalities gives us:  Γ(π−1  B (U), OB) = Γ(π−1  B+,Y (π−1(U)), OB+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Since π−1  B (U) ⊂ Cox(Y/X) is affine we obtain a natural morphism  φU : π−1  B+,Y (π−1(U)) → π−1  B (U)  over U induced by the isomorphisms on global sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The constructed morphisms  are functorial for open embeddings U ⊂ V of affine subsets on X and glue to a global  morphism B+ → B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The morphism B+ → B is birational as it is an isomorphism over Uπ ⊂ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover iB is an isomorphism over Uπ:  π−1  B (Uπ) = π−1  B+,Y (Uπ) = SpecUπ(  �  E∈Cl(Y/X)  OUπtE) = Uπ × TB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By the construction,  π−1  B (Di) = π−1  B (VB(t−1  i )) = VB+(t−1  i ) = Di+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Locally for any open affine V ⊂ π−1(U) the induced homomorphisms  OB(π−1  B (U)) = Γ(U, π∗(CY/X)) = Γ(π−1(U), CY/X) → Γ(V, CY/X) = OB+(π−1  B+,Y (V ))  determine the homomorphisms  (OB(π−1  B (U)))T = Γ(U, π∗(CY/X)T ) → Γ(V, CT  Y/X) = OB+((π−1  B+,Y (V )))T ,  and define the global morphism B+ � TB = Y → B � TB = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the  morphism πB : B = Cox(Y/X) → X, (respectively πB+,Y : B+ = Cox(Y/X)+ →  X) will be called the full cobordization of π (respectively the cobordization of π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If I is an ideal on X, then by the full cobordant blow-up σ : B → X at I  (respectively cobordant blow-up σ+ : B+ → X at I we mean the full cobordization  (respectively cobordization) of the normalized blow-up blJ (X) → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Cox trivial space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational morphism of normal  schemes, and E = � Ei be its exceptional divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let Uπ = Y ∖ E ⊂ X be  the maximal open subset of X and of Y where π is an isomorphism exactly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  the Cox trivial space is B− = X × TB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover we have  i−1  B (B−) = B+ ×B B− = Uπ × TB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2 we have  B− := B ∖  k�  i=1  Di = B ∖ V (t−1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · t−1  k ) = Spec(OX[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk, t−1  k ]) = X × TB  B+ ×B B− := B+ ∖  k�  i=1  Di = B+ ∖ VB+(t−1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · t−1  k ) =  = Spec(  �  E∈Cl(Y/X)  OY (E)tE)[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk, t−1  k ]) = Spec(OUπ[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk, t−1  k ])  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  11  ♣  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Open immersion of Cox spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Generating forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X be an affine scheme and π : Y → X be a proper birational  morphism of normal integral schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Assume that YF is affine, for a certain  form F = ft−E on Y , with f ∈ H0(Y, OY (−E)) = H0(X, π∗(OY (−E)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  (B+)F = BF is affine and π−1  B+,Y (YF ) = (B+)F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover  CY/X(YF ) = (CY/X(Y ))F = (H0(B, OB))F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' If y ∈ YF then F = ft−E is invertible in the stalk (CY/X)y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Indeed  div(ft−E) = 0 at y so E = div(f) is principal at y, and thus (ft−E)−1 = f −1tE  is the inverse of ft−E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This shows that the form F is invertible in CY/X(YF ),  and the function F is invertible on the scheme π−1  B+,Y (YF ) ⊂ B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus we have  an open immersion π−1  B+,Y (YF ) ֒→ B+F .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Since F is invertible on π−1  B+,Y (YF )  the natural homorphism CY/X(Y ) → CY/X(YF ) factors through the localization  (CY/X(Y ))F → CY/X(YF ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  On the other hand if  G = gt−E′ ∈ CY/X(YF )  is a form on YF then, by definition,  divY (G · F n) = divY (G) + n · divY (F) ≥ 0  on Y for sufficiently large n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Hence G·F n ∈ CY/X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This shows that (CY/X(Y ))F →  CY/X(YF ) is surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' But this morphism is defined by the restrictions of forms,  so functions on open subsets of B+, and thus it is also injective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Hence it is an  isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This defines an isomorphism of the global sections  (CY/X(Y ))F = H0(B+, OB+)F = H0((B+)F , OB+)  → H0(π−1  B+,Y (YF ), OB+) = CY/X(YF )  If YF is affine then we obtain then π−1  B+,Y (YF ) is also affine, and the open im-  mersion π−1  B+,Y (YF ) ֒→ (B+)F has the left inverse (B+)F → π−1  B+,Y (YF ) determined  by the global sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Since the schemes are separated, it is an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Finally we observe that H0(X, π∗(OY (E)) = H0(Y, OY (E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Hence  H0(Y, CY/X) = H0(X, π∗(CY/X)) = H0(X, AY/X) = H0(B, OB),  and  H0(BF , OB) = AY/X(X))F = CY/X(Y ))F = CY/X(YF ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Irrelevant ideal and open immersion of Cox spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The notion of irrelevant  ideals was used in [ADHL15] in the context of Cox rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Here we consider the  analogous definition and results for morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  12  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational morphism of normal  schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that X can be covered by open subsets Xi such Yi := π−1(Xi)  admits an open affine cover (Yi)Fj, where Fij = fijt−Eij is a form on Yi for  fij ∈ OYi(−Eij).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then there is a natural open TB-equivariant embedding  B+ = Cox(Y/X)+ ֒→ B = Cox(Y/X),  It induces the morphism of the good quotients:  B+ � TB = Y  → B � TB = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover B ∖ B+ is of codimension ≥ 2 in B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The problem is local on X, so we can replace X with Xi, and drop the  subscripts i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, the open affine cover YFj of Y where Fj ∈ Iirr  defines the open affine cover B+Fi = SpecY ((CY/X)Fi) = π−1  B+,Y (Yi) of B+ mapping  it isomorphically onto open subsets BFi = SpecX((AY/X)Fi) ⊂ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This induces  the open immersion  B+ ֒→ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  For “moreover part” let Uπ = Y ∖ E ⊂ Y be the maximal open subset, where  π : Y → X is an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then Uπ can be identified with an open subset of  X, and the complement X ∖ Uπ of the open set is of codimension ≥ 2, and  B+ ∖ D = Uπ × TB ⊂ B− = B ∖ D = X × TB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  if of codimension ≥ 2 in B− = B ∖ D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  On the other hand, by Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='11, the divisors Di = VB(t−1  i  ) are irreducible  on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently the difference Di ∖ B+ = Di ∖ Di+ is of codimension ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus  B ∖ B+ = (B− ∖ B+) ∪ (D ∖ D+)  is of codimension ≥ 2 in B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  The notion of irrelevant ideal on Cox coordinate spces was originally introduced  in [ADHL15] (Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2 and Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3(iii))  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the the irrelevant ideal Iirr ⊂ AY/X we mean the ideal  radically generated by the forms F in AY/X, such that YF is open affine over X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Under the conditions from Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, Iirr is the radical  coherent ideal determined by the reduced closed subscheme B ∖ B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus we can  write B+ = B ∖ V (Iirr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The problem is local on X, and we can assume that X is affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It follows  from the construction that B+ = B ∖ V (I), where I is generated by all F ∈ AY/X,  such that YF is affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus rad(I) = Iirr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox construction for regular schemes X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Recall a well-known fact:  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Y be a normal scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the complement of any open  affine subset V ⊂ Y is the support of a Weil divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus there is a finite open cover of Y by open affine subsets Vi = Y ∖ Di, where  Di are Weil divisors on Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  13  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By definition, V is the set of points of Y where all the functions f ∈  Γ(V, OY ) ⊂ κ(Y ) are regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Since Y is normal, this means that the supports  of the divisors div−(f) of the negative components of div(f) cover Y ∖ V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Conse-  quently, Y ∖ V is the union of the Weil divisors contained in it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus this union is  finite, and Y ∖ V is the support of the Weil divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This defines an open cover Vi = Y ∖ Di which can be assumed to be finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational morphism of normal schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let p ∈ X be a regular point on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' There is an open affine neighborhood U of p  in X, and an open cover of YU = π−1(U) by open affine subsets YF = YU ∖ VY (F),  where F is a form over U ⊂ X and on YU ⊂ Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We can assume that X is affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the previous lemma, we can find an  open affine cover  Vj := Y ∖ (Dj ∪ Ej)  of Y defined by the divisors Dj ∪ Ej, where Ej are some possibly reducible ex-  ceptional divisors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Taking the images of Dj in X, we obtain a finite collection of  divisors D′  j = π(Dj) on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider an open affine neighborhood  U := Xg = X ∖ V (g)  of p ∈ X, for g ∈ H0(X, OX), such that all the divisors D′  j are principal on U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus we can write D′  j = divU(fj), where fj ∈ O(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The pullbacks of the principal divisor D′  j = divU(fj) on U are of the form  π∗(D′  j) = Dj +Ej on YU = π−1(U), where Ej = � nijEi is an exceptional divisor,  with nij ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' They define the forms  Fj := fjt−Ej+Ej  on YU such that  divY (Fj) = divY (fj) − Ej + Ej = Dj + Ej.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  and thus VY (Fj) = Dj ∪ Ej on YU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  YU ∖ V (Fj) = YU ∖ (Dj ∪ Ej) = (Vj)g = Vj ∖ VY (g)  is an open affine cover of YU = π−1(U) = π−1(Xg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The lemma is valid under the assumption that p ∈ X is a Q-  factorial point, so any Weil divisor at p is Q-Cartier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  As a corollary from the above, we obtain the following:  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that X is regular, and π : Y → X is a proper  birational morphism of normal schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' There is a natural open TB-equivariant  embedding  B+ = B ∖ V (Iirr) ֒→ B  It induces the morphism of the good quotients:  B+ � TB = Y  → B � TB = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordant blow-ups of ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  14  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The strict and the weak transform under cobordant morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let I be any ideal on a normal scheme X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a  proper birational morphism from a normal scheme Y , and σ = πB : B → X be the  full cobordization of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then by the strict transform of the ideal I we mean the  ideal  σs(I) := (f ∈ OB | t−αf ∈ OB · I, for some α ∈ Zk  ≥0) ⊂ OB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The weak transform of the ideal I is given by  σ◦(I) := tα0I,  where  α0 := max{α | I ⊂ t−αOX},  is defined for the partial componentwise order on the set of components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordant blow-ups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let J be an ideal on a normal scheme X, such that codim(V (J ) ≥  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let π : Y → X be the normalized blow-up of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let E = � aiEi be the  exceptional divisor of π, such that OY (−E) = OY · J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Set α = (a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ak).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Denote by σ : B → X be the corresponding full cobordant blow-up of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  (1) σ−1(X ∖ V (J )) = (X ∖ V (J )) × TB is trivial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) B+ = B ∖ VB(σ◦(J )) = B ∖ VB(tαJ ), where  σ◦(J ) = OB · t−EJ = OB · tαJ  is the weak transform of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) J · OB+ = t−αOB+ is a locally principal monomial ideal on B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let U ⊂ X be an open affine subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The ideal of sections J (U) is gener-  ated by some f1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , fk ∈ J (U) ⊂ OX(U) = OY (π−1(U)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The pullbacks of the  functions f1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , fk ∈ J (U) generate the ideal  IE = OY (−E) = OY · J  on YU := π−1(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover on each YU ∖ VY (Fi), where Fi := fit−E we have  exactly divYU (fi) = E|YU .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  On the other hand consider the open cover of  YU = π−1(U) = Proj  ∞  �  i=0  J i(U)ti,  where t is a dummy unknown by the open subsets  (YU)fit = π−1(U)fit = (Proj  ∞  �  i=0  J i(U)ti)fit = (Spec(  ∞  �  i=0  J i(U))fit)0,  where fit ∈ J 1(U)t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Since fjt is invertible on (YU)fjt and fit/fjt = fi/fj are  regular we wee that O(YU )fj t · J is generated by fj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So E = divY (fj) on (YU)fit,  and consequently the form Fj = fjt−E is invertible on (YU)fjt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Computing div(fit) on the cover (YU)fjt of YU gives us  div(fit) = div(fit/fjt) = div(fi/fj) = div(fi) − E = div(Fi) = div(fit−E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently we conclude that (YU)fit = (YU)Fi is affine and cover YU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus, by  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, there is an open immersion B+ ⊂ B, where B+ is covered by  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  15  B+Fi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, by the above, the ideal J tα on B+Fi is generated by fit−E, and  thus equal to  J tα  |B+Fi = OB+Fi · OYFi (−E)t−E = OB+Fi · fit−E = OB+Fi · Fi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  But Fi = fit−E is invertible on B+Fi of degree −E, whence  OB+Fi · J = OB+Fi · J tα · t−α = OB+Fit−α,  which implies that  OB+ · J = OB+t−α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (4)  On the other hand J tα ⊂ OB, since any element ftα ∈ J (U)tα is in  Oπ−1(U)(−E)tα which is the −E gradation of OB over U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This also shows that  J tα = σ◦(J ), as by equality (4) for B+, the form t−α = tE is the maximal factor  which divides OB · J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Finally, by the above  V (σ◦(J )) = V (f1t−E, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , fkt−E) = V (F1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Fk) = B ∖ B+ = V (Iirr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Remark 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It follows from the above that the inverse image OB+ ·J of ideal J  under the cobordant blow-up is the ideal of the exceptional divisor tE, analogously  to the standard blow-up of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' However, this is no longer true for the full cobordant  blow-up J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordant flips.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let φ1 : X1 → Z, and φ2 : X2 → Z be proper birational morphisms  from normal schemes X1, X2 to Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that the induced proper birational map  X1 ��� X2 over Z is an isomorphism in codimension one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  B := B(X1/Z) = B(X2/Z),  is equipped with the action of torus TB = Cl(X1/Z) = Cl(X2/Z), and there is  a natural birational map B(X1/Z)+ ��� B(X2/Z)+ over B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover if φ1, φ2  satisfy the condition of Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, then B(X1/Z)+ and B(X2/Z)+ are open  subschemes of B which coincide in codimension 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Functoriality of Cox spaces for open immersions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The construction of  the full cobordization is functorial for open immersions up to torus factors:  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational morphism of normal integral  schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let U ⊂ Y be an open subset, and YU := π−1(U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Ek be the  irreducible exceptional divisors of π : Y → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let πB : B = Cox(Y/X) → X be the  full cobordization of a proper birational morphism π : Y → X, and πB+ : B+ → X  is its cobordization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let  TB∖BU := Spec( Z[ti, t−1  i  | Ei ⊂ Y ∖ YU ] ),  Then  BU := π−1  B (U) = B(YU/U) × TB∖BU ,  BU+ := π−1  B+(U) = B(YU/U)+ × TB∖BU .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  16  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For any open subset U ⊂ X, and YU = π−1(U), we can construct a subgroup  Cl(YU/U) ⊆ Cl(Y/X), with the canonical splitting Cl(Y/X) → Cl(YU/U).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Write  Cl(Y/X) = Cl(YU/U)⊕Cl0(YU/U), where Cl0(YU/U) is generated by Ei ⊂ Y ∖YU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  π−1  B (U) = SpecU(  �  E∈Cl(Y/X)  π∗(OY (E)|U)tE =  SpecU(  �  E∈Cl(YU/U)  π∗(OY (E))|UtE) ⊗OU (  �  E∈Cl0(YU /U)  π∗(OY (E))|UtE)  SpecU(  �  E∈Cl(YU/U)  π∗(OY (E))|UtE) ⊗OU (  �  E∈Cl0(YU /U)  OUtE) = B(YU/U) × TB∖BU  Similarly  π−1  B+(U) = SpecYU (  �  E∈Cl(Y/X)  OYU (E)tE) =  SpecYU (  �  E∈Cl(YU /U)  OYU (E)tE) ⊗OYU (  �  E∈Cl0(YU /U)  OYU (E)tE)  SpecYU (  �  E∈Cl(YU /U)  OYU (E)tE) ⊗OYU (  �  E∈Cl0(YU /U)  OYU tE)  = B(YU/U)+ ×YU (YU × TB∖BU ) = B(YU/U)+ × TB∖BU  ♣  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Relative Cox construction for toric morphisms  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Toric varieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Recall some basic properties of toric varieties over a field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (See [KKMSD73], [Oda88], [Dan78], [Ful98]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Fans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let κ be a field, and let  T = Spec(κ[x1, x−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk, x−1  k ] = Spec(κ[M])  be the torus, where M = Hom(T, Gm) ≃ Zk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The elements of M can be described  by the Laurent monomials xα ∈ M, where α ∈ Zk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Denote by N := Hom(Gm, T ) the group of algebraic homomorphisms t → tβ =  (tb1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tbk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This determines a nondegenerate pairing (·, ·) N × M → Z defined by the com-  position:  Hom(Gm, T ) × Hom(T, Gm) → Hom(Gm, Gm)  , xα ◦ tβ = t(β,α).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus N = M ∗ ≃ Hom(M, Z) is dual to M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By a fan ∆ in NQ, we mean a collection of strictly convex cones, which is closed  under the face relation, and such that two cones intersect along the common face.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If τ is a face of σ, written as τ ≤ σ then Xτ ⊂ Xσ is an open immersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Toric varieties from fans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' With any rational strictly convex cone σ in NQ =  N ⊗ Q we associate its dual  σ∨ := {y ∈ MQ | (x, y) ≥ 0  for all  x ∈ σ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The cone σ∨ determnies the monoid Pσ := σ∨ ∩ M, and the relevant affine toric  variety Xσ = Spec(κ[Pσ]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  17  We say that a cone σ in NQ is regular or nonsingular if it is generated by a part  of a basis of the lattice e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek ∈ N, written  σ = ⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek⟩ := Q≥0e1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' + Q≥0ek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Similarly a cone σ = ⟨v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vk⟩ in NQ is simplicial it if it generated by a linearly  independent set {v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vk} ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  With a fan Σ we associate the toric variety XΣ obtained by glueing Xσ, where  σ ∈ Σ, along Xτ, where τ ≤ σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The torus T = Spec(κ(M)) acts on toric variety  XΣ with an open dense orbit T = Spec(κ(M)) corresponding to {0} ∈ Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The fan Σ will be called regular (respectively simplicial) if all its cones are regular  (respectively simplicial).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The regular (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' simplicial) fans Σ are in the bijective correspondence with  the smooth (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Q-factorial) toric varieties XΣ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  For any r ∈ Z≥0 by Σ(r) denote the set of cones σ of dimension r in Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The  cones in Σ(r) correspond to the orbits Oσ and thus to the irreducible T -stable  closed subvarieties Oσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In particular, the irreducible T -stable divisors correspond  to the one-dimensional faces in Σ(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Toric valuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Any integral vector v ∈ N determines a monomial valuation  val(v), which can be defined for f = � cm · m ∈ κ[M], as  val(v)(f) = val(v)(  �  cm · m) = min  cm̸=0(v, m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The center Zval(v) of the valuation val(v) is the union of orbits Oτ, which corre-  spond to the cones τ in  Star(τ, Σ) = {τ | σ ≤ τ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The associated ideals on XΣ are given locally on Xσ as  Ival(v),a,Xσ = (m ∈ Pσ | (v, m) ≥ a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By a vertex of Σ, we mean the primitive vector, so the integral vector with  relatively coprime coordinates, which lies in a one-dimensional face of Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The set  of vertices of Σ will be denoted by Vert(Σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Each vector v ∈ Vert(Σ) defines the  one-dimensional face ⟨v⟩, and the valuation val(v), which is precisely the valuation  of the associated T -stable irreducible divisor D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Decomposition of fans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the support of a fan Σ we mean the union of its  cones |Σ| = �  σ∈Σ σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The decomposition of the fan Σ is a fan Σ′ such that any cone σ′ ∈ Σ′ is contained  in σ ∈ Σ, and |Σ′| = |Σ|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  For any subset Σ0 of the fan Σ, denote by Σ0 the set of all faces of the cones in  Σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The typical examples of the decompositions are given by the star subdivisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Σ be a fan and v be a primitive vector in the relative interior  of τ ∈ Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the star subdivision v · Σ of Σ at v is defined to be  v · Σ = (Σ ∖ Star(τ, Σ)) ∪ {⟨v⟩ + σ | σ ∈ Star(τ, Σ) ∖ Star(τ, Σ)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The vector v will be called the center of the star subdivision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The decompositions ∆ of a fan Σ are in bijective correspondence  with the proper birational T -equivariant morphisms X∆ → XΣ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The star subdivision v · Σ corresponds to the blow-up of the valuation, which is  the normalized blow-up of Ival(v),a,XΣ for a sufficiently divisible a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  18  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Maps of fans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By a map of fans (Σ′, N′) → (Σ, N) we mean a linear map  φ : N′ ⊗ Q → N ⊗ Q of vector spaces, such that  (1) φ(N′) ⊂ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) For any σ′ ∈ Σ′ there is is σ ∈ Σ such that φ(σ′) ⊂ σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The map of fans corresponds to a TN′-equivariant morphism of toric varieties  (XΣ′, TN′) → (XΣ, TN), where the action of TN′ = Spec κ[M′] on XΣ is defined by  the homomorphism of tori  TN′ = Spec κ[M′] → TN = Spec κ[M],  induced by N′ → N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The decomposition Σ′ of a fan Σ corresponds to the proper  birational morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Good quotients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let φ : (σ′, N′) → (σ, N) be a surjective map of cones, such  that φ(σ′) = σ, and φ(N′) = N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let N′′ := ker(N′ → N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the exact sequence  0 → N′′ → N′ → N → 0,  has its dual  0 → M → M′ → M′′ → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus M can be identified with the sublattice of M ′′ defined as  M = {m ∈ M ′′ | (n, m) = 0  for  all n ∈ N′′}  Consequently, κ[M] = κ[M′′]TN′′ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover the dual map determine the inclusion  σ∨ ֒→ (σ′)∨ for which (σ′)∨ ∩ MQ = σ∨, and  (Pσ′)TN′′ = Pσ′ ∩ M = Pσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Hence  O(Xσ′)TN′′ = κ[Pσ′]TN′′ = κ[Pσ] = O(Xσ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus  Xσ′ → Xσ ≃ Xσ′ � TN′′  is a good quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If additionally φ : σ′ → σ is injective, so it is an isomorphism of cones, then the  inverse image of any orbit is a single orbit, and thus the corresponding morphism  Xσ′ → Xσ ≃ Xσ′/TN′′ is a geometric quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If the map of fans φ : (Σ′, N′) → (Σ, N) is surjective, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' φ(|Σ′|) = |Σ| and  φ(N′) = N, and for any cone δ ∈ Σ, the inverse image φ−1(δ)∩|Σ′| is a unique cone  δ′ ∈ Σ′, then the corresponding morphism XΣ′ → XΣ is affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently, by  the previous argument, it is a good quotient with respect to TN ′′ = ker(TN′ → TN),  where N′′ = ker(N′ → N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If additionally, the map |Σ′| → |Σ| is bijective then XΣ′ → XΣ is a geometric  quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox construction for toric varieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We recall here the standard Cox  construction for toric varieties from the convex geometry point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This pre-  sentation relies greatly on [Cox95], [ADHL15], and will be then adapted to the  relative situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  19  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Given a toric variety X with associated fan Σ in the space  NQ ≃ Qn containing the standard lattice N ≃ Zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We shall assume that the fan Σ  is nondegenerate that is the set Vert(Σ) generate the vector space NQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let Vert(Σ) = {v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vk} denote the set of vertices of Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek denote  the standard basis of Zk ⊂ Qk, and let  σB := ⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek⟩ = {  k  �  i=1  aivi | ai ∈ Q≥0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The cone σB defines a regular fan ΣB in NQ  B = Qk, consisting of all the faces of σB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  It corresponds to the affine space  XσB = Spec(κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk]) = Ak  κ  Consider the linear map πB : NQ  B = Qk → NQ = Qn defined on the basis e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek,  such that πB(ei) = vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We construct the subfan ΣB+ of σB to be the set of all  the faces σ of σB such that πB(σ) is contained in a face of Σ ([ADHL15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This  determines a morphism πB : ΣB+ → Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Note that it follows from the definition  that for any face δ = ⟨vi1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' vik⟩ of Σ, there is a unique face  δ0 = π−1  B (δ) = ⟨ei1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' eik⟩ ∈ Cox(Σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox coordinate ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Div(X) be the group of Weil divisors on X = XΣ,  and Div(X)+ be the monoid of the effective Weil divisors and zero on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let  Vert(Σ) = {v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vk} denote the set of vertices of Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The corresponding Weil  divisors D1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Dk ∈ Div(X) freely generate Div(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' [Cox95] The Cox coordinate ring is defined to be  C(X) := κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk] = κ[Div(X)+] =  �  D∈Div(X)+  κxD,  with the natural identification xi = xDi, and xD = xα and the induced multiplica-  tion xD1 · xD2 = xD1+D2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Denote by Prin(X) the subgroup of Div(X) of the principal divisors on X, which  is generated by div(m), where m ∈ M, giving an isomorphism  M ≃ Prin(X),  m �→  �  (vi, m)Di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We use here the assumption that Σ is nondegenerate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let Cl(X) = Div(X)/Prin(X) be the Weil divisor class group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Although the Cox  coordinate ring, as defined, comes with the natural Div(X)-gradation, one can also  consider its Cl(X) = Div(X)/Prin(X)-gradation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then for any class [E] ∈ Cl(X)  of the divisor E ∈ Div(X) the space of effective Weil divisors in [E] on X is T -  stable and thus generated by all T - invariant effective divisors  E + div(m) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus one can describe the [E]- gradation to be  C(X)[E] =  �  D∈[E]  κ · xD =  �  m∈M,div(m)+E≥0  κxE · xdiv(m) ≃ H0(X, OX(E)) · xE,  20  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  Thus choosing any set E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Ek of Div(X) which determines a basis of the lattice  Cl(X), one identifies Cl(X), with the subgroup of Div(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Under this noncanonical  identification we can write as in [Cox95] and [ADHL15]:  C(X) =  �  E∈Cl(X)  H0(X, OX(E)) · xE  On the other hand the canonical Cl(X)-gradation on C(X) determines the nat-  ural action of the torus  TX := Spec(κ[Cl(X)]) ≃ Spec(κ[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tr, t−1  r ],  where Cl(X) ≃ Zr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox coordinate space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Cox coordinate ring defines the Cox coordinate  space (as in [Cox95] and [ADHL15]) to be  B = Cox(X) := Spec(C(X)) = Spec(  �  E∈Cl(X)  H0(X, OX(E)) · xE) ≃ Ak,  It is the toric variety associated with the fan ΣB of all the faces of σB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Good and geometric quotients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let  B+ = Cox(X)+ := XΣB+ ⊂ B  be the open toric subscheme of B associated with ΣB+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The subscheme B+ is called  the Cox characteristic space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The morphism B+ → X corresponding to ΣB+ → Σ  is toric and affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It defines the homomorphism of the relevant tori  φ : TB := Spec(κ[Div(X)]) → T := Spec(κ[M]),  corresponding to the inclusion M ֒→ Div(X) and defining the exact sequence  0 → M → Div(X) → Cl(X) → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently, the kernel of φ can be identified canonically with TX := Spec(κ[Cl(X)]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Since TX acts trivially on T ⊂ X, the morphism B+ → X is TX-invariant and  affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover for any δ ∈ Σ, and δ0 = π−1(δ), we have that π(δ0) = δ, and  Xδ0 � TX = Xδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus, the affine TX-invariant morphism B+ → X is a good  quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the form F on X we mean a Cl(X)-homogenous function of  gradation [E] in  H0(X, OX(E))xE = H0(B, OB)[E] = C(X)[E] = (OB)[E].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Each such TB-semiinvariant form can be described as  F = xD = xα = xm · xE,  where D ∈ Div(X), D = E + div(xm), and xm ∈ H0(X, OX(E)), for E being a  linear combination of Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  With any form F = fxE ∈ H0(X, OX(E))xE we can associate its divisor  divX(F) = E + div(f), and its vanishing locus V (F) = supp(div(F)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This ex-  tends to a homomorphism  Div(X) → Div(X),  D → div(xD),  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  21  which is identical on generators Ei of Cl(X) ⊂ Div(X), and thus on their linear  combinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' On the other hand, any class [D] ∈ Cl(X) can be written as the  difference  [D] = [E′] ∖ [E′′]  of effective linear combinations E′ and E′′ of the generators Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then E′ + div(xm) = D + E′′ is effective, for a certain m ∈ M, and we have the  equality for the form F := xmxE′:  div(F) = div(xmxE′) = div(xD) + div(E′′),  whence  D + E′′ = E′ + div(xm) = div(xD) + E′′  and thus  divX(xD) = D,  for any D ∈ Div(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently V (xD) = supp(D) for any form xD, where  D ∈ Div(X)+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In particular, the vanishing locus div(xi) = div(xDi) = Di corresponds to the  vertex vi ∈ Vert(Σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox characteristic space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The subscheme B+ can be described using the TB-  semiinvariant forms on X as in [ADHL15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the construction, B+ can be covered  by the open affine subsets Bδ := π−1(Xδ), where δ ∈ ΣB+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For each δ ∈ ΣB+ con-  sider the form ˇxδ := �  vi̸∈δ xi on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Its vanishing locus is equal to the complement  X ∖ Xδ =  �  vi̸∈δ  Di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  So we can write Xδ = X ∖ VX(ˇxδ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Similarly Bδ = B ∖ VB(ˇxδ) = Bˇxδ, where ˇxδ is  considered as a function on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently  B+ = B ∖ V (Iirr),  where  Iirr := (ˇxδ | δ ∈ Σ) ⊂ O(B) = C(X)  is the irrelevant ideal (see [Cox95],[ADHL15]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover the morphism Bδ → Xδ, can be described as  Bδ = Bˇxδ = Spec(κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk]ˇxδ) → Xδ = Xˇxδ = X ∖ VX(ˇxδ)  Note however then that the condition f ∈ H0(Xˇxδ, OX(E)) is equivalent to  div(f) + E + div(ˇxn  δ ) ≥ 0  for n ≫ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The latter condition can be written as  fxE · ˇxn  δ ∈ H0(X, OX(E + n[div(ˇxδ)]) · xE+n[div(ˇxδ)]  Consequently  κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk]ˇxδ = (  �  E∈Cl(X)  H0(X, OX(E)) · xE)ˇxδ =  �  E∈Cl(X)  H0(Xδ, OX(E)) · xE  The latter leads to the formula for the Cox characteristic space to be  B+ = Cox(X) = SpecX(  �  E∈Cl(X)  OX(E) · xE)  as in [ADHL15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  22  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox relative spaces over affine toric schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In this section, we shall  study the general relative Cox construction developed in Chapter 1 in the context  of birational toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' To a great extent, it is analogous to the original Cox  construction for toric varieties (as in [Cox95]) presented in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  On the other hand, one can link it to the original construction of Satriano, who  developed a similar notion in the context of the toric Artin stacks in [Sat13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The following result shows the relation between the toric Cox construction for  toric varieties and the general Cox construction for proper morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let σ be a regular cone, and ∆ be its subdivision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : X∆ → Xσ  be the induced proper birational morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the toric Cox coordinate space  Cox(X∆) and the toric Cox characteristic space Cox(X∆)+ for toric variety X∆  coincide with the relative Cox coordinate space B = Cox(X∆/Xσ) and relative  Cox characteristic space B+ = Cox(X∆/Xσ)+ for the proper birational morphism  X∆ → Xσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The construction of the spaces is formally identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The reason is that  the gradation in both cases is the group Cl(X∆) = Cl(X∆/Xσ), which is freely  generated by the exceptional toric divisors Ei with no relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' System of local parameters on affine toric schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Pσ = σ∨ ∩ M be  the monoid associated with the affine toric variety Xσ = Spec(κ[Pσ]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Denote by  P ∗  σ ≃ Zr the subgroup of the invertible elements in Pσ, and let P σ := Pσ/P ∗  σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The  natural homomorphism of monoids Pσ → P σ = Pσ/P ∗  σ splits, and one can write  noncanonically  Pσ = P σ × P ∗  σ,  Let u1 = m1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , us = ms ∈ Pσ be the minimal set of generators of the monoid  P σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This set is determined uniquely and consists of the elements m ∈ P σ, which  cannot be written as m = m′ · m′′ for the nontrivial elements m′, m′′ ∈ P σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The set of generators of u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , us ∈ P σ ⊂ Pσ will be called a  system of local toric parameters on Xσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox relative spaces over affine toric schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let σ0 be any cone in NQ, and ∆ be its subdivision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider the  induced toric morphism π : X∆ → Xσ0 = Spec(κ[Pσ0]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Ek be the  toric exceptional divisors of π corresponding to the vertices v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vk ∈ Vert(∆) ∖  Vert(σ0), and the exceptional valuations νi = val(vi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let B and B+ denote the full cobordization and, respectively, the cobordization  of the morphism X∆ → Xσ0  Then  (1) B = Spec OXσ[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ustαk], where and u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk ∈ Pσ  is a system of local toric parameters and αi = (ai1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , aik), with aij :=  νj(ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) B is a toric variety B ≃ Xσ0 × Ak, and the corresponding cone is  σB = σ0 × ⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) The natural morphism  B = Spec OXσ0 [t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk] → Xσ0  is given by the projection πΣ : σB → σ0, mapping ei �→ vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  23  (4) B+ ⊂ XσB can be described as the set ΣB+ of the faces σ of σB such that  πΣ(σ) ⊆ δ, where δ ∈ ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In particular, B+ ⊂ B is an open inclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' First we will show that X∆ can be covered by the open affine subsets (X∆)F ,  where F is a form on X∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The problem translates into a toric situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For any  cone δ ∈ ∆ let ω be a maximal common face of δ and σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider a character  χδ ∈ σ∨  0 which is zero on ω and strictly positive on σ0 ∖ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The character χδ defines  a regular function on Xσ0, for which  ni := χδ(vi) = νi(χδ) > 0,  for any vertex  vi ∈ Vert(δ) ∖ Vert(ω) = Vert(δ) ∖ Vert(σ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In particular div(χδ) − Eδ ≥ 0, where Eδ := �  Ei∩Xδ̸=∅ niEi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then, for the form  Fδ := χδx−Eδ, its support  supp(div(Fδ)) = supp(div(χδ)) − Eδ)  on X∆ is the union of all the toric divisors which are in X∆ ∖ Xδ and which  correspond to the vertices in Vert(∆) ∖ Vert(δ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently supp(div(Fδ)) =  X∆ ∖ Xδ, and XFδ = Xδ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This implies, by Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, that the natural  morphism  B+ =  �  δ∈∆  Bδ ֒→ B  is an open immersion, where Bδ := BFδ is open affine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (1) For any i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , k let ti be the coordinate corresponding to −Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Set  ˇti := (t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ˇti, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk)  ˇt−1  i  := (t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ˇt−1  i , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k )  By Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5 one can write:  AY/X =  �  ai∈Z  k�  i=1  Iνi,ai · ta1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tak  k =  k�  i=1  �  ai∈Z  Iνi,ai · tai  i [ˇti,ˇt−1  i ],  Let u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk ∈ P σ = Pσ/P ∗  σ ⊂ Pσ be the generators of P σ, and let νi(uj) = aij ∈  Z≥0 for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , k, and j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  Iνi,a = (ub1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · ubn  n ) |  k  �  j=1  bjaij ≥ a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Comparing gradations we easily see that for each i,  �  ai∈Z  Iνi,atai  i  = OX[t−1  i , ujtaij  i  ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  So  AY/X =  k�  i=1  OX[t−1  i  , ujtaij  i  ][ˇti,ˇt−1  i ] = OX[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk],  where αi = (ai1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , aik).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  24  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  (2)  B = Spec OXσ[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk] =  = Spec(κ[u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk, v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vr][t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk] =  = Spec(κ[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk, v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vr] ≃  ≃ Spec(κ[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk, v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vr]) ≃ Xσ0 × Ak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) The toric map  B = Spec(κ[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk, v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vr] →  Xσ0 = Spec(κ[u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , us, v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vr]),  corresponds to the map of cones  πB : σB ≃ σ0 × ⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek⟩ → σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Under this correspondence  val(ei)(t−1  j ) = δij,  val(ei)(ujtαj) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  On the other hand val(v)(t−1  i  ) = 0 for any integral vector v ∈ σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By the above we can write  B = Spec(κ[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k ] × Spec(κ[u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk, v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vr])  The toric valuation µi on B associated to the divisor Di = VB(t−1  i ) satisfies  µi(ujtαj) = 0, and µi(t−1  i′ ) = 0 for i ̸= i′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It corresponds to the vector ei, as val(ei)  fulfills precisely the same relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The quotient morphism πB : B → Xσ0 takes a toric valuation val(v) on B, for  any integral v ∈ σB to the restriction to O(Xσ0) corresponding to val(πΣ(v)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It  maps the vertices of the face σ0 ⊂ σB to the very same vertices of σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The image  of the vector ei is the vertex πΣ(ei) = vi ∈ Vert(∆) ∖ Vert(σ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This follows from  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9 or can be seen by direct computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the previous considerations,  vi corresponds to νi on X∆, and ei to the valuation µi of t−1  i  on B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The restriction  of the toric valuation µi to κ[u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk], gives  µi(uj) = µi(ujtαj · t−αj) = µi(tαj) = aij = νi(uj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (4) By the considerations at the beginning of the proof, and Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, we  can write B+ as the union of open affine subsets Bδ = BFδ = π−1  B+(Xδ):  B+ =  �  δ∈∆  Bδ ⊂ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The induced map of fans ΣB+ → ∆ corresponds to the good quotient B+ → B+�T ,  and is defined by the linear map:  πΣ : NQ  B = NQ  B+ → NQ = NQ  Y = NQ  Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus any cone δ ∈ ∆ can be written as the image δ = πΣ(δ′), where δ′ ∈ ΣB+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In particular any vertex vi ∈ Vert(∆) ∖ Vert(σ0) is the image vi = π(ei) of ei ∈  Vert(ΣB) = Vert(ΣB+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently, the fan ΣB+ is determined by the faces τ of  ΣB such that πΣ(τ) ∈ ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox relative spaces for toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' General case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  25  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Coborization of proper toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let ∆ be a subdivision of a fan Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We can further generalize the characterization of the cobordization of any proper  birational toric morphism π : X∆ → XΣ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let ∆ be a fan subdivision of a fan Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y = X∆ → X =  XΣ be the associated proper toric morphism of toric varieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vk be the  vertices of Vert(∆) ∖ Vert(Σ) corresponding to the toric valuations νi = val(vi),  associated with the exceptional divisors E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Ek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let σ0 = ⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek⟩ be the  regular cone defined by the free basis e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let πΣ : |Σ| × σ0 → |Σ| be the linear map of the supports of fans such that  πΣ(ei) = vi, and identical on |Σ|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider the subfan ΣB of Σ × σ0 consisting of  the faces of Σ × σ0 mapping to faces of Σ, under the projection πΣ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the full  cobordization B → X of π can be described as the toric morphism associated with  the projection πΣ|ΣB : ΣB → Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The morphism B+ ⊂ B is an open inclusion which corresponds to the subfan  ΣB+ of ΣB of all the faces of Σ × σ0 mapping to the faces of ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5, and reducing to the affine case, we see that B+ ⊂ B is an  open immersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let T0 := Spec(κ[M]) ⊂ XΣ be the torus acting on XΣ, and on X∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let  TB := Spec(κ[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk, t−1  k ]), where the coordinates t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , correspond  to e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek on Xσ0 = κ[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k ]) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, we can write B as  B = Spec(AY/X), where  AY/X =  �  ai∈Z  k�  i=1  Iνi,ai · ta1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tak  k ⊂ OX[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk, t−1  k ]  Consequently, B contains a toric variety  B = SpecX(AY/X) ⊃ B− = SpecX(OX[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk, t−1  k ]) = XΣ × TB,  and hence contains a torus T0 × TB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover the torus T0 × TB acts on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  On the other hand, by Lemmas 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5 the scheme B is the union of  toric varieties Bσ containing T0 × TB, associated with σ ∈ Σ, such that  Bσ := π−1  B (Xσ) = B(X∆|σ/Xσ) × T (Xσ) =  SpecXσ(OXσ[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ustαk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus B is a toric variety, let ΣB its corresponding fan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The affine toric morphism  B → X determines the homomorphism of tori T0 × TB → T0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It corresponds to the  map of fans (ΣB, N0 × NB) → (Σ, N0), defined by the natural projection N0 × NB  Consider the toric variety XΣ × Spec(κ[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k ]), associated with the fan  Σ × σ0, with the lattice N0 × NB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The linear map  πΣ : (|Σ| × σ0, N0 × NB) → (|Σ|, N0),  satisfies πΣ(ei) = vi, and πΣ|N0 = idN0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The full cobordization morphism B → XΣ takes the divisor Di = VB(t−1  i ) to  Ei by Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus it defines the same map on the lattices πΣ : NB → N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover, by Lemmas 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5, each toric variety  Bσ = B(X∆|σ/Xσ) × TB∖Bσ ⊂ B  corresponds to the subfan determined by the cone σ ×τ(σ) of Σ×σ0, where τ(σ) ≤  σ0 is generated by all ei with vi ∈ σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  26  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  Thus, by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5(4), ΣB consists exactly of the faces of Σ × σ0 mapping  into faces of Σ, under the projection πΣ : ei �→ vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently, B+ corresponds  to the subfan ΣB+ of ΣB of all the faces mapping to the faces of ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The dual complex of the exceptional divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The dual complex of toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y = X∆ → XΣ be a proper  toric morphism, where ∆ is a subdivision of Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that X = XΣ is smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the full cobordization B of π is a smooth toric variety with the toric morphism  πB : B → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently the exceptional divisors D = VB(t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k ) of πB  and D+ = D ∩ B+ of πB+ are SNC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' On the other hand the components Di+ map  to the components Ei of the exceptional toric divisor E of π : Y → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  One can define the divisorial stratifications SD, and SD+ on B, and B+ with the  strata determined by the nonempty sets  sI :=  �  i∈I  Di ∖  �  j∈J  Dj,  where I ∪ J = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , k}, I ∩ J = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Note that the closure sI can be written in the  form  sI =  �  i∈I  Di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Likewise the stratification SE od E on Y is determined by the nonempty closed  sets sIE := �  i∈I Ei, which determine the strata sE  I obtained by removing from sIE  all the proper subsets sJ E ⊂ sIE, with J ⊃ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  These three stratifications are coarser than the orbit stratifications;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' thus, each  stratum is the union of orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The divisorial stratifications SD and SD+ define the  dual complexes ∆D and ∆D+ ⊂ ∆D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The vertices ei of ∆D and ∆D+ correspond  to the divisors Di or, respectively Di+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We associate with a stratum s = �  i∈I Di ∖  �  j∈J Dj, the simplex σs := ∆(ei | i ∈ I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Similarly, we can define the dual complex ∆E associated with the toric excep-  tional divisor E on Y (which is usually not SNC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Again the vertices ei of ∆E  correspond to the divisors Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We associate with any set of divisors {Ei | i ∈ I}  such that �  i∈I Ei ̸= ∅ the simplex σI := ∆(ei | i ∈ I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Summarizing we obtain the  following characterization of the complexes:  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' A simplex σ in ∆D( respectively in ∆D+ or ∆E) corresponds bi-  jectively to a set of divisors Di ( respectively Di+ or Ei) having a nonempty inter-  section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let B → X be the full cobordization of π : Y = X∆ → X = XΣ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let D be the exceptional divisor on B, and SD be the induced stratification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  for any stratum s ∈ SD, the image πB(s) is closed in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The problem is local on X so we can assume that X = Xσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let B = Xσ×Xδ,  where δ = ⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek⟩ the regular cone generated by a free basis {e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The morphism B → X corresponds to the projection πΣ : σB = σ × δ → σ,  mapping ei to vi ∈ Vert(∆) ∖ Vert(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Any stratum s = �  i∈I Di ∖ �  j∈J Dj in SD is closed on the open affine subset  B′ = B ∖ �  j∈J Dj of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By replacing B with the open affine subset B′ = Bt−1  J ,  where tJ = �  j∈J tj, we assume that s = �  i∈I Di and all the exceptional vertices ei  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  27  of σ × δ , where i ∈ I, span the cone δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then s is the union of orbits corresponding  to the cones in Star(δ, σB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let δ0 := πΣ(δ) be the image of δ, which is a subcone in σ generated by πΣ(ei).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Denote by σ0 ≤ σ the unique face such that int(δ0) ⊂ σ0 ≤ σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus, since σ is regular, and the map πΣ is surjective, the image πB(s) of s is  defined by the orbits corresponding to the cones in Star(σ0, σ), and thus it is closed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The center of valuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Recall that for any valuation ν of the quotient field  κ(X), we denote its center on X by ZX(ν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider any stratum s ∈ SD such that s = �  i∈I Di ∖ �  j∈J Dj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then  πB(s) =  �  i∈I  ZX(νi),  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Note that, by Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9, the image πB(Di) = ZX(νi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then πB(s) ⊆  �  i∈I ZX(νi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The problem is local on X, and we use the notation and the description  from the proof of the previous Lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The stratum s contains a generic toric orbit  corresponding to the cone δ = ⟨ei | i ∈ I⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Its image πB(s) is closed and corresponds  to the Star(σ0, σ), where σ0 is the smallest face containing the images {vi | i ∈ I},  where val(vi) = νi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  On the other hand, �  i∈I ZX(νi) corresponds to the faces of σ containing all vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Both sets are identical and πB(s) = �  i∈I ZX(νi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The morphism πB+,Y : B+ → Y determines a bijective correspon-  dence between the sets of divisors {Di+ | i ∈ I} such that � Di+ ̸= 0, and the sets  {Ei | i ∈ I} for which � Ei ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We need to show that �  i∈I Di+ ̸= ∅ iff �  i∈I Ei ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6,  πB+,Y (Di+) = Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus if �  i∈I Di+ is nonempty then  �  i∈I  πB+,Y (Di+) =  �  i∈I  Ei ⊇ πB+,Y (  �  i∈I  Di+) ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Conversely, if �  i∈I Ei is nonempty then the vertices vi corresponding to Ei form  the subcone τ = ⟨vi | i ∈ I⟩ of a face δ ∈ ∆, with Vert(τ) ⊆ Vert(δ) ∖ Vert(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently, by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5(4), τ is the image of the face δ′ = ⟨ei | i ∈ I⟩ ∈ ∆B+,  whence �  i∈I Di+ is nonempty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The natural surjective map SD+ → SE determines an isomor-  phism of the dual complexes ∆D+ ≃ ∆E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Also, we have  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The natural morphism SD+ → SD determines the inclusion of  the dual complexes ∆D+ ≃ ∆D, so that ∆D+ is a subcomplex of ∆D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the construction, the faces of ∆D (and ∆D+) correspond to the sets of  divisors {Di | i ∈ I} such that �  i∈I Di ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Now, if �  i∈I Di+ ̸= ∅ then obviously  �  i∈I Di ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Newton polytopes of monomial ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  28  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Newton polytopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider the lattice of monomials  M = {xα | α ∈ Zk} ≃ Zk,  and let N = Hom(M, Z) be its dual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let I = (xα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xαk) ⊂ κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn] be a  toric ideal generated by the monomials corresponding to the elements of  αi ∈ Zn  ≥0 ⊂ σ∨  0 = ⟨e∗  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , e∗  n⟩ = Qn  ≥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By the associated Newton polytope of I we mean  P = PI := conv(α1 + Qn  ≥0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , αk + Qn  ≥0) ⊆ Qn  ≥0 ⊆ MQ = M ⊗ Q = Qn  Conversely any polytope (or polyhedron) P = P + Qn  ≥0 determines the ideal  I = IP := (xα | α ∈ P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' There is a bijective correspondence I �→ PI, P �→ IP , between  integrally closed toric ideals I ⊂ κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn], and polytopes P = P + Qn  ≥0 with  integral vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The orbit stratification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' One can identify e∗  i with xi, so we can write σ∨  0 =  ⟨x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Denote by NQ the dual space of MQ, and σ0 ⊂ NQ the dual of σ∨  0 as  in Sections 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For any τ ⊂ NQ set  τ ⊥ := {y ∈ MQ | (x, y) = 0  for all x ∈ τ},  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' There is a natural bijective correspondence between  the faces τ of σ0  the faces τ∗ := τ ⊥ ∩ σ∨  0 of σ∨  0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  the open affine subsets Xτ ⊂ Xσ0  the minimal closed orbits Oτ ⊂ Xτ which are in Xσ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover under the above identification the closure Oτ of the orbit Oτ is defined  by the ideal (xi | xi ̸∈ τ ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The face τ of σ0 determines the open subset  Xτ = Spec(κ[τ∨ ∩ M]) = Spec(κ[Pτ]) = Spec(κ[P ∗  τ ]) × Spec(κ[P τ])  of Xσ0, where  Pτ = τ∨ ∩ M = Pσ0 + P ∗  τ = Pσ0 − (τ ∗ ∩ M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus τ ∗ ∩ M = P ∗  τ ∩ Pσ0 consists of the elements of Pσ0 = σ∨  0 ∩ M, which are  invertible in Pτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The closed orbit Oτ ⊂ Xτ is described by the ideal generated by  the set of noninvertible elements  Pτ ∖ P ∗  τ := (τ ∨ ∖ τ ∗ ∖ (−τ ∗)) ∩ M ⊂ Pτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus its closure Oτ in Xσ0 is defined by the ideal (xi | xi ̸∈ τ ∗) corresponding to the  monoid ideal Pσ0 ∖ P ∗  τ = (σ∨  0 ∖ τ ∗) ∩ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Conversely, any face τ ∗ of σ∨  0 determines  the closure Oτ ⊂ Xσ0 of the orbit Oτ with the monoid ideal (σ∨  0 ∖ τ ∗) ∩ M, and  the face τ = (τ ∗)⊥ ∩ σ0 of σ0 ⊂ NQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  By the construction, Oτ is the smallest T -stable closed subset of Xτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' If τ ⊂ τ′ is  the inclusion of the faces then Xτ ⊂ Xτ ′ is an open immersion, and Oτ contains Oτ ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently the orbits Oτ form the stratification of Xσ0 = Spec(κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  29  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let I ⊂ κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk] be a monomial ideal and PI ⊂ σ∨  0 be its  Newton polytope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the toric subset V (I) is exactly the union of the orbits Oτ  such that τ ∗ is disjoint from PI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The orbit Oτ is contained in V (I) if and only if the ideal of Oτ contains I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus the corresponding monoid ideal (σ∨  0 ∖ τ∗) ∩ M contains P ∩ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The latter is  equivalent to the condition τ∗ ∩ P = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Supporting faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The monomial ideal I = (xα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xαk) defines a piecewise  linear convex function FI := min(αi, v) on σ0 := ⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , en⟩ which is dual to σ∨  0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Likewise any polytope P ⊂ σ∨  0 determines a piecewise linear convex function  FP := min((w, v) | w ∈ P)  on σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If P = P(I) then both functions coincide:  FP = FI = min(v, αi) = min((v, w) | w ∈ P))  By the dual fan or normal fan of P, we mean the fan ∆P = ∆I is determined by  the maximal cones τ ⊂ σ0, where FP is linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By definition, ∆P is a decomposition  of σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Conversely, the function FP on σ0, determines the polytope  P = {w ∈ σ∨  0 | (·, w)|σ0 ≥ FP |σ0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Recall the standard fact from the convex geometry:  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' There is a bijective correspondence between the faces P of the  polytope P0, and the faces τP of the fan ∆P0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  P �→ τP := (P0 − P)∨ = {v ∈ σ0 | (v, w) ≥ 0, w ∈ P0 − P} ∈ ∆P0  τ �→ Pτ = {w ∈ P | FP |σ = (·, w)|σ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover dim(P) = n − dim(σP ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For any i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , n, let  ai := min{xi(p) | p ∈ P}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then  Pi := {p ∈ P | (xi − ai)(p) = 0}  is the face of P corresponding to the one-dimensional face ⟨ei⟩ determine by the  vertex ei of σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the supporting facets of P0 we mean the faces corresponding  to the vertices of Vert(∆P0) ∖ Vert(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The affine hull of a supporting face will be  called a supporting hyperplane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the supporting faces, we mean the faces, which  are the intersections of some supporting facets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  As a corollary from Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8, we obtain  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let ∆ be the subdivision of regular cone σ0 associated with the  normalized blow-up π : Y = X∆ → X = Xσ0 of the monomial ideal I ⊂ κ[Pσ] =  κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let B → X = Xσ0 = An be the full cobordant blow-up of I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  the following sets are in the bijective correspondence  (1) The supporting hyperplanes Hi of P(I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  30  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  (2) The vertices vi of Vert(∆) ∖ Vert(σ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) The exceptional divisors Di of B → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (4) The exceptional divisors Ei of Y → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (5) The toric exceptional valuations νi = val(vi) on X associated with Ei on  Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (6) The vertices of the dual complexes ∆E ≃ ∆D+ and ∆D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The supporting faces exist if codim(V (I)) ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' On the other  hand, if I is principal, then ∆ = σ0, and thus P admits no supporting faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' With the above notation and assumptions:  (1) Any exceptional valuation ν determines the supporting hyperplane Hν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) With a face σ of ∆E one can associate the set ωσ of the exceptional valua-  tions corresponding to the vertices Vert(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) Any face σ of the dual complex ∆E determines the supporting face Pσ of  P, where  Pσ =  �  ν∈ωσ  Hν ∩ P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (4)  inv◦  ωσ(I) := (uα ∈ I | ν(I) = ν(xα), ν ∈ ωσ) =  = invPσ(I) := (xα ∈ I | α ∈ Pσ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Here  ν(I) := min{ν(f) | f ∈ I}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  One can see the above relations in the following example:  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let I = (xk, xy, yl) ⊂ κ[x, y].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The Newton polytope P of I is generated by the vertices P1 = (k, 0), P2 =  (1, 1), P3 = (0, l) of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The supporting planes H1, and H2 are determined, respec-  tively, by the supporting facets P12 = conv({(k, 0), (1, 1)}), and P23 = conv({(1, 1), (0, l)}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  They correspond to the vectors v1 = (v11, v12), v2 = (v21, v22) such that  kv11 = v11 + v12,  v21 + v22 = lv21  Thus v1 = (1, k − 1), v2 = (l − 1, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The decomposition ∆P consists of three 2-  dimesional cones σ1 = ⟨e1, v1⟩, σ2 = ⟨v1, v2⟩, σ3 = ⟨v2, e2⟩, and their 1-dimesional  faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' These 2-dimesional faces in ∆P correspond to the vertices (k, 0), (1, 1), (0, l)  of P, and the associated monomials xk, xy, yl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The vectors v1, v2 ∈ Vert(∆p) cor-  respond to the exceptional valuations ν1 = val(v1), ν2 = val(v2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In particular  inv◦  ν1(I) = invP12(I) = (xk, xy),  inv◦  ν2(I) = invP23(I) = (xy, yl),  inv◦  ν1,ν2(I) = invP2(I) = (xy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Note that the vertices in Vert(P), which are, in our case, defined by xk, xy, yl,  label the maximal faces in ∆P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We see that the monomials in inv◦  ω(I) = invP (I) correspond to the maximal  cones in the star of the relevant face in ∆P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This face is described as the dual  to P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Equivalently, it is defined as the smallest face containing the set of the  vertices of ∆P determined by ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In particular, the generators xk, xy occurring in  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  31  inv◦  ν1(I) = inv◦  P12(I) = (xk, xy) correspond to the maximal cones in the star of the  face ⟨v1⟩ ∈ ∆P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The full cobordant blow-up of I = (xk, xy, yl) is given by  B = Spec(κ[t−1  1 , t−1  2 , xt1tl−1  2  , ytk−1  1  t2]),  and using Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4,  B+ = Spec(κ[t−1  1 , t−1  2 , xt1tl−1  2  , ytk−1  1  t2]) ∖ V (tk  1tl  2(xk, xy, yl)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Geometric quotients for toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y = X∆ → XΣ be a toric morphism, associated with the  decomposition ∆ of Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that Σ is simplicial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then its cobordization B+ → Y = B+/TB is a geometric quotient iff ∆ is  simplicial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The problem is local on X, and can be reduced to the affine toric morphism  X∆ → Xσ corresponding to the subdivision ∆ of a simplicial cone σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then, by  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, ΣB is simplicial, and so is ΣB+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The natural projection ΣB+ → ∆ is defined bijectively on the vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover,  the faces of ∆ are the images of cones in ΣB+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus ΣB+ → ∆ is bijective on faces  if and only if ∆ is simplicial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' On the other hand, the condition that ΣB+ → ∆ is  bijective on faces is equivalent to B+ → Y being a geometric quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y = X∆ → X = XΣ be a proper birational toric morphism  of toric varieties, with X regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then B+ ⊂ B contains open maximal subsets  Bs ⊂ B+ admitting geometric quotient Bs/TB which is projective birational over  Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The morphism Y → X corresponds to the subdivision ∆ of Σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider  the sequence of the star subdivisions centered at Vert(∆) of ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the definition  of the star subdivision, the process transforms ∆ into a simplicial fan ∆′ with  Vert(∆′) = Vert(∆), as all the vertices in the faces form linearly independent sets  being the centers of the star subdivisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  So the valuations of the exceptional  divisors corresponding to Vert(∆) = Vert(∆′) remain unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then, by Propo-  sition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2 we obtain that B(Y/X) = B(Y ′/X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' On the other hand, by the second  part of Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, we have the open inclusions of toric subsets:  Bs := B(Y ′/X)+ ⊂ B(Y/X)+ ⊂ B(Y/X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By the previous Lemma, Bs → Bs/TB = X∆′ is a geometric quotient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordization of locally toric morphisms  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Locally toric morphisms of locally toric schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Locally toric schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' A normal scheme X over a field κ is locally toric if any point  p ∈ X admits an open neighborhood U, and a regular morphism φ : U → Xσ =  Spec(κ[Pσ]), called a toric chart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  An ideal I on a locally toric X is called locally monomial if for any point p ∈ X,  there exists a toric chart U → Xσ = Spec(κ[Pσ]), and a monomial ideal Iσ ⊆ κ[Pσ],  defined by a subset of Pσ, such that I|U = Iσ · OX|U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  32  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The primary reason we consider locally toric schemes over a field  κ, and not just over Z, is that the morphisms to Spec(Z) are, in general, not flat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus the toric charts over Z into Spec(Z[Pσ]) which are defined by the monomials  in Pσ = σ∨ ∩N are not regular (not flat), and some proofs would require a different  formalism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Locally monomial valuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X be a locally toric scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' A valuation of κ(X) with values  in Z will be called locally monomial if for any point p in the center Z(ν) ⊂ X, there  exists a toric chart U → Xσ, and a vector v ∈ σ ∩N, such that Iν,a = OX ·Ival(v),a,  for any a ∈ Z≥0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Locally toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' A proper birational morphism π : Y → X of normal schemes  over a field κ is called locally toric if for any point p ∈ X there is an open neigh-  borhood U, a toric chart φ : U → Xσ, and the fiber square:  π−1(U)  ψ→  X∆  πU ↓  πA ↓  U  ψ→  Xσ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  where πU := π|π−1(U) : π−1(U) → U is the restriction of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let J be a locally monomial ideal on a locally monomial  scheme X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The normalized blow-up of J is a locally toric morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Functoriality of cobordization of locally toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Local toric presentation of cobordization of locally toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a locally toric proper birational morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  for any point p ∈ X there exists an open neighborhood U of p ∈ X, a toric chart  φU : U → Xσ and a fiber square  YU := π−1U  φ→  X∆  πU ↓  πA ↓  U  φU  →  Xσ,  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  such that  (1) There is a bijective correspondence between the irreducible exceptional di-  visors of πU and πA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' That is, any irreducible exceptional divisor of πU is  the inverse image of an irreducible exceptional divisor of πA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) There is a bijective correspondence between the strata of the divisorial strat-  ifications of the exceptional divisors EU of YU → U and E∆ of X∆ → Xσ,  which defines the isomorphism Cl(YU/U) → Cl(X∆/Xσ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, any  stratum of the stratification SE is the inverse image of a stratum in SE∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) For any E′  U = � ni(EU)i and the corresponding (E∆)′ = � niE∆  i  we have  OYU ((E∆)′) = OY · (OX∆((E∆)′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (4) B(πU) = B(πA) ×Xσ U  B+(πU) = B+(πA)+ ×Xσ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (5) Any irreducible exceptional Weil divisor Ei of π defines a locally monomial  valuation νi with respect to any given toric chart U → Xσ associated with  the morphism π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  33  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (1) Since φU is regular, the inverse images φ−1  U (sτ) of the toric strata sτ,  where τ ≤ σ, define a stratification on U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, the induced morphisms on the  strata φ−1  U (sτ) → sτ are regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We can assume that the given point p ∈ X maps to a point q ∈ Xσ, which is in  the orbit Oσ ⊂ Xσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For any τ ≤ σ, the closure sτ := Oτ of the toric orbit Oτ on  Xσ is normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, since φU is regular, the inverse image φ−1  U (sτ) is normal,  and thus, it is the disjoint union of the irreducible components of the codimension  equal to the codimension of sτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently, by shrinking U around p, if necessary, we can assume that the  inverse image of the closures of the toric strata (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=', the orbits) on Xσ are irreducible  subsets of U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The inverse image of E∆ is the union of the normal divisorial components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Their  images under πU are of the codimension ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So they are the exceptional divisors  of πU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Moreover all the irreducible exceptional divisors of πU are contained in  φ−1(E∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The image πA(E∆  i ) contains the orbit Oσ with φ−1  U (Oσ) ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then, by the  assumption, φ−1(E∆  i ) ̸= ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We need to show that each φ−1(E∆  i ) is an irreducible divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The image of the  exceptional divisor E∆  i  under πA defines the closure of the toric orbit  πA(E∆  i ) = sτ = Oτ  on Xσ, for some face τ ≤ σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Denote by q the generic point of E∆  i , and by q0 the  generic point of sτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  For any divisorial component, Eij in φ−1(E∆  i ), let pj be its generic point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By  the assumption π(pj) ∈ U determines a unique point p0 which is the generic point  of the stratum s on U so that  s = φ−1  U (sτ) = p0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By definition, the generic point q of the toric divisor E∆  i  on X∆ is in the fiber  Fq0 = π−1  A (q0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus the generic points pj of the components Eij of φ−1(E∆  i ) are  in the fiber  Fp0 = π−1(p0  i ) = Spec(κ(p0  i )) ×Spec(κ(q0  i )) Fq0  i  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let ∆τ := ∆|τ be the restriction of ∆ to τ which determines the induced decom-  position of τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The fiber of  Fp0 = Spec(κ(p0)) ×Spec(κ(q0)) Fq0 = Y ×X Spec(κ(p0))  of π : Y = X ×Xσ X∆ → X is isomorphic to the fiber of the induced morphism  Xκ(p0)  ∆τ  → Xκ(p0)  τ  over p0 = Spec(κ(p0)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover the natural morphism Fp0 → Fq0 is induced by  the fiber square  Xκ(p0)  ∆τ  φ∆  →  Xκ(q0)  ∆τ  π ↓  πA ↓  Xκ(p0)  τ  φ→  Xκ(q0)  τ  ↓  ↓  Spec(κ(p0))  →  Spec(κ(q0))  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  34  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  The above morphism is bijective on the toric orbits and their generic points, as  they correspond to the faces of ∆ or respectively σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the inverse image of the  point qj ∈ Fq0 ⊂ Xκ(q0)  ∆τ  corresponds to a unique face in ∆(1) and a unique point p  in Fp0 ⊂ Xκ(p0)  ∆τ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Hence the inverse image of the toric divisor E∆  i  with the generic point q is the  unique exceptional divisor Ei with the generic point p = pj over q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) The same reasoning shows that the inverse image φ−1  ∆ (s∆  j ) = sj of the closure  of a toric stratum s∆  j on Xσ determines a unique stratum sj on YU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We use the  same relation for the fibers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  π−1(p0  j) = Fp0  j = Spec(κ(p0  j)) ×Spec(κ(q0  j )) Fq0  j  where pj is the generic point of sj, qj = φ(pj), p0  j = π(pj) and q0  j = πA(qj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) We need to show first that  OY (nEi) = OY (OX∆(nE∆  i ))  By the above, the generic point p of Ei is exactly the generic point of the fiber  φ−1(q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The induced homomorphism of the completions of the local rings is given  by  �  OX∆,q → �  OY,p = �  OX∆,q ⊗κ(q) κ(p)  Thus we get  mn  q · OX∆,p = mn  q ⊂ OY,p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Both points p and q admit a regular neighborhood and its local rings are DVR  defining the valuation νi of Ei, and ν∆  i  of E∆  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  One verifies that Iνi,a,Y = OY · I∆  νi,a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' First observe that the valuation center of  νi on Y can be described as  ZY (νi) = VY (Iνi,a,Y ) = Ei = φ−1(E∆  i ) = V (OY · I∆  νi,a)  For any point p′ ∈ Z(νi), and its image q′ = φ(p) ∈ Z(ν∆  i ) we have  �  OY,p = �  OX∆,p ⊗κ(p) κ(q)[[u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' uk]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently the monomial valuation ν∆  i  on OX∆,p′ = OXδ,p′ of E∆  i  associated  with a vertex of ∆ extends to a certain unique monomial valuation ν′  i on �  OY,p such  that  �Iν′  i,a,p′ = I∆  νi,a · �  OY,p′ = I∆  νi · ( �  OX∆,p′ ⊗κ(p′) κ(q′)[[u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' uk]])  which by flatness implies  Iν′  i,a,p′ = I∆  νi,a · OY,p′  Note that the generic point p of Ei specializes at p′, and the generic point q of E∆  specializes at q′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Passing to p and q and localizing we obtain that  Iν′  i,a,p = I∆  νi,a,q · OY,p = Iνi,a,p,  whence both valuations are equal νi = ν′  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus Iνi,a,p′ = I∆  νi,a,q′ · OY,p′ and the  vanishing locus of the ideal  Iνi,a,YU = OYU · I∆  νi,a,X∆  is irreducible by part (1) and defines the center of the valuation νi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  35  Now, for any effective divisor (E∆)′ = � aiE∆  i , and its inverse image (EU)′ =  � ai(EU)i we have, by flatness  OYU (−(EU)′) =  �  Iνi,ai,YU = OYU · (  �  Iνi,ai,X∆) =  = OYU · OX∆((E∆)′) = OYU ⊗OX∆ OX∆((E∆)′)  In general, for any (E∆)′ = � aiE∆  i , we can find a nontrivial monomial m ∈  Pσ = σ∨ ∩ M such that for n ≫ 0,  OY ((E∆)′) = m−nOY ((E∆)′ − n · div(m)),  where −((E∆)′ − n · div(m)) is effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently  OYU ((EU)′) = m−nOYU ((EU)′ − n · divY (m)) =  = OYU · m−n · OX∆((E∆)′ − n · div(m)) = OYU OX∆(E∆) = OYU ⊗OX∆ OX∆(E∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (4) and (5) Since the morphism U → Xσ is affine, and thus YU → X∆ is such  we have  BU+ = SpecYU (  �  E∈Cl(YU /U)  OYU (E)) = SpecYU (OYU · (  �  E∆∈Cl(X∆/Xσ)  OX∆(E∆)) =  = SpecX∆ OYU ⊗OX∆ (  �  E∆∈Cl(X∆/Xσ)  OX∆(E∆)) = YU ×X∆ B+(πA)+ =  = (U ×Xσ X∆) ×U ×XσB+(πA) = U ×Xσ B+(πA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By definition, and since all the schemes are normal  πA∗(Iν∆  i ,a,X∆) = πA∗(OX∆(a, E∆  i )) = Iνσ  i ,a,Xσ ⊂ πA∗(OX∆(E∆)) = OXσ  are the toric ideals generated by monomials associated with the toric valuation νσ  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Similarly  π∗(Iνi,a,Y )) = π∗(OY (aE)) = Iνi,a,X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By the above and since ψ is flat, we have  Iνi,a,U = π∗(OYU (−Ei)) = π∗(OYU · OX∆(−E∆  i )) =  π∗(OYU ⊗ OX∆(−E∆  i )) = OU ⊗ πA∗(OX∆(−E∆  i )) = OU · Iνi,a,Xσ  is a locally monomial valuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus for E = � aiEi, we have  π∗(OYU (E)) =  �  Iνi,ai,U =  �  OU ·Iνi,a,Xσ = OU ·  �  Iνi,ai,Xσ = OU ·π∗(OX∆(E))  Hence, by the above  BU = SpecU(  �  E∈Cl(YU /U)  π∗(OYU (E)) = SpecU(OU · (  �  E∆∈Cl(X∆/Xσ)  π∗(OX∆(E∆)) =  = SpecU(OU ⊗OXσ (  �  E∆∈Cl(X∆/Xσ)  π∗(OX∆(E∆)) = U ×Xσ B(X∆/Xσ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  36  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Local description of the exceptional divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' As a corollary from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2  we obtain:  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a locally toric morphism of locally toric schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let πB : B → X be its full cobordization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  For any point p ∈ X, there is a toric chart φU : U → Xσ, such that for the  induced morphism BU = π−1  B (U) → X∆, there is a bijective correspondence between  the strata s = φ−1(sτ) of the divisorial stratifications of the exceptional divisor DBU  on BU, (respectively DBU+ on BU+) and the strata (sτ) of the exceptional divisor  DB(X∆/Xσ) on B(X∆/Xσ) (respectively DB(X∆/Xσ)+ on B(X∆/Xσ)+ ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The reasoning is the same as in the proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We can assume,  as in the proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2(2), that the inverse image φ−1  U (si) ⊂ U consists of  a single stratum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By Lemmas 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, we have the following fiber square diagram for the  cobordizations, with horizontal morphisms being regular:  BU  φ→  B(X∆/Xσ)  πU ↓  πB ↓  U  φU  →  Xσ = An,  ,  and the analogous fiber square for BU+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently, the inverse image of the  exceptional divisor on DB(X∆/Xσ) is the exceptional divisor DBU .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Its components  are of the form V B(X∆/Xσ)(t−1  i  ) and are associated with the components E∆  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Their inverse images are the irreducible components V BU(t−1  i )) corresponding to  the exceptional components Ei = φ−1(E∆  i ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Since φU is regular, the inverse image φ−1(s) of the closure s of any stratum s of  DB(X∆/Xσ) is normal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus it is the disjoint union of the irreducible components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  To prove that φ−1(s) is irreducible on YU, we need to show that there is a single  generic point p in the fiber φ−1(q) over the generic point q of s, and such that p  is of the same codimension in U as s in B(X∆/Xσ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This can be reduced to the  problem of the morphism of the fibers  π−1(p0) = Fp0 → π−1(q0) = Fq0,  where p0 = πB(p), and q0 = πU(q) are the generic point of the relevent strata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  But this follows from the relation for the fibers of toric morphisms, as in the  proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2(2),  π−1(p0  i ) = Fp0  i = Spec(κ(p0  i )) ×Spec(κ(q0  i )) Fq0  i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Description of cobordization of locally toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Local functoriality of relative Cox spaces for smooth morphims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational locally toric morphism  of locally toric varieties over a field κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let φ : X′ → X be a regular morphism over  κ, and π′ : Y ′ → X′ will be the base change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then for any p′ ∈ Y ′ there are open  neighborhoods U ′ of p′, and U of p := φ(p′), with the induced smooth morphism  φ|U′ : U ′ → U such that  B(YU/U) ×X X′ ≃ B(Y ′  U′/U ′)  B(YU/U)+ ×X X′ ≃ B(Y ′  U′/U ′)+  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  37  Thus the full cobordization and cobordization of proper birational locally toric  morphisms are functorial for regular morphisms up to torus factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This is a direct consequence of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2 and definition of locally toric  morphisms  ♣  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Local description of cobordization of locally toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational locally toric morphism over  a field κ, and πB : B → X be its full cobordization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  (1) B+ ⊂ B is the natural open immersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) For any point p ∈ X there is an open neighborhood U of p, with a toric  chart U → Xσ, and the torus  TB∖BU := Spec( κ[xi, x−1  i  | Ei ⊂ B ∖ BU ] ),  and an induced regular morphism  BU = σ−1(U) = B(YU/U) × TB∖BU → Xσ × Ak × TB∖BU  (3) If X is regular then B is regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, the problem reduces locally to a toric situation via toric  chart U → Xσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (1) By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5, B(X∆/Xσ)+ ֒→ B(X∆/Xσ) is an open inclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus,  by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, B+ ⊂ B is also such.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) Also locally by Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, we can write BU = B(YU/U) × TB∖BU .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' On  the other hand, by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2(4) B(YU/U) → B(X∆/Xσ) is regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Finitely by  Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5(2), B(X∆/Xσ) = Xσ × Ak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) Follows from (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Local description of cobordization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordization of locally monomial maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X be a locally monomial scheme over a field κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We say  that u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk is a locally toric system of parameters on X if there is a chart  φ : U → Xσ, and a local system of toric parameters x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk on Xσ, such that  ui = φ∗(xi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  As a Corollary from Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4 we obtain the following:  Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational locally toric morphism of  locally toric schemes over a field κ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then locally on X we can write up to torus  factors  AY/X = π∗(CY/X) = OX[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk],  where  (1) u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk is a locally toric system of parameters  on an open U ⊂ X  defining a toric chart for the morphism π,  (2) tαi := tai1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · taik  k , with aij := νi(uj) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In particular, if X is regular then B and B+ ⊂ B are regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We use the fact from Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, that the valuations are locally monomial  with respect to u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk, and Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  38  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The cobordization of monomial morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Y → X be a proper bira-  tional locally toric morphism over κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn be a system of local parameters at a point p on a locally toric X  defining a toric chart for a Y → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the full cobordization of π : Y → X can  be represented as:  B = SpecX(OX[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , x′  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , x′  n]/(x′  1t−α1 − x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , x′  kt−αk − xk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus B = V (x′  1t−α1−x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , x′  kt−αk−xk) ⊂ X×An+k is locally a closed subscheme  of X × An+k defined by a system of local parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It is regular for a regular X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently, the full cobordization B → X can be described by a single chart up  to a torus factor with the following coordinates:  t−1  i  for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , k is the inverse of the coordinate ti representing the action  of torus T = Spec(κ[Cl(Y/X)] = Spec(κ[t1, t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tn, t−1  n ]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  x′  i = xi · tαi for 1 ≤ i ≤ k, and  x′  j = xj for j > n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The open subsets Bx′  i = B ∖ V (x′  i), associated with the forms x′  i = xitαi cover  the cobordization B+ = B ∖ V (Iirr) producing several ”charts” similarly to the  standard blow-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  These open affine subsets can be conveniently described by  using toric geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' They correspond to the maximal faces of the decomposition  ∆ of the cone σ associated with the local toric chart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If π : Y  → X is the cobordant blow-up of a locally monomial J , where  codim(V (J ) ≥ 2, then the subset B+, by Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, can be described as  B+ = B ∖ V (J tα), where α = (a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ak), and ai are the coefficients of the  exceptional divisor E = � aiEi of π : Y → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In this case, the charts of B+  can also be interpreted by the vertices of the Newton polytope of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (See Example  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='14)  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In the particular case, when considering the stack-theoretic quo-  tients of the blow-up of a locally monomial ideal on a regular scheme, one obtains  the definition of a multiple weighted blow-up BlJ = [B+ � T ] introduced in [AQ21]  by Abramovich-Quek via the Satriano construction in [Sat13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The more general  definition of BlJ ,b is discussed in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Weighted cobordant blow-ups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Recall that the weighted stack-theoretic blow-  ups were considered in the context of resolution in [McQ19] and [ATW19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The  definition of the weighted cobordant blow-up was introduced in [W�lo22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' One can  view these notions from the more general perspective of Cox cobordant blow-ups  or the multiple weighted blow-ups of Abramovich-Quek from [AQ21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk) be a partial system of local parameters on a  regular scheme X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let J be a center of the form (xa1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xak  k ), where a1 ≤ a2 ≤  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' ≤ ak are positive integers, and k > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be the normalized  blow-up of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the weighted cobordant blow-up of J we mean the cobordization  BJ + → X of π : Y → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The corresponding monomial ideal on the toric chart Ak  κ defines a piecewise  linear function G := mini(aie∗  i ) on the regular coordinate cone σ = ⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek⟩,  where e∗  i (ej) = δij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The functions aie∗  i determine the ray  ρ := {v ∈ σ | a1e∗  1(v) = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' = ake∗  k(v)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  39  The ray ρ is generated by the primitive vector  w = (w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , wk) = w1e1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' + wkek,  with relatively prime components and such that  w1a1 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' = wkak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The normalized blow-up of J is described by the decomposition ∆ of σ into  maximal subcones where G is linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus ∆ is the star subdivision ρ·⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek⟩ at a ray ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The vector w determines  the valuation νE of the unique irreducible exceptional divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then, by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5(1), the full cobordant blow-up of X at the center J is  defined by  BJ = SpecX(OX[t−1, tw1x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , twkxk]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Here we have  wi = νE(xi) = (w, e∗  i )  The cobordant weighted blow-up is simply (BJ )+ = B ∖ V (σ◦(J )), where, by  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, we have σ◦(J ) = ta · J , where a = ν(J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus  σ◦(J ) = (xa1  1 ta1w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xak  k takwk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We see that the cobordant weighted blow-up is the cobordization of an ordinary  toric weighted blow-up corresponding to the star subdivision at the center v ∈ σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We will discuss this construction in the context of the blow-ups of valuative Q-ideals  in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Observe that both notions: the one in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7, and the one given by the  formula BJ = SpecX(OX[t−1, tw1x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , twkxk]), as in [W�lo22], are different in the  trivial case k = 1 and the blow-up of (xa1  1 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then Y → X is an isomorphism, and  B = B+ = B− ≃ Y ≃ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' However the formula from [W�lo22] gives us  B = SpecX(OX[t−1, tw1x1]),  which defines the isomorphism of the quotients:  B/Gm ≃ B+/Gm ≃ B−/Gm ≃ Y ≃ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In this case, B+ is a locally trivial Gm-bundle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So both constructions of B+ differ  locally by the torus factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Geometric quotients for locally toric morphisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In general, when con-  sidering the cobordization B+ of a locally toric morphism π : Y → X, one obtains  the good quotient B+ � T ≃ Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, below shows that if X is regular  then, by replacing B+ with an open subset Bs ⊆ B+ one obtains the geometric quo-  tient Bs/T with a proper birational morphism Bs/T → B+�T ≃ Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='xConsequently,  Bs has a geometric quotient Bs/T with abelian quotient singularities and the trans-  formation Bs → X can be be used in the resolution instead of B+ → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a locally toric morphism, with X regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then its cobordization B+ determines the geometric quotient B+ → B+/T ≃ Y  iff Y has abelian quotient singularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The problem is local and can be reduced to the toric morphism π : X∆ → Xσ  corresponding to the subdivision ∆ of a regular cone σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then, by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5,  the full cobordization B of π is a regular scheme corresponding to the cone ΣB,  and B+ is its open toric subscheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The natural projection σB+ → ∆ corresponds  40  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  to the geometric quotient iff ∆ is a simplicial fan, and thus Y has abelian quotient  singularities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational locally toric morphism of  locally toric schemes over a field, with X regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then B+ = Cox(Y/X)+ ⊂ B =  Cox(Y/X) contains open maximal subsets Bs ⊂ B+ admitting geometric quotient  Bs/TB with the projective birational morphism  Bs/TB → B+/TB = Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Ek be the irreducible exceptional divisors of π : Y → X, and  ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νk be the associated exceptional valuations on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2(5), the  valuations are locally toric on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider the sequence of the blow-ups at the  valuations νi as in [W�lo20, Proposition 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' These are precisely the normalized  blow-ups of Iνi,a,X for a sufficiently divisible a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Locally, in the compatible toric charts, U → Xσ the sequence of the blow-ups  correspond to a sequence of the star subdivisions at the vertices Vert(∆) ∖ Vert(σ)  (see [W�lo20, Lemma 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' As the result we create a new subdivision ∆′ of ∆ with  Vert(∆′) = Vert(∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This decomposition is simplicial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Indeed, let δ0 be any cone in  ∆′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the property of the star subdivisions, for any vertex v0 ∈ Vert(δ) ∖ Vert(σ)  one can write δ0 = ⟨v0⟩ + δ1, where δ1 is a face of δ0 of codimension one in δ0,  and v0 is linearly independent of Vert(δ1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We can run this argument inductively  until we can represent δ0 as δ0 = ⟨v0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vr⟩ + δr, where v0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , vr ∈ Vert(δ0) are  linearly independent of Vert(δr) ⊂ Vert(σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus all the vertices of δ0 are linearly  independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By construction, the valuations of the exceptional divisors corresponding to  Vert(∆) ∖ Vert(σ) remain unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then B(Y/X) = B(Y ′/X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' On the other  hand, by the description of the toric case from Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5(4), we obtain the open  inclusions  Bs := B(Y ′/X)+ ⊆ B(Y/X)+ = B+ ⊆ B(Y/X) = B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordant resolution of singularities  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The dual complex of the exceptional divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' One can extend the con-  siderations and the results from Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The exceptional divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational locally toric  morphism, where X is a regular scheme over a field κ, and E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Ek be the  irreducible components of the exceptional divisor E of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let πB : B → X be the  full cobordization of π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5, B is regular and there is an SNC divisor  D = VB(t−1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='· t−1  k ) with irreducible components Di = VB(t−1  i ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So is the divisor  D+ = D|B+ on B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, the exceptional divisor E of π : Y → X is locally  toric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We can associate with the SNC divisors D on B, D+ on B+, and with the divisor  E on Y the divisorial stratifications SD, SD+, and SE, extending the definitions  from Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The strata of SD are defined by the irreducible components of  the locally closed sets :  �  i∈I  Di ∖  �  j∈J  Dj,  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  41  where I ∪J = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=', k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Replacing Di with Di+ we obtain the definition for SD+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently, any stratum s ∈ SD+ extends to a stratum in SD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The closures of the strata sE ∈ SE are defined by the irreducible components  of the intersections �  i∈I Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The strata sE are obtained by removing from sE  the proper closed subsets s′E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The stratifications SD, SD+ and SE determine the  dual simplicial complexes ∆D, ∆D+, and ∆E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Since D and D+ are SNC, the  simplices in ∆D, (respectively ∆D+) are in the bijective correspondence with the  strata of SD (respectively of SD+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, by the above, ∆D+ is a subcomplex  of ∆D corresponding to the strata of SD which intersect B+ ⊂ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Also, under this  identification Vert(∆D) = Vert(∆D+).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The divisor E is usually not SNC, and the strata alone do not determine the  faces of ∆E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The vertices vi of ∆E correspond to the divisors Ei ↔ vi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The  simplices σ = ∆(ei | i ∈ I) in ∆E correspond to the pairs (sE  σ , Eσ) consisting of  a stratum sσ ∈ SE and a collection of divisors Eσ = {Ei | i ∈ I), such that sσE  is an irreducible component of �  i∈I Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus, in this case, the correspondence  between the faces of ∆E and the strata of SE is not bijective, and the closures of  strata could be represented by the intersections of components �  i∈I Ei defined by  different subsets I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (See also Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=')  Summarizing we have  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' A simplex σ in ∆B (respectively ∆D+, ∆E) is represented by a pair  ({Di | i ∈ I},  (  �  Di)0)  consisting of a collection of the irreducible divisors Di, (respectively Di+, Ei) which  have a nonempty intersection and an irreducible component (� Di)0 of � Di (re-  spectively � Di+,  � Ei).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' With the previous assumptions and notations:  (1) There is a bijective correspondence between the divisors Di, Di+, Ei, and  the valuations νi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) (a) If s ∈ SD then s is a component of a locally closed set  �  Di⊇s  Di ∖  �  Di̸⊇s  Di  (b) The image πB(s) is closed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It is an irreducible component of the closed  set  πB(  �  Di⊇s  Di ∖  �  Di̸⊇s  Di) =  �  Di⊇s  ZX(νi) =  �  Di⊇s  πB(Di) =  �  Di⊇s  π(Ei)  where ZX(ν) denotes the center of a valuation ν on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, the  sets �  Di⊇s Di are locally irreducible over X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (c) The morphism πB determines a bijective correspondence between the  strata defined by the irreducible components of �  Di⊇s Di ∖ �  Di̸⊇s Di  and the irreducible components of �  Di⊇s ZX(νi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) The morphism πB+,Y determines a bijective correspondence between the  components of �  i∈I Di+ and the components of �  i∈I Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This correspon-  dence defines the isomorphism of the dual complexes ∆D+ ≃ ∆E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  42  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  (4) The morphism of the stratifications SD+ → SD maps a stratum s+ of SD+  into an open subset of a stratum s of SD .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It determines the inclusion of  the dual complexes ∆B+ ֒→ ∆B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (1) The correspondence follows from Lemmas 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9, and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2)-(5) By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, we can reduce the situation locally to the  toric case, where we use Lemmas 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3, and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6, and Corollaries 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7 and  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Dual complex of valuations of a locally toric morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let N = {ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νk}  be the set of the exceptional valuations of π : Y → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The vertices of Vert(∆E),  and thus of Vert(∆B) and Vert(∆B+) are in the bijective correspondence with the  valuations in N, and the exceptional divisors Ei, Di+, and Di:  νi ↔ Ei = ZY (νi) ↔ Di+ ↔ Di.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently, one can associate with the faces of ∆E, ∆B+, and ∆B the subsets  of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This determines the complexes ∆N  B , ∆N  B+, ∆N  E , called the dual valuation  complexes, together with natural isomorphisms of the simplicial complexes  ∆B → ∆N  B ,  , ∆B+ → ∆N  B+,  ∆E → ∆N  E  Then, by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3, ∆N  E = ∆B+ determine the same subcomplex of ∆N  B .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The simplices of the valuation complexes will be called the valuation faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The  valuation faces come with natural face inclusions inherited from ∆N  B , ∆N  B+, ∆N  E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3 we get:  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (1) A valuation face σ in ∆N  B is represented by a pair (ω, Z0  X(ω))  defined by the collection of valuations ω = ωσ in N, such that  ZX(ω) :=  �  ν∈ω  ZX(ν) ̸= ∅,  and an irreducible component Z0  X(ω) of ZX(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) A simplex σ of ∆N  E = ∆N  B+ corresponds to a subset ω ⊂ N, such that  ZY (ω) :=  �  ν∈ω  ZY (ν) ̸= ∅,  and an irreducible component, denoted as Z0  Y (ω) of the set  ZY (ω) :=  �  ν∈ω  ZY (ν).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The face relations are given by the inclusions of the sets of valuations and the  associated components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus, the dual valuation complexes could be thought of as ordinary  dual complexes of the exceptional divisors with the associated valuation structure so  that the vertices define the relevant exceptional valuations, and the faces determine  the sets of the valuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  43  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Dual complex associated with a locally monomial ideal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' If J is locally mono-  mial ideal on a regular scheme, such that codim(V (I)) ≥ 2, then one can asso-  ciate with J the normalized blow-up π : Y → X, and the full cobordant blow-up  πB : B → X of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The morphism π : Y → X is locally toric, and we shall call the  dual complexes ∆D, ∆D+ ≃ ∆E and the corresponding dual valuation complexes  ∆N  D, ∆N  D+ ≃ ∆N  E associated with J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Graded rings defined by the valuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Graded rings defined by valuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In the considerations below, let ω =  {ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νr} be a set of valuations on a regular scheme X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We associate with each  valuation νi a dummy variable ti for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Set  t := (t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk)  and  t−1 := (t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consider the partial componentwise order on Zr  ≥o.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For α := (a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ar) ∈ Zr  ≥0  we define the ideals  J α  ω :=  �  νi∈ω  Iνi,ai ⊂ OX,  J >α  ω  :=  �  β>α  J β  ω .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (5)  This determines the Zk  ≥0-graded Rees algebra  Aω :=  �  a∈Z≥0  J α  ω tα ⊂ OX[t],  where tα = ta1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tar  r , and the associated gradation  grω(OX) =  �  a∈Z≥0  (J α  ω /J >α  ω  )tα = Aω/(Aω ∩ t−1Aω]) = Aω[t−1]/(t−1 · Aω[t−1]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (6)  In particular, for α = 0 = (0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , 0) we have locally on X:  Jω := J >0  ω  = IZX(ω),  where  ZX(ω) :=  k�  i=1  ZX(νi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then grω(OX) is a sheaf of graded OX/Jω = OV (Jω)-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume the valuations in the set ω = {ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νr} are monomial  for a certain partial system of local parameters u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , un on a regular scheme X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then  (1) Jω = �k  i=1 Iνi,1 = (uj | νi(uj) > 0, for some νi ∈ ω) , and  (2) grω(OX) = OV (Jω)[u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαk], where ui ∈ J αi  ω  ∖ J >αi  ω  , and αi =  (ai1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ain), with νi(uj) = aij ∈ Z≥0 for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , r, and j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , n  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (1) Note that IZX(νi) = (uj | νi(uj) > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus  Jω = IZX(ω) =  �  ν∈ω  IZX(νi) = (uj | νi(uj) > 0, for some νi ∈ ω)  44  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  (3) By definition of Aω, the equality (5), and the Proof of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Aω[t−1] = (  �  ai∈Z≥0  r�  i=1  Iνi,ai · ta1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tar  r )[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  r ] =  = OX[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  r , u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , untαn]) = OX[t−1, u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , untαk],  where αi = (ai1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ain), and νi(uj) = aij ∈ Z≥0 for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , r, and j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus by the equality (6):  grω(OX) = Aω[t−1]/(t−1 · Aω[t−1] =  = (OX[t−1, u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , untαk])/(t−1) ≃  = (OX/Jω)[u1tα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , untαk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  We shall call the corresponding scheme  Nω(X) := SpecV (Jω)(grω(OX)) = SpecZX(ω)(grω(OX))  the weighted normal bundle of X at the set of valuations ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  One can extend this to any valuation face in ∆N  B , associated with a full cobordant  blow-up B → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the weighted normal bundle of X at the valuation face ω ∈  ∆N  B we mean the scheme  Nω(X) := SpecZ0  X(ω)(grω(OX))  over the component Z0  X(ω) of ZX(ω) associated with the face ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  As ∆N  E ⊂ ∆N  B the above definition is also valid for any valuation face ω ∈ ∆N  E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The ideals of the initial forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' With any function f ∈ OX,p, regular at  p ∈ V (J ), such that f ∈ J α  ω ∖ J >α  ω  , for a certain a ∈ N one can associate the  unique homogenous element, called the initial form  inω(f) = (f + J >α  ω  ) ∈ (J α  ω /J >α  ω  )tα  ω ⊂ grω(OX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Similarly, we associate with an ideal sheaf I, the filtration Iα  ω := I ∩ J α  ω and set  I>α  ω  = I ∩ J >α  ω  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We define the ideal of the initial forms of I to be the ideal  inω(I) =  �  α∈Z≥0  Iα  ω/I>α  ω  =  �  α∈Z≥0  (Iα  ω + J >α  ω  )/J >α  ω  ⊂ grω(OX)  on NJ (X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  For the ideal sheaf I, its weak ideal of the initial forms on NJ (X) is given by  in◦  ω(I) = grω(OX) · Iα0  ω /I>α0  ω  ⊂ grω(OX),  where I ⊂ J α0  ω , and I ̸⊂ J >α0  ω  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For any function f ∈ OX,  inω(f) = inω(OX · f) = in◦  ω(OX · f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  45  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Composition of gradations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let ω = {ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νr} be a set of valuations which are monomial for  a common partial system of local parameters u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , un on a regular X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider  its partition into subsets ω1 = {ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νs}, and ω2 = {νs+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νr}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let t :=  (t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tr) ( respectively tω1 := (t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ts)) be the set of the unknowns ti associated  to the valuations νi ∈ ω, ( respectively and νi ∈ ω1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Jω1 = (u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uℓ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  (1) The set ω2 = {νs+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νr} determines the set of monomial valuations  ω2 = {νs+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νr} on the multi-graded ring  grω1(OX) = OV (Jω1 )[u1tα1  ω1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uℓtαn  ω1 ] ≃ OV (Jω1 )[u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uℓ],  with the ideals  Iνi,ai = inω1(Iνi,ai)  (2) grω2(grω1(OX) ≃ grω(OX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) If I ⊂ OX then  (a) inω(I) = inω2(inω1(I)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (b) in◦  ω(I) = in◦  ω2(in◦  ω1(I)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (1) For j ≤ ℓ, inωw1(uj) is identified with uj in OV (Jω1 )[u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uℓ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Other-  wise if j > ℓ, then inωw1 (uj) is a parameter in OV (Jω1) = OX/Jω1 = OX/(u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uℓ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently νj determine the monomial valuations νj on grω(OX) with inω1(Iνj,a) =  (Iνj,a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) and (3) For the multiindex α = (α1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' α2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' where αi correspond to ωi for  i = 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' consider a function f ∈ J α  ω ∖ J >α  ω  :  f ∈ J α  ω ∖ J >α  ω  = J α1  ω1 ∩ J α2  ω2 ∖ (J >α1  ω1  ∩ J α2  ω2 + J α1  ω1 ∩ J >α2  ω2  )  The ideal inω1(J α2  ω2 ) ⊂ grω1(OX) is homogenous and inω1(f) is in α1-gradation  of inω1(J α2  ω2 )α1 ⊂ (grω1(OX))α1:  inω1(J α2  ω2 )α1 = J α1  ω1 ∩ J α2  ω2  J >α1  ω1  ∩ J α2  ω2  ⊆ (grω1(OX))α1 = J α1  ω1  J >α1  ω1  and  inω1(J >α2  ω2  )α1 = J α1  ω1 ∩ J >α2  ω2  + J >α1  ω1  ∩ J α2  ω2  J >α1  ω1  ∩ J α2  ω2  Consequently,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' by the above,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  inω2(inω1(f)) ∈ inω2(inω1(J α2  ω2 )α1) = (inω1(J α2  ω2 ))α1  (inω1(J >α2  ω2  ))α1  =  =  J α1  ω1 ∩ J α2  ω2  J α1  ω1 ∩ J >α2  ω2  + J >α1  ω1  ∩ J α2  ω2  = J α  ω  J >α  ω  = (grω1(OX))α  On the other hand the initial form  inω(f) ∈ J α  ω  J >α  ω  = (grω1(OX))α,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  determines the same element:  inω(f) = inω2(inω1(f)) ∈ (grω(OX))α = grω2((grω1(OX))α1)α2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  which implies (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  46  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The weighted normal bundles at valuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The following extends a  classical result of Huneke-Swanson on extended Rees algebras and smooth blow-ups  [HS06, Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5], and the recent results of Rydh in [QR19] and W�lodarczyk  in [W�lo22, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4] on the weighted normal cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a locally toric proper birational morphism to a  regular scheme X over a field κ, with the exceptional components Ei, for i = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , k  and let πB : B → X be its full cobordization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then for any stratum s = sω ∈ SD of  the exceptional divisor D = V (t−1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · t−1  k ) on B and the corresponding valuation  face ω in ∆N  B there is an isomorphism:  s ≃ Nω(X) × ˇtω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  where Tˇtω := Spec(κ[ˇtω,ˇt−1  ω ]), for the set ˇtω of the unknowns corresponding to the  remaining exceptional valuations which are not in ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We can replace X with its open subset and assume ZX(ω) is irreducible so  that πB(s) = Z0  X(ω) = ZX(ω) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By separating variables into tω and ˇtω we can factor any monomial tα = tα  ω · ˇtα  ω  uniquely into the product of the relevant monomials tα  ω and ˇtα  ω respectively in tω  and ˇtω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then by Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3(2), we can write s = V (t−1  ω ) in a neighborhood of  s, and s = V (t−1  ω ) ∖ V (ˇt−1  ω ) as there is only one component of V (t−1  ω ) mapping to  πB(s) = Z0  X(ω) = ZX(ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By definition B = Spec(A[t−1]), where  A =  �  α∈Zk  ≥0  J αtα,  J α :=  k�  i=1  Iνi,ai ⊂ OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let  Aω =  �  α  J α  ω tα  ω,  J α  ω :=  �  νi∈ω  Iνi,ai ⊂ OX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus for the open subset Bω ⊂ B where ˇt−1  ω  are invertible we can write:  Bω := Bˇt−1  ω  = SpecX(A[t−1][ˇtω]) = SpecX(Aω[t−1  ω ])[ˇtω,ˇt−1  ω ])  Consequently s = VBω(t−1  ω ) ⊂ Bω, by Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3(2), so we can write  Os = Aω[t−1  ω ][ˇtω,ˇt−1  ω ]/(t−1  ω ) = (Aω[t−1  ω ]/((t−1  ω · Aω[t−1  ω ]))[ˇtω,ˇt−1  ω ] =  = (Aω/((t−1  ω · Aω) ∩ Aω))[ˇtω,ˇt−1  ω ] = grω(OX)[ˇtω,ˇt−1  ω ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The latter equality follows from Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The weak and the strict transforms and the ideal of the initial forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The  identification from Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1 can be extended to the strict transforms of the  ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The following generalizes the result from [W�lo22, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4] for the  weighted blow-ups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X be a regular scheme over a field Let B → X be the full  cobordant blow-up of a locally monomial center J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let I ⊂ OX be an ideal sheaf  on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let σs(I) ⊂ OB be the strict transform of I, and σ◦(I) ⊂ OB be its weak  transform (see Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then for any s ∈ SD, the natural isomorphism  Os ≃ OB[ˇtω,ˇt−1  ω ]/(t−1  ω ) → grω(OX)[ˇtω,ˇt−1  ω ]  takes  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  47  (1) σs(I)|s onto inω(I)[ˇtω,ˇt−1  ω ] ⊂ grω(OX)[ˇtω,ˇt−1  ω ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) σ◦(I)|s onto in◦  ω(I)[ˇtω,ˇt−1  ω ] ⊂ grω(OX)[ˇtω,ˇt−1  ω ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let f ∈ I such that f ∈ J α ∖ J >α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the definition of  OB = (  �  α≥0  J αtα)[t−1]  we conclude that σs(f) = tαf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then f ∈ J α  ω ∖ J >α  ω  , and in a neighborhood of s we have that ˇt−1  ω  is invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the strict transform  σs(f) = tαf = tα  ωˇtα  ωf ∈ J αtα ⊂ J α  ω tα  ω[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  and its reduction modulo (t−1  ω OB ∩J α  ω )tα = J >α  ω  tα can be written as the homoge-  nous element  σs(f) = tαf + tαJ >a  ω  = tα  ωˇtα  ωf + tα  ωˇtα  ω · J >a  ω  in  OB[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ]/(t−1  ω · OB[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ]) = grω(OX)[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ]  in the gradation  J α  ω tα  ω[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ]/(t−1  ω OB[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ] ∩ OB[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ])  = (J α  ω /J >a  ω )tα  ω[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ] ⊂ grω(OX)[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ]  On the other hand f determines its initial form  inω(f) = (f + J >α  ω  )tω ∈ (J α  ω /J >α  ω  )tα  ω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  and thus,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' by the above σs(f) naturally and bijectively corresponds to  ˇtα  ω inω(f) ∈ (J α  ω /J >α  ω  )tα  ω[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ] ⊂ grω(OX)[ˇtω,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='ˇt−1  ω ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The latter differs from inω(f) by the unit ˇtα  ω:  ˇtα  ω inω(f) ∼ inω(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordant resolution by locally monomial centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Weighted normal cone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X be a regular scheme over a field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Y ⊂ X be a closed  reduced subscheme with the ideal IY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let ω be a set of monomial valuations for a  partial system of local parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The subscheme Cω(Y ) = V (inω IY ) ⊂ Nω(X)  will be called the weighted normal cone of Y at ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X be a regular universal catenary scheme over a field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let  Y ⊂ X be a subscheme of pure codimension d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let ω be a set of monomial valuations  for a common partial local system of parameters u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then Cω(Y ) is  of pure codimension d in Nω(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let ω = {ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νr} and ω1 = {ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νr−1} be its subset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then, by  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7, we can write  inω(I) = inνr(inω1(I)),  where νr is monomial on  Nω1(X) = Spec(grω1(OX)) = Spec(OV (Jω1 )[u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uℓ])  48  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  is also universally catenary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Here we assume without loss of generality that Jω1 =  u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uℓ for ℓ ≤ k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By the inductive argument for inω1(I) on Nω1(X) we can reduce the situation  to a single monomial valuation ν = νr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let ν(u1) = w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ν(uk) = wk, and find some integers a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ak such that  a1w1 = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' = akwk,  Consider the full cobordant blow-up B of I = (ua1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uak  k )  B = SpecX(OX[t−1, u1tw1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktwk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We apply the argument from [W�lo22, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the assumption, B is  catenary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let d be the codimension of Y in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then for the morphism  πB− : B− = B ∖ V (t−1) = X × Gm → X,  the inverse image π−1  B−(Y ) is of pure codimension d in B−.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So it is its scheme-  theoretic closure Y ′ := πB−(Y ), which is the strict transform V (σs(I)) of Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Note that t−1 is not a zero divisor in  Y ′ = V (σs(I)) = Spec(OB/σs(I)),  since t−1f ∈ σs(I) implies f ∈ σs(I), by definition of the strict transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then, by the Krull Hauptidealsatz, we have that each component of Y ′ ∩V (t−1)  is of codimension 1 in Y ′, and of codimension d + 1 in B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We conclude that each  component of  Y ′ ∩ V (t−1) = V (Ot−1 · σs(I)) = Cν(Y ) ⊂ Nν(X)  is of codimension d in V (t−1) = Nν(X).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordant resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' For any scheme Y , let Sing(Y ) denote its singular  locus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  For any ideal I on X by Sing(V (I)) we mean the singular locus of the  scheme  V (I) = SpecX(OX/I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The following theorem extends [W�lo22, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X be a regular universally catenary scheme over a field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let  Y ⊂ X be an integral, closed subscheme of pure codimension d defined by IY .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Assume there is a locally monomial ideal J ⊃ IY on X, with the cosupport  V (J ) of codimension ≥ 2, and with the associated exceptional divisor E on the  normalized blow-up σ : Y = blJ (X) → X, and the dual valuation complex ∆N  E such  that  (1) Sing(V (IY )) ⊆ V (J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) For any valuation face ω ∈ ∆N  E ⊂ ∆N  B , and the ideal inω(IY ) ⊂ grJω(OX)1  we have  SingNω(X)(V (inω IY )) ⊆ V (in◦  ω J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  1Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  49  (respectively  (2’) For any valuation face ω ∈ ∆N  E ⊂ ∆N  B , we have  SingNω(X)(V (in◦  ω IY )) ⊆ V (in◦  ω J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=')  Then the cobordant blow-up B+ → X of J defines a cobordant resolution of Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  That is, the strict transform Y ′ = V (σs(IY )) of Y (respectively the weak transform  Y ′ = V (σ◦(IY )) of Y ) is a regular subscheme of B+ of the codimension equal to  the codimension of Y in X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The problem is local on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus, up to a torus factor, we can assume that  the full cobordant blow-up of J is given locally on X by  σ : B = Spec(OX[t−1, tα1u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tαkuk]) → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then for the restriction morphism πB− : B− = X × T → X, the inverse im-  age π−1  B−(Y ) is irreducible of codimension d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  So is its closure Y ′ := σ−1(Y ) =  V (σc(IY )), which is the strict transform of Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Since V (J ) is of codimension ≥ 2,  the divisor D = VB(t−1) is exceptional for B → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Observe that  Sing(Y ′) ∖ D = Sing(Y ′) ∩ B− ⊂ V ◦  B−(J ) ⊆ VB(σ◦(J ))  On the other hand, the exceptional divisor D+ = D|B+ is the union of the strata  s+ ∈ SD+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3(4),(5), each such a stratum s+ extends to s ∈ SD,  and corresponds to the valuation face ω ∈ ∆N  D+ = ∆N  E ⊂ ∆N  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Since the singular locus of V (inω IY ) is contained in V (in◦  ω(J )) and by Lemmas  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3, we have  Sing(Y ′ ∩ s) = SingNω(X)(V (inω IY )) × ˇtω ⊆ V (in◦  ω J ) × ˇtω = VB(σ◦(J )|s),  Then using Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1 we conclude that the subscheme  Y ′ ∩ s ≃ V (inω IY )) × ˇtω  is of pure codimension d in s ≃ Nω(X) × ˇtω, and  (Y ′ ∩ s) ∩ B+ = ((Y ′ ∩ s) ∖ VB(σ◦(J ))  is regular of codimension d in s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Hence for p ∈ ((Y ′ ∩ s) ∖ VB(σ◦(J )), we can find parameters v1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' vd ∈ Os,p ·  IY ′ = (OB,p · IY ′)/(t−1  ω ) at p which vanish on Y ′ ∩ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' But these parameters come  from local parameters in IY ′ on B at p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So they define a regular subscheme Y ′′  of B+ of codimension d, containing locally Y ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus Y ′′ locally coincides with Y ′  which must be regular at p ∈ s∖VB(σ◦(J )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consequently Sing(Y ′) is contained in  VB(σ◦(J )), and, by Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, Y ′ is a regular subscheme of B+ = B∖VB(σ◦(J ))  of codimension d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The proof for the weak transform σ◦(I) (with stronger assumptions in condition  (2’)) is identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  As a corollary, we obtain the following:  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X be a smooth variety over a field κ of any characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let Y ⊂ X be a closed integral subscheme of X Assume there is a locally monomial  ideal J ⊃ IY on X , with the cosupport V (J ) of codimension ≥ 2, and with the  associated exceptional divisor E on the normalized blow-up σ : Y = blJ (X) → X,  and the dual valuation complex ∆N  E such that  50  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  (1) Sing(V (IY )) ⊆ V (J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) For any valuation face ω ∈ ∆N  E , the ideal the singular locus  SingNω(X)(V (inω IY )) ⊆ V (in◦  ω J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then there is a resolution of Y at Z, that is, a projective birational morphism  φ : Y res → Y from a smooth variety Y res with the exceptional locus Z ⊂ Y , such  that φ−1(Z) is an SNC divisor on Y ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Take the cobordant resolution B+ → X from Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We use Section  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4 to embed cobordant blow-up B+ as a smooth subspace of the relative affine  space An  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This implies that B+ � T is locally toric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The locally toric singularities of B+ � T can be canonically resolved by the  combinatorial method of [W�lo20, Theorem 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This produces the projective  birational resolution Y ′ → Y of Y such that the inverse image of the singular point  is an SNC divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Resolution of hypersurfaces via the Newton method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Newton polytope of a monomial ideal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X = Ak  Z = Spec(OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk]),  where Z is a smooth scheme over κ, and I ⊂ OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk] is an ideal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' One can  extend the notion of the Newton polytope of monomial ideals I = (xα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xαk) ⊂  κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn] considered previously in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1 in the case Z = Spec(κ), where  κ is a field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  As before, by the associated Newton polytope of I we mean  PI := conv(α1 + Qn  ≥0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , αk + Qn  ≥0) ⊆ Qn  ≥0  Conversely, with a polytope P ⊂ Qn  ≥0 we associate the monomial ideal  IP := (xα | α ∈ P ∩ Zn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The initial forms defined by faces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (see [AQ21]) If I = (xα)α∈A ⊂ OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn] is a monomial  ideal and PI is its Newton polytope and P ≤ PI be its face, we define the initial  form with respect to a face of the PI to be:  invP (I) := (xα | α ∈ A ∩ P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The definition invP (I) is a particular case of the notion o the initial form inv◦  ω(I)  with respect to a valuation face ω ∈ ∆N  E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='13 we obtain  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let ∆N  E be the valuation dual complex associated with a monomial  ideal I, and let P = PI be its Newton polytope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Any valuation face ω ∈ ∆N  E of the associated dual valuation complex ∆N  E defines  the induced face  Pω := P ∩  �  ν∈ω  Hν  of the Newton polytope P, for the supporting hyperplanes Hν associated with ν and  we have:  inv◦  ω(I) = invPω(I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  51  Conversely for any supporting face P ′ of P there is a valuation face ω ∈ ∆N  E ,  such that inv◦  ω(I) = invPω(I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The above correspondence is not bijective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Several valuation faces  ω could define the same supporting face of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The information encoded in the dual  valuation complex is richer and can be applied to a more general setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Newton polytopes of polynomials and ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the Newton polytope of  the function  f =  �  cαxα ∈ O(Z)[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk],  where cα ∈ O(Z) we mean the Newton polytope of the monomial ideal  Jf := (xα | cα ̸= 0),  generated by the exponents α occurring in the presentation of f with nonzero  coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Note that Jf is the smallest monomial ideal which contains f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This definition can be extended to any ideal I ⊂ OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We associate  with I the monomial ideal J = JI generated by If, where f ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Newton  polytope PI of I is simply the Newton polytope of the monomial ideal J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If P ≤ PI is a face of the Newton polytope PI, and f = �  α∈A cαxα ∈ I we put  invP (f) :=  �  α∈A∩P  cαxα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then invP (I) is the ideal generated by invP (f), where f ∈ I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let ∆N  E be the dual valuation complex associated with a monomial ideal J ⊂  OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Recall that, by Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, and using identification :  grωOZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk] = OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk], for any valuation face ω ∈ ∆N  E we write  invω(f) :=  �  α∈Aω,f  cαxα ∈ grω(OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk]) = OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  where  Aω,f = {α ∈ A | ν(xα) = ν(f), ν ∈ ω}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Similarly for the ideal I ⊂ OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk] the ideal of the initial forms inv◦  ω(I)  is generated by all invω(f), where f ∈ I, and ν(f) = ν(I) for all ν ∈ ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The following is an immediate consequence of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, and the above:  Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Pf (respectively PI) be the Newton polytope of f = � cαxα  (respectively of an ideal I ⊂ OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk]), and let Jf (respectively JI) be the  associated monomial ideal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then for any valuation face ω ∈ ∆N  E of the associated  dual valuation complex ∆N  E and the corresponding face Pω of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  invω(f) = invPω(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (respectively  inv◦  ω(I) = invPω(I)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  52  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Resolution by the Newton polytopes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The following is a particular case of  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5 for hypersurfaces, written in a more straightforward setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' X = An  Z = Spec OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk], where Z is a regular scheme  over a field κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let  f =  �  α∈Af  cαxα ∈ OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk]  where cα ̸= 0 for α ∈ Af.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let J = (xα | α ∈ Af)sat be the induced monomial ideal,  and Pf = PJ be its Newton polytope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that  (1) The cosupport V (J ) is of codimension ≥ 2,  (2) Sing(V ((f)) ⊆ V (J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) For any supporting face P of Pf, Sing(V (inP (f)) ⊂ V (inP (J )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the cobordant blow-up B+ → X of J resolves the singularity of V (f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' That is,  the strict transform Y ′ = V (σs(f)) of Y (which coincides with the weak transform  V (σ◦(f)) of Y ) is a regular subscheme of B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4, and the assumption (3) we get that  Sing(invω(f)) = Sing(inv◦  ω(f)) ⊂ V (in◦  ω(J )),  for any ω ∈ ∆N  E and the corollary follows from Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The theorem shows that in the case of hypersurface V (f) the  critical combinatorial information is related to the faces P of the Newton polytope  Pf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Generally, one considers the dual valuation complex ∆N  E associated with the  ideal I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In such a case, invP (f) is replaced with more general invω(I), and the  role of the Newton polytope of a monomial ideal is limited (see Theorems 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5,  Theorems 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' However, it still can be used in the context of the order of the  ideals in OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk] (see Theorems 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  One can easily extend these results to the products of schemes:  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X = �  Z Xj, where each Xj = Anj  Z  = Spec(OZ[xj]) =  Spec OZ[xj1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xjkj], where Z is a regular scheme over a field κ for j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let  fj =  �  α∈Afj  cjαxjα ∈ OZ[xj1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xjkj ]  where cjα ̸= 0 for α ∈ Afj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let  Jj = (xα  j | α ∈ Afj)sat ⊂ OZ[xj]  be the induced monomial ideal, and Pfj := PJj be its Newton polytope in Qkj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Assume that for any j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , r  (1) The cosupport V (Jj) is of codimension ≥ 2,  (2) Sing(V (fj)) ⊆ V (Jj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) For any supporting face P of Pfj,Sing(V (inP (f)) ⊆ V (inP (Ji)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the cobordant blow-up B+ → X of �r  j=1 OX · Ji resolves the singularity of  V (f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , fk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  That is, the strict transform Y ′ = V (σs((f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , fk)) of Y is a  regular subscheme of B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  53  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The cobordant blow-up of �r  j=1 OX · Ji is equal to the product over Z of  the cobordant blow-ups Bj+ of Ji on Spec(OZ[xj]), each of which is smooth over  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Abramovich-Quek resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The following result is due to Abramovich-  Quek (with some minor modifications):  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' [AQ21, Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2] Let X = An  Z = Spec OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn],  where Z is a regular scheme over a field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider the induced SNC divisor D :=  V (x1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · xn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let  f =  �  α∈Af  cαxα ∈ O(Z)[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk]  where cα ̸= 0 for α ∈ Af.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let J = Jf := (xα | α ∈ Af) be the associated monomial  ideal, and Pf := PJ be its Newton polytope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that the cosupport V (J ) is of  codimension ≥ 2, and for any face P of Pf, the ideal (inP (f)) determines a smooth  subscheme outside of D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the cobordant blow-up B+ → X of J resolves the singularity of V (f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' That  is, the strict transform Y ′ = V (σs(f)) = V (σ◦(f)) of Y is a regular subscheme of  B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Note that unlike in the original formulation the coefficients cα are  not necessarily invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1 is further generalized for the ideals in the  context of order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' See Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let σ∨  0 = Qn  ≥0 = ⟨x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn⟩ be the cone corresponding to the ring  OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  It suffices to show that conditions (2), (3) of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9 are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  To prove condition (3) let P ′ be any supporting face of Pf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5,  there is a stratification of X with strata sτ, where τ is a face of σ0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It is determined  by the pull-back of the orbit stratification on Xσ0, via X = Xσ0 × Z → Xσ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Assume that sτ is not in V (in◦  P ′(J )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This means, by Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6, that τ ∗  intersects P ′ so we consider the face P := P ′ ∩ τ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5, we  can write the closure of the stratum sτ as  sτ := V (xi | xi ̸∈ τ∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  On the other hand, since P ⊂ τ∗, the polynomial inP (f) ∈ OZ[xi ∈ τ ∗] ⊂  OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn] can be identified with  inP (f)|sτ ∈ OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn]/(xi | xi ̸∈ τ ∗) ≃ OZ[xi ∈ τ ∗].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Now inP (f) is simply equal to  inP (f)|sτ = inP ′(f)|sτ ,  By the assumption inP (f) ∈ OZ[xi ∈ τ∗] is a local parameter on  Spec(OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn] ∖ V (  �  xi)  =  (Spec(OZ[xi ∈ τ ∗]) ∖ V (  �  xi∈τ ∗  xi))  ×  (Spec(OZ[xi ̸∈ τ ∗]) ∖ V (  �  xi̸∈τ ∗  xi)),  54  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  and on  (Spec(OZ[xi ∈ τ ∗]) ∖ V (  �  xi∈τ ∗  xi)) ≃  ≃ V (xi | xi ̸∈ τ∗) ∖ V (  �  xi∈τ ∗  xi)) = sτ ∖ V (  �  xi∈τ ∗  xi)) = sτ  Consequently inP (f)|sτ = inP ′(f)|sτ defines a local parameter on the stratum sτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This implies that inP ′(f) is a local parameter on all strata sτ outside of V (in◦  P ′(J )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The proof of condition (2) is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider any face τ of σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' If sτ is not in  V (J ), then, by Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6, τ intersects Pf so we consider the face P := Pf ∩τ ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently, by the assumption  (inP (f))|sτ = f|sτ ∈ OZ[xi ∈ τ∗]  defines a local parameter on the stratum  sτ = sτ ∖ V (  �  xi∈τ ∗  xi),  This implies that f is a local parameter on all strata sτ outside of V (J ), showing  condition (2) of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9 and completing the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Z be a regular scheme over a field κ, and X = �  Z Xj, where  Xj := Anj  Z = Spec O(Z)[xj1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xjkj ] for j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let  fj =  �  α∈Afj  cjαxjα ∈ OZ[xj1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xjkj ]  where cjα ̸= 0 for α ∈ Afj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Jj := (xα  j | α ∈ Afj) be the induced monomial  ideal, and Pfj := PJj be its Newton polytope in Qkj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that for any j =  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , r the cosupport V (Jj) is of codimension ≥ 2, and for any face P of Pfj,  the ideal (inP (fj)) determines a smooth subscheme outside of V (xj1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · xjkj ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the cobordant blow-up B+ → X of �r  j=1 OX · Ji resolves the singularities  of V (f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , fk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' That is, the strict transform Y ′ = V (σs((f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , fk)) of Y is a  regular subscheme of B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Examples of resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let X = SpecZ(OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk]), where Z is a smooth variety  over a field κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider the closed subscheme Y on X defined by a function f ∈  H0(X, OX) of the form  f =  k  �  i=1  cαi(v)xαi,  where cαi(v) ∈ O(Z)∗ are invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Assume that for the presentation of f, one of the following holds:  char(κ) = 0, and for any αi except possibly one, there is a variable xji such  that a power x  aji  ji  of xji, occurs in xαi and xji does not occur in the others  xαj for j ̸= i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  char(κ) = p, and for any αi except possibly one there is a variable xji such  that a power x  aji  ji  of xji, occurs in xαi, with p ∤ aji and xji does not occur  in the others xαj for j ̸= i except as some k · p-th power for k ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  55  Then the cobordant blow-up B+ → X of J = (xα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xαk) resolves singularity,  so that the strict transform πs  B(f) determines a regular subscheme σs(Y ) of B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let D(f) be the ideal generated by f, and all the derivatives D(f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' At any  point p of Sing(f) , we have that ordp(f) ≥ 2 which implies Sing(V (f)) = V (D(f)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  But the ideal D(f) contains all but possibly one monomials xαi ∼ xj(i)Dxj(i)(f) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Since f = �k  i=1 cαi(v)xαi, and all but at most one monomial xαi are in D(f) we  conclude that D(f) ⊇ J = (xα1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xαk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So  Sing(Y ) = V (D(f)) ⊆ V (J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Similarly  Sing(inP (f)) = V (D(inP (f)) ⊆ V ((in◦  P (J )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus the conditions of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9 are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let f = xa1  1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' + xak  k ∈ κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk], where the characteristic  p divides at most one ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the cobordant blow-up of (xa1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xak  k ) resolves  singularity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6, it is given by  B = SpecX(OX[t−1, x1tw1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xktw  k ])  B+ = B ∖ VB(σs(J )) = B ∖ VB(x1tw1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xktwk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The morphism B+ → X is interpreted in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4 as the cobordant blow-up  of the weighted center J = (x1/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , x1/wk  k  ), such that OB+ · J = OB+ · t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  xp  1 + axp  2x3 + bx1xp  4xp2  5 ∈ κ[x1, x2, x3, x4, x5, ],  where a, b ∈ κ∗can be resolved by the single cobordant blow-up of  J = (xp  1, xp  2x3, x1xp  4xp2  5 )  over a field κ of characteristic p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Here for xp  2x3 the variable x3 does not occur in  the other terms, and for x1xp  4xp2  5 the coordinate x1 occurs in the other terms as xp  1  power or does not show at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  x2  1x5  2 + 7x7  4x5  3 + 25x1x6  3 ∈ κ[x1, x2, x3, x4]  can be resolved by the cobordant blow-up of  J = (x2  1x5  2, x7  4x5  3, x1x6  3)  over a field κ of char(κ) ̸= 5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We use x2 for x2  1x5  2, and x4 for x7  4x5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Z be a smooth variety over a field κ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let  X = SpecZ(OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xn]) = SpecZ(OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xr]),  where  xi := (xki−1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xki−1),  for k0 = 1 < k1 < .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' < kr = n + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider the closed subscheme Y of X defined  by the set of the polynomial functions fj ∈ H0(X, OX), where j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , r of the  form  fj =  rj  �  i=1  cαij(v)xαij  j  ,  56  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  where cαij(v) ∈ O(Z)∗ are invertible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Assume that for any j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , r and for the presentation of fj one of the  following holds:  char(κ) = 0, and for any αij except possibly one, there is a variable xji  such that a power x  aji  ji  of xji, occurs in xαij and xji does not occur in the  others xαi′j for i′ ̸= i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  char(κ) = p, and for any αij except possibly one there is a variable xji such  that a power x  aji  ji  of xji occurs in xαij , with p ∤ aji and xji does not occur  in the others xαi′j for i′ ̸= i except as some k · p-th power for k ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the cobordant blow-up B+ → X of  J =  r  �  j=1  (xα1  j , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xαk  j )  resolves singularity, so that the strict transform σs(f1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , fr) determines a smooth  subvariety of B+.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The space X can be written as the fiber product  X =  �  Z  Aki−ki−1  Z  =  �  Z  SpecZ(OZ[xj]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The cobordant blow-up of J is equal to the product over Z of the cobordant blow-  ups Bj+ of (xα1  j , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xαk  j ) on SpecZ(OZ[xj]), and each of Bj+ is smooth over Z by  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The system of equations  xp  1 + ax1xp  2x3 + bx4xp  5xp2  6  = 0  yp3  1 + cyp2  2 y3y6 + dy1yp  4yp2  5 y2  6  = 0  in  κ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , x6, y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , y5],  where a, b, c, d ∈ κ∗, can be resolved by the single cobordant blow-up of  J = (xp  1, xp  2x3, x1x4xp  5xp2  6 ) · (yp3  1 , yp2  2 y3, y4yp  5yp2  6 )  in characteristic p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let fj = xa1  1j + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' + xak  kjj ∈ κ[xij], where j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , k and the  characteristic p divides at most one aij for any j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then the cobordant blow-up of  �  j(xa1  1j , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xak  kjj) resolves singularity of V (fj)j=1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=',k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Partial resolution by the order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The method can be linked to different  invariants, particularly to the order  ordp(I) := max{k | Ip ⊂ mk  p},  where mp ⊂ OX,p is the maximal ideal of a point p ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let I be an ideal on a regular scheme X, and d ∈ N be an  integer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We define  supp(I, d) := {p ∈ X | ordp(I) ≥ d}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The following theorem extends [W�lo22, Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1]:  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  57  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let I be an ideal on a regular scheme X over a field, and let  d ∈ N be any natural number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume that there exists a locally monomial center  J , with codim(V (J ) ≥ 2, with the associated dual valuation complex ∆N  E , and such  that  (1) supp(I, d) ⊆ V (J ) ⊂ X,  (2) supp(inω(I), d) ⊆ V (in◦  ω(J )) ⊂ Nω(X), for any ω ∈ ∆N  E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (respectively  (2’) supp(in◦  ω(I), d) ⊆ V (in◦  ω(J )) ⊂ Nω(X), for any ω ∈ ∆N  E .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=')  Then for the cobordant blow-up σ+ : B+ → X of J , the maximal order of the  strict transform σs(I) (respectively the weak transform σ◦(I)) on B+ is strictly  smaller than d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let q ∈ D+ = D ∖ VB(σ◦(J )), where D = V (t−1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' t−1  k ) is the exceptional  divisor of B → X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then there is ω ∈ ∆N  E , and the corresponding stratum s in SD  such that  q ∈ s ∖ V (σ◦(J )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3, there is a natural isomorphism s → Spec(grω(O)[ˇtω,ˇt−1  ω ]),  which takes σs(I)|s to inω(I)[ˇtω,ˇt−1  ω ] (and σ◦(J )|s to in◦  ω(J )[ˇtω,ˇt−1  ω ]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Conse-  quently  ordq(σs(I)) ≤ ordq(σs(I)|s) = ordq(inω(I)[ˇtω,ˇt−1  ω ]) < d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If  q ∈ B ∖ D ∖ V (σs(J )) = B− ∖ V (σs(J )) = (X ∖ V (J )) × T,  then since πB(q) ∈ X ∖ V (J ) we conclude that  ordq(σs(I)) = ordπB(q)(I) < d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The proof for σ◦(I) is the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Newton method of decreasing order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' As a corollary from Theorem  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, and Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4 we obtain:  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' X = An  Z = Spec OX[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk], where Z is regular over a field  κ of characteristic p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let I ⊂ OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk] be an ideal, and J = JI, be its  associated monomial ideal with the Newton polytope PJ = PI and d ∈ N be any  natural number such that  (1) codim(V (J )) ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (2) supp(I, d) ⊆ V (J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  (3) for any supporting face P of PJ , supp(inP (I), d) ⊂ V (invP (J )).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the maximal order of the weak transform σ◦(I) on B+ under cobordant blow-  up of J is strictly smaller than d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Thus we get  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' X = An  Z = Spec OX[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk], where Z is regular over a field  κ of characteristic p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let I ⊂ OZ[x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , xk] be an ideal, and J = JI, be its  associated monomial ideal with with codim(V (J ) ≥ 2, and let PJ = PI be its  Newton polytope and d ∈ N be any natural number such that for any face P of PJ ,  supp(inP (I), d) ⊂ D := V (x1·, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · xk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then the maximal order of the weak transform σ◦(I) under cobordant blow-up  B+ → X of J is strictly smaller than d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  58  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The proof uses similar arguments as the proof of Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We need  to show that the conditions of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1 are satisfied  For condition (3) of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, let P ′ be any supporting face of PI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider  the closure of the stratum sτ, where τ is a face of σ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  If sτ is not in V (in◦  P ′(J )) consider the face P := P ′ ∩ τ ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  supp(inP ′(I))|sτ , d) = supp(inP (f)|sτ , d)  is contained in sτ ∖ sτ = V (�  xi∈τ ∗ xi) so it is not in sτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This implies that  supp(inP ′(I)), d) is contained V (in◦  P ′(J ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The proof of condition (2) of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1 is the same, except we replace P ′  with PJ , in◦  P ′(J ) with J = in◦  PJ (J ) , and P with P = PJ ∩ τ ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus the corollary is a consequence of Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Remark 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Theorems 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2 generalize respectively Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9, and  Corollary 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We put I = (f), and d = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then Sing(V (f)) = supp((f), 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (See also Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='14)  Let Y ⊂ X = Spec κ[x, y, z] be described by the ideal  I = (xk + xy + yl,  zkl + xk−2zkl−1 + yk−2zkl−1)  of order 2, where gcd(k, l) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider the corresponding admissible monomial  ideal  J = (xk, xy, yl, zkl, xk−2zkl−1, yk−2zkl−1)  and its associated Newton polytope P generated by the exponents  (k, 0, 0), (1, 1, 0), (0, l, 0), (0, 0, kl) ⊂ σ∨ = ⟨e∗  1, e∗  2, e∗  3⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This corresponds to two supporting faces P1, P2 defined, respectively, by  (k, 0, 0), (1, 1, 0), (0, 0, kl),  and  (1, 1, 0), (0, l, 0), (0, 0, kl).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  They intersect at the face P12 = (1, 1, 0), (0, 0, kl).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The faces P1, P2 corresponds to the primitive vectors v1 = (a1, a2, a3) such that  a1k = a1 + a2 = a3kl,  and v2 = (b1, b2, b3), where  b1 + b2 = lb2 = klb3  in the dual plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' So  v1 = (l, l(k − 1), 1),  v2 = (k(l − 1), k, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  This defines the set of two extremal valuations ν1, ν2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then  inP1(I) = (xk + xy, zkl),  inP2(f) = (xy + yl, zkl),  inP12(f) = (xy, zkl).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By considering the ideals of the derivatives D(inP (f)) we see that in all cases  supp(inP (I), 2) = V (x, y, z)  Similarly supp(I, 2) = V (x, y, z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  59  The cobordant blow-up of J = (xk, x2y, yl) is described as  B = SpecX(OX[t−1  1 , t−1  2 , xtl  1tk(l−1)  2  , ytl(k−1)  1  tk  2, zt1t2] =  Spec(κ[t−1  1 , t−1  2 , xtl  1tk(l−1)  2  , ytl(k−1)  1  tk  2, zt1t2])  B+ = B ∖ V (σs(J )) = B ∖ tαJ ,  where σs(J ) = tαJ , and the coefficients are given by the exceptional divisor E =  α1E1 + α2E2 of the toric normalized blow-up of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  α1 = ν1(f) = a1k = a1 + a2 = a3kl = kl,  and  α2 = ν2(f) = b1 + b2 = lb2 = klb3 = kl  Thus  B+ = B ∖ V ((xk, xy, yl, zkl) · tkl  1 tkl  2 ),  By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='9, the cobordant blow-up B+ → X of J = (xk, xy, yl, zkl) decreases  the order of I to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Generalized cobordant blow-ups and Q-ideals  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordization with respect to subgroups Γ ⊂ Cl(Y/X) ⊗ Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be a proper birational morphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Γ ⊂  Cl(Y/X) ⊗ Q be a finitely generated subgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We define the full cobordization  (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' cobordization of π) with respect to Γ to be  B = BΓ := SpecX(π∗(  �  E∈Γ  OX(E))  B+ = BΓ  + = SpecY (  �  E∈Γ  OY (E)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The natural morphism BΓ  + → BΓ is an open immersion if  locally on X there are forms F = fx−E, with E ∈ Γ such that XF are open affine  and cover X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The proposition follows from the first part of the proof of Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be the normalized blow-up of the an I on a  normal scheme X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let Γ ⊂ Cl(Y/X) ⊗ Q be a finitely generated subgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  we define the full cobordant blow-up of I with respect to Γ (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' the cobordant  blow-up of I with respect to Γ) to be the full cobordization (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' cobordization  of) π with respect to Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' π : Y → X be the normalized blow-up of an ideal J on a nor-  mal scheme X, and let E0 be the exceptional Cartier divisor such that OY (−E0) =  OY · J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' If a finitely generated group Γ ⊂ Cl(Y/X) ⊗ Q contains divisor E0, then  BΓ  + = BΓ ∖ V (It−E0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The proof is identical to the proof of Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  60  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Simple cobordant blow-up of ideal I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be the normalized blow-up of an ideal I on a  normal scheme X, with the exceptional divisor E0, such that OY (−E0) = OY · I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By the simple cobordant blow-up of I on X we mean the cobordization BΓ  + of  π : Y → X with respect to the subgroup Γ = Z · E0 ⊂ Cl(Y/X) generated by E0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The simple cobordant blow-up of I is given by  B = SpecX(OX[t−1, It])int,  B+ = B ∖ V (It).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' It follows that OY (−nE0) = OY · In.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover π∗(OY (−nE0)) = (In)int  is the integral closure of In.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently  B = BΓ  I = SpecX(π∗(  �  n∈Z  OY (nE0)tnE0) = SpecX(OX[t−1, It])int,  under the identification of tE0 with t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4,  B+ = B ∖ V (σs(I)) = B ∖ V (It).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  and thus is described by the standard Rees extended algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordant blow-ups of Q-ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Valuative Q-ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The valuative Q-ideals were introduced in [ATW19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Here  we consider its particular version considered in [W�lo22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By valuative Q-ideals, or, simply, Q-ideals on a normal scheme  X we mean the equivalence classes of formal expressions I1/n, where I is the ideal  on X, and n ∈ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We say that two Q-ideals I1/n, and J 1/m are equivalent if the  integral closures of Im, and J n are the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In particular, if D is a Cartier effective divisor on X then any Q-Cartier effective  divisor  1  m · D determines the Q-ideal OX(−D)  1  m .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By the vanishing locus of J = I1/n we mean V (J ) = V (I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  One can define the operation of addition and multiplication on Q-ideals:  I1/n + J 1/m := (Im + J n)1/mn,  I1/n · J 1/m = (Im · J n)1/mn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  For any valuative Q-ideal J = I1/n on X we define the associated ideal of  sections on X:  JX := {f ∈ OX | f n ∈ Iint},  where Iint is the integral closure of I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In particular, for the effective Cartier divisor  D, we have the equalities  (OX(−D)1/m)X = OX(− 1  mD) = {f ∈ OX | div(f) − 1  mD ≥ 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  With any valuative Q-ideal J we associate the Rees algebra on X :  OX[J t]X =  �  n∈Z≥0  (J n)Xtn ⊂ OX[t],  and the extended Rees algebra on X:  OX[t−1, J t]X =  �  n∈Z≥0  J n  Xtn ⊕  �  −n∈Z<0  t−n ⊂ OX[t, t−1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  61  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cobordant blow-up of Q-ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let J = I1/m be a Q-ideal on X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider  the normalized blow-up π : Y → X of I, with the exceptional divisor E0 such that  OY (−E0) = OY · I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then OY ·I1/m is the Q-ideal OY (−E0)1/m, which corresponds to the Q-Cartier  exceptional divisor  1  mE0 on Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently, by the blow-up of the Q-ideal J = I1/m we mean the the normal-  ized blow-up π : Y → X of I, with the associated Q-Cartier divisor  1  mE0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Definition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By the simple cobordant blow-up/full cobordant blow-up of the  Q-ideal J = I1/m we mean the cobordization/full cobordization of the normalized  blow-up Y → X of J with respect to the group Γ = Z · 1  mE0 ⊂ Cl(Y/X) ⊗ Q  generated by  1  mE0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let σ : B → X be the simple full cobordant blow-up of the Q-ideal  J = I1/m on a normal scheme X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Then  B = SpecX(OX[t−1, J t])X  (1) B+ = B ∖ V (J t)  (2) OB+ · J = t−1 · OB+  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let π : Y → X be the normalized blow-up of I, E0 is the exceptional divisor  on Y such OX · I = OY (−E0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus, by [W�lo22, Proof of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4],  π∗(OY (− n  mE0) = (f ∈ π∗(OY ) = OX : f n ∈ π∗(OY (−mE0)) = (Im)int) = J m  X .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  giving the formula for B:  B = SpecX(π∗(  �  n∈Z  OY (n · (1/m) · E0)tn)) = SpecX(OX[t−1, J t])X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4,  B+ = B ∖ V (I · t−E0) = B ∖ V (J t−(1/m)E0) = B ∖ V (J t),  as (1/m)E0 generates Γ, and t(1/m)E0 corresponds to t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus the inverse image  of  OB+ · I1/m = OB+ · J = t−1OB+ · J t = OB+ · t−1  is a Cartier exceptional divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We use here the fact that the Q-ideal J t|B+ = OB+,  as J t = (Ita)1/a = (I · t−E0)1/a is trivial on B+ = B ∖ V (It−E0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  ♣  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Weighted cobordant blow-ups revisited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let πB : B → X be the simple  cobordant blow-up of the weighted center J = (u1/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , u1/wk  k  ), where u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk  is a partial system of local parameters on a regular scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Assume, first, that the  weights wi are relatively prime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The center J can be written as J = I1/m, where  I = (um/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , um/wk  k  ),  is the ideal, and the weights wi|m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let E0 be the exceptional divisor of the blow-up π : Y → X of J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let νE0 be  the associated exceptional valuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Using the toric chart, defined by u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk  one reduces the situation to the blow-up of the toric Q-ideal J on a toric variety  Xσ, where σ = ⟨e1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ek⟩ is regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The Q-ideal J = I1/m defines a piecewise  linear convex function  FJ = min( 1  w1  e∗  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , 1  wk  e∗  k) = 1/m · min( m  w1  e∗  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , m  wk  e∗  k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  62  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  The normalized blow-up of J defines a decomposition ∆ of σ into the maximal  subcones where FJ is linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let w := (w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , wk) , and  FJ (ei) = 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , FJ (w) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then ∆ is the star subdivision at ⟨w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Moreover, the vector mw corresponds to  mFJ = FI in the sense that they define the same Weil divisors , and w and  corresponds to E0, so the valuation νE0 on Y is associated with w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In particular,  νE0(ui) = e∗  i (w) = wi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Consequently, OY · (um/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , um/wk  k  ) = OY (−mE0) is the ideal of the Cartier  divisor mE0 on Y , associated with the integral function mFJ , and the Q-ideal  J = (u1/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , u1/wk  k  ) corresponds to the Q-divisor (1/m) · mE0 = E0 which is a  Weil divisor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The cobordant blow-up associated with the group Γ = Z·E0 = Cl(Y/X) is given  by the standard formula from Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3:  B = SpecX(π∗(  �  n∈Z  OY (nE0))tn = SpecX(OX[t−1, J t])X =  = SpecX(  �  ai∈Z  Iν,ai · ta1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tak  k ) =  = SpecX(OX[t−1, u1tw1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktwk]),  where wi = νE0(ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In general, for arbitrary weights, the simple cobordant blow-up of (u1/w1  1  , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , u1/wk  k  )  is associated with the group Γ = Z· 1  w0 E0 =  1  w0 ·Cl(Y/X), where w0 := gcd(w1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , wk),  and with the valuation w0ν, with  w0ν(xi) = wi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Now  Iw0ν,a = (ub1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · ubk  k ) |  k  �  j=1  bjwi ≥ a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Comparing gradations we see  �  a∈Z  Iw0ν,ata = OX[t−1, uitwi].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then  B = SpecX(π∗(  �  n∈Z  OY (n · (1/w0) · E0)tn =  = SpecX(  �  ai∈Z  Iw0ν,a · ta) = SpecX(OX[t−1, tw1x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , twkxk]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  By the above B+ = B ∖ V (J t) = B ∖ V (tw1x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , twkxk), and OB+ · J =  OB+ · t−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  These weighted cobordant blow-ups were studied in [W�lo22] and used for the  resolution of varieties in characteristic zero and some classes of singularities in pos-  itive and mixed characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' To a great extent, they are equivalent to the stack-  theoretic weighted blow-ups introduced and considered in [McQ19], and [ATW19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  63  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Multiple weighted cobordant blow-ups of Abramovich-Quek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In the  paper [AQ21], the authors consider the generalization of the weighted blow-ups,  so-called, multi-weighted blow-ups BlJ ,b, associated with a Q-ideal J and a vec-  tor b = (b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , bk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' They are constructed locally in toric charts in the language  of fantastacks and stack-theoretic quotients via Satriano combinatorial approach  [Sat13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' The multi-weighted blow-ups are used to prove the logarithmic resolution  on smooth toroidal ambient Artin stacks in characteristic zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  We give here a geometric interpretation of this construction in the language of  cobordizations with respect to a subgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' In particular, this approach does not  rely on coordinates or combinatorics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let π : Y → X be the normalized blow-up of a locally monomial center J on  a regular scheme over a field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Denote by E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , Ek the irreducible exceptional  divisors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Let ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νk be the associated exceptional valuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We consider the  full cobordant blow-up of J with respect to the subgroup  Γb := Z 1  b1  E1 ⊕ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' ⊕ Z 1  bk  Ek ⊂ Cl(Y/X) ⊗ Q,  for any positive integers b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , bk, and b = (b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , bk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Write  B = SpecX(π∗(  �  E∈Γb  OX(E)),  B+ = SpecY (  �  E∈Γb  OY (E)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  The generators  1  b1 E1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , 1  bk Ek are associated with the monomial valuations  νb  1 := b1ν1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , νb  k := bkνk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Then locally on X using the Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='2, and the proof of Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5(1) we  can write  B = SpecX(  �  ai∈Z  k�  i=1  Iνb  i ,ai · ta1  1 · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tak  k ) =  =  k�  i=1  OX[t−1  i , ujtνb  i (uj)  i  ][ˇti,ˇt−1  i ] =  = SpecX(OX[t−1  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , t−1  k , u1tαb  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uktαb  k]),  where  ˇti := t1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , ˇti, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , tk  u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , uk, is a system of coordinates on open U ⊂ X defining monomial  generators for J , and  tαb  i := tab  i1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tab  ik  k ,  with  ab  ij := νb  i (uj) = biνi(uj) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Note that under this correspondence t−1  i  �→ t  1  bi Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Let  E0 = a1E1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' + akEk  (7)  be the exceptional divisor of π : Y → X, for the relevant ai ∈ Z≥0, such that  OY (−E0) = OY · J .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' By Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='4,  B+ = B ∖ V (J t−E0) = B ∖ V (J tαb),  64  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' W�LODARCZYK  where tαb corresponds to t−E0, under t−1  i  �→ t  1  bi Ei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Thus by (7), αb = (b1a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , bkak),  and  B+ = B ∖ V (J t−E0) = B ∖ V (J tb1a1  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' · tbkak  k  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  In particular, if X is regular over a field and J is a locally monomial ideal on  X, then the full cobordant blow-up B of J with respect to Γb is regular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Multiple weighted blow-ups associated with Q-ideals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Consider the normalized  blow-up π : Y → X of a monomial Q-ideal J , with the associated exceptional  divisor E0 = a1E1 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' + akEk with rational, positive coefficients ai, as in Section  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' We choose b = (b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , bk) with bi ∈ Z>0, such that  Γb = Z 1  b1  E1 ⊕ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' ⊕ Z 1  bk  Ek ⊂ Cl(Y/X) ⊗ Q,  is the minimal subgroup of Cl(Y/X) ⊗ Q containing E0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Thus any monomial Q-ideal I and b = (b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' , bk) ∈ Zk  >0 determines a unique  associated cobordant blow-up B+ → X with respect to the group Γb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' This way, tak-  ing the stack-theoretic quotient, we obtain the Abramovich-Quek multiple weighted  blow-up [B+ � T ] → X from [AQ21], which is necessarily regular for a regular X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  References  [ADHL15]  Ivan Arzhantsev, Ulrich Derenthal, J¨urgen Hausen, and Antonio Laface, Cox rings,  2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' viii+530.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 3307753  [AKMW02]  Dan Abramovich, Kalle Karu, Kenji Matsuki, and Jaros�law W�lodarczyk, Torification  and factorization of birational maps, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 15 (2002), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 3, 531–572  (electronic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1896232 (2003c:14016)  [AQ21]  Dan Abramovich and Ming Hao Quek, Logarithmic resolution via multi-weighted  blow-ups, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [ATW17]  Dan Abramovich, Michael Temkin, and Jaros�law W�lodarczyk, Principalization of  ideals on toroidal orbifolds, JEMS, to appear, (2017), arXiv:1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='03185.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [ATW19]  , Functorial embedded resolution via weighted blowings up, arXiv e-prints  (2019), arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='07106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [ATW20]  Dan Abramovich, Michael Temkin, and Jaros�law W�lodarczyk, Relative desingular-  ization and principalization of ideals, arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='03659.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [BM97]  Edward Bierstone and Pierre D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Milman, Canonical desingularization in character-  istic zero by blowing up the maximum strata of a local invariant, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 128  (1997), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 2, 207–302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1440306 (98e:14010)  [BR19]  Daniel Bergh and David Rydh, Functorial destackification and weak factorization  of orbifolds, arXiv e-prints (2019), arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='00872.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [Cox95]  David A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Cox, The homogeneous coordinate ring of a toric variety, 1995, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 17–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  MR 1299003  [Dan78]  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Danilov, The geometry of toric varieties, Uspekhi Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Nauk 33 (1978),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 2(200), 85–134, 247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 495499  [DH98]  Igor V Dolgachev and Yi Hu, Variation of geometric invariant theory quotients, Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Hautes ´Etudes Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (1998), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 87, 5–56, With an appendix by Nicolas  Ressayre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1659282  [EH02]  Santiago Encinas and Herwig Hauser, Strong resolution of singularities in charac-  teristic zero, Comment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Helv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 77 (2002), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 4, 821–845.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1949115  [ER21]  Dan Edidin and David Rydh, Canonical reduction of stabilizers for Artin stacks  with good moduli spaces, Duke Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 170 (2021), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 5, 827–880.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 4255045  [EV03]  Santiago Encinas and Orlando Villamayor, A new proof of desingularization over  fields of characteristic zero, Proceedings of the International Conference on Algebraic  Geometry and Singularities (Spanish) (Sevilla, 2001), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 19, 2003, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 339–353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  MR 2023188  COX RINGS OF MORPHISMS AND RESOLUTION OF SINGULARITIES  65  [Ful98]  William Fulton, Intersection theory, second ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=', Ergebnisse der Mathematik und  ihrer Grenzgebiete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Folge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' A Series of Modern Surveys in Mathematics [Results in  Mathematics and Related Areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 3rd Series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' A Series of Modern Surveys in Mathe-  matics], vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 2, Springer-Verlag, Berlin, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1644323  [Hir64]  Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of  characteristic zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' I, II, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' of Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (2) 79 (1964), 109–203;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' ibid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (2) 79 (1964),  205–326.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 0199184  [HK00]  Yi Hu and Sean Keel, Mori dream spaces and GIT, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 48, 2000, Dedicated to  William Fulton on the occasion of his 60th birthday, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 331–348.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1786494  [HS06]  Craig Huneke and Irena Swanson, Integral closure of ideals, rings, and modules,  London Mathematical Society Lecture Note Series, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 336, Cambridge University  Press, Cambridge, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 2266432  [KKMSD73] George Kempf, Finn Faye Knudsen, David Mumford, and Bernard Saint-Donat,  Toroidal embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' I, Lecture Notes in Mathematics, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 339, Springer-Verlag,  Berlin, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 0335518 (49 #299)  [Kol07]  J´anos Koll´ar, Lectures on resolution of singularities, Annals of Mathematics Studies,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 166, Princeton University Press, Princeton, NJ, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 2289519 (2008f:14026)  [McQ19]  Michael McQuillan, Very fast, very functorial, and very easy resolution of singular-  ities, 2019, preprint, written with the collaboration of G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Marzo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [Oda88]  Tadao Oda, Convex bodies and algebraic geometry—toric varieties and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  I, 1988, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 89–94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 966447  [QR19]  Ming Hao Quek and David Rydh, Weighted blow-ups, 2019, in preparation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [Que20]  Ming Hao Quek, Logarithmic resolution via weighted toroidal blowings up, arXiv  e-prints (2020), arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='05939.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [Rei]  Miles Reid, What is a flip?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=', Colloquium Talk, Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Of Utah, Dec , 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [Sat13]  Matthew Satriano, Canonical Artin stacks over log smooth schemes, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 274  (2013), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 3-4, 779–804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 3078247  [Tha94a]  Michael Thaddeus, Stable pairs, linear systems and the Verlinde formula, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 117 (1994), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 2, 317–353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1273268  [Tha94b]  , Toric quotients and flips, Topology, geometry and field theory, World Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=', River Edge, NJ, 1994, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 193–213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1312182  [Tha96]  , Geometric invariant theory and flips, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 9 (1996), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 3,  691–723.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1333296  [Vil89]  Orlando Villamayor, Constructiveness of Hironaka’s resolution, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' ´Ecole  Norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Sup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' (4) 22 (1989), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 1, 1–32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 985852  [W�lo00]  Jaros�law W�lodarczyk, Birational cobordisms and factorization of birational maps,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Algebraic Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 9 (2000), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 3, 425–449.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 1752010 (2002d:14019)  [W�lo03]  , Toroidal varieties and the weak factorization theorem, Invent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 154  (2003), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 2, 223–331.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 2013783 (2004m:14113)  [W�lo05]  , Simple Hironaka resolution in characteristic zero, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 18  (2005), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' 4, 779–822 (electronic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' MR 2163383  [W�lo20]  Jaros�law W�lodarczyk, Functorial resolution except for toroidal locus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' Toroidal com-  pactification, Advances in Mathematics Volume 407, 8, October 2022, 108551.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  [W�lo22]  Jaros�law W�lodarczyk, Functorial resolution by torus actions, arXiv e-prints (2022)  arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='13846 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='  Department of Mathematics, Purdue University, 150 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content=' University Street,, West  Lafayette, IN 47907-2067  Email address: wlodarcz@purdue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
+page_content='edu' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/iNFMT4oBgHgl3EQf4jES/content/2301.12452v1.pdf'}
diff --git a/jNE4T4oBgHgl3EQfsQ20/content/tmp_files/2301.05215v1.pdf.txt b/jNE4T4oBgHgl3EQfsQ20/content/tmp_files/2301.05215v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e7788efb0a1ffb3b44a8db3fd7908e59722e07c1
--- /dev/null
+++ b/jNE4T4oBgHgl3EQfsQ20/content/tmp_files/2301.05215v1.pdf.txt
@@ -0,0 +1,583 @@
+A LUCAS ANALOGUE OF EULERIAN NUMBERS
+JOS´E AGAPITO RUIZ
+Abstract. The generalized Lucas numbers are polynomials in two variables with non-
+negative integer coefficients. Lucas versions of some combinatorial numbers with known
+formulas in terms of quotient and products of nonnegative integers have been recently
+given by replacing the integers in those formulas with their corresponding Lucas analogues.
+We instead use a recursive approach. In this sense, we give a recursive formula for Lucas-
+Narayana numbers derived from a recent formula in terms of Lucasnomials (the explicit
+Lucas version of binomial numbers). We propose a recursive definition for a Lucas ana-
+logue of the classical Eulerian numbers, which shows immediately that they are polynomials
+in two variables with nonnegative integer coefficients. We prove that they are palindromic
+like their standard counterparts. The recursive approach allows us to give Lucas analogues
+of many relevant combinatorial constants. In particular, Lucas versions for both Stirling
+numbers of the second kind and Motzkin numbers are presented.
+1. Introduction
+The generalized Lucas numbers are defined recursively by {0} = 0, {1} = 1, and
+(1)
+{n} = s{n − 1} + t{n − 2} ,
+for any integer n ≥ 2. It follows immediately from (1) that the generalized Lucas numbers
+{n} are polynomials in s and t with nonnegative integer coefficients. On specialization of s
+and t one can recover, for example, the nonnegative integers (s = 2, t = −1), the q-integers
+[n]q = qn−1
+q−1 = 1 + q + · · · + qn−1 (s = 1 + q, t = −q), the Chebyshev polynomials of the
+second kind Un−1(x) (U0(x) = 1, U1(x) = 2x, s = 2x, t = −1), and the Fibonacci sequence Fn
+(s = t = 1), which is at the core of recursion (1). Here are a few instances of the generalized
+Lucas numbers:
+{2} = s,
+{3} = s2 + t,
+{4} = s3 + 2st,
+{5} = s4 + 3s2t + t2,
+{6} = s5 + 4s3t + 3st2 .
+A useful combinatorial interpretation of {n} is derived from the standard interpretation
+of Fibonacci numbers via tiling. In this regard, we consider two types of tiles: monominoes
+(which cover one unit squares) and dominoes (which cover two unit squares), so that for a
+given configuration T using these tiles, we define its weight to be
+(2)
+wt T = s# of monominoes in T t# of dominoes in T .
+Furhermore, for any set T of tilings of this kind, the weight of T is defined to be
+(3)
+wt T =
+�
+T ∈T
+wt T .
+Clearly, wt T is a polynomial in s and t when T is finite, otherwise it is a formal power series.
+Let T (n) be the set of all tilings of a row of n squares. Figure 1 shows all possible tilings
+for n = 4. It is then easy to see by induction that for every n ≥ 1, we have
+{n} = wt T (n − 1) .
+Key words and phrases. Eulerian numbers, Lucas analogues, Recursive formulas.
+2020 Mathematics Subject Classification. Primary 03, 05, 11.
+1
+arXiv:2301.05215v1  [math.CO]  12 Jan 2023
+
+2
+J. AGAPITO RUIZ
+Figure 1: The tilings in T (4)
+The cardinality of T (n − 1) is precisely the Fibonacci number Fn (clearly, for T (0) = ∅ we
+assume |T (0)| = 1). Now, by tiling rows with a decreasing number of squares and piling them
+up we can make sense of the expression
+(4)
+{n}! = {n}{n − 1} · · · {2}{1} .
+This is the Lucas analogue of the factorial, the Lucastorial number. By convention {0}! = 1.
+Using the setting of Young diagrams, Identity (4) gives the weight of the set of all tilings of
+the standard staircase partition δn = (n − 1, n − 2, . . . , 1); namely
+wt T (δn) = {n}!
+Likewise, one can obtain a Lucas version of any expression given in terms of products and
+quotients of nonnegative integers by simply replacing each ocurrence of n in the expression
+with {n}. For instance, given 0 ≤ k ≤ n, the Lucasnomial is defined by
+(5)
+�n
+k
+�
+=
+{n}!
+{k}!{n − k}! .
+From this point of view, Lucasnomials are rational expressions in s and t a priori. However
+they are indeed polynomials in s and t with nonnegative integer coefficients. This follows from
+some combinatorial interpretations given by Gessel and Viennot [6], Benjamin and Plott [3],
+and Sagan and Savage [7]). More recently, using a model that involves lattice paths inside
+tilings of Young diagrams, Bennett et al.[4] have given another combinatorial interpretation
+for Lucasnomials that not only is simpler than the previous ones but also is more flexible for
+combinatorial proofs of identities involving Lucasnomials. Their combinatorial interpretation
+is also extendable to other familiar sequences of numbers like the Catalan numbers and their
+relatives. It is worth mentioning that Amdeberhan et. al. [2] have also studied the generalized
+Lucas sequence and the Lucas analogues of Binomial and Catalan numbers from an algebraic
+and number theoretical perspective.
+In general, given any array of numbers An,k, its Lucas analogue will be denoted by A{n,k}.
+An alternative natural way to obtain Lucas analogues of standard arrays of numbers is by
+generalizing their recursive relations in a straightforward manner. For instance, it is well-
+known that the following formula holds for binomial numbers Bn,k =
+�n
+k
+�
+,
+(6)
+Bn,k = Bn−1,k + Bn−1,k−1 .
+However, since {1} = 1, we do not get anything new by replacing 1 with {1} in (6). Therefore,
+we have to choose a different recursive relation. In this regard, there is a less familiar recursive
+formula for binomial numbers that we can work with; that is
+(7)
+Bn,k = (k + 1)Bn−1,k − (n − k − 1)Bn−1,k−1 .
+Keeping in mind that {n} = n when s = 2 and t = −1, a natural way of defining the Lucas
+analogue of (7) is
+(8)
+B{n,k} = {k + 1}B{n−1,k} + t{n − k − 1}B{n−1,k−1} .
+
+A LUCAS ANALOGUE OF EULERIAN NUMBERS
+3
+An immediate conclusion from (8) is that B{n,k} is a polynomial in s and t with nonnegative
+integer coefficients. Moreover, using as initial conditions B{n,0} = B{n,n} = 1 for n ≥ 0 and
+B{n,k} = 0 whenever n < k or k < 0, we can recover by induction the formula
+B{n,k} =
+{n}!
+{k}!{n − k}! .
+Hence, the Lucas version for binomial numbers obtained from generalizing the recursive rela-
+tion (7) agrees with the explicit formula for Lucasnomials.
+Another familiar array of nonnegative integers with combinatorial interpretations is the
+array of Narayana numbers, defined for 1 ≤ k ≤ n as
+(9)
+Nn,k = 1
+n
+�n
+k
+��
+n
+k − 1
+�
+.
+The corresponding Lucas-Narayana numbers are then given by
+(10)
+N{n,k} =
+1
+{n}
+�n
+k
+� �
+n
+k − 1
+�
+.
+The fact that Lucas-Narayana numbers are indeed polynomials in s and t with nonnegative
+integer coefficients was conjectured in [4], and later proved by Sagan and Tirrell [8] using
+special factoring properties of {n}. Recently, Garret and Killpatrick [5] gave a combinatorial
+proof of this fact by showing that the Lucas-Narayana numbers N{n,k} satisfy the formula
+(11)
+N{n,k} =
+�n − 1
+k − 1
+�2
++ t
+�n − 1
+k
+� �n − 1
+k − 2
+�
+,
+for 2 ≤ k ≤ n − 1 and n ≥ 1. Formula (11) shows that N{n,k} is a polynomial in s and t with
+nonnegative integer coefficients because it is expressed as a sum of products of Lucasnomials
+with coefficients in N[s, t]. Now, manipulating Formula (11) algebraically, we get a recursive
+formula for Lucas-Narayana numbers.
+Proposition 1. For any integers 2 ≤ k ≤ n − 1 and n ≥ 1, the Lucas-Narayana numbers are
+given by
+(12)
+N{n,k} = {k}{n − 1}
+{n − k}
+N{n−1,k} + t {n − k}{n − 1}
+{k}
+N{n−1,k−1} ,
+with initial conditions N{0,0} = 1, N{n,k} = 1 for n = k or k = 1, N{j,0} = 0 for j > 0, and
+N{n,k} = 0 for n < k.
+Formula (12) is the Lucas analogue of the not well-known recurrence relation satisfied by the
+classical Narayana numbers,
+Nn,k = k(n − 1)
+n − k Nn−1,k − (n − k)(n − 1)
+k
+Nn−1,k−1
+.
+We can recover from Proposition 1 the closed formula (10), by using induction again. Note
+that the polynomial nature of N{n,k} with nonnegative integer coefficients is not immediate
+from the recursive formula (12) this time.
+These two examples illustrate the elementary approach we will take for the rest of the
+paper.
+We show in Section 2 that a straightforward Lucas version of a recursive relation
+satisfied by the classical Eulerian numbers En,k gives a way of defining the Lucas-Eulerian
+numbers E{n,k}. It follows immediately from the definition that they are polynomials in s
+and t with nonnegative integer coefficients. We show that they are palindromic. Using the
+recursive definition of E{n,k}, we get a formula for E{n,1} that encourage us to conjecture a
+similar formula for the general case E{n,k}. In Section 3, we elaborate on the difficulties that
+arise when trying to give a Lucas analogue of a known alternating sum formula for Eulerian
+
+4
+J. AGAPITO RUIZ
+numbers that be compatible with our Lucas-Eulerian numbers. We end in Section 4 by making
+further comments on open problems and on Lucas analogues of Stirling numbers of the second
+kind and Motzkin numbers.
+2. Lucas-Eulerian numbers
+Among several equivalent variants of a known recurrence relation satisfied by the classical
+Eulerian numbers, we have the following formula
+(13)
+En,k = (k + 1)En−1,k + (n − k + 1)En−1,k−1 .
+A straightforward Lucas analogue of Formula 13 defines the Lucas-Eulerian numbers.
+Definition 1. The Lucas-Eulerian numbers are defined recursively by the formula
+(14)
+E{n,k} = {k + 1}E{n−1,k} + {n − k + 1}E{n−1,k−1} ,
+for any integers 0 ≤ k ≤ n, with initial conditions E{n,0} = E{n,n} = 1 for n ≥ 0 and
+E{n,k} = 0 for n < k or k < 0.
+n\k
+0
+1
+2
+3
+4
+5
+0
+1
+0
+0
+0
+0
+0
+1
+1
+1
+0
+0
+0
+0
+2
+1
+2s
+1
+0
+0
+0
+3
+1
+3s2 + t
+3s2 + t
+1
+0
+0
+4
+1
+4s3 + 3st
+6s4 + 8s2t + 2t2
+4s3 + 3st
+1
+0
+5
+1
+5s4 + 6s2t + t2
+10s6 + 25s4t + 16s2t2 + 2t3
+10s6 + 25s4t + 16s2t2 + 2t3
+5s4 + 6s2t + t2
+1
+Table 1: A sample of Lucas-Eulerian numbers
+It immediately follows from Definition 1 that the Lucas-Eulerian numbers are polynomials
+in s and t with nonnegative integer coefficients. Moreover, Table 1 indicates that they are
+palindromic. Note that for Lucasnomials B{n,k} and Lucas-Narayana numbers N{n,k}, this
+property is immediate because they both have closed formulas from where it is easy to check
+that B{n,k} = B{n,n−k} and N{n,k} = N{n,n−k+1}.
+Theorem 2. The Lucas-Eulerian numbers are palindromic.
+Proof. This is an immediate consequence of the bijection k �→ n − k = k′, which amounts to
+write
+E{n,n−k} = {n − k + 1}E{n−1,n−k} + {n − n + k + 1}E{n−1,n−k−1}
+as
+E{n,k′} = {k′ + 1}E{n−1,k′} + {n − k′ + 1}E{n−1,k′−1} .
+□
+Unlike Binomial and Narayana numbers, whose Lucas analogues have straightforward gen-
+eralizations of their explicit closed formulas, there is not an equivalent formula known for the
+classical Eulerian numbers; that is, in terms of a quotient of products of nonnegative inte-
+gers. There is a formula in terms of alternating sums though, but unfortunately the natural
+extension of the Lucas recurrence to negative numbers does not give a Lucas analogue of such
+formula that be polynomial in s and t with nonnegative integer coefficients. We elaborate
+more on this observation in Section 3.
+Using Definition 1 repeatedly we get an interesting formula for E{n,1}. We have
+(15)
+E{n,1} = {2}E{n−1,1} + {n} =
+n
+�
+j=0
+{n − j}{2}j .
+
+A LUCAS ANALOGUE OF EULERIAN NUMBERS
+5
+Expanding out the sum in Formula (15), and replacing {2} with x, we get the polynomial
+�
+An,1
+�
+(x) = {n}x0 + {n − 1}x1 + · · · + {1}xn−1 + {0}xn ,
+which is the Lucas version of the polynomial An,1(x) = xnPn,1
+� 1
+x
+�
+, where
+Pn,1(x) =
+�
+x d
+dx
+� �1 − xn+1
+1 − x
+�
+= x + 2x2 + · · · + nxn .
+Therefore, we have E{n,1} =
+�
+An,1
+�
+({2}). Note that when n + 1 is prime, the polynomials
+ϕn(x) = 1 + x + x2 + · · · + xn = 1 − xn+1
+1 − x
+,
+are the cyclotomic polynomials Φn+1(x) used in the definition of Lucas atoms [8]. They provide
+a convenient factorization of {n}. Recall also that there is a well-known formula that generates
+the classical Eulerian polynomials, here denoted by En(x), in terms of the operator x d
+dx and
+the geometric series
+1
+1−x; namely
+�
+x d
+dx
+� �
+1
+1 − x
+�
+=
+En(x)
+(1 − x)n+1 .
+It is then reasonable to think that a general formula for E{n,k} may be given by the Lucas
+version of a polynomial obtained by applying the operator x d
+dx to a suitable transformation of
+ϕn(x).
+Conjecture. The Lucas-Eulerian numbers are given by E{n,k} =
+�
+An,k
+�
+({k + 1}), where
+�
+An,k
+�
+is the Lucas version of the polynomial An,k(x) defined as
+An,k(x) =
+�
+x d
+dx
+� �
+T(ϕn(x))
+�
+,
+where T is a suitable transformation of ϕn(x).
+3. On an alternating sum formula for Eulerian numbers
+For any integers 0 ≤ k < n, setting En,n = 1 for all n ≥ 0 and En,k = 0 for n < k, a
+classical formula that holds for Eulerian numbers is
+(16)
+En,k =
+k+1
+�
+j=0
+(−1)k+1−j
+�
+n + 2
+k + 1 − j
+�
+jn+1 .
+A natural question that comes to mind is what the Lucas analogue of this formula should be.
+An immediate answer is to replace binomial coefficients and powers of nonnegative integers
+with their Lucas versions. But what is the Lucas version of −1?
+n\k
+1
+0
+0
+1
+1
+2
+s3 + s3t + +2st2
+3
+s4 + s4t + 3s2t2 + t3
+4
+s5 + s5t + 4s3t2 + 3st3
+5
+s6 + s6t + 5s4t2 + 6s2t3 + t4
+Table 2: E′
+{n,1}
+n\k
+1
+0
+0
+1
+1
+2
+2s + s3 + s3
+t
+3
+3s2 + t + s4 + s4
+t
+4
+4s3 + 3st + s5 + s5
+t
+5
+5s4 + 6s2t + t2 + s6 + s6
+t
+Table 3: E′′
+{n,1}
+
+6
+J. AGAPITO RUIZ
+We have seen in Section 1 that for convenient recursive formulas that hold for Binomial and
+Narayana numbers, using Lucasnomials and replacing −1 with t was enough to get consistent
+formulas for their Lucas analogues. Hence, let us do the same here. Define the Lucas number
+E′
+{n,k} =
+k+1
+�
+j=0
+tk+1−j
+�
+n + 2
+k + 1 − j
+�
+{j}n+1 .
+We can easily check that E{n,k} ̸= E′
+{n,k} (compare Table 1 with Table 2). Another plausible
+Lucas version of formula (16) is obtained by extending the recurrence (1) to negative integers.
+In particular, we have {−1} = 1
+t so that we get the Lucas number
+E′′
+{n,k} =
+k+1
+�
+j=0
+� 1
+t
+�k+1−j
+�
+n + 2
+k + 1 − j
+�
+{j}n+1 .
+Once more, we have E′′
+{n,k} ̸= E{n,k} (compare Table 1 with Table 3). This time though, we
+see that E′′
+{n,1} and E{n,1} are almost equal except for an extra term sn+1 + sn+1
+t
+for n ≥ 2.
+We wonder what the Lucas version of the alternating sum formula (16) is that be compatible
+with our Lucas analogue of Eulerian numbers.
+4. Further comments
+We expect to find an uncomplicated formula for Lucas-Eulerian numbers in general by using
+induction. It is not easy to obtain a formula for E{n,k} similar to the one given for E{n,1},
+as stated in the conjecture. This difficulty is due in part to the fact that Lucas generalized
+numbers are neither additive nor multiplicative, for instance {2}+{3} ̸= {5} and {2}{3} ̸= {6}.
+Moreover, Lucas-Eulerian numbers are not always factorized in terms of Lucas atoms (we refer
+to [8] for definitions and notations). Try for example to factorize E{3,1} = 3s2+t. Nevertheless,
+we can write E{3,1} as a linear combination of Lucas atoms as follows
+3s2 + t = 4(s2 + t) − (s2 + 3t) = 4P3(s, t) − P6(s, t) .
+Despite the elementary way of defining Lucas-Eulerian numbers, we have been unable to
+find a combinatorial interpretation for them. We hope that the reader will be tempted to find
+such an interpretation.
+The recursive approach used here to define Lucas-Eulerian numbers can be used to define
+Lucas versions of a vast collection of combinatorial constants for which recursive relations are
+known. For instance, the Lucas analogue of the Stirling numbers St2n,k of the second kind
+are given by
+(17)
+St2{n,k} = {k}St2{n−1,k} + St2{n−1,k−1} ,
+with the usual initial conditions St2{0,0} = 1, St2{n,k} = 1 for n = k or k = 1, St2{j,0} = 0
+for j > 0, and St2{n,k} = 0 for n < k.
+n\k
+0
+1
+2
+3
+4
+5
+0
+1
+0
+0
+0
+0
+0
+1
+0
+1
+0
+0
+0
+0
+2
+0
+1
+1 + s
+0
+0
+0
+3
+0
+1
+1 + s + s2
+1
+0
+0
+4
+0
+1
+1 + s + s2 + s3
+1 + s + s2 + t
+1
+0
+5
+0
+1
+1 + s + s2 + s3 + s4
+1 + s + 2s2 + +s3 + s4 + t + st + 2s2t + t2
+1 + s + s2 + s3 + t + 2st
+1
+Table 4: A sample of Lucas-Stirling numbers of the second kind
+
+A LUCAS ANALOGUE OF EULERIAN NUMBERS
+7
+It follows from (17) that the Lucas-Stirling numbers of the second kind are polynomials in s
+and t with nonnegative integer coefficients. Table 4 shows some of them. We are not aware of
+any work on these numbers in the literature.
+Here is another enlightening example; for n ≥ 2 and with initial conditions M0 = M1 = 1, the
+standard Motzkin numbers Mn are known to satisfy the following recursive formula,
+(18)
+Mn = 2n + 1
+n + 2 Mn−1 + 3n − 3
+n + 2 Mn−2 .
+The natural Lucas analogue of relation (18) is
+(19)
+M{n} = {2n + 1}
+{n + 2} M{n−1} + {3n − 3}
+{n + 2} M{n−2} ,
+with initial conditions M{0} = M{1} = 1. Formula (19) gives rational expressions in s and t
+for M{n} in general. For instance,
+M{2} = s4 + 3s2t + t2 + s2 + t
+s3 + 2st
+.
+On the other hand, Motzkin numbers also satisfy a formula in terms of binomials coefficients
+and Catalan numbers, whose straightforward Lucas analogue is
+(20)
+M{n} =
+⌊n/2⌋
+�
+k=0
+� n
+2k
+�
+C{k} ,
+where C{k} =
+1
+k+1
+�
+2k
+k
+�
+.
+Since Lucasnomials and Lucas-Catalan numbers are polynomials
+in s and t with nonnegative integer coefficients [4], so are the Lucas-Motzkin numbers by
+Formula (20). This apparent contradiction with (19) is due to the fact that the recursive
+formula used to define the Lucas numbers M{n} is not the right one. In the same way we
+did in Section 1, by using a recursive relation different from the common one that holds for
+binomial numbers, here we have to pick a different recursive relation whose Lucas analogue be
+compatible with Formula (20).
+In ongoing work, we elaborate more on this observation [1].
+References
+[1] J. Agapito, A Lucas analogue of Riordan arrays. Preprint 2023.
+[2] T. Amdeberhan, X. Chen, V. H. Moll, B. Sagan, Generalized Fibonacci Polynomials and Fibonomial
+Coefficients. Ann. Comb. 18 (2014), 541–562.
+[3] A. Benjamin, S. Plott, A combinatorial approach to Fibonomial coefficients, Fibonacci Quart., 46/47
+(2008/2009), no. 1, 7–9.
+[4] C. Bennett, J. Carrillo, J. Machacek, B. Sagan, Combinatorial interpretations of Lucas analogues of
+binomial coefficients and Catalan numbers. Ann. Comb. 24 (2020), no. 3, 503–530.
+[5] K. Garret, K. Killpatrick, A combinatorial proof of a formula for the Lucas-Narayana polynomials. Discrete
+Math. 345 (2022), no. 12, 7 pp.
+[6] I. Gessel, G. Viennot, Binomial determinants, paths, and hook length formulae, Adv. in Math. 58 (1985),
+no. 3, 300–321.
+[7] B. Sagan, C. Savage, Combinatorial interpretations of binomial coefficient analogues related to Lucas
+sequences. Integers, 10:A52 (2010), 697–703.
+[8] B. Sagan and J. Tirrell, Lucas atoms, Adv. Math. 372 (2020) 107387
+Centro de an´alise funcional, estruturas lineares e aplicac¸˜oes, faculdade de ciˆencias,
+universidade de lisboa, 1749-016 Lisboa, portugal
+Email address: jaruiz@ciencias.ulisboa.pt
+
diff --git a/jNE4T4oBgHgl3EQfsQ20/content/tmp_files/load_file.txt b/jNE4T4oBgHgl3EQfsQ20/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d131b8cdcd4964fefed3c362763ea3dce66431a0
--- /dev/null
+++ b/jNE4T4oBgHgl3EQfsQ20/content/tmp_files/load_file.txt
@@ -0,0 +1,256 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf,len=255
+page_content='A LUCAS ANALOGUE OF EULERIAN NUMBERS  JOS´E AGAPITO RUIZ  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' The generalized Lucas numbers are polynomials in two variables with non-  negative integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Lucas versions of some combinatorial numbers with known  formulas in terms of quotient and products of nonnegative integers have been recently  given by replacing the integers in those formulas with their corresponding Lucas analogues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  We instead use a recursive approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' In this sense, we give a recursive formula for Lucas-  Narayana numbers derived from a recent formula in terms of Lucasnomials (the explicit  Lucas version of binomial numbers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' We propose a recursive definition for a Lucas ana-  logue of the classical Eulerian numbers, which shows immediately that they are polynomials  in two variables with nonnegative integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' We prove that they are palindromic  like their standard counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' The recursive approach allows us to give Lucas analogues  of many relevant combinatorial constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' In particular, Lucas versions for both Stirling  numbers of the second kind and Motzkin numbers are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Introduction  The generalized Lucas numbers are defined recursively by {0} = 0, {1} = 1, and  (1)  {n} = s{n − 1} + t{n − 2} ,  for any integer n ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' It follows immediately from (1) that the generalized Lucas numbers  {n} are polynomials in s and t with nonnegative integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' On specialization of s  and t one can recover, for example, the nonnegative integers (s = 2, t = −1), the q-integers  [n]q = qn−1  q−1 = 1 + q + · · · + qn−1 (s = 1 + q, t = −q), the Chebyshev polynomials of the  second kind Un−1(x) (U0(x) = 1, U1(x) = 2x, s = 2x, t = −1), and the Fibonacci sequence Fn  (s = t = 1), which is at the core of recursion (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Here are a few instances of the generalized  Lucas numbers:  {2} = s,  {3} = s2 + t,  {4} = s3 + 2st,  {5} = s4 + 3s2t + t2,  {6} = s5 + 4s3t + 3st2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  A useful combinatorial interpretation of {n} is derived from the standard interpretation  of Fibonacci numbers via tiling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' In this regard, we consider two types of tiles: monominoes  (which cover one unit squares) and dominoes (which cover two unit squares), so that for a  given configuration T using these tiles, we define its weight to be  (2)  wt T = s# of monominoes in T t# of dominoes in T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Furhermore, for any set T of tilings of this kind, the weight of T is defined to be  (3)  wt T =  �  T ∈T  wt T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Clearly, wt T is a polynomial in s and t when T is finite, otherwise it is a formal power series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Let T (n) be the set of all tilings of a row of n squares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Figure 1 shows all possible tilings  for n = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' It is then easy to see by induction that for every n ≥ 1, we have  {n} = wt T (n − 1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Eulerian numbers, Lucas analogues, Recursive formulas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  2020 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Primary 03, 05, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='05215v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='CO]  12 Jan 2023  2  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' AGAPITO RUIZ  Figure 1: The tilings in T (4)  The cardinality of T (n − 1) is precisely the Fibonacci number Fn (clearly, for T (0) = ∅ we  assume |T (0)| = 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Now, by tiling rows with a decreasing number of squares and piling them  up we can make sense of the expression  (4)  {n}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' = {n}{n − 1} · · · {2}{1} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  This is the Lucas analogue of the factorial, the Lucastorial number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' By convention {0}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Using the setting of Young diagrams, Identity (4) gives the weight of the set of all tilings of  the standard staircase partition δn = (n − 1, n − 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' , 1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' namely  wt T (δn) = {n}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Likewise, one can obtain a Lucas version of any expression given in terms of products and  quotients of nonnegative integers by simply replacing each ocurrence of n in the expression  with {n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' For instance, given 0 ≤ k ≤ n, the Lucasnomial is defined by  (5)  �n  k  �  =  {n}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  {k}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' {n − k}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  From this point of view, Lucasnomials are rational expressions in s and t a priori.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' However  they are indeed polynomials in s and t with nonnegative integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' This follows from  some combinatorial interpretations given by Gessel and Viennot [6], Benjamin and Plott [3],  and Sagan and Savage [7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' More recently, using a model that involves lattice paths inside  tilings of Young diagrams, Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' [4] have given another combinatorial interpretation  for Lucasnomials that not only is simpler than the previous ones but also is more flexible for  combinatorial proofs of identities involving Lucasnomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Their combinatorial interpretation  is also extendable to other familiar sequences of numbers like the Catalan numbers and their  relatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' It is worth mentioning that Amdeberhan et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' [2] have also studied the generalized  Lucas sequence and the Lucas analogues of Binomial and Catalan numbers from an algebraic  and number theoretical perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  In general, given any array of numbers An,k, its Lucas analogue will be denoted by A{n,k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  An alternative natural way to obtain Lucas analogues of standard arrays of numbers is by  generalizing their recursive relations in a straightforward manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' For instance, it is well-  known that the following formula holds for binomial numbers Bn,k =  �n  k  �  ,  (6)  Bn,k = Bn−1,k + Bn−1,k−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  However, since {1} = 1, we do not get anything new by replacing 1 with {1} in (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Therefore,  we have to choose a different recursive relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' In this regard, there is a less familiar recursive  formula for binomial numbers that we can work with;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' that is  (7)  Bn,k = (k + 1)Bn−1,k − (n − k − 1)Bn−1,k−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Keeping in mind that {n} = n when s = 2 and t = −1, a natural way of defining the Lucas  analogue of (7) is  (8)  B{n,k} = {k + 1}B{n−1,k} + t{n − k − 1}B{n−1,k−1} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  A LUCAS ANALOGUE OF EULERIAN NUMBERS  3  An immediate conclusion from (8) is that B{n,k} is a polynomial in s and t with nonnegative  integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Moreover, using as initial conditions B{n,0} = B{n,n} = 1 for n ≥ 0 and  B{n,k} = 0 whenever n < k or k < 0, we can recover by induction the formula  B{n,k} =  {n}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  {k}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' {n − k}!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Hence, the Lucas version for binomial numbers obtained from generalizing the recursive rela-  tion (7) agrees with the explicit formula for Lucasnomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Another familiar array of nonnegative integers with combinatorial interpretations is the  array of Narayana numbers, defined for 1 ≤ k ≤ n as  (9)  Nn,k = 1  n  �n  k  ��  n  k − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  The corresponding Lucas-Narayana numbers are then given by  (10)  N{n,k} =  1  {n}  �n  k  � �  n  k − 1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  The fact that Lucas-Narayana numbers are indeed polynomials in s and t with nonnegative  integer coefficients was conjectured in [4], and later proved by Sagan and Tirrell [8] using  special factoring properties of {n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Recently, Garret and Killpatrick [5] gave a combinatorial  proof of this fact by showing that the Lucas-Narayana numbers N{n,k} satisfy the formula  (11)  N{n,k} =  �n − 1  k − 1  �2  + t  �n − 1  k  � �n − 1  k − 2  �  ,  for 2 ≤ k ≤ n − 1 and n ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Formula (11) shows that N{n,k} is a polynomial in s and t with  nonnegative integer coefficients because it is expressed as a sum of products of Lucasnomials  with coefficients in N[s, t].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Now, manipulating Formula (11) algebraically, we get a recursive  formula for Lucas-Narayana numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Proposition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' For any integers 2 ≤ k ≤ n − 1 and n ≥ 1, the Lucas-Narayana numbers are  given by  (12)  N{n,k} = {k}{n − 1}  {n − k}  N{n−1,k} + t {n − k}{n − 1}  {k}  N{n−1,k−1} ,  with initial conditions N{0,0} = 1, N{n,k} = 1 for n = k or k = 1, N{j,0} = 0 for j > 0, and  N{n,k} = 0 for n < k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Formula (12) is the Lucas analogue of the not well-known recurrence relation satisfied by the  classical Narayana numbers,  Nn,k = k(n − 1)  n − k Nn−1,k − (n − k)(n − 1)  k  Nn−1,k−1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  We can recover from Proposition 1 the closed formula (10), by using induction again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Note  that the polynomial nature of N{n,k} with nonnegative integer coefficients is not immediate  from the recursive formula (12) this time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  These two examples illustrate the elementary approach we will take for the rest of the  paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  We show in Section 2 that a straightforward Lucas version of a recursive relation  satisfied by the classical Eulerian numbers En,k gives a way of defining the Lucas-Eulerian  numbers E{n,k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' It follows immediately from the definition that they are polynomials in s  and t with nonnegative integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' We show that they are palindromic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Using the  recursive definition of E{n,k}, we get a formula for E{n,1} that encourage us to conjecture a  similar formula for the general case E{n,k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' In Section 3, we elaborate on the difficulties that  arise when trying to give a Lucas analogue of a known alternating sum formula for Eulerian  4  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' AGAPITO RUIZ  numbers that be compatible with our Lucas-Eulerian numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' We end in Section 4 by making  further comments on open problems and on Lucas analogues of Stirling numbers of the second  kind and Motzkin numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Lucas-Eulerian numbers  Among several equivalent variants of a known recurrence relation satisfied by the classical  Eulerian numbers, we have the following formula  (13)  En,k = (k + 1)En−1,k + (n − k + 1)En−1,k−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  A straightforward Lucas analogue of Formula 13 defines the Lucas-Eulerian numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Definition 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' The Lucas-Eulerian numbers are defined recursively by the formula  (14)  E{n,k} = {k + 1}E{n−1,k} + {n − k + 1}E{n−1,k−1} ,  for any integers 0 ≤ k ≤ n, with initial conditions E{n,0} = E{n,n} = 1 for n ≥ 0 and  E{n,k} = 0 for n < k or k < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  n\\k  0  1  2  3  4  5  0  1  0  0  0  0  0  1  1  1  0  0  0  0  2  1  2s  1  0  0  0  3  1  3s2 + t  3s2 + t  1  0  0  4  1  4s3 + 3st  6s4 + 8s2t + 2t2  4s3 + 3st  1  0  5  1  5s4 + 6s2t + t2  10s6 + 25s4t + 16s2t2 + 2t3  10s6 + 25s4t + 16s2t2 + 2t3  5s4 + 6s2t + t2  1  Table 1: A sample of Lucas-Eulerian numbers  It immediately follows from Definition 1 that the Lucas-Eulerian numbers are polynomials  in s and t with nonnegative integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Moreover, Table 1 indicates that they are  palindromic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Note that for Lucasnomials B{n,k} and Lucas-Narayana numbers N{n,k}, this  property is immediate because they both have closed formulas from where it is easy to check  that B{n,k} = B{n,n−k} and N{n,k} = N{n,n−k+1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' The Lucas-Eulerian numbers are palindromic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' This is an immediate consequence of the bijection k �→ n − k = k′, which amounts to  write  E{n,n−k} = {n − k + 1}E{n−1,n−k} + {n − n + k + 1}E{n−1,n−k−1}  as  E{n,k′} = {k′ + 1}E{n−1,k′} + {n − k′ + 1}E{n−1,k′−1} .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  □  Unlike Binomial and Narayana numbers, whose Lucas analogues have straightforward gen-  eralizations of their explicit closed formulas, there is not an equivalent formula known for the  classical Eulerian numbers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' that is, in terms of a quotient of products of nonnegative inte-  gers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' There is a formula in terms of alternating sums though, but unfortunately the natural  extension of the Lucas recurrence to negative numbers does not give a Lucas analogue of such  formula that be polynomial in s and t with nonnegative integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' We elaborate  more on this observation in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Using Definition 1 repeatedly we get an interesting formula for E{n,1}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' We have  (15)  E{n,1} = {2}E{n−1,1} + {n} =  n  �  j=0  {n − j}{2}j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  A LUCAS ANALOGUE OF EULERIAN NUMBERS  5  Expanding out the sum in Formula (15), and replacing {2} with x, we get the polynomial  �  An,1  �  (x) = {n}x0 + {n − 1}x1 + · · · + {1}xn−1 + {0}xn ,  which is the Lucas version of the polynomial An,1(x) = xnPn,1  � 1  x  �  , where  Pn,1(x) =  �  x d  dx  � �1 − xn+1  1 − x  �  = x + 2x2 + · · · + nxn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Therefore, we have E{n,1} =  �  An,1  �  ({2}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Note that when n + 1 is prime, the polynomials  ϕn(x) = 1 + x + x2 + · · · + xn = 1 − xn+1  1 − x  ,  are the cyclotomic polynomials Φn+1(x) used in the definition of Lucas atoms [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' They provide  a convenient factorization of {n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Recall also that there is a well-known formula that generates  the classical Eulerian polynomials, here denoted by En(x), in terms of the operator x d  dx and  the geometric series  1  1−x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' namely  �  x d  dx  � �  1  1 − x  �  =  En(x)  (1 − x)n+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  It is then reasonable to think that a general formula for E{n,k} may be given by the Lucas  version of a polynomial obtained by applying the operator x d  dx to a suitable transformation of  ϕn(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' The Lucas-Eulerian numbers are given by E{n,k} =  �  An,k  �  ({k + 1}), where  �  An,k  �  is the Lucas version of the polynomial An,k(x) defined as  An,k(x) =  �  x d  dx  � �  T(ϕn(x))  �  ,  where T is a suitable transformation of ϕn(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' On an alternating sum formula for Eulerian numbers  For any integers 0 ≤ k < n, setting En,n = 1 for all n ≥ 0 and En,k = 0 for n < k, a  classical formula that holds for Eulerian numbers is  (16)  En,k =  k+1  �  j=0  (−1)k+1−j  �  n + 2  k + 1 − j  �  jn+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  A natural question that comes to mind is what the Lucas analogue of this formula should be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  An immediate answer is to replace binomial coefficients and powers of nonnegative integers  with their Lucas versions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' But what is the Lucas version of −1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  n\\k  1  0  0  1  1  2  s3 + s3t + +2st2  3  s4 + s4t + 3s2t2 + t3  4  s5 + s5t + 4s3t2 + 3st3  5  s6 + s6t + 5s4t2 + 6s2t3 + t4  Table 2: E′  {n,1}  n\\k  1  0  0  1  1  2  2s + s3 + s3  t  3  3s2 + t + s4 + s4  t  4  4s3 + 3st + s5 + s5  t  5  5s4 + 6s2t + t2 + s6 + s6  t  Table 3: E′′  {n,1}  6  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' AGAPITO RUIZ  We have seen in Section 1 that for convenient recursive formulas that hold for Binomial and  Narayana numbers, using Lucasnomials and replacing −1 with t was enough to get consistent  formulas for their Lucas analogues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Hence, let us do the same here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Define the Lucas number  E′  {n,k} =  k+1  �  j=0  tk+1−j  �  n + 2  k + 1 − j  �  {j}n+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  We can easily check that E{n,k} ̸= E′  {n,k} (compare Table 1 with Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Another plausible  Lucas version of formula (16) is obtained by extending the recurrence (1) to negative integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  In particular, we have {−1} = 1  t so that we get the Lucas number  E′′  {n,k} =  k+1  �  j=0  � 1  t  �k+1−j  �  n + 2  k + 1 − j  �  {j}n+1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Once more, we have E′′  {n,k} ̸= E{n,k} (compare Table 1 with Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' This time though, we  see that E′′  {n,1} and E{n,1} are almost equal except for an extra term sn+1 + sn+1  t  for n ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  We wonder what the Lucas version of the alternating sum formula (16) is that be compatible  with our Lucas analogue of Eulerian numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Further comments  We expect to find an uncomplicated formula for Lucas-Eulerian numbers in general by using  induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' It is not easy to obtain a formula for E{n,k} similar to the one given for E{n,1},  as stated in the conjecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' This difficulty is due in part to the fact that Lucas generalized  numbers are neither additive nor multiplicative, for instance {2}+{3} ̸= {5} and {2}{3} ̸= {6}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Moreover, Lucas-Eulerian numbers are not always factorized in terms of Lucas atoms (we refer  to [8] for definitions and notations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Try for example to factorize E{3,1} = 3s2+t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Nevertheless,  we can write E{3,1} as a linear combination of Lucas atoms as follows  3s2 + t = 4(s2 + t) − (s2 + 3t) = 4P3(s, t) − P6(s, t) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Despite the elementary way of defining Lucas-Eulerian numbers, we have been unable to  find a combinatorial interpretation for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' We hope that the reader will be tempted to find  such an interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  The recursive approach used here to define Lucas-Eulerian numbers can be used to define  Lucas versions of a vast collection of combinatorial constants for which recursive relations are  known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' For instance, the Lucas analogue of the Stirling numbers St2n,k of the second kind  are given by  (17)  St2{n,k} = {k}St2{n−1,k} + St2{n−1,k−1} ,  with the usual initial conditions St2{0,0} = 1, St2{n,k} = 1 for n = k or k = 1, St2{j,0} = 0  for j > 0, and St2{n,k} = 0 for n < k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='n\\k  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1 + s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1 + s + s2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1 + s + s2 + s3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1 + s + s2 + t  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1 + s + s2 + s3 + s4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1 + s + 2s2 + +s3 + s4 + t + st + 2s2t + t2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1 + s + s2 + s3 + t + 2st  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='Table 4: A sample of Lucas-Stirling numbers of the second kind  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='A LUCAS ANALOGUE OF EULERIAN NUMBERS  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='7  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='It follows from (17) that the Lucas-Stirling numbers of the second kind are polynomials in s  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='and t with nonnegative integer coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Table 4 shows some of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' We are not aware of  any work on these numbers in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Here is another enlightening example;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' for n ≥ 2 and with initial conditions M0 = M1 = 1, the  standard Motzkin numbers Mn are known to satisfy the following recursive formula,  (18)  Mn = 2n + 1  n + 2 Mn−1 + 3n − 3  n + 2 Mn−2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  The natural Lucas analogue of relation (18) is  (19)  M{n} = {2n + 1}  {n + 2} M{n−1} + {3n − 3}  {n + 2} M{n−2} ,  with initial conditions M{0} = M{1} = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Formula (19) gives rational expressions in s and t  for M{n} in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' For instance,  M{2} = s4 + 3s2t + t2 + s2 + t  s3 + 2st  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  On the other hand, Motzkin numbers also satisfy a formula in terms of binomials coefficients  and Catalan numbers, whose straightforward Lucas analogue is  (20)  M{n} =  ⌊n/2⌋  �  k=0  � n  2k  �  C{k} ,  where C{k} =  1  k+1  �  2k  k  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  Since Lucasnomials and Lucas-Catalan numbers are polynomials  in s and t with nonnegative integer coefficients [4], so are the Lucas-Motzkin numbers by  Formula (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' This apparent contradiction with (19) is due to the fact that the recursive  formula used to define the Lucas numbers M{n} is not the right one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' In the same way we  did in Section 1, by using a recursive relation different from the common one that holds for  binomial numbers, here we have to pick a different recursive relation whose Lucas analogue be  compatible with Formula (20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  In ongoing work, we elaborate more on this observation [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  References  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Agapito, A Lucas analogue of Riordan arrays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Preprint 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  [2] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Amdeberhan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Chen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Moll, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Sagan, Generalized Fibonacci Polynomials and Fibonomial  Coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Comb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' 18 (2014), 541–562.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Benjamin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Plott, A combinatorial approach to Fibonomial coefficients, Fibonacci Quart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=', 46/47  (2008/2009), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' 1, 7–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  [4] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Bennett, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Carrillo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Machacek, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Sagan, Combinatorial interpretations of Lucas analogues of  binomial coefficients and Catalan numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Comb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' 24 (2020), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' 3, 503–530.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  [5] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Garret, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Killpatrick, A combinatorial proof of a formula for the Lucas-Narayana polynomials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Discrete  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' 345 (2022), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' 12, 7 pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  [6] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Gessel, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Viennot, Binomial determinants, paths, and hook length formulae, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' in Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' 58 (1985),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' 3, 300–321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  [7] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Sagan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Savage, Combinatorial interpretations of binomial coefficient analogues related to Lucas  sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Integers, 10:A52 (2010), 697–703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='  [8] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Sagan and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Tirrell, Lucas atoms, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content=' 372 (2020) 107387  Centro de an´alise funcional, estruturas lineares e aplicac¸˜oes, faculdade de ciˆencias,  universidade de lisboa, 1749-016 Lisboa, portugal  Email address: jaruiz@ciencias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='ulisboa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
+page_content='pt' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE4T4oBgHgl3EQfsQ20/content/2301.05215v1.pdf'}
diff --git a/jdE1T4oBgHgl3EQf0AWa/content/tmp_files/2301.03451v1.pdf.txt b/jdE1T4oBgHgl3EQf0AWa/content/tmp_files/2301.03451v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d632f03e43fd0e8aecb10ce837345df1aee85724
--- /dev/null
+++ b/jdE1T4oBgHgl3EQf0AWa/content/tmp_files/2301.03451v1.pdf.txt
@@ -0,0 +1,1344 @@
+ 
+Label-free incoherent super-resolution optical microscopy 
+Nikhil Jayakumar1, Firehun T Dullo2, Jean-Claude Tinguley1, Krizia Sagini3,4, Alicia Llorente3,4,5, Balpreet 
+Singh Ahluwalia*1 
+1Department of Physics and Technology, UiT The Arctic University of Norway, Tromsø, 9037, Norway 
+2Department of Microsystems and Nanotechnology, SINTEF Digital, Gaustadalleen 23C, 0373 Oslo, Norway 
+3 Department of Molecular Cell Biology, Institute for Cancer Research, Oslo University Hospital, The 
+Norwegian Radium Hospital, 0379 Oslo, Norway 
+4Centre for Cancer Cell Reprogramming, Faculty of Medicine, University of Oslo, Montebello, 0379 Oslo, Norway 
+5Department for Mechanical, Electronics and Chemical Engineering, Oslo Metropolitan University, Oslo, Norway 
+ 
+*Balpreet.singh.ahluwalia@uit.no 
+Abstract: The photo-kinetics of fluorescent molecules has enabled the circumvention of far-field optical 
+diffraction-limit. Despite its enormous potential, the necessity to label the sample may adversely influence the 
+delicate biology under investigation. Thus, continued development efforts are needed to surpass the far-field label-
+free diffraction barrier. The coherence of the detected light in label-free mode hinders the application of existing 
+super-resolution methods based on incoherent fluorescence imaging. In this article, we present the physics and 
+propose a methodology to circumvent this challenge by exploiting the photoluminescence of silicon nitride 
+waveguides for near-field illumination of unlabeled samples. The technique is abbreviated EPSLON, Evanescently 
+decaying Photoluminescence Scattering enables Label-free Optical Nanoscopy. We demonstrate that such an 
+illumination has properties that mimics the photo-kinetics of nano-sized fluorescent molecules. This allows to 
+develop a label-free incoherent system that is linear in intensity, and stable with time thereby permitting the 
+application of techniques like structured illumination microscopy (SIM) and intensity-fluctuation based optical 
+nanoscopy (IFON) in label-free mode to circumvent the diffraction limit. We experimentally demonstrate label-
+free super-resolution imaging of nanobeads (polystyrene and gold), extra-cellular vesicles and human placenta 
+tissue. We believe EPSLON is a step forward within the nascent field of label-free super-resolution microscopy 
+that holds the key to investigate delicate biological systems in its natural state without the need for exogenous 
+labels.   
+Introduction 
+The ability of light beams to interfere is quantified by their degree of coherence. Light beams originating from 
+within the coherence volumes can only overlap and generate a sustained interference pattern [1, 2]. In fluorescence 
+microscopy, the transversal coherence lengths are typically on the order of a few nanometers. This is because the 
+fluorescent molecules, a few nanometers in size, emit independently and stochastically. It leads to a linear mapping 
+between the sample plane fluorophore concentration and image plane intensity. This implies that the photo-kinetics 
+of these molecules may be utilized to circumvent the far-field diffraction-limit, as in structured illumination 
+microscopy [3, 4] or fluorescence-based IFON algorithms [5-10]. However, the absence of such exogenous 
+molecules in label-free microscopy restricts the far-field transversal coherence lengths to a few hundreds of 
+nanometers [11, 12]. This hinders the application of fluorescence-based super-resolution algorithms in the label-
+free regime for generating reliable super-resolved images [13]. Another hinderance in label-free microscopy is 
+lack of selectivity and specificity that results in strong scattering and multiple scattering from the entire sample. 
+To circumvent these challenges, it can be foreseen that near-field illumination, to reduce multiple scattering issues, 
+via nano-sized light sources with stochastic photo-kinetics and sufficient quantum yield is required. Therefore, 
+through this article, we provide the concepts and a key to unlock the challenge of generating far-field label-free 
+super-resolved optical images using fluorescence based super-resolution algorithms: photoluminescence (PL) of 
+silicon nitride (Si3N4) [14, 15] waveguide functions as exogenous nano-sized illumination sources with stochastic 
+photo-kinetics. In addition, the photonic-chip helps in engineering the illumination to induce fluctuations in 
+intensity via multi-mode interference (MMI) /speckle-like patterns [16-18] or via well-defined interference fringes 
+that permits the application of fluorescence based IFON algorithms or SIM respectively to enhance the resolution. 
+Poor-contrast and diffraction-limited resolution are major impediments to the development of label-free optical 
+microscopy. To mitigate the issue of poor contrast, various approaches have emerged: phase contrast microscopy 
+[19], differential interference contrast [20], interferometric scattering microscopy [21], interferometric techniques 
+[22], holographic non-interferometric techniques [23], Fourier Ptychography [24], rotating coherent scattering 
+
+microscopy [25], manipulating the coherence of light sources used for illumination [26], ultraviolet microscopy 
+[27], optical waveguides [28, 29] etc. However, circumventing the diffraction-limit in label-free regime is still at 
+a nascent stage in life sciences, as opposed to fluorescence microscopy [30]. This could be attributed to the ease 
+of utilizing/manipulating the photo-kinetics of nano-sized fluorescent molecules to gain information beyond the 
+diffraction-limit. The different approaches developed for label-free super-resolution microscopy, albeit with their 
+respective experimental challenges especially for life sciences applications, includes near-field scanning optical 
+microscopy [31], super-lens [32], micro-sphere assisted super-resolution imaging [33], super-resolution via 
+scattering [33, 34], optical super-oscillation techniques [35], hyperbolic materials for super-resolution imaging 
+[36], utilizing the intrinsic autofluorescence of biological specimens in tandem with fluorescence-based super-
+resolution algorithms [37, 38] etc.  
+In this article, we propose the use of Si3N4 waveguides to solve the abovementioned challenges associated with 
+label-free microscopy. The concept permits the application of fluorescence based super-resolution algorithms on 
+unlabeled samples, generating high-contrast label-free super-resolved images, without photo-toxicity and 
+photobleaching plaguing the imaging process. Our work helps synthesize a label-free incoherent imaging system 
+and is termed Evanescently decaying Photoluminescence Scattering enables Label-free Optical Nanoscopy 
+(EPSLON), which builds and extends the concepts outlined by Goodman [39], Ruh et.al. [25], Wicker and 
+Heinztmann [13] and previous work based on photonic-chip microscopy [29]. These concepts of EPSLON which 
+enable circumventing the label-free far-field diffraction-limit are explained and experimentally demonstrated in 
+Fig. 1 and Fig. 2. We describe how a Si3N4 waveguide is a solution to these challenges and validate our concepts 
+experimentally via high-contrast label-free super-resolved images of polystyrene beads, gold nanoparticles, 
+weakly scattering specimens like extra-cellular vesicles and human placenta tissue, Fig. 3-5.     
+Conceptual framework and Results  
+Problem statement 
+Here we describe why fluorescence based super-resolution algorithms when applied to coherently scattering 
+samples do not yield any resolution gain beyond the diffraction-limit, which is also discussed by Wicker and 
+Heintzmann [13]. To explain this concept, the image formation process at the camera plane is regarded as an 
+interference phenomenon. To illustrate the image formation process in label-free mode, we consider two 
+coherently scattering phase-objects illuminated by a monochromatic plane-wave 𝐸𝑖(𝑟⃗, 𝑡) = 𝑒𝑖(𝑘⃗⃗.𝑟⃗ − 𝜔𝑡). The scalar 
+fields scattered by the phase-objects can then be represented as 𝐸1(𝑟1⃗⃗⃗⃗, 𝑡) = 𝑝1(𝑟1⃗⃗⃗⃗) cos(𝑘⃗⃗. 𝑟1⃗⃗⃗⃗ − 𝜔𝑡) and 𝐸2(𝑟2⃗⃗⃗⃗, 𝑡) =
+ 𝑝2(𝑟2⃗⃗⃗⃗) cos(𝑘⃗⃗. 𝑟2⃗⃗⃗⃗ − 𝜔𝑡), where 𝑝1(𝑟1⃗⃗⃗⃗) and 𝑝2(𝑟2⃗⃗⃗⃗) are the amplitudes of the scattered fields and are linked to the 
+applied electric fields via the polarizability of the particles, α(𝑟⃗, 𝑡). The intensity registered by the camera is then 
+𝐼(𝑟⃗) = 〈|(𝐸1(𝑟1⃗⃗⃗⃗, 𝑡) + 𝐸2(𝑟2⃗⃗⃗⃗, 𝑡)) ⨷ ℎ(𝑟⃗)|
+2〉, where 〈 〉 represents time averaging by the detector, ℎ(𝑟⃗) is the 
+coherent point spread function of the imaging system and ⨷ represents the convolution operation. Due to statistical 
+similarity or coherence between the overlapping scattered fields, the intensity registered by the camera is non-
+linearly related to the particle concentration and is a function of 𝛥𝜑 = 𝑘⃗⃗. 𝑟2⃗⃗⃗⃗ − 𝑘⃗⃗. 𝑟1⃗⃗⃗⃗ = 𝜑2 − 𝜑1. It implies that the 
+image generated by the camera varies with either a change in the illumination angle 𝑘⃗⃗, or with the relative positions 
+of the particles 𝑟2⃗⃗⃗⃗ − 𝑟1⃗⃗⃗⃗.  
+Next, to illustrate the image formation process in fluorescence microscopy we replace the phase-objects with 
+fluorescent molecules. Analogous to the strengths of the scattered fields, |𝑎1(𝑟1⃗⃗⃗⃗)|2 and |𝑎2(𝑟2⃗⃗⃗⃗)|2, are the brightness 
+of the molecules that typically depends on the illumination intensity at the location of the molecule. The molecules 
+can also be assumed to emit independently [40] and stochastically typically on the order of nanoseconds [41]. The 
+following properties of these molecules can be utilized by collecting only the Stoke shifted light emitted by the 
+molecules:  
+(i) 
+Stochastic emission between the molecules causes the phase difference between the emitted fields to be 
+a function of time, 𝛥𝜑(𝑡). It implies that the molecule emissions are incoherent with respect to one 
+another or in other words we can say that the transversal coherence length is determined by the size of an 
+individual molecule. This gives rise to similar images for different illumination angles of the incident 
+plane wave, i.e., the particle concentration and image plane intensity obey a linear relationship as the 
+intensity registered by the camera becomes independent of 𝛥𝜑(𝑡). It is this property that allows the usage 
+of structured light in SIM [13, 42] or the intrinsic photo-kinetics of the molecules in IFON algorithms to 
+enhance the resolution [29],  
+
+(ii) 
+Excited lifetime on the order of nanoseconds of the molecules excites many independent interference or 
+speckle patterns, that gets averaged within the integration time of the camera thus mitigating the speckle-
+noise and  
+(iii) 
+Molecular specificity offered by these molecules enables multi-color imaging of different cell organelles. 
+It can be concluded that the suppression of speckle noise and molecular specificity offered by the 
+molecules enables high-contrast imaging and the linear relationship between molecular concentration and 
+image plane intensity helps in enhancing the resolution via fluorescence-based super-resolution 
+algorithms.   
+Hence, to improve the label-free resolution via fluorescence-based algorithms, we need to ensure that there exists 
+no statistical similarity between the scattered fields originating from different locations. This calls for the spatial 
+coherence function to be δ-function correlated, i.e.,   
+𝐽(𝑟1⃗⃗⃗⃗, 𝑟2⃗⃗⃗⃗) = 〈𝐸𝑇(𝑟1⃗⃗⃗⃗, 𝑡)𝐸∗
+𝑇(𝑟2⃗⃗⃗⃗, 𝑡)〉 = 𝛫𝐼𝑇(𝑟1⃗⃗⃗⃗) δ(𝑟1⃗⃗⃗⃗ − 𝑟2⃗⃗⃗⃗)                                               (1) 
+where 𝐽(𝑟1⃗⃗⃗⃗, 𝑟2⃗⃗⃗⃗) is the spatial coherence function and determines the spatial correlation of the fields, 𝐸𝑇(𝑟⃗, 𝑡) =
+𝐸1(𝑟⃗, 𝑡) + 𝐸2(𝑟⃗, 𝑡) is the total field reaching the camera, 𝛫 is a real constant and 𝐼𝑇 is the image generated by the 
+camera. This will ensure an incoherent imaging system. Eqn. (1) can be assumed to be satisfied in fluorescence 
+microscopy because the transversal spatial coherence length is determined by the size of the fluorescent molecules 
+and the image generated by the camera indicates the spatial locations of the fluorescent molecules.  
+Thus, to circumvent the label-free diffraction-limit using fluorescence-based super-resolution algorithms, we need 
+to develop a light source with δ-function correlations and then acquire an image stack exhibiting intensity-
+fluctuations to apply SIM or intensity-fluctuation based algorithms. This can be realized experimentally via the 
+EPSLON configuration. Fig. 1(a-c) compares the conventional imaging configurations and their corresponding 
+image plane intensity distribution with EPSLON, Fig. 1(d). EPSLON satisfies Eqn. 1 and is experimentally 
+demonstrated in Fig. 1e-1j. In Fig. 1e-1f, schematic diagrams of waveguide-based label-free coherent and 
+incoherent imaging systems EPSLON are shown. The coherent and corresponding EPSLON images are compared 
+in Fig. 1g, where speckle suppression due to loss in phase information in the scattered light is clearly evidenced in 
+the EPSLON configuration image. This loss in phase information also implies that identical images must be 
+generated for arbitrary illumination angles in EPSLON configuration, as opposed to label-free coherent imaging. 
+This is demonstrated experimentally in Fig. 1h-1j where the coherent and its corresponding incoherent EPSLON 
+images are provided.           
+EPSLON: a solution for high-contrast far-field label-free super-resolution microscopy 
+To employ a light source with δ-function correlations, we resort to the high-index contrast (Δn ≈ 2) Si3N4 optical 
+waveguide deposited using plasma enhanced chemical vapor deposition (PECVD) scheme. Waveguide fabrication 
+and properties of the guided modes and its spatial frequency extend is provided in Supplementary section 1 and in 
+previous works [43, 44]. The choice of Si3N4 over other high index contrast optical waveguides, such as tantalum 
+pentoxide, Ta2O5, or titanium dioxide TiO2, is attributed to the room-temperature visible PL generated inside the 
+core during the transfer of optical power along its length. Determining the origin and lifetime of this emission is 
+not within the scope of this work. The origin and photophysical properties of this PL is a widely researched area 
+[45-47]. It is found to be dependent on the waveguide fabrication scheme employed and could be attributed to 
+intrinsic fluorescence of the material [14]. The PL emission spectrum is broad [15] and the lifetime of these states 
+is found to vary on the order of a few nanoseconds to a few hundred microseconds depending on the origin of the 
+PL [16, 49-50]. Such an emission could be visualized as a very large number of fluorescent molecules embedded 
+in a material and emitting stochastically. Hence, if the PL light is used for near-field illumination of samples, then 
+Eqn. (1) will be satisfied for the incoherently scattered fields. This helps in synthesizing a label-free incoherent 
+system, Fig. 1. 
+The next problem to tackle is that of generating an image stack with intensity-fluctuations for the fluorescence-
+based algorithms. Structuring the illumination beam, manipulating the photophysical properties of the fluorescence 
+molecules are some of the ways typically employed for generating image stacks with intensity-fluctuations. In 
+EPSLON, this problem is resolved by resorting to Si3N4 waveguides of the following types: (1) Straight 
+waveguides with strip geometry and large widths that supports a large number of the guided modes, generating 
+MMI patterns (Fig. 2a) [29], (2) Four-arm junction multi-moded strip waveguides for speckle illumination from 
+
+different azimuthal angles (Fig. 2b) [29] and, (3) a single moded SIM chip with rib geometry and phase modulation 
+for one-dimensional structured illumination (Fig. 2c) [50].  
+Image formation process in EPSLON 
+Laser is coupled into a Si3N4 waveguide via a microscope objective MO1, (Supplementary Fig. 3). The coupled 
+optical power gets distributed among the multiple coherent guided modes, which correspond to the eigen vectors 
+of the guiding structure. As the modes guide power along the length of the waveguide, they also induce a broadband 
+PL along the length as shown in Fig. 2d-2e. The Si3N4 waveguide employed in this work demonstrated PL in all 
+the commonly used wavelengths in bio-imaging, 488 nm, 561 nm, and 647/660 nm (Fig. 2e). This PL of Si3N4 
+waveguide does not exhibit any bleaching effect over long periods of times (Fig. 2f), as opposed to the 
+autofluorescence in polymer waveguides [51] and varies linearly with the excitation power (Fig. 2g). 
+To explain the origin of fluctuations in intensity, we consider the case of a multi-moded straight waveguide. 
+Fluctuations over time, 𝐼𝑐𝑜𝑟𝑒
+𝑚
+(𝑟,⃗⃗⃗ 𝑡), can be induced by oscillating MO1 using a piezo-stage across the input facet of 
+the waveguide (Supplementary Fig. 3) which excites different sets of modes 𝜓𝑚(𝑟⃗, 𝑡) with relative amplitudes 0 ≤
+𝑎𝑚(𝑡) ≤ 1. The instantaneous PL intensity at each location in the core is dependent on the coherent superposition 
+of the modes and can be represented mathematically as 𝐼𝑐𝑜𝑟𝑒
+𝑚
+(𝑟,⃗⃗⃗ 𝑡) = 𝜂(𝜆)|∑
+𝑎𝑚(𝑡)𝜓𝑚(𝑟⃗, 𝑡)
+𝑚
+|2, where 𝜂(𝜆) is 
+assumed to be a constant across the material for a specific wavelength that can be deduced from Fig. 2g, 𝜓𝑚(𝑟⃗, 𝑡) =
+𝐸𝑚(𝑥, 𝑦)𝑒(𝑖ß𝑚𝑧−𝑖𝜔𝑡) corresponds to the scalar representation of the mth guided mode with fixed transversal profile 
+𝐸𝑚(𝑥, 𝑦) and propagation constant ß𝑚. As the PL emission occurs inside a high-index core, a part of the PL light 
+gets confined to the core due to total-internal reflection at the core-cladding interface and the remaining part gets 
+transmitted into the far-field, which is visible as an omnipresent background or noise. Now the presence of any 
+index perturbation at the core-cladding interface scatters this evanescently decaying PL light into the far-field (Fig. 
+1d), i.e., both the coherent as well as the Stoke shifted incoherent PL light gets scattered into the far-field. By 
+invoking a first order Born approximation for evanescent field excitation of biological specimens 𝑆(𝑟⃗) =
+∬ 𝛼(𝑟⃗𝑘)𝛿(𝑟⃗ − 𝑟⃗𝑘)
+ 
+𝑆
+𝑑𝑟⃗𝑘  with α being the polarizability, it is seen that these scattered fields contain the information 
+of the sample. Only these scattered fields are collected by the microscope objective MO2 and relayed onto the 
+camera via tube lens because of the decoupled illumination and detection scheme offered by waveguides 
+(Supplementary Fig. 3). Through the usage of appropriate bandpass filters, the coherently scattered light is filtered 
+out and only the incoherent light gets detected. The oscillation of MO1 is synchronized with the detector in such a 
+way that an image is acquired at each excitation point of the waveguide. By invoking Eqn. (1) and neglecting 
+noise, an EPSLON image (Fig. 1d) at the camera plane in general may be described mathematically as 
+     
+               𝐼𝑚(𝑟⃗) = 𝜂|𝑆(𝑟⃗) ∑
+𝑎𝑚(𝑡)𝜓𝑚(𝑟⃗, 𝑡)
+𝑚
+|2 ⨷ |ℎ(𝑟⃗)|2  
+ 
+ 
+                     (2) 
+The abovementioned concepts and experimental results can be summarized into the following: (i) Speckle noise 
+is mitigated in EPSLON images as opposed to label-free waveguide based coherent images due to stochastic 
+fluctuations between the scattered fields, Fig. 1g. (ii) Stochastic fluctuations implies that phase relationships 
+between the scattered fields are lost in EPSLON images as opposed to label-free coherent images. This also leads 
+to identical images for different illumination angles, Fig. 1(h-j) and (iii) Intensity-fluctuations are induced over 
+time due to time dependence of 𝑎𝑚(𝑡) and 𝜓𝑚(𝑟⃗, 𝑡). This is evident in the line plots in Fig. 1j and in the MMI 
+patterns shown as insets in Fig. 2a-2c. This is also validated using simulations in Supplementary Fig. 4. Thus, 
+EPSLON when used in tandem with fluorescence-based super-resolution algorithms helps develop a high-contrast 
+label-free super-resolution imaging system.   
+Applications of EPSLON 
+The potential of EPSLON is first demonstrated on nanobeads, 195 nm polystyrene beads and 200 nm gold 
+nanoparticles (GNP), using the three different waveguide geometries mentioned earlier. For brevity, the 
+diffraction-limited label-free image and its corresponding reconstructed image in the following sections are termed 
+DL and EPSLON. For the straight and four-arm junction waveguide, images are acquired using a detection MO 
+with numerical aperture NA = 0.45. The acquired image stack is given as input to a fluorescence-based super-
+resolution algorithm called as Super-resolution method based on Auto-Correlation two-step Deconvolution 
+(SACD) [9]. The choice of SACD over other IFON algorithms is attributed to the better performance of the 
+algorithm at low signal to background ratios [52]. Now to validate the super-resolved images generated by SACD, 
+the same sample is imaged with a 0.7 NA detection MO, which serves as the ground truth image. In Fig. 3a, the 
+line profiles indicate the intensity variations across the particles in the insets. The line profile of the green inset 
+
+clearly indicates that EPSLON resolves the nanobeads shown in the blue inset in the DL image. This observation 
+is validated by the ground truth image, and it is seen that EPSLON, and the ground truth image agree. A similar 
+experiment is then repeated using the four-arm junction waveguide as shown in Fig. 3b. The use of such a 
+waveguide geometry helps in introducing additional illumination frequencies (Supplementary Fig. 2). It is evident 
+that the line profile in Fig. 3b of the green inset in the EPSLON image shows dips, implying resolving the beads 
+enclosed in the blue inset in the DL image. This is validated again by the ground truth image, i.e., the EPSLON 
+and ground truth images agree.  
+Next, we demonstrate label-free 1-D SIM in EPSLON configuration. The nanobeads are deposited on the SIM 
+structure shown in Fig. 3c. The angle between the interfering waveguides used in the experiment is 60º. This will 
+create an interference pattern with a fringe period 𝑓 =
+𝜆𝑒𝑥
+2𝑛𝑓 sin𝜃
+2
+ where 𝜆𝑒𝑥 is the excitation wavelength, 𝑛𝑓 ≈ 1.7 is 
+the refractive index of the guided mode and 𝜃 is the angle between the interfering waveguides. For better 
+visualization purposes, the interference fringe pattern shown in Fig. 2c is generated by waveguides interfering at 
+an angle 𝜃 = 20º. For the 1-D SIM experiment, images are acquired using a detection MO with NA = 1.2. Phase 
+shifted frames required for the SIM reconstruction is generated by temporarily changing the index on one of the 
+arms of the interfering waveguides. The three phase shifted frames are then given as input to the Fiji plugin of 
+FairSIM [53]. The reconstructed images and its Fourier spectra are provided in Fig. 3c. The SIM reconstruction 
+can clearly resolve the beads enclosed in the red inset in the DL image. The beads in the green inset in the EPSLON 
+image are separated by a distance of 274 nm, shown in the line profile, which lies below the Abbe diffraction limit 
+𝜆𝑑𝑒𝑡
+𝑁𝐴𝑑𝑒𝑡+𝑛𝑓 sin𝜃
+2
+≈ 330 𝑛𝑚, where 𝜆𝑑𝑒𝑡 is the detected wavelength and 𝑁𝐴𝑑𝑒𝑡 is the numerical aperture of the 
+detection MO.  
+Next, to showcase the potential of EPSLON for life sciences, we choose biological samples such as extra-cellular 
+vesicles (EVs) and human placenta tissue. Small EVs are gaining attention due to their role in intercellular 
+communication and possible clinical applications, especially for targeted drug delivery. Nevertheless, their 
+molecular biology, as well as their therapeutic potential, is far to be completely understood. Further understanding 
+of the spatiotemporal aspects of EVs rely on the ability to image processes such as EV secretion, uptake and 
+biodistribution. However, imaging and tracking of small EVs has been challenging due to their small sizes (50-
+200 nm), and often require the use of labeling strategies, that may alter EV release and structure, prior to 
+visualization [54]. These problems are mitigated in EPSLON: the decoupled speckle-illumination and detection 
+paths helps visualize these structures beyond the diffraction-limit with high-contrast and without photobleaching 
+as demonstrated in Fig. 4a. The EVs used in this experiment have a size distribution of 75-250 nm, Supplementary 
+Fig. 5, and are fluorescently labeled. EPSLON and total-internal reflection fluorescence (TIRF) imaging of the 
+same region of interest is performed. Fluorescent dyes are chosen in a way to ensure that there is no fluorescent 
+signal reaching the camera during EPSLON imaging. Images are acquired in both EPSLON and TIRF mode using 
+a detection MO with NA = 0.45. It is seen in Fig. 4a and Fig. 4b that the EPSLON and TIRF images are in good 
+agreement. The line profile in the red and green insets in Fig. 4b show a blob of light and therefore, unable to 
+clearly resolve the particles. To resolve these particles, the DL image stack is given as input to the reconstruction 
+algorithm to generate the EPSLON image. From Fig. 4b it is seen that in the EPSLON image the particles are 
+clearly resolved as shown by the line profiles. To validate the EPSLON image, the same region of interest is 
+imaged with a higher NA = 0.9 detection MO. The EPSLON matches well with the ground truth image.  
+Finally, we showcase the potential of EPSLON on histological samples human placenta tissue. These samples are 
+an ideal candidate for chip-based imaging as clinical applications of these histological samples demand high-
+throughput imaging that is supported by chip-illumination over large areas [18]. Here, images are acquired using 
+a detection MO with NA = 0.10, termed DL image in Fig. 5. The large field-of-view super-resolved EPSLON 
+image is also shown. To validate the EPSLON image, we image the same region of interest with a higher NA = 
+0.25 detection MO. We choose two regions within the field-of-view, ‘‘1’’ and ‘‘2’’ in the DL image in Fig. 5. The 
+corresponding regions in the EPSLON and ground truth image are also blown up and shown alongside. The line 
+profile of the zoomed regions shows clear resolution enhancement in the EPSLON image over the DL image and 
+the EPSLON and ground truth images are in excellent agreement. EPSLON supports both superior contrast and 
+super-resolution imaging with a low magnification imaging objective lens, which is essential for scanning large 
+areas for histopathology applications.  
+Discussion and Outlook 
+
+Fluorescence based algorithms have been previously applied to coherently scattering specimens [36, 55]. However, 
+the reconstructed images generated must be interpreted with caution with regards to resolution beyond the 
+diffraction-limit as coherence of the scattered light cannot be neglected [13, 29]. In our proof-of-concept work 
+EPSLON, we circumvent this issue for two-dimensional samples by realizing a light source with δ-function 
+correlations, i.e., by using the PL property of Si3N4 waveguides for near-field illumination of unlabeled samples. 
+In addition, PL emission takes place within the core matrix and a part of it gets transmitted into the far-field, which 
+prevents realizing an ideal chip-based imaging system where only the scattered light off the sample reaches the 
+camera. As a result, the signal to background ratio of weakly scattering specimens is poor and hence, imaging in 
+this current work was restricted to lower magnification objectives. Despite the limited photon budget, we have 
+demonstrated proof-of-concept label-free super-resolution results on nanobeads, EVs and human placenta tissue. 
+The experimental particulars are provided in Table 1 and Table 2 in the supplementary material. In future works, 
+we propose novel chip designs as in Ref. [56, 57] which will improve the poor signal to background ratio. The 
+other challenge of lack of specificity in label-free imaging can be mitigated by resorting to machine learning based 
+tools [58].  
+This work lays the foundation for synthesizing a label-free incoherent imaging system that is compatible with the 
+myriad of fluorescence based super-resolution algorithms to circumvent the spatial diffraction-limit. We believe 
+that EPSLON will trigger further developments of label-free super-resolution incoherent optical microscopy 
+methods and its application in biology. This work could also initiate further developments within integrated optics 
+to harness the PL properties of different materials. Interestingly, PL in waveguides is an undesirable phenomenon 
+as it increases the propagation losses of the guiding structures. However, here we demonstrated that PL of Si3N4 
+waveguide can be harnessed for near-field illumination to develop an incoherent imaging system for surpassing 
+the diffraction limit in label-free regime.  
+ 
+References 
+1. Wolf, E., 2007. Introduction to the Theory of Coherence and Polarization of Light. Cambridge university 
+press. 
+2. Fujimoto, J.G., Pitris, C., Boppart, S.A. and Brezinski, M.E., 2000. Optical coherence tomography: an 
+emerging technology for biomedical imaging and optical biopsy. Neoplasia, 2(1-2), pp.9-25. 
+3. Heintzmann, R. and Cremer, C.G., 1999, January. Laterally modulated excitation microscopy: 
+improvement of resolution by using a diffraction grating. In Optical biopsies and microscopic techniques 
+III (Vol. 3568, pp. 185-196). SPIE. 
+4. Gustafsson, M.G., 2000. Surpassing the lateral resolution limit by a factor of two using structured 
+illumination microscopy. Journal of microscopy, 198(2), pp.82-87. 
+5. Dertinger, T., Colyer, R., Iyer, G., Weiss, S. and Enderlein, J., 2009. Fast, background-free, 3D super-
+resolution optical fluctuation imaging (SOFI). Proceedings of the National Academy of 
+Sciences, 106(52), pp.22287-22292. 
+6. Gustafsson, N., Culley, S., Ashdown, G., Owen, D.M., Pereira, P.M. and Henriques, R., 2016. Fast live-
+cell 
+conventional 
+fluorophore 
+nanoscopy 
+with 
+ImageJ 
+through 
+super-resolution 
+radial 
+fluctuations. Nature communications, 7(1), pp.1-9. 
+7. Yahiatene, I., Hennig, S., Müller, M. and Huser, T., 2015. Entropy-based super-resolution imaging (ESI): 
+From disorder to fine detail. Acs Photonics, 2(8), pp.1049-1056. 
+8. Cox, S., Rosten, E., Monypenny, J., Jovanovic-Talisman, T., Burnette, D.T., Lippincott-Schwartz, J., 
+Jones, G.E. and Heintzmann, R., 2012. Bayesian localization microscopy reveals nanoscale podosome 
+dynamics. Nature methods, 9(2), pp.195-200. 
+9. Zhao, W., Zhao, S., Han, Z., Ding, X., Hu, G., Wang, X., Mao, H., Jiu, Y., Hu, Y., Tan, J. and Ding, X., 
+2022. Enhancing detectable fluorescence fluctuation for high-throughput and four-dimensional live-cell 
+super-resolution imaging. bioRxiv.  
+10. Agarwal, K. and Macháň, R., 2016. Multiple signal classification algorithm for super-resolution 
+fluorescence microscopy. Nature communications, 7(1), pp.1-9. 
+11. Ryabukho, V.P., Lyakin, D.V., Grebenyuk, A.A. and Klykov, S.S., 2013. Wiener–Khintchin theorem for 
+spatial coherence of optical wave field. Journal of Optics, 15(2), p.025405. 
+12. Goodman, J.W., 2007. Speckle phenomena in optics: theory and applications. Roberts and Company 
+Publishers. 
+
+13. Wicker, K. and Heintzmann, R., 2014. Resolving a misconception about structured illumination. Nature 
+Photonics, 8(5), pp.342-344. 
+14. Kistner, J., Chen, X., Weng, Y., Strunk, H.P., Schubert, M.B. and Werner, J.H., 2011. Photoluminescence 
+from silicon nitride—no quantum effect. Journal of Applied Physics, 110(2), p.023520. 
+15. Coucheron, D.A., Helle, Ø.I., Wilkinson, J.S., Murugan, G.S., Domínguez, C., Angelskår, H. and 
+Ahluwalia, B.S., 2021. Study of waveguide background at visible wavelengths for on-chip 
+nanoscopy. Optics Express, 29(13), pp.20735-20746. 
+16. Diekmann, R., Helle, Ø.I., Øie, C.I., McCourt, P., Huser, T.R., Schüttpelz, M. and Ahluwalia, B.S., 2017. 
+Chip-based wide field-of-view nanoscopy. Nature Photonics, 11(5), pp.322-328. 
+17. Jayakumar, N., Helle, Ø.I., Agarwal, K. and Ahluwalia, B.S., 2020. On-chip TIRF nanoscopy by applying 
+Haar wavelet kernel analysis on intensity fluctuations induced by chip illumination. Optics 
+Express, 28(24), pp.35454-35468. 
+18. Villegas-Hernández, L.E., Dubey, V., Nystad, M., Tinguely, J.C., Coucheron, D.A., Dullo, F.T., 
+Priyadarshi, A., Acuña, S., Ahmad, A., Mateos, J.M. and Barmettler, G., 2022. Chip-based multimodal 
+super-resolution microscopy for histological investigations of cryopreserved tissue sections. Light: 
+Science & Applications, 11(1), pp.1-17. 
+19. Zernike, F., 1955. How I discovered phase contrast. Science, 121(3141), pp.345-349. 
+20. Chen, M., Phillips, Z.F. and Waller, L., 2018. Quantitative differential phase contrast (DPC) microscopy 
+with computational aberration correction. Optics express, 26(25), pp.32888-32899. 
+21. Taylor, R.W., Mahmoodabadi, R.G., Rauschenberger, V., Giessl, A., Schambony, A. and Sandoghdar, 
+V., 2019. Interferometric scattering microscopy reveals microsecond nanoscopic protein motion on a live 
+cell membrane. Nature Photonics, 13(7), pp.480-487. 
+22. Park, Y., Depeursinge, C. and Popescu, G., 2018. Quantitative phase imaging in biomedicine. Nature 
+photonics, 12(10), pp.578-589. 
+23. Baek, Y. and Park, Y., 2021. Intensity-based holographic imaging via space-domain Kramers–Kronig 
+relations. Nature Photonics, 15(5), pp.354-360. 
+24. Zheng, G., Horstmeyer, R. and Yang, C., 2013. Wide-field, high-resolution Fourier ptychographic 
+microscopy. Nature photonics, 7(9), pp.739-745. 
+25. Ruh, D., Mutschler, J., Michelbach, M. and Rohrbach, A., 2018. Superior contrast and resolution by 
+image formation in rotating coherent scattering (ROCS) microscopy. Optica, 5(11), pp.1371-1381. 
+26. Redding, B., Choma, M.A. and Cao, H., 2012. Speckle-free laser imaging using random laser 
+illumination. Nature photonics, 6(6), pp.355-359. 
+27. Ojaghi, A., Fay, M.E., Lam, W.A. and Robles, F.E., 2018. Ultraviolet hyperspectral interferometric 
+microscopy. Scientific reports, 8(1), pp.1-6. 
+28. Liu, X., Kuang, C., Hao, X., Pang, C., Xu, P., Li, H., Liu, Y., Yu, C., Xu, Y., Nan, D. and Shen, W., 2017. 
+Fluorescent nanowire ring illumination for wide-field far-field subdiffraction imaging. Physical Review 
+Letters, 118(7), p.076101. 
+29. Jayakumar, N., Dullo, F.T., Dubey, V., Ahmad, A., Ströhl, F., Cauzzo, J., Guerreiro, E.M., Snir, O., 
+Skalko-Basnet, N., Agarwal, K. and Ahluwalia, B.S., 2022. Multi-moded high-index contrast optical 
+waveguide for super-contrast high-resolution label-free microscopy. Nanophotonics, 11(15), pp.3421-
+3436. 
+30. Schermelleh, L., Ferrand, A., Huser, T., Eggeling, C., Sauer, M., Biehlmaier, O. and Drummen, G.P., 
+2019. Super-resolution microscopy demystified. Nature cell biology, 21(1), pp.72-84. 
+31. Betzig, E. and Chichester, R.J., 1993. Single molecules observed by near-field scanning optical 
+microscopy. Science, 262(5138), pp.1422-1425. 
+32. Pendry, J.B., 2000. Negative refraction makes a perfect lens. Physical review letters, 85(18), p.3966. 
+33. Wang, Z., Guo, W., Li, L., Luk'Yanchuk, B., Khan, A., Liu, Z., Chen, Z. and Hong, M., 2011. Optical 
+virtual imaging at 50 nm lateral resolution with a white-light nanoscope. Nature communications, 2(1), 
+pp.1-6. 
+34. Darafsheh, A., Limberopoulos, N.I., Derov, J.S., Walker Jr, D.E. and Astratov, V.N., 2014. Advantages 
+of microsphere-assisted super-resolution imaging technique over solid immersion lens and confocal 
+microscopies. Applied Physics Letters, 104(6), p.061117. 
+35. Rogers, E.T., Lindberg, J., Roy, T., Savo, S., Chad, J.E., Dennis, M.R. and Zheludev, N.I., 2012. A super-
+oscillatory lens optical microscope for subwavelength imaging. Nature materials, 11(5), pp.432-435. 
+
+36. Lee, Y.U., Li, S., Wisna, G.B.M., Zhao, J., Zeng, Y., Tao, A.R. and Liu, Z., 2022. Hyperbolic material 
+enhanced scattering nanoscopy for label-free super-resolution imaging. Nature communications, 13(1), 
+pp.1-8. 
+37. Lin, C., Peñaranda, J.S.D., Dendooven, J., Detavernier, C., Schaubroeck, D., Boon, N., Baets, R. and Le 
+Thomas, N., 2022. UV photonic integrated circuits for far-field structured illumination autofluorescence 
+microscopy. Nature Communications, 13(1), pp.1-9. 
+38. Dong, B., Almassalha, L.M., Stypula-Cyrus, Y., Urban, B.E., Chandler, J.E., Nguyen, T.Q., Sun, C., 
+Zhang, H.F. and Backman, V., 2016. Superresolution intrinsic fluorescence imaging of chromatin 
+utilizing native, unmodified nucleic acids for contrast. Proceedings of the National Academy of 
+Sciences, 113(35), pp.9716-9721. 
+39. Goodman, J. W. Introduction to Fourier Optics (Roberts & Company, 2005). 
+40. Gustafsson, M.G., 2005. Nonlinear structured-illumination microscopy: wide-field fluorescence imaging 
+with theoretically unlimited resolution. Proceedings of the National Academy of Sciences, 102(37), 
+pp.13081-13086. 
+41. Berezin, M.Y. and Achilefu, S., 2010. Fluorescence lifetime measurements and biological 
+imaging. Chemical reviews, 110(5), pp.2641-2684. 
+42. Chowdhury, S., Dhalla, A.H. and Izatt, J., 2012. Structured oblique illumination microscopy for enhanced 
+resolution imaging of non-fluorescent, coherently scattering samples. Biomedical optics express, 3(8), 
+pp.1841-1854. 
+43. Prieto, F., Sepúlveda, B., Calle, A., Llobera, A., Domínguez, C., Abad, A., Montoya, A. and Lechuga, 
+L.M., 2003. An integrated optical interferometric nanodevice based on silicon technology for biosensor 
+applications. Nanotechnology, 14(8), p.907. 
+44. Tinguely, J.C., Helle, Ø.I. and Ahluwalia, B.S., 2017. Silicon nitride waveguide platform for fluorescence 
+microscopy of living cells. Optics express, 25(22), pp.27678-27690. 
+45. Dhakal, A., Wuytens, P., Raza, A., Le Thomas, N. and Baets, R., 2017. Silicon nitride background in 
+nanophotonic waveguide enhanced Raman spectroscopy. Materials, 10(2), p.140. 
+46. Aydinli, A., Serpengüzel, A. and Vardar, D., 1996. Visible photoluminescence from low temperature 
+deposited hydrogenated amorphous silicon nitride. Solid state communications, 98(4), pp.273-277. 
+47. Vlasukova, L.A., Komarov, F.F., Parkhomenko, I.N., Milchanin, O.V., Leont’ev, A.V., Mudryi, A.V. and 
+Togambaeva, A.K., 2013. Optical properties of silicon nitride films formed by plasma-chemical vapor 
+deposition. Journal of Applied Spectroscopy, 80(1), pp.89-92. 
+48. Giorgis, F., Vinegoni, C. and Pavesi, L., 2000. Optical absorption and photoluminescence properties of 
+a− Si 1− x N x: H films deposited by plasma-enhanced CVD. Physical Review B, 61(7), p.4693. 
+49. Smith, J., Monroy-Ruz, J., Rarity, J.G. and C. Balram, K., 2020. Single photon emission and single spin 
+coherence of a nitrogen vacancy center encapsulated in silicon nitride. Applied Physics Letters, 116(13), 
+p.134001. 
+50. Helle, Ø.I., Dullo, F.T., Lahrberg, M., Tinguely, J.C., Hellesø, O.G. and Ahluwalia, B.S., 2020. Structured 
+illumination microscopy using a photonic chip. Nature Photonics, 14(7), pp.431-438. 
+51. Engdahl, A.K., Belle, S., Wang, T.C., Hellmann, R., Huser, T. and Schüttpelz, M., 2021. Large Field-of-
+View Super-Resolution Optical Microscopy Based on Planar Polymer Waveguides. ACS Photonics, 8(7), 
+pp.1944-1950. 
+52. Opstad, I.S., Acuña, S., Hernandez, L.E.V., Cauzzo, J., Škalko-Basnet, N., Ahluwalia, B.S. and Agarwal, 
+K., 2020. Fluorescence fluctuations-based super-resolution microscopy techniques: an experimental 
+comparative study. arXiv preprint arXiv:2008.09195. 
+53. Müller, M., Mönkemöller, V., Hennig, S., Hübner, W. and Huser, T., 2016. Open-source image 
+reconstruction of super-resolution structured illumination microscopy data in ImageJ. Nature 
+communications, 7(1), pp.1-6. 
+54. Chuo, S.T.Y., Chien, J.C.Y. and Lai, C.P.K., 2018. Imaging extracellular vesicles: current and emerging 
+methods. Journal of biomedical science, 25(1), pp.1-10. 
+55. Chang, B.J., Lin, S.H., Chou, L.J. and Chiang, S.Y., 2011. Subdiffraction scattered light imaging of gold 
+nanoparticles using structured illumination. Optics letters, 36(24), pp.4773-4775. 
+56. Chazot, C.A., Nagelberg, S., Rowlands, C.J., Scherer, M.R., Coropceanu, I., Broderick, K., Kim, Y., 
+Bawendi, M.G., So, P.T. and Kolle, M., 2020. Luminescent surfaces with tailored angular emission for 
+compact dark-field imaging devices. Nature photonics, 14(5), pp.310-315. 
+57. Kuai, Y., Chen, J., Fan, Z., Zou, G., Lakowicz, J. and Zhang, D., 2021. Planar photonic chips with tailored 
+angular transmission for high-contrast-imaging devices. Nature communications, 12(1), pp.1-9. 
+
+58. Kandel, M.E., He, Y.R., Lee, Y.J., Chen, T.H.Y., Sullivan, K.M., Aydin, O., Saif, M.T.A., Kong, H., 
+Sobh, N. and Popescu, G., 2020. Phase imaging with computational specificity (PICS) for measuring dry 
+mass changes in sub-cellular compartments. Nature communications, 11(1), pp.1-10. 
+ 
+Ethical statement 
+Full-term placentae from 10 different Caucasian healthy patients were collected anonymously immediately after 
+delivery at the University Hospital of North Norway. Written consent was obtained from the participants according 
+to the protocol approved by the Regional Committee for Medical and Health Research Ethics of North Norway 
+(REK Nord reference no. 2010/2058–4). 
+ 
+Acknowledgements 
+We wish to acknowledge the fruitful discussions with Dr. Florian Strohl (UiT) and Prof. Krishna Agarwal (UiT) 
+that helped us complete this work in a timely fashion, Prof. Ganesh Acharya, Prof. Mona Nystad (UiT) and Luis 
+Villegas (UiT) for providing us with the tissue placenta sections. Dr. Hong Mao for his constant support throughout 
+our experiments. We would also like to express our sincere thanks to Dr. Weisong Zhao (Harbin Institute of 
+Technology) for his valuable inputs and cooperation that enabled in the timely completion of this manuscript.  
+This project has received funding from the European Union’s Horizon 2020 research and innovation program 
+under the Marie Skłodowska-Curie Grant Agreement No. 766181, project “DeLIVER” and from the Research 
+Council of Norway (NANO 2021–288565); BIOTEK 2021 (BIOTEK 2021–285571). 
+ 
+Authors and Affiliations 
+Dept. of Physics and Technology, UiT The Arctic University of Norway, Tromsø 9037, Norway 
+Nikhil Jayakumar, Jean-Claude Tinguley, Balpreet Singh Ahluwalia 
+Dept. of Microsystems and Nanotechnology, SINTEF Digital, Gaustadalleen 23C, 0373 Oslo, Norway 
+Firehun T Dullo 
+Dept. of Molecular Cell Biology, Institute for Cancer Research, Oslo University Hospital, Oslo, Norway 
+Krizia Sagini, Alicia Llorente 
+Centre for Cancer Cell Reprogramming, Faculty of Medicine, University of Oslo, Montebello, 0379 Oslo, 
+Norway 
+Krizia Sagini, Alicia Llorente 
+Dept. for Mechanical, Electronics and Chemical Engineering, Oslo Metropolitan University, Oslo, Norway 
+Alicia Llorente 
+ 
+Author Contribution 
+NJ conceived and conceptualized the idea. NJ and BSA designed the experiments. FTD and JCT designed the 
+waveguide chip and mask for fabrication. FTD also performed the FIMMWAVE simulations. KS and AL provided 
+the extra-cellular vesicles for imaging and wrote the EV preparation protocol. NJ performed the experiments, 
+analyzed the results and prepared the manuscript with inputs from FTD, JCT and BSA. All authors commented on 
+the manuscript. BSA secured and supervised the project. 
+Conflict of interest statement: B.S.A. have applied for patent for chip-based optical nanoscopy. B.S.A is the 
+co-founder of the company Chip NanoImaging AS, which commercializes on-chip super-resolution microscopy 
+systems. All other authors declare no conflicts of interest regarding this article. 
+ 
+
+ 
+Figure 1 Overview of ELSPON: (a-d) Comparison between fluorescence and label-free microscopy. (a) 
+Epifluorescence: coherent light λexc is used for excitation of fluorescent molecules and the camera detects the Stoke 
+shifted incoherent light emitted by the molecules λem. Stochastic fluctuations of the Stoke shifted light and 
+specificity offered by the molecules helps suppress speckle noise enabling high-contrast imaging. (b) TIRF: 
+coherent light for near-field illumination of fluorescently labeled samples and incoherent light gets detected by the 
+camera. Near-field illumination helps to further improve the contrast as compared to the epifluorescence by 
+illuminating thin sections of the sample. (c) Label-free coherent imaging: coherent light for illumination and 
+coherent light gets detected by the camera. Multiple scattering and coherent nature of the scattered light leads to 
+speckle noise, (d) EPSLON: incoherent light for near-field illumination of unlabeled samples and incoherent light 
+scattered by the sample, λaf, forms the image. The incoherent nature of the detected light in addition to the near-
+field illumination helps generate high-contrast label-free images. (e) Schematic of optical waveguide-based label-
+free coherent imaging. The guided coherent light generates an evanescent field that interacts with the sample placed 
+at the core-cladding interface, and thereby transmits high-spatial frequencies of the sample into the far-field. (f) 
+Schematic of EPSLON imaging using Si3N4 waveguide. The guided coherent light induces incoherent 
+photoluminescence (PL) in the core of the waveguide that interacts with the sample and gets transmitted into the 
+far-field. (g) 200 nm gold nanoparticles imaged in coherent and EPSLON mode, scale bar 100 μm. The issues of 
+coherent noise, poor-contrast associated with conventional label-free techniques is mitigated in EPSLON due to 
+δ-function correlations existing in the detected light. (h) To induce fluctuations in image intensity over time, 
+different modes of the waveguide are excited by scanning the coupling objective along the input facet of the 
+waveguide. At each instance of time t1, t2, t3 etc. the scatterers get excited by different MMI patterns, and an image 
+is acquired. Scale bar 10 μm. (i) Experimental demonstration of coherence of scattered light using two 200 nm 
+gold nanoparticles, scale bar 10 μm. The excitation of different modes causes the phase difference Δ𝜑 between the 
+scattered light off the particles to change, leading to different images at different instances of time in label-free 
+coherent imaging. This is demonstrated by the line profile of the bead images provided alongside. (j) Experimental 
+realization of stochastic nature of the detected light in label-free imaging. The same nanoparticles shown in (i) are 
+imaged in EPSLON mode, scale bar 10 μm. In EPSLON, stochastic fluctuations between the scattered incoherent 
+PL light reaching the camera leads to identical images at different instances of time. This can be seen from the line 
+profiles of the bead images provided alongside.                   
+ 
+
+a
+Epi-
+b
+C
+Label-free,
+d
+EPSLON:
+Imageplane
+TIRF
+Imageplane
+Image plane
+Imageplane
+fluorescence
+coherent
+Label-free.
+incoherent
+M.O
+M.O
+M.O
+M.O
+Sampleplane
+Sampleplane
+Sampleplane
+Sampleplane
+80
+O
+O
+exc
+f
+tomicroscope
+g
+Label-free,
+e
+Label-free,
+tomicroscope
+EPSLON
+EPSLON
+coherent
+coherent
+scatterer
+af
+filter
+M.O
++A
+M.O
+exc
+eXC
+exc
+exo
+M.O.
+M.O.
+waveguidechip
+waveguidechip
+scatterers
+h
+Label-free.
+3
+Greyvalue (norm.)
+coherent
+Greyvalue (norm.)
+EPSLON
+AO
+facetscan
+2
+Ad
+A2
+Ao,
+Az
+Aos
+0
+1
+2
+-
+2
+3
+4
+Distance (μm)
+Distance (μm) 
+ 
+Figure 2: Structuring the incoherent photoluminescent illumination using Si3N4 waveguides and its 
+properties. (a-c) Structuring photoluminescence using different waveguide geometries. (a) Straight waveguide 
+that supports multiple modes in the core, scale bar 20 μm. The red insets are a part of the imaging region on the 
+straight waveguide that is blown up to show the MMI pattern at different instances of time, scale bar 5 μm. 
+Schematic diagram shows the geometry and width of the straight waveguide fabricated on a wafer. (b) Four-arm 
+crossing waveguide provides more illumination spatial frequencies, scale bar 20 μm. The green inset is the blown-
+up region of the imaging area on the four-arm crossing waveguide, showing different speckle patterns at different 
+instances of time, scale bar 5 μm. Schematic diagram shows the geometry and width of the four-arm crossing 
+waveguide. (c) SIM chip where two single-mode waveguides are made to overlap at the imaging area enclosed by 
+the blue inset, scale bar 20 μm. The blown-up regions show the interference fringe pattern at three different phases, 
+2 μm. Schematic diagram shows the geometry of the SIM chip for two-dimensional SIM works. (d) By averaging 
+out several MMI patterns, a uniform illumination profile over large field-of-view can be generated, scale bar 100 
+μm. (e) Ratio of incoherent PL scattering to coherent scattering for a single waveguide at three different 
+wavelengths is plotted. Here the waveguide is excited at 488 nm, 561 nm and 640 nm and the corresponding 
+emissions may be detected in FITC, TRITC and CY5 channels. (f) PL emission as a function of time is plotted 
+here. No bleaching was observed for about 2 hours of imaging indicating a stable emission that is suitable for long-
+term cell imaging. (g) PL emission varies linearly with the input coupling power, implying a linear system. 
+ 
+
+a
+q
+t
+C
+Straight
+Four-arm
+SIM
+25-1000μm
+200-400μm
+25μm
+Multi-wavelength
+Uniformillumination
+emission
+Stableemission
+Linearemission
+d
+Excitation wavelength (nm)
+1.0
+1.0
+e
+488
+561
+640
+g
+3
+?0.8
+0.02
+Aod
+0.15
+0.6
+0.01
+0.2
+0.05
+50
+100
+0.2
+0.4
+0.6
+0.8
+1.0
+Time (minutes)
+Normalized inputpower(a.u.)
+FITCTRITCCy5TRITCCy5 Cy5
+Fluorescencefiltet 
+ 
+Figure 3: EPSLON for label-free super-resolution imaging of nanobeads using various waveguide 
+geometries.  (a,b,c) Label-free diffraction limited image termed DL, super-resolved image termed EPSLON and 
+ground truth image of nanobeads are shown. (a) Label-free super-resolved images of 200 nm gold nanoparticles 
+using a straight waveguide is demonstrated. The diffraction-limited DL image, super-resolved EPSLON image 
+and ground truth optical images are given alongside, scale bar 5 μm. The red and green line plot corresponds to 
+intensity variation in the red and green insets in DL and EPSLON image respectively. (b) Label-free super-resolved 
+images of 150 nm gold nanoparticles using a four-arm waveguide is demonstrated, scale bar 5 μm. In the straight 
+waveguide, illumination frequencies are predominantly distributed along one-axis and therefore, resolution 
+enhancement is possible only along that axis. To mitigate this issue, a four-arm waveguide is used that provides 
+more illumination frequencies along the azimuthal orientation, thereby permits resolution enhancement along two 
+orthogonal directions. The two red insets in the DL image enclose unresolved beads oriented along two orthogonal 
+directions corresponding to the illumination frequency direction. The line profile of the intensity variation in the 
+green inset clearly indicates resolving the two beads enclosed by the red inset which is validated by the ground 
+truth image. (c) Label-free 1-D SIM of 200 nm gold nanoparticles is demonstrated, scale bar 5 μm. The line profile 
+indicates the intensity variations in the red and green insets in the diffraction-limited DL and FairSIM reconstructed 
+EPSLON images respectively. The line profile clearly shows the separation of two particles spaced 274 nm, which 
+is beyond the diffraction-limit of the imaging system. The Fourier domain representation of the diffraction-limited 
+and reconstructed image are also provided alongside, scale bar 2 μm-1.   
+ 
+ 
+
+a
+Label-freeIFON usingstraightwaveguide
+DL
+EPSLON
+Groundtruth
+1.0
+DL
+EPSLON
+20.4
+0.0
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+Distance (μm)
+b
+Label-freeIFONusingfour-armwaveguide
+DL
+EPSLON
+Groundtruth
+DL
+1.0
+EPSLON
+0.67
+intensity
+0.4
+0.2
+0.0
+0.5
+1.0
+1.5
+0.0
+Distance (μm)C
+EPsLONforone-dimensionallabel-freeSlM
+DL
+EPSLON
+274nm
+1.0
+DL
+EPSLON
+0.8
+0.6
+cn
+0.4
+0.2
+0.0
+0.2
+0.6
+1.2
+0.2
+0.0
+0.4
+0.8
+1.0
+Distance (um) 
+Figure 4: EPSLON for circumventing photobleaching and for label-free super-resolution imaging of EVs 
+(a) Time-lapse imaging comparison of extra-cellular vesicles between TIRF and EPSLON configurations. 
+EPSLON helps to image nanosized EVs over long periods of time without photobleaching and with better signal-
+to-background ratio as opposed to TIRF, scale bar 5 μm. This fact is quantified in the graph where signal-to-
+background ratio as a function of time is plotted. (b) Super-resolution imaging of EVs in label-free regime using 
+EPSLON configuration. EVs are imaged in both TIRF and EPSLON mode, scale bar 2 μm. The red, green, blue, 
+and yellow insets correspond to EVs in diffraction-limited TIRF image, label-free diffraction-limited image termed 
+DL, label-free super-resolved EPSLON image and TIRF ground truth image. The line profiles corresponding to 
+each of these insets showing the intensity variation are also shown alongside. EPSLON resolves the unresolved 
+EVs in the diffraction-limited images and this result is validated by the TIRF ground truth image acquired with a 
+higher NA objective.     
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+Distance (μm)
+a
+b
+20X/0.45NATIRF
+1.0
+Osec
+2 sec
+8 sec
+0.8
+TIRF
+0.6
+0.4
+0
+4
+20X/0.45NADL
+1.0
+EPSLON
+0.8
+0.6
+0.4
+0
+1
+2
+3
+intensity (a.u.
+1.5
+EPSLON
+1.0
+1.4
+0.5
+1.3
+1.3
+0.0
+0
+1.2
+1.2
+60X/0.9NATIRF
+1.00
+1.1
+0.75
+1.0
+3
+0.50
+0
+2
+4
+6
+8
+Time(s)
+0.25 
+Figure 5: EPSLON for label-free super-resolution imaging of human placenta tissue sections: Large field-
+of-view label-free diffraction-limited image termed DL, super-resolved EPSLON image and ground truth images 
+are shown, scale bar 25 μm. Two regions marked ‘‘1’’ and ‘‘2’’ in the DL image are blown-up and shown 
+alongside. The corresponding regions in the EPSLON and ground truth images are also magnified and shown, 
+scale bar 10 μm. Line profiles along the white dotted lines in the magnified boxes of the DL image fails to resolve 
+any intricate features as shown by the line plots. EPSLON images provide more details as seen in the images and 
+they are validated by the ground truth images, which are also evidenced by the line plots.    
+ 
+ 
+ 
+   
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+Figure.5:EPSLONforlabel-freesuper-resolutionofhuman
+DL
+EPSLON
+Groundtruth
+placentatissuesections
+1.00
+0.75
+Intensity (a.u.
+0.50
+Diffraction-limited
+0.25
+0
+EPSLON
+um
+Groundtruth
+1.00
+0.75
+0.50
+Ground truth 
+ 
+Label-free incoherent super-resolution optical microscopy 
+Nikhil Jayakumar, Firehun T Dullo, Jean-Claude Tinguley, Krizia Sagini, Alicia Llorente, Balpreet Singh 
+Ahluwalia 
+1Department of Physics and Technology, UiT The Arctic University of Norway, Tromsø, 9037, Norway 
+2Department of Microsystems and Nanotechnology, SINTEF Digital, Gaustadalleen 23C, 0373 Oslo, Norway 
+3 Department of Molecular Cell Biology, Institute for Cancer Research, Oslo University Hospital, The 
+Norwegian Radium Hospital, 0379 Oslo, Norway 
+4Centre for Cancer Cell Reprogramming, Faculty of Medicine, University of Oslo, Montebello, 0379 Oslo, Norway 
+5Department for Mechanical, Electronics and Chemical Engineering, Oslo Metropolitan University, Oslo, Norway 
+*Balpreet.singh.ahluwalia@uit.no 
+ 
+Supplementary Information 
+1. Waveguide fabrication 
+A 2 µm thick oxide layer was thermally grown on a silicon wafer, followed by the deposition of 150 nm 
+thick Si3N4 layer using plasma enhanced chemical vapor deposition (PECVD). The 2D channel 
+waveguides were defined by photolithography process and etched using reactive ion etching (RIE). 
+Then, silicon oxide layer was deposited using PECVD on the patterned nitride layer for protection. 
+Finally, the oxide layer was patterned and removed from certain regions of each waveguide to create the 
+imaging regions. The oxide layer was removed using combination of both dry and wet etching [1].  
+      
+2. Waveguide modes 
+ 
+Figure. 1: (a) Effective indices of the guided modes for various Si3N4 waveguide widths. A schematic diagram of 
+the cross-section of the waveguide is provided as an inset in the plot. (b) Mode profiles for the fundamental and 
+higher-order TE - modes. The geometry of the waveguide in the simulation model is 150 nm thick and 0.25 - 4 
+µm wide. The guided modes for a strip Si3N4 waveguide were simulated using the commercial software 
+FIMMWAVE (Photon Design, Oxford, UK), and its effective indices were calculated using the full-vectorial film 
+mode matching (FMM) method. 
+ 
+ 
+
+(a)
+(b)
+1.71
+TEOO
+Effective index (n_eff)
+H20
+1.66
+TE01
+S3N4
+TE02
+Si02
+1.61
+TEO0
+TE01
+TE03
+TE04
+1.56
+TE05
+TE06
+1.51
+TE07
+TE02
+TE03
+TE08
+TE09
+1.46
+0
+0.5
+1
+1.5
+2
+2.5
+3
+3.5
+4
+Waveguidewidth(um) 
+Figure. 2: Waveguide geometries employed in EPSLON for beam shaping and their corresponding 
+illumination frequencies. The multi-moded interference (MMI) pattern of straight and four-crossing waveguide 
+is captured using a 20X/0.45 NA objective, scale bar 25 μm, while that of the SIM chip is captured using a 60X/1.2 
+NA objective, scale bar 5 μm. To see the well-defined fringe patterns in case of SIM chips, the interference angle 
+between the overlapping single moded waveguides is chosen to be 20 degrees. The orange markers on the figures 
+indicate the extend and orientation of the illuminating frequencies. Scale bar 500 mm-1 for the straight and four-
+arm junction waveguide and 1 μm-1 for the SIM chip. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+Straight
+Four-cross
+SIM
+25 μm
+25 μm
+5 μm
+pattern
+500mm-1
+500mm-1
+1 μm-1
+Ilumination spatial
+frequencies 
+3. Schematic diagram of the imaging setup for EPSLON 
+ 
+ 
+Figure. 3. Schematic diagram of experimental setup for EPSLON. Laser guided by a single mode fiber (SMF) 
+held on a XY piezo stage by vacuum chuck is collimated and directed to the back-focal plane of coupling objective 
+Olympus LMPanFL N 50×/0.5 NA MO1. The light is focused by MO1 and coupled into Si3N4 waveguide mounted 
+on a XYZ piezo stage. The coupled laser light in the waveguide, induces a broadband photoluminescence in the 
+core. Any index perturbation scatters the PL light, shown in red, into the far-field via detection objective MO2, 
+tube lens with spectral filters onto a sCMOS Hamamatsu C13440-20CU camera. The spectral filters are chosen to 
+reject the coherent laser light and transmit only the incoherent photoluminescent light.  
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ExperimentalsetupforEPSLON
+SCMOS
+Tube lenswith
+spectral filter
+MO2
+SMF
+SigNWaveguide
+Piezo
+7
+MO1
+X
+Piezostage4. Optical modes of the waveguide to induce intensity-fluctuations: simulation study 
+ 
+ 
+Figure. 4: Two particle resolution comparison between waveguide-based coherent and incoherent 
+(EPSLON) imaging. Three separate cases are considered for comparison between coherent and incoherent 
+EPSLON imaging. For brevity, only the fundamental mode with amplitude a1 and higher-order mode with 
+amplitude a2 are considered interacting with the sample in each case. The colorbar provided alongside indicates 
+the phase variation of the field across the cross-section or width of the waveguide. The sample consists of two 150 
+nm sized particles which are placed with a center-to-center distance of 350 nm apart on the core-cladding interface 
+of a 10 μm Si3N4 waveguide. The particles scatter 500 nm wavelength light into a detection objective with NA = 
+1. The image generated at the camera plane for the coherent and EPSLON cases are shown, scale bar 500 nm. The 
+loss in phase information in EPSLON imaging leads to similarity in images for the different excitation cases.   
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+Mode 1
+Mode 1
+Mode 1
+Mode 1
+Mode1
+Mode 1
+ai= 1
+a2= 1
+ai=1
+a2 = 0.1
+ai= 1
+a2 = 1
+Coherent
+EPSLON
+Coherent
+EPSLON
+Coherent
+EPSLON 
+5. Small EV preparation and characterization 
+Small EVs were isolated from fresh urine samples collected in the morning from healthy donors. The 
+collection of urine samples was approved by the Norwegian Regional Committees for Medical and Health 
+Research Ethics and the participants gave informed written consent. Small EVs were isolated by differential 
+centrifugation as previously described [2]. Briefly, urine (around 200 ml) was centrifuged at 2000×g for 15 
+min at room temperature (RT) to remove cells and cell debris, and then at 10,000×g for 30 min at RT to 
+separate large particles/vesicles. The resulting supernatant was centrifuged at 100,000×g for 70 min at RT in 
+a Ti70 fixed-angle rotor (Beckmann Coulter, IN, USA) to pellet small particles. The pellet was washed with 
+20 ml phosphate-buffered saline (PBS) and centrifuged again at 100,000×g for 70 min at 4°C in a Ti70 rotor. 
+The pellet was then resuspended in 6.5 ml PBS, vortexed and centrifuged at 100,000×g for 70 min at 4°C in 
+an MLA-80 fixed-angle rotor (Beckmann Coulter, IN, USA). The supernatant was then removed, and the 
+pellet resuspended in 200 μl PBS (filtered through a 0.02-μm Anotop 25 filter) and stained with CellMask™ 
+Deep Red plasma membrane dye (C10046, Invitrogen, MA, USA) according to manufacturer’s instructions. 
+Briefly, small EVs were incubated with CellMask™ Deep Red (diluted 1:500) for 10 min at 37°C, then the 
+unbounded dye was removed and stained EVs washed with filtered PBS using ultrafiltration devices (Amicon 
+Ultra 0.5 mL - 3K, UFC5003234, Millipore, MA, USA) at RT. The sample was then stored at 4°C until further 
+use. A small aliquot of the sample was used to measure the size and number of particles in the 100,000×g 
+pellets using a Nanosight NS500 instrument (Malvern Panalytical, Malvern, UK). The sample was diluted to 
+the optimal working concentration of the instrument (2 × 108 to 1 × 109 particles per ml) with filtered PBS, 
+and then measured. Five videos of 60 sec were acquired and subsequently analyzed with the NTA 3.4 software, 
+which identifies and tracks the center of each particle under Brownian motion to measure the average distance 
+the particles move on a frame-by-frame basis. As shown in Fig. 5, the majority of the small EVs has a diameter 
+between 100-175 nm (65,9% of the total) with a mode of 101 nm. 
+ 
+ 
+Figure. 5: Small EVs were isolated by sequential centrifugation from healthy donor urine and their size was 
+measured by NTA. The size distribution of small EVs is shown as percentage of particles having the indicated 
+size normalized by the total number of particles.  
+ 
+ 
+ 
+ 
+0
+10
+20
+30
+40
+50
+50-75
+75-100
+100-125
+125-150
+150-175
+175-200
+200-225
+225-250
+250-275
+275-300
+300-325
+325-350
+350-375
+375-400
+400-425
+425-450
+450-475
+475-500
+% particles
+(normalized to total particles)
+nm
+
+ 
+6. Human-placenta tissue preparation and characterization 
+ 
+Placental tissue samples are first fixed in formalin and then embedded in paraffin [3]. 4 μm sections of 
+the tissue samples are then cut from these paraffin blocks using microtome (HM 355S Automatic 
+Microtome, Thermo Fisher Scientific, Waltham, Massachusetts, USA). The cut sections are then placed 
+on poly-L-lysine coated Si3N4 waveguide chips, and deparaffinized in xylene (3 × 5 min), followed by 
+rehydration in descendent series of ethanol: 100% (2 × 10 min), 96% (2 × 10 min) and 70% (10 min). 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ 
+ 
+ 
+ 
+ 
+ 
+7. Experimental particulars 
+The following spectral filters are used in this work: 
+Table 1: 
+Sl. No. 
+Filter Name 
+Spectral range 
+(LP: LongPass, BP: BandPass) 
+1 
+FITC 
+515 nm LP + 535\30  nm BP 
+2 
+TRITC 
+585 nm LP \ 630\75 nm BP 
+3 
+CY5 
+655 nm LP \ 690\50 nm BP 
+ 
+Table 2: 
+Figure # 
+Sample 
+λill 
+Spectral 
+filter \ 
+MO2 
+Exposure 
+Reconstruction 
+Algorithm 
+# Images 
+Comments 
+3a 
+195 nm 
+Polystyrene 
+beads 
+488 nm 
+TRITC \ 
+0.45 NA 
+100 ms 
+SACD [4] 
+500 
+Order 2 used 
+for 
+reconstruction 
+3b 
+150 nm Gold 
+nanoparticles 
+640 nm 
+CY5 \ 0.45 
+NA 
+1 sec 
+SACD 
+100 
+Order 2 used 
+for 
+reconstruction 
+3c 
+200 nm Gold 
+nanoparticles 
+640 nm 
+CY5 \ 1.2 
+NA 
+100 ms 
+FairSIM [5] 
+3 
+ 
+4 
+(75 –250) nm 
+Extracellular 
+vesicles 
+488 nm 
+for PL  
+TRITC \ 
+0.45 NA 
+1 sec 
+SACD 
+50 
+Order 2 used 
+for 
+reconstruction 
+ 
+ 
+640 nm 
+for TIRF 
+CY5 \ 0.45 
+NA, 1.2 
+NA 
+100 ms 
+ 
+50 
+ 
+5 
+Human Placenta 
+Tissue 
+488 nm 
+TRITC\ 
+0.25 NA 
+(PL 
+image) and 
+0.45 NA 
+(Ground 
+truth) 
+50 ms 
+SACD 
+20 
+Order 2 used 
+for 
+reconstruction. 
+Each image is 
+acquired for 
+50 ms and 20 
+images are 
+averaged to 
+create (50 
+ms*20 = 1 
+sec) to create 
+one input 
+image for 
+SACD. 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+ 
+
+ 
+ 
+ 
+ 
+8. References 
+ 
+1. Prieto, F., Sepúlveda, B., Calle, A., Llobera, A., Domínguez, C., Abad, A., Montoya, A. and Lechuga, 
+L.M., 2003. An integrated optical interferometric nanodevice based on silicon technology for biosensor 
+applications. Nanotechnology, 14(8), p.907. 
+2. Ramirez-Garrastacho, M., Berge, V., Linē, A. and Llorente, A., 2022. Potential of miRNAs in urinary 
+extracellular vesicles for management of active surveillance in prostate cancer patients. British journal of 
+cancer, 126(3), pp.492-501. 
+3. Slaoui, M. and Fiette, L., 2011. Histopathology procedures: from tissue sampling to histopathological 
+evaluation. In Drug safety evaluation (pp. 69-82). Humana Press. 
+4. Müller, M., Mönkemöller, V., Hennig, S., Hübner, W. and Huser, T., 2016. Open-source image 
+reconstruction of super-resolution structured illumination microscopy data in ImageJ. Nature 
+communications, 7(1), pp.1-6. 
+5. Zhao, W., Zhao, S., Han, Z., Ding, X., Hu, G., Wang, X., Mao, H., Jiu, Y., Hu, Y., Tan, J. and Ding, X., 
+2022. Enhancing detectable fluorescence fluctuation for high-throughput and four-dimensional live-cell 
+super-resolution imaging. bioRxiv. 
+ 
+ 
+
diff --git a/jdE1T4oBgHgl3EQf0AWa/content/tmp_files/load_file.txt b/jdE1T4oBgHgl3EQf0AWa/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5f89469548bb5187c29e2b6767ff0f4e0729b124
--- /dev/null
+++ b/jdE1T4oBgHgl3EQf0AWa/content/tmp_files/load_file.txt
@@ -0,0 +1,1351 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf,len=1350
+page_content='Label-free incoherent super-resolution optical microscopy Nikhil Jayakumar1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Firehun T Dullo2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Jean-Claude Tinguley1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Krizia Sagini3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Alicia Llorente3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Balpreet Singh Ahluwalia*1 1Department of Physics and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' UiT The Arctic University of Norway,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Tromsø,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 9037,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway 2Department of Microsystems and Nanotechnology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' SINTEF Digital,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Gaustadalleen 23C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 0373 Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway 3 Department of Molecular Cell Biology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Institute for Cancer Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Oslo University Hospital,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The Norwegian Radium Hospital,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 0379 Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway 4Centre for Cancer Cell Reprogramming,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Faculty of Medicine,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' University of Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Montebello,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 0379 Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway 5Department for Mechanical,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Electronics and Chemical Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Oslo Metropolitan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway  Balpreet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='singh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='ahluwalia@uit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='no Abstract: The photo  kinetics of fluorescent molecules has enabled the circumvention of far  field optical diffraction  limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Despite its enormous potential, the necessity to label the sample may adversely influence the delicate biology under investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Thus, continued development efforts are needed to surpass the far  field label  free diffraction barrier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The coherence of the detected light in label  free mode hinders the application of existing super  resolution methods based on incoherent fluorescence imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In this article, we present the physics and propose a methodology to circumvent this challenge by exploiting the photoluminescence of silicon nitride waveguides for near  field illumination of unlabeled samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The technique is abbreviated EPSLON, Evanescently decaying Photoluminescence Scattering enables Label  free Optical Nanoscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' We demonstrate that such an illumination has properties that mimics the photo  kinetics of nano  sized fluorescent molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This allows to develop a label  free incoherent system that is linear in intensity, and stable with time thereby permitting the application of techniques like structured illumination microscopy (SIM) and intensity  fluctuation based optical nanoscopy (IFON) in label  free mode to circumvent the diffraction limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' We experimentally demonstrate label  free super  resolution imaging of nanobeads (polystyrene and gold), extra  cellular vesicles and human placenta tissue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' We believe EPSLON is a step forward within the nascent field of label  free super  resolution microscopy that holds the key to investigate delicate biological systems in its natural state without the need for exogenous labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Introduction The ability of light beams to interfere is quantified by their degree of coherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Light beams originating from within the coherence volumes can only overlap and generate a sustained interference pattern [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In fluorescence microscopy, the transversal coherence lengths are typically on the order of a few nanometers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This is because the fluorescent molecules, a few nanometers in size, emit independently and stochastically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' It leads to a linear mapping between the sample plane fluorophore concentration and image plane intensity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This implies that the photo  kinetics of these molecules may be utilized to circumvent the far  field diffraction  limit, as in structured illumination microscopy [3, 4] or fluorescence  based IFON algorithms [5  10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' However, the absence of such exogenous molecules in label  free microscopy restricts the far  field transversal coherence lengths to a few hundreds of nanometers [11, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This hinders the application of fluorescence  based super  resolution algorithms in the label  free regime for generating reliable super  resolved images [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Another hinderance in label  free microscopy is lack of selectivity and specificity that results in strong scattering and multiple scattering from the entire sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To circumvent these challenges, it can be foreseen that near  field illumination, to reduce multiple scattering issues, via nano  sized light sources with stochastic photo  kinetics and sufficient quantum yield is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Therefore, through this article, we provide the concepts and a key to unlock the challenge of generating far  field label  free super  resolved optical images using fluorescence based super  resolution algorithms: photoluminescence (PL) of silicon nitride (Si3N4) [14, 15] waveguide functions as exogenous nano  sized illumination sources with stochastic photo  kinetics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In addition, the photonic  chip helps in engineering the illumination to induce fluctuations in intensity via multi  mode interference (MMI) /speckle  like patterns [16  18] or via well  defined interference fringes that permits the application of fluorescence based IFON algorithms or SIM respectively to enhance the resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Poor  contrast and diffraction  limited resolution are major impediments to the development of label  free optical microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To mitigate the issue of poor contrast, various approaches have emerged: phase contrast microscopy [19], differential interference contrast [20], interferometric scattering microscopy [21], interferometric techniques [22], holographic non  interferometric techniques [23], Fourier Ptychography [24], rotating coherent scattering  microscopy [25], manipulating the coherence of light sources used for illumination [26], ultraviolet microscopy [27], optical waveguides [28, 29] etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' However, circumventing the diffraction-limit in label-free regime is still at a nascent stage in life sciences, as opposed to fluorescence microscopy [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This could be attributed to the ease of utilizing/manipulating the photo-kinetics of nano-sized fluorescent molecules to gain information beyond the diffraction-limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The different approaches developed for label-free super-resolution microscopy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' albeit with their respective experimental challenges especially for life sciences applications,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' includes near-field scanning optical microscopy [31],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' super-lens [32],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' micro-sphere assisted super-resolution imaging [33],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' super-resolution via scattering [33,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 34],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' optical super-oscillation techniques [35],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' hyperbolic materials for super-resolution imaging [36],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' utilizing the intrinsic autofluorescence of biological specimens in tandem with fluorescence-based super- resolution algorithms [37,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 38] etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In this article, we propose the use of Si3N4 waveguides to solve the abovementioned challenges associated with label-free microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The concept permits the application of fluorescence based super-resolution algorithms on unlabeled samples, generating high-contrast label-free super-resolved images, without photo-toxicity and photobleaching plaguing the imaging process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Our work helps synthesize a label-free incoherent imaging system and is termed Evanescently decaying Photoluminescence Scattering enables Label-free Optical Nanoscopy (EPSLON), which builds and extends the concepts outlined by Goodman [39], Ruh et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' [25], Wicker and Heinztmann [13] and previous work based on photonic-chip microscopy [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' These concepts of EPSLON which enable circumventing the label-free far-field diffraction-limit are explained and experimentally demonstrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' We describe how a Si3N4 waveguide is a solution to these challenges and validate our concepts experimentally via high-contrast label-free super-resolved images of polystyrene beads, gold nanoparticles, weakly scattering specimens like extra-cellular vesicles and human placenta tissue, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Conceptual framework and Results Problem statement Here we describe why fluorescence based super-resolution algorithms when applied to coherently scattering samples do not yield any resolution gain beyond the diffraction-limit, which is also discussed by Wicker and Heintzmann [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To explain this concept, the image formation process at the camera plane is regarded as an interference phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To illustrate the image formation process in label-free mode, we consider two coherently scattering phase-objects illuminated by a monochromatic plane-wave 𝐸𝑖(𝑟⃗, 𝑡) = 𝑒𝑖(𝑘⃗⃗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='𝑟⃗ − 𝜔𝑡).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The scalar fields scattered by the phase-objects can then be represented as 𝐸1(𝑟1⃗⃗⃗⃗, 𝑡) = 𝑝1(𝑟1⃗⃗⃗⃗) cos(𝑘⃗⃗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  𝑟1⃗⃗⃗⃗ − 𝜔𝑡) and 𝐸2(𝑟2⃗⃗⃗⃗, 𝑡) = 𝑝2(𝑟2⃗⃗⃗⃗) cos(𝑘⃗⃗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 𝑟2⃗⃗⃗⃗ − 𝜔𝑡), where 𝑝1(𝑟1⃗⃗⃗⃗) and 𝑝2(𝑟2⃗⃗⃗⃗) are the amplitudes of the scattered fields and are linked to the applied electric fields via the polarizability of the particles, α(𝑟⃗, 𝑡).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The intensity registered by the camera is then 𝐼(𝑟⃗) = 〈|(𝐸1(𝑟1⃗⃗⃗⃗, 𝑡) + 𝐸2(𝑟2⃗⃗⃗⃗, 𝑡)) ⨷ ℎ(𝑟⃗)| 2〉, where 〈 〉 represents time averaging by the detector, ℎ(𝑟⃗) is the coherent point spread function of the imaging system and ⨷ represents the convolution operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Due to statistical similarity or coherence between the overlapping scattered fields, the intensity registered by the camera is non- linearly related to the particle concentration and is a function of 𝛥𝜑 = 𝑘⃗⃗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 𝑟2⃗⃗⃗⃗ − 𝑘⃗⃗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 𝑟1⃗⃗⃗⃗ = 𝜑2 − 𝜑1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' It implies that the image generated by the camera varies with either a change in the illumination angle 𝑘⃗⃗, or with the relative positions of the particles 𝑟2⃗⃗⃗⃗ − 𝑟1⃗⃗⃗⃗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Next, to illustrate the image formation process in fluorescence microscopy we replace the phase-objects with fluorescent molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Analogous to the strengths of the scattered fields, |𝑎1(𝑟1⃗⃗⃗⃗)|2 and |𝑎2(𝑟2⃗⃗⃗⃗)|2, are the brightness of the molecules that typically depends on the illumination intensity at the location of the molecule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The molecules can also be assumed to emit independently [40] and stochastically typically on the order of nanoseconds [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  The following properties of these molecules can be utilized by collecting only the Stoke shifted light emitted by the molecules: (i) Stochastic emission between the molecules causes the phase difference between the emitted fields to be a function of time, 𝛥𝜑(𝑡).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' It implies that the molecule emissions are incoherent with respect to one another or in other words we can say that the transversal coherence length is determined by the size of an individual molecule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This gives rise to similar images for different illumination angles of the incident plane wave, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', the particle concentration and image plane intensity obey a linear relationship as the intensity registered by the camera becomes independent of 𝛥𝜑(𝑡).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' It is this property that allows the usage of structured light in SIM [13,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 42] or the intrinsic photo-kinetics of the molecules in IFON algorithms to enhance the resolution [29],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  (ii) Excited lifetime on the order of nanoseconds of the molecules excites many independent interference or speckle patterns,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' that gets averaged within the integration time of the camera thus mitigating the speckle- noise and (iii) Molecular specificity offered by these molecules enables multi-color imaging of different cell organelles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' It can be concluded that the suppression of speckle noise and molecular specificity offered by the molecules enables high-contrast imaging and the linear relationship between molecular concentration and image plane intensity helps in enhancing the resolution via fluorescence-based super-resolution algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Hence, to improve the label-free resolution via fluorescence-based algorithms, we need to ensure that there exists no statistical similarity between the scattered fields originating from different locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This calls for the spatial coherence function to be δ-function correlated, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 𝐽(𝑟1⃗⃗⃗⃗, 𝑟2⃗⃗⃗⃗) = 〈𝐸𝑇(𝑟1⃗⃗⃗⃗, 𝑡)𝐸∗ 𝑇(𝑟2⃗⃗⃗⃗, 𝑡)〉 = 𝛫𝐼𝑇(𝑟1⃗⃗⃗⃗) δ(𝑟1⃗⃗⃗⃗ − 𝑟2⃗⃗⃗⃗)                                               (1) where 𝐽(𝑟1⃗⃗⃗⃗, 𝑟2⃗⃗⃗⃗) is the spatial coherence function and determines the spatial correlation of the fields, 𝐸𝑇(𝑟⃗, 𝑡) = 𝐸1(𝑟⃗, 𝑡) + 𝐸2(𝑟⃗, 𝑡) is the total field reaching the camera, 𝛫 is a real constant and 𝐼𝑇 is the image generated by the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This will ensure an incoherent imaging system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  (1) can be assumed to be satisfied in fluorescence microscopy because the transversal spatial coherence length is determined by the size of the fluorescent molecules and the image generated by the camera indicates the spatial locations of the fluorescent molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Thus, to circumvent the label-free diffraction-limit using fluorescence-based super-resolution algorithms, we need to develop a light source with δ-function correlations and then acquire an image stack exhibiting intensity- fluctuations to apply SIM or intensity-fluctuation based algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This can be realized experimentally via the EPSLON configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1(a-c) compares the conventional imaging configurations and their corresponding image plane intensity distribution with EPSLON, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' EPSLON satisfies Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1 and is experimentally demonstrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1e-1j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1e-1f, schematic diagrams of waveguide-based label-free coherent and incoherent imaging systems EPSLON are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The coherent and corresponding EPSLON images are compared in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1g, where speckle suppression due to loss in phase information in the scattered light is clearly evidenced in the EPSLON configuration image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This loss in phase information also implies that identical images must be generated for arbitrary illumination angles in EPSLON configuration, as opposed to label-free coherent imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This is demonstrated experimentally in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1h-1j where the coherent and its corresponding incoherent EPSLON images are provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  EPSLON: a solution for high-contrast far-field label-free super-resolution microscopy To employ a light source with δ-function correlations, we resort to the high-index contrast (Δn ≈ 2) Si3N4 optical waveguide deposited using plasma enhanced chemical vapor deposition (PECVD) scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Waveguide fabrication and properties of the guided modes and its spatial frequency extend is provided in Supplementary section 1 and in previous works [43, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The choice of Si3N4 over other high index contrast optical waveguides, such as tantalum pentoxide, Ta2O5, or titanium dioxide TiO2, is attributed to the room-temperature visible PL generated inside the core during the transfer of optical power along its length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Determining the origin and lifetime of this emission is not within the scope of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The origin and photophysical properties of this PL is a widely researched area [45-47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' It is found to be dependent on the waveguide fabrication scheme employed and could be attributed to intrinsic fluorescence of the material [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The PL emission spectrum is broad [15] and the lifetime of these states is found to vary on the order of a few nanoseconds to a few hundred microseconds depending on the origin of the PL [16, 49-50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Such an emission could be visualized as a very large number of fluorescent molecules embedded in a material and emitting stochastically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Hence, if the PL light is used for near-field illumination of samples, then Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  (1) will be satisfied for the incoherently scattered fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This helps in synthesizing a label-free incoherent system, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The next problem to tackle is that of generating an image stack with intensity-fluctuations for the fluorescence- based algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Structuring the illumination beam, manipulating the photophysical properties of the fluorescence molecules are some of the ways typically employed for generating image stacks with intensity-fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In EPSLON, this problem is resolved by resorting to Si3N4 waveguides of the following types: (1) Straight waveguides with strip geometry and large widths that supports a large number of the guided modes, generating MMI patterns (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2a) [29], (2) Four-arm junction multi-moded strip waveguides for speckle illumination from  different azimuthal angles (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2b) [29] and, (3) a single moded SIM chip with rib geometry and phase modulation for one-dimensional structured illumination (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2c) [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Image formation process in EPSLON Laser is coupled into a Si3N4 waveguide via a microscope objective MO1, (Supplementary Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The coupled optical power gets distributed among the multiple coherent guided modes, which correspond to the eigen vectors of the guiding structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' As the modes guide power along the length of the waveguide, they also induce a broadband PL along the length as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2d-2e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The Si3N4 waveguide employed in this work demonstrated PL in all the commonly used wavelengths in bio-imaging, 488 nm, 561 nm, and 647/660 nm (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This PL of Si3N4 waveguide does not exhibit any bleaching effect over long periods of times (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2f), as opposed to the autofluorescence in polymer waveguides [51] and varies linearly with the excitation power (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2g).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To explain the origin of fluctuations in intensity, we consider the case of a multi-moded straight waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Fluctuations over time, 𝐼𝑐𝑜𝑟𝑒 𝑚 (𝑟,⃗⃗⃗ 𝑡), can be induced by oscillating MO1 using a piezo-stage across the input facet of the waveguide (Supplementary Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3) which excites different sets of modes 𝜓𝑚(𝑟⃗, 𝑡) with relative amplitudes 0 ≤ 𝑎𝑚(𝑡) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  The instantaneous PL intensity at each location in the core is dependent on the coherent superposition of the modes and can be represented mathematically as 𝐼𝑐𝑜𝑟𝑒 𝑚 (𝑟,⃗⃗⃗ 𝑡) = 𝜂(𝜆)|∑ 𝑎𝑚(𝑡)𝜓𝑚(𝑟⃗, 𝑡) 𝑚 |2, where 𝜂(𝜆) is assumed to be a constant across the material for a specific wavelength that can be deduced from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2g, 𝜓𝑚(𝑟⃗, 𝑡) = 𝐸𝑚(𝑥, 𝑦)𝑒(𝑖ß𝑚𝑧−𝑖𝜔𝑡) corresponds to the scalar representation of the mth guided mode with fixed transversal profile 𝐸𝑚(𝑥, 𝑦) and propagation constant ß𝑚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' As the PL emission occurs inside a high-index core, a part of the PL light gets confined to the core due to total-internal reflection at the core-cladding interface and the remaining part gets transmitted into the far-field, which is visible as an omnipresent background or noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Now the presence of any index perturbation at the core-cladding interface scatters this evanescently decaying PL light into the far-field (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1d), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', both the coherent as well as the Stoke shifted incoherent PL light gets scattered into the far-field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' By invoking a first order Born approximation for evanescent field excitation of biological specimens 𝑆(𝑟⃗) = ∬ 𝛼(𝑟⃗𝑘)𝛿(𝑟⃗ − 𝑟⃗𝑘)  𝑆 𝑑𝑟⃗𝑘  with α being the polarizability, it is seen that these scattered fields contain the information of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Only these scattered fields are collected by the microscope objective MO2 and relayed onto the camera via tube lens because of the decoupled illumination and detection scheme offered by waveguides (Supplementary Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Through the usage of appropriate bandpass filters, the coherently scattered light is filtered out and only the incoherent light gets detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The oscillation of MO1 is synchronized with the detector in such a way that an image is acquired at each excitation point of the waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' By invoking Eqn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (1) and neglecting noise, an EPSLON image (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1d) at the camera plane in general may be described mathematically as  𝐼𝑚(𝑟⃗) = 𝜂|𝑆(𝑟⃗) ∑  𝑎𝑚(𝑡)𝜓𝑚(𝑟⃗, 𝑡)  𝑚  |2 ⨷ |ℎ(𝑟⃗)|2  (2) The abovementioned concepts and experimental results can be summarized into the following: (i) Speckle noise is mitigated in EPSLON images as opposed to label-free waveguide based coherent images due to stochastic fluctuations between the scattered fields, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (ii) Stochastic fluctuations implies that phase relationships between the scattered fields are lost in EPSLON images as opposed to label-free coherent images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This also leads to identical images for different illumination angles, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1(h-j) and (iii) Intensity-fluctuations are induced over time due to time dependence of 𝑎𝑚(𝑡) and 𝜓𝑚(𝑟⃗, 𝑡).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This is evident in the line plots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1j and in the MMI patterns shown as insets in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2a-2c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This is also validated using simulations in Supplementary Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Thus, EPSLON when used in tandem with fluorescence-based super-resolution algorithms helps develop a high-contrast label-free super-resolution imaging system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Applications of EPSLON The potential of EPSLON is first demonstrated on nanobeads, 195 nm polystyrene beads and 200 nm gold nanoparticles (GNP), using the three different waveguide geometries mentioned earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' For brevity, the diffraction-limited label-free image and its corresponding reconstructed image in the following sections are termed DL and EPSLON.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' For the straight and four-arm junction waveguide, images are acquired using a detection MO with numerical aperture NA = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  The acquired image stack is given as input to a fluorescence-based super- resolution algorithm called as Super-resolution method based on Auto-Correlation two-step Deconvolution (SACD) [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The choice of SACD over other IFON algorithms is attributed to the better performance of the algorithm at low signal to background ratios [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Now to validate the super-resolved images generated by SACD, the same sample is imaged with a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='7 NA detection MO, which serves as the ground truth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3a, the line profiles indicate the intensity variations across the particles in the insets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The line profile of the green inset  clearly indicates that EPSLON resolves the nanobeads shown in the blue inset in the DL image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This observation is validated by the ground truth image, and it is seen that EPSLON, and the ground truth image agree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' A similar experiment is then repeated using the four-arm junction waveguide as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The use of such a waveguide geometry helps in introducing additional illumination frequencies (Supplementary Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' It is evident that the line profile in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3b of the green inset in the EPSLON image shows dips, implying resolving the beads enclosed in the blue inset in the DL image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This is validated again by the ground truth image, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', the EPSLON and ground truth images agree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Next, we demonstrate label-free 1-D SIM in EPSLON configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The nanobeads are deposited on the SIM structure shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The angle between the interfering waveguides used in the experiment is 60º.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This will create an interference pattern with a fringe period 𝑓 = 𝜆𝑒𝑥 2𝑛𝑓 sin𝜃 2 where 𝜆𝑒𝑥 is the excitation wavelength, 𝑛𝑓 ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='7 is the refractive index of the guided mode and 𝜃 is the angle between the interfering waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' For better visualization purposes, the interference fringe pattern shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2c is generated by waveguides interfering at an angle 𝜃 = 20º.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' For the 1-D SIM experiment, images are acquired using a detection MO with NA = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Phase shifted frames required for the SIM reconstruction is generated by temporarily changing the index on one of the arms of the interfering waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The three phase shifted frames are then given as input to the Fiji plugin of FairSIM [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The reconstructed images and its Fourier spectra are provided in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The SIM reconstruction can clearly resolve the beads enclosed in the red inset in the DL image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The beads in the green inset in the EPSLON image are separated by a distance of 274 nm, shown in the line profile, which lies below the Abbe diffraction limit 𝜆𝑑𝑒𝑡 𝑁𝐴𝑑𝑒𝑡+𝑛𝑓 sin𝜃 2 ≈ 330 𝑛𝑚, where 𝜆𝑑𝑒𝑡 is the detected wavelength and 𝑁𝐴𝑑𝑒𝑡 is the numerical aperture of the detection MO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Next, to showcase the potential of EPSLON for life sciences, we choose biological samples such as extra-cellular vesicles (EVs) and human placenta tissue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Small EVs are gaining attention due to their role in intercellular communication and possible clinical applications, especially for targeted drug delivery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nevertheless, their molecular biology, as well as their therapeutic potential, is far to be completely understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Further understanding of the spatiotemporal aspects of EVs rely on the ability to image processes such as EV secretion, uptake and biodistribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' However, imaging and tracking of small EVs has been challenging due to their small sizes (50- 200 nm), and often require the use of labeling strategies, that may alter EV release and structure, prior to visualization [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  These problems are mitigated in EPSLON: the decoupled speckle-illumination and detection paths helps visualize these structures beyond the diffraction-limit with high-contrast and without photobleaching as demonstrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The EVs used in this experiment have a size distribution of 75-250 nm, Supplementary Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 5, and are fluorescently labeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' EPSLON and total-internal reflection fluorescence (TIRF) imaging of the same region of interest is performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Fluorescent dyes are chosen in a way to ensure that there is no fluorescent signal reaching the camera during EPSLON imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Images are acquired in both EPSLON and TIRF mode using a detection MO with NA = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' It is seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4a and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4b that the EPSLON and TIRF images are in good agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The line profile in the red and green insets in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4b show a blob of light and therefore, unable to clearly resolve the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To resolve these particles, the DL image stack is given as input to the reconstruction algorithm to generate the EPSLON image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4b it is seen that in the EPSLON image the particles are clearly resolved as shown by the line profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To validate the EPSLON image, the same region of interest is imaged with a higher NA = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='9 detection MO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The EPSLON matches well with the ground truth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Finally, we showcase the potential of EPSLON on histological samples human placenta tissue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  These samples are an ideal candidate for chip-based imaging as clinical applications of these histological samples demand high- throughput imaging that is supported by chip-illumination over large areas [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Here, images are acquired using a detection MO with NA = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='10, termed DL image in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The large field-of-view super-resolved EPSLON image is also shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To validate the EPSLON image, we image the same region of interest with a higher NA = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='25 detection MO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' We choose two regions within the field-of-view, ‘‘1’’ and ‘‘2’’ in the DL image in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The corresponding regions in the EPSLON and ground truth image are also blown up and shown alongside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The line profile of the zoomed regions shows clear resolution enhancement in the EPSLON image over the DL image and the EPSLON and ground truth images are in excellent agreement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' EPSLON supports both superior contrast and super-resolution imaging with a low magnification imaging objective lens, which is essential for scanning large areas for histopathology applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Discussion and Outlook  Fluorescence based algorithms have been previously applied to coherently scattering specimens [36, 55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' However, the reconstructed images generated must be interpreted with caution with regards to resolution beyond the diffraction-limit as coherence of the scattered light cannot be neglected [13, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In our proof-of-concept work EPSLON, we circumvent this issue for two-dimensional samples by realizing a light source with δ-function correlations, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', by using the PL property of Si3N4 waveguides for near-field illumination of unlabeled samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In addition, PL emission takes place within the core matrix and a part of it gets transmitted into the far-field, which prevents realizing an ideal chip-based imaging system where only the scattered light off the sample reaches the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' As a result, the signal to background ratio of weakly scattering specimens is poor and hence, imaging in this current work was restricted to lower magnification objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Despite the limited photon budget, we have demonstrated proof-of-concept label-free super-resolution results on nanobeads, EVs and human placenta tissue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The experimental particulars are provided in Table 1 and Table 2 in the supplementary material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In future works, we propose novel chip designs as in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' [56, 57] which will improve the poor signal to background ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The other challenge of lack of specificity in label-free imaging can be mitigated by resorting to machine learning based tools [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  This work lays the foundation for synthesizing a label-free incoherent imaging system that is compatible with the myriad of fluorescence based super-resolution algorithms to circumvent the spatial diffraction-limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' We believe that EPSLON will trigger further developments of label-free super-resolution incoherent optical microscopy methods and its application in biology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This work could also initiate further developments within integrated optics to harness the PL properties of different materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Interestingly, PL in waveguides is an undesirable phenomenon as it increases the propagation losses of the guiding structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' However, here we demonstrated that PL of Si3N4 waveguide can be harnessed for near-field illumination to develop an incoherent imaging system for surpassing the diffraction limit in label-free regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  References 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Wolf, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Introduction to the Theory of Coherence and Polarization of Light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Cambridge university press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Fujimoto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Pitris, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Boppart, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Brezinski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optical coherence tomography: an emerging technology for biomedical imaging and optical biopsy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Neoplasia, 2(1-2), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='9-25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Heintzmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Cremer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 1999, January.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Laterally modulated excitation microscopy: improvement of resolution by using a diffraction grating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In Optical biopsies and microscopic techniques III (Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3568, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 185-196).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' SPIE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Gustafsson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Journal of microscopy, 198(2), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='82-87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Dertinger, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Colyer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Iyer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Weiss, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Enderlein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Fast, background-free, 3D super- resolution optical fluctuation imaging (SOFI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences, 106(52), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='22287-22292.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Gustafsson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Culley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Ashdown, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Owen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Pereira, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Henriques, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Fast live- cell conventional fluorophore nanoscopy with ImageJ through super-resolution radial fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature communications, 7(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Yahiatene, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hennig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Müller, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Huser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Entropy-based super-resolution imaging (ESI): From disorder to fine detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Acs Photonics, 2(8), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1049-1056.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Cox, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Rosten, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Monypenny, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Jovanovic-Talisman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Burnette, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Lippincott-Schwartz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Jones, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  and Heintzmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Bayesian localization microscopy reveals nanoscale podosome dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature methods, 9(2), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='195-200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Zhao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Han, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Ding, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Mao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Jiu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Tan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Ding, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Enhancing detectable fluorescence fluctuation for high-throughput and four-dimensional live-cell super-resolution imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' bioRxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Agarwal, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Macháň, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Multiple signal classification algorithm for super-resolution fluorescence microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature communications, 7(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Ryabukho, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Lyakin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Grebenyuk, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Klykov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Wiener–Khintchin theorem for spatial coherence of optical wave field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Journal of Optics, 15(2), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='025405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Speckle phenomena in optics: theory and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Roberts and Company Publishers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Wicker, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Heintzmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Resolving a misconception about structured illumination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature Photonics, 8(5), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='342-344.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Kistner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Weng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Strunk, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Schubert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Werner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Photoluminescence from silicon nitride—no quantum effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Journal of Applied Physics, 110(2), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='023520.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Coucheron, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Helle, Ø.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Wilkinson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Murugan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Domínguez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Angelskår, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Ahluwalia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Study of waveguide background at visible wavelengths for on-chip nanoscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optics Express, 29(13), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='20735-20746.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Diekmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Helle, Ø.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Øie, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', McCourt, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Huser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Schüttpelz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Ahluwalia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Chip-based wide field-of-view nanoscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature Photonics, 11(5), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='322-328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Jayakumar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Helle, Ø.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Agarwal, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Ahluwalia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' On-chip TIRF nanoscopy by applying Haar wavelet kernel analysis on intensity fluctuations induced by chip illumination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optics Express, 28(24), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='35454-35468.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Villegas-Hernández, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Dubey, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Nystad, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Tinguely, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Coucheron, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Dullo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Priyadarshi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Acuña, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Ahmad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Mateos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Barmettler, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Chip-based multimodal super-resolution microscopy for histological investigations of cryopreserved tissue sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Light: Science & Applications, 11(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Zernike, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 1955.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' How I discovered phase contrast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Science, 121(3141), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='345-349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Phillips, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Waller, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Quantitative differential phase contrast (DPC) microscopy with computational aberration correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optics express, 26(25), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='32888-32899.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Taylor, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Mahmoodabadi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Rauschenberger, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Giessl, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Schambony, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Sandoghdar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Interferometric scattering microscopy reveals microsecond nanoscopic protein motion on a live cell membrane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature Photonics, 13(7), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='480-487.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Park, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Depeursinge, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Popescu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Quantitative phase imaging in biomedicine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature photonics, 12(10), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='578-589.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Baek, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Park, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Intensity-based holographic imaging via space-domain Kramers–Kronig relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature Photonics, 15(5), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='354-360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Zheng, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Horstmeyer, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Yang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Wide-field, high-resolution Fourier ptychographic microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature photonics, 7(9), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='739-745.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Ruh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Mutschler, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Michelbach, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Rohrbach, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Superior contrast and resolution by image formation in rotating coherent scattering (ROCS) microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optica, 5(11), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1371-1381.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Redding, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Choma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Cao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Speckle-free laser imaging using random laser illumination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature photonics, 6(6), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='355-359.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Ojaghi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Fay, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Lam, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Robles, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Ultraviolet hyperspectral interferometric microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Scientific reports, 8(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Kuang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Pang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Xu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Yu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Xu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Nan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Shen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Fluorescent nanowire ring illumination for wide-field far-field subdiffraction imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Physical Review Letters, 118(7), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='076101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Jayakumar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Dullo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Dubey, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Ahmad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Ströhl, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Cauzzo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Guerreiro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Snir, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Skalko-Basnet, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Agarwal, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Ahluwalia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Multi-moded high-index contrast optical waveguide for super-contrast high-resolution label-free microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nanophotonics, 11(15), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='3421- 3436.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Schermelleh, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Ferrand, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Huser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Eggeling, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Sauer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Biehlmaier, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Drummen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Super-resolution microscopy demystified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature cell biology, 21(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='72-84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Betzig, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Chichester, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Single molecules observed by near-field scanning optical microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Science, 262(5138), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1422-1425.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Pendry, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Negative refraction makes a perfect lens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Physical review letters, 85(18), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='3966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Guo, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=", Luk'Yanchuk, B." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Khan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Hong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature communications, 2(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Darafsheh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Limberopoulos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Derov, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Walker Jr, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Astratov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Advantages of microsphere-assisted super-resolution imaging technique over solid immersion lens and confocal microscopies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Applied Physics Letters, 104(6), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='061117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Rogers, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Lindberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Roy, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Savo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Chad, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Dennis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Zheludev, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  A super- oscillatory lens optical microscope for subwavelength imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature materials, 11(5), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='432-435.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Lee, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Wisna, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Zeng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Tao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Hyperbolic material enhanced scattering nanoscopy for label-free super-resolution imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature communications, 13(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Lin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Peñaranda, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Dendooven, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Detavernier, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Schaubroeck, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Boon, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Baets, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Le Thomas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' UV photonic integrated circuits for far-field structured illumination autofluorescence microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature Communications, 13(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Dong, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Almassalha, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Stypula-Cyrus, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Urban, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Chandler, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Nguyen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Sun, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Backman, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Superresolution intrinsic fluorescence imaging of chromatin utilizing native, unmodified nucleic acids for contrast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences, 113(35), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='9716-9721.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Introduction to Fourier Optics (Roberts & Company, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Gustafsson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Proceedings of the National Academy of Sciences, 102(37), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='13081-13086.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Berezin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Achilefu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Fluorescence lifetime measurements and biological imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Chemical reviews, 110(5), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2641-2684.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Chowdhury, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Dhalla, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Izatt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Structured oblique illumination microscopy for enhanced resolution imaging of non-fluorescent, coherently scattering samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Biomedical optics express, 3(8), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1841-1854.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Prieto, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Sepúlveda, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Calle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Llobera, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Domínguez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Abad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Montoya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Lechuga, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' An integrated optical interferometric nanodevice based on silicon technology for biosensor applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nanotechnology, 14(8), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Tinguely, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Helle, Ø.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Ahluwalia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Silicon nitride waveguide platform for fluorescence microscopy of living cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optics express, 25(22), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='27678-27690.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Dhakal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Wuytens, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Raza, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Le Thomas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Baets, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Silicon nitride background in nanophotonic waveguide enhanced Raman spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Materials, 10(2), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Aydinli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Serpengüzel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Vardar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Visible photoluminescence from low temperature deposited hydrogenated amorphous silicon nitride.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Solid state communications, 98(4), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='273-277.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Vlasukova, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Komarov, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Parkhomenko, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Milchanin, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Leont’ev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Mudryi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Togambaeva, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optical properties of silicon nitride films formed by plasma-chemical vapor deposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Journal of Applied Spectroscopy, 80(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='89-92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Giorgis, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Vinegoni, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Pavesi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optical absorption and photoluminescence properties of a− Si 1− x N x: H films deposited by plasma-enhanced CVD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Physical Review B, 61(7), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4693.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Smith, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Monroy-Ruz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Rarity, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Balram, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Single photon emission and single spin coherence of a nitrogen vacancy center encapsulated in silicon nitride.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Applied Physics Letters, 116(13), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='134001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Helle, Ø.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Dullo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Lahrberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Tinguely, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hellesø, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Ahluwalia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Structured illumination microscopy using a photonic chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature Photonics, 14(7), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='431-438.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Engdahl, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Belle, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hellmann, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Huser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Schüttpelz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Large Field-of- View Super-Resolution Optical Microscopy Based on Planar Polymer Waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' ACS Photonics, 8(7), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1944-1950.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Opstad, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Acuña, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hernandez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Cauzzo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Škalko-Basnet, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Ahluwalia, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Agarwal, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Fluorescence fluctuations-based super-resolution microscopy techniques: an experimental comparative study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' arXiv preprint arXiv:2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='09195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Müller, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Mönkemöller, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hennig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hübner, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Huser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature communications, 7(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Chuo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Chien, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Lai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Imaging extracellular vesicles: current and emerging methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Journal of biomedical science, 25(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Chang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Chou, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Chiang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Subdiffraction scattered light imaging of gold nanoparticles using structured illumination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optics letters, 36(24), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4773-4775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Chazot, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Nagelberg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Rowlands, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Scherer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Coropceanu, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Broderick, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Bawendi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', So, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Kolle, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Luminescent surfaces with tailored angular emission for compact dark-field imaging devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Nature photonics, 14(5), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='310-315.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Kuai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Fan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Zou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Lakowicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Planar photonic chips with tailored angular transmission for high-contrast-imaging devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature communications, 12(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Kandel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', He, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Lee, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Sullivan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Aydin, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Saif, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Kong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Sobh, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Popescu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Phase imaging with computational specificity (PICS) for measuring dry mass changes in sub-cellular compartments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature communications, 11(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Ethical statement Full-term placentae from 10 different Caucasian healthy patients were collected anonymously immediately after delivery at the University Hospital of North Norway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Written consent was obtained from the participants according to the protocol approved by the Regional Committee for Medical and Health Research Ethics of North Norway (REK Nord reference no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2010/2058–4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Acknowledgements We wish to acknowledge the fruitful discussions with Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Florian Strohl (UiT) and Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Krishna Agarwal (UiT) that helped us complete this work in a timely fashion, Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Ganesh Acharya, Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Mona Nystad (UiT) and Luis Villegas (UiT) for providing us with the tissue placenta sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Hong Mao for his constant support throughout our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' We would also like to express our sincere thanks to Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Weisong Zhao (Harbin Institute of Technology) for his valuable inputs and cooperation that enabled in the timely completion of this manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 766181, project “DeLIVER” and from the Research Council of Norway (NANO 2021–288565);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' BIOTEK 2021 (BIOTEK 2021–285571).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Authors and Affiliations Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' of Physics and Technology, UiT The Arctic University of Norway, Tromsø 9037, Norway Nikhil Jayakumar, Jean-Claude Tinguley, Balpreet Singh Ahluwalia Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' of Microsystems and Nanotechnology, SINTEF Digital, Gaustadalleen 23C, 0373 Oslo, Norway Firehun T Dullo Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' of Molecular Cell Biology, Institute for Cancer Research, Oslo University Hospital, Oslo, Norway Krizia Sagini, Alicia Llorente Centre for Cancer Cell Reprogramming, Faculty of Medicine, University of Oslo, Montebello, 0379 Oslo, Norway Krizia Sagini, Alicia Llorente Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' for Mechanical, Electronics and Chemical Engineering, Oslo Metropolitan University, Oslo, Norway Alicia Llorente  Author Contribution NJ conceived and conceptualized the idea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' NJ and BSA designed the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' FTD and JCT designed the waveguide chip and mask for fabrication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' FTD also performed the FIMMWAVE simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' KS and AL provided the extra-cellular vesicles for imaging and wrote the EV preparation protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' NJ performed the experiments, analyzed the results and prepared the manuscript with inputs from FTD, JCT and BSA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' All authors commented on the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' BSA secured and supervised the project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Conflict of interest statement: B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' have applied for patent for chip-based optical nanoscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='A is the co-founder of the company Chip NanoImaging AS, which commercializes on-chip super-resolution microscopy systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' All other authors declare no conflicts of interest regarding this article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Figure 1 Overview of ELSPON: (a-d) Comparison between fluorescence and label-free microscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (a) Epifluorescence: coherent light λexc is used for excitation of fluorescent molecules and the camera detects the Stoke shifted incoherent light emitted by the molecules λem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Stochastic fluctuations of the Stoke shifted light and specificity offered by the molecules helps suppress speckle noise enabling high-contrast imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (b) TIRF: coherent light for near-field illumination of fluorescently labeled samples and incoherent light gets detected by the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Near-field illumination helps to further improve the contrast as compared to the epifluorescence by illuminating thin sections of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (c) Label-free coherent imaging: coherent light for illumination and coherent light gets detected by the camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Multiple scattering and coherent nature of the scattered light leads to speckle noise, (d) EPSLON: incoherent light for near-field illumination of unlabeled samples and incoherent light scattered by the sample, λaf, forms the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The incoherent nature of the detected light in addition to the near- field illumination helps generate high-contrast label-free images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (e) Schematic of optical waveguide-based label- free coherent imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The guided coherent light generates an evanescent field that interacts with the sample placed at the core-cladding interface, and thereby transmits high-spatial frequencies of the sample into the far-field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  (f) Schematic of EPSLON imaging using Si3N4 waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The guided coherent light induces incoherent photoluminescence (PL) in the core of the waveguide that interacts with the sample and gets transmitted into the far-field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (g) 200 nm gold nanoparticles imaged in coherent and EPSLON mode, scale bar 100 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The issues of coherent noise, poor-contrast associated with conventional label-free techniques is mitigated in EPSLON due to δ-function correlations existing in the detected light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (h) To induce fluctuations in image intensity over time, different modes of the waveguide are excited by scanning the coupling objective along the input facet of the waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' At each instance of time t1, t2, t3 etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' the scatterers get excited by different MMI patterns, and an image is acquired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Scale bar 10 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (i) Experimental demonstration of coherence of scattered light using two 200 nm gold nanoparticles, scale bar 10 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The excitation of different modes causes the phase difference Δ𝜑 between the scattered light off the particles to change, leading to different images at different instances of time in label-free coherent imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This is demonstrated by the line profile of the bead images provided alongside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (j) Experimental realization of stochastic nature of the detected light in label-free imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The same nanoparticles shown in (i) are imaged in EPSLON mode, scale bar 10 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  In EPSLON, stochastic fluctuations between the scattered incoherent PL light reaching the camera leads to identical images at different instances of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This can be seen from the line profiles of the bead images provided alongside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  a  Epi b  C  Label free,  d  EPSLON:  Imageplane  TIRF  Imageplane  Image plane  Imageplane  fluorescence  coherent  Label free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  incoherent  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='O  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='O  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='O  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='O  Sampleplane  Sampleplane  Sampleplane  Sampleplane  80  O  O  exc  f  tomicroscope  g  Label free,  e  Label free,  tomicroscope  EPSLON  EPSLON  coherent  coherent  scatterer  af  filter  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='O  +A  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='O  exc  eXC  exc  exo  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  waveguidechip  waveguidechip  scatterers  h  Label free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  3  Greyvalue (norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=')  coherent  Greyvalue (norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=')  EPSLON  AO  facetscan  2  Ad  A2  Ao,  Az  Aos  0  1  2 2  3  4  Distance (μm)  Distance (μm)  Figure 2: Structuring the incoherent photoluminescent illumination using Si3N4 waveguides and its properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (a-c) Structuring photoluminescence using different waveguide geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (a) Straight waveguide that supports multiple modes in the core, scale bar 20 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The red insets are a part of the imaging region on the straight waveguide that is blown up to show the MMI pattern at different instances of time, scale bar 5 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Schematic diagram shows the geometry and width of the straight waveguide fabricated on a wafer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (b) Four-arm crossing waveguide provides more illumination spatial frequencies, scale bar 20 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The green inset is the blown- up region of the imaging area on the four-arm crossing waveguide, showing different speckle patterns at different instances of time, scale bar 5 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Schematic diagram shows the geometry and width of the four-arm crossing waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (c) SIM chip where two single-mode waveguides are made to overlap at the imaging area enclosed by the blue inset, scale bar 20 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The blown-up regions show the interference fringe pattern at three different phases, 2 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Schematic diagram shows the geometry of the SIM chip for two-dimensional SIM works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (d) By averaging out several MMI patterns, a uniform illumination profile over large field-of-view can be generated, scale bar 100 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (e) Ratio of incoherent PL scattering to coherent scattering for a single waveguide at three different wavelengths is plotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Here the waveguide is excited at 488 nm, 561 nm and 640 nm and the corresponding emissions may be detected in FITC, TRITC and CY5 channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (f) PL emission as a function of time is plotted here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' No bleaching was observed for about 2 hours of imaging indicating a stable emission that is suitable for long- term cell imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (g) PL emission varies linearly with the input coupling power, implying a linear system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  a  q  t  C  Straight  Four arm  SIM  25 1000μm  200 400μm  25μm  Multi wavelength  Uniformillumination  emission  Stableemission  Linearemission  d  Excitation wavelength (nm)  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0  e  488  561  640  g  3  ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='02  Aod  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='05  50  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0  Time (minutes)  Normalized inputpower(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=')  FITCTRITCCy5TRITCCy5 Cy5  Fluorescencefiltet  Figure 3: EPSLON for label-free super-resolution imaging of nanobeads using various waveguide geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (a,b,c) Label-free diffraction limited image termed DL, super-resolved image termed EPSLON and ground truth image of nanobeads are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (a) Label-free super-resolved images of 200 nm gold nanoparticles using a straight waveguide is demonstrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The diffraction-limited DL image, super-resolved EPSLON image and ground truth optical images are given alongside, scale bar 5 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The red and green line plot corresponds to intensity variation in the red and green insets in DL and EPSLON image respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (b) Label-free super-resolved images of 150 nm gold nanoparticles using a four-arm waveguide is demonstrated, scale bar 5 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In the straight waveguide, illumination frequencies are predominantly distributed along one-axis and therefore, resolution enhancement is possible only along that axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To mitigate this issue, a four-arm waveguide is used that provides more illumination frequencies along the azimuthal orientation, thereby permits resolution enhancement along two orthogonal directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The two red insets in the DL image enclose unresolved beads oriented along two orthogonal directions corresponding to the illumination frequency direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The line profile of the intensity variation in the green inset clearly indicates resolving the two beads enclosed by the red inset which is validated by the ground truth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  (c) Label-free 1-D SIM of 200 nm gold nanoparticles is demonstrated, scale bar 5 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The line profile indicates the intensity variations in the red and green insets in the diffraction-limited DL and FairSIM reconstructed EPSLON images respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The line profile clearly shows the separation of two particles spaced 274 nm, which is beyond the diffraction-limit of the imaging system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The Fourier domain representation of the diffraction-limited and reconstructed image are also provided alongside, scale bar 2 μm-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  a Label-freeIFON usingstraightwaveguide DL EPSLON Groundtruth 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 DL EPSLON 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 Distance (μm) b Label-freeIFONusingfour-armwaveguide DL EPSLON Groundtruth DL 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 EPSLON 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='67 intensity 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 Distance (μm)C EPsLONforone-dimensionallabel-freeSlM DL EPSLON 274nm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 DL EPSLON 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='6 cn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 Distance (um) Figure 4: EPSLON for circumventing photobleaching and for label-free super-resolution imaging of EVs (a) Time-lapse imaging comparison of extra-cellular vesicles between TIRF and EPSLON configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' EPSLON helps to image nanosized EVs over long periods of time without photobleaching and with better signal- to-background ratio as opposed to TIRF, scale bar 5 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' This fact is quantified in the graph where signal-to- background ratio as a function of time is plotted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (b) Super-resolution imaging of EVs in label-free regime using EPSLON configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' EVs are imaged in both TIRF and EPSLON mode, scale bar 2 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The red, green, blue, and yellow insets correspond to EVs in diffraction-limited TIRF image, label-free diffraction-limited image termed DL, label-free super-resolved EPSLON image and TIRF ground truth image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The line profiles corresponding to each of these insets showing the intensity variation are also shown alongside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  EPSLON resolves the unresolved EVs in the diffraction-limited images and this result is validated by the TIRF ground truth image acquired with a higher NA objective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Distance (μm) a b 20X/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45NATIRF 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 Osec 2 sec 8 sec 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='8 TIRF 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4 0 4 20X/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45NADL 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 EPSLON 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4 0 1 2 3 intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 EPSLON 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2 60X/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='9NATIRF 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='0 3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='50 0 2 4 6 8 Time(s) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='25 Figure 5: EPSLON for label-free super-resolution imaging of human placenta tissue sections: Large field- of-view label-free diffraction-limited image termed DL, super-resolved EPSLON image and ground truth images are shown, scale bar 25 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Two regions marked ‘‘1’’ and ‘‘2’’ in the DL image are blown-up and shown alongside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The corresponding regions in the EPSLON and ground truth images are also magnified and shown, scale bar 10 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Line profiles along the white dotted lines in the magnified boxes of the DL image fails to resolve any intricate features as shown by the line plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' EPSLON images provide more details as seen in the images and they are validated by the ground truth images, which are also evidenced by the line plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5:EPSLONforlabel freesuper resolutionofhuman  DL  EPSLON  Groundtruth  placentatissuesections  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='75  Intensity (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='50  Diffraction limited  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='25  0  EPSLON  um  Groundtruth  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='75  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='50  Ground truth  Label-free incoherent super-resolution optical microscopy Nikhil Jayakumar,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Firehun T Dullo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Jean-Claude Tinguley,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Krizia Sagini,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Alicia Llorente,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Balpreet Singh Ahluwalia 1Department of Physics and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' UiT The Arctic University of Norway,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Tromsø,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 9037,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway 2Department of Microsystems and Nanotechnology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' SINTEF Digital,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Gaustadalleen 23C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 0373 Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway 3 Department of Molecular Cell Biology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Institute for Cancer Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Oslo University Hospital,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The Norwegian Radium Hospital,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 0379 Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway 4Centre for Cancer Cell Reprogramming,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Faculty of Medicine,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' University of Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Montebello,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 0379 Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway 5Department for Mechanical,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Electronics and Chemical Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Oslo Metropolitan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Oslo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Norway *Balpreet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='singh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='ahluwalia@uit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='no  Supplementary Information 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Waveguide fabrication A 2 µm thick oxide layer was thermally grown on a silicon wafer, followed by the deposition of 150 nm thick Si3N4 layer using plasma enhanced chemical vapor deposition (PECVD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The 2D channel waveguides were defined by photolithography process and etched using reactive ion etching (RIE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Then, silicon oxide layer was deposited using PECVD on the patterned nitride layer for protection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Finally, the oxide layer was patterned and removed from certain regions of each waveguide to create the imaging regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The oxide layer was removed using combination of both dry and wet etching [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Waveguide modes  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 1: (a) Effective indices of the guided modes for various Si3N4 waveguide widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' A schematic diagram of the cross-section of the waveguide is provided as an inset in the plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' (b) Mode profiles for the fundamental and higher-order TE - modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The geometry of the waveguide in the simulation model is 150 nm thick and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='25 - 4 µm wide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The guided modes for a strip Si3N4 waveguide were simulated using the commercial software FIMMWAVE (Photon Design, Oxford, UK), and its effective indices were calculated using the full-vectorial film mode matching (FMM) method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  (a) (b) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='71 TEOO Effective index (n_eff) H20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='66 TE01 S3N4 TE02 Si02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='61 TEO0 TE01 TE03 TE04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='56 TE05 TE06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='51 TE07 TE02 TE03 TE08 TE09 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='46 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 4 Waveguidewidth(um) Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2: Waveguide geometries employed in EPSLON for beam shaping and their corresponding illumination frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The multi-moded interference (MMI) pattern of straight and four-crossing waveguide is captured using a 20X/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45 NA objective, scale bar 25 μm, while that of the SIM chip is captured using a 60X/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2 NA objective, scale bar 5 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' To see the well-defined fringe patterns in case of SIM chips, the interference angle between the overlapping single moded waveguides is chosen to be 20 degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The orange markers on the figures indicate the extend and orientation of the illuminating frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Scale bar 500 mm-1 for the straight and four- arm junction waveguide and 1 μm-1 for the SIM chip.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Straight Four-cross SIM 25 μm 25 μm 5 μm pattern 500mm-1 500mm-1 1 μm-1 Ilumination spatial frequencies 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Schematic diagram of the imaging setup for EPSLON  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Schematic diagram of experimental setup for EPSLON.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Laser guided by a single mode fiber (SMF) held on a XY piezo stage by vacuum chuck is collimated and directed to the back-focal plane of coupling objective Olympus LMPanFL N 50×/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 NA MO1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The light is focused by MO1 and coupled into Si3N4 waveguide mounted on a XYZ piezo stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The coupled laser light in the waveguide, induces a broadband photoluminescence in the core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Any index perturbation scatters the PL light, shown in red, into the far-field via detection objective MO2, tube lens with spectral filters onto a sCMOS Hamamatsu C13440-20CU camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The spectral filters are chosen to reject the coherent laser light and transmit only the incoherent photoluminescent light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  ExperimentalsetupforEPSLON SCMOS Tube lenswith spectral filter MO2 SMF SigNWaveguide Piezo 7 MO1 X Piezostage4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Optical modes of the waveguide to induce intensity-fluctuations: simulation study  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4: Two particle resolution comparison between waveguide-based coherent and incoherent (EPSLON) imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Three separate cases are considered for comparison between coherent and incoherent EPSLON imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' For brevity, only the fundamental mode with amplitude a1 and higher-order mode with amplitude a2 are considered interacting with the sample in each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The colorbar provided alongside indicates the phase variation of the field across the cross-section or width of the waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The sample consists of two 150 nm sized particles which are placed with a center-to-center distance of 350 nm apart on the core-cladding interface of a 10 μm Si3N4 waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The particles scatter 500 nm wavelength light into a detection objective with NA = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The image generated at the camera plane for the coherent and EPSLON cases are shown, scale bar 500 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The loss in phase information in EPSLON imaging leads to similarity in images for the different excitation cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Mode 1 Mode 1 Mode 1 Mode 1 Mode1 Mode 1 ai= 1 a2= 1 ai=1 a2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1 ai= 1 a2 = 1 Coherent EPSLON Coherent EPSLON Coherent EPSLON 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Small EV preparation and characterization Small EVs were isolated from fresh urine samples collected in the morning from healthy donors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The collection of urine samples was approved by the Norwegian Regional Committees for Medical and Health Research Ethics and the participants gave informed written consent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Small EVs were isolated by differential centrifugation as previously described [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Briefly, urine (around 200 ml) was centrifuged at 2000×g for 15 min at room temperature (RT) to remove cells and cell debris, and then at 10,000×g for 30 min at RT to separate large particles/vesicles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The resulting supernatant was centrifuged at 100,000×g for 70 min at RT in a Ti70 fixed-angle rotor (Beckmann Coulter, IN, USA) to pellet small particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The pellet was washed with 20 ml phosphate-buffered saline (PBS) and centrifuged again at 100,000×g for 70 min at 4°C in a Ti70 rotor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The pellet was then resuspended in 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 ml PBS, vortexed and centrifuged at 100,000×g for 70 min at 4°C in an MLA-80 fixed-angle rotor (Beckmann Coulter, IN, USA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The supernatant was then removed, and the pellet resuspended in 200 μl PBS (filtered through a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='02-μm Anotop 25 filter) and stained with CellMask™ Deep Red plasma membrane dye (C10046, Invitrogen, MA, USA) according to manufacturer’s instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Briefly, small EVs were incubated with CellMask™ Deep Red (diluted 1:500) for 10 min at 37°C, then the unbounded dye was removed and stained EVs washed with filtered PBS using ultrafiltration devices (Amicon Ultra 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='5 mL - 3K, UFC5003234, Millipore, MA, USA) at RT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The sample was then stored at 4°C until further use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' A small aliquot of the sample was used to measure the size and number of particles in the 100,000×g pellets using a Nanosight NS500 instrument (Malvern Panalytical, Malvern, UK).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The sample was diluted to the optimal working concentration of the instrument (2 × 108 to 1 × 109 particles per ml) with filtered PBS, and then measured.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Five videos of 60 sec were acquired and subsequently analyzed with the NTA 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='4 software, which identifies and tracks the center of each particle under Brownian motion to measure the average distance the particles move on a frame-by-frame basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 5, the majority of the small EVs has a diameter between 100-175 nm (65,9% of the total) with a mode of 101 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 5: Small EVs were isolated by sequential centrifugation from healthy donor urine and their size was measured by NTA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The size distribution of small EVs is shown as percentage of particles having the indicated size normalized by the total number of particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  0  10  20  30  40  50  50 75  75 100  100 125  125 150  150 175  175 200  200 225  225 250  250 275  275 300  300 325  325 350  350 375  375 400  400 425  425 450  450 475  475 500  % particles  (normalized to total particles)  nm  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Human-placenta tissue preparation and characterization  Placental tissue samples are first fixed in formalin and then embedded in paraffin [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4 μm sections of the tissue samples are then cut from these paraffin blocks using microtome (HM 355S Automatic Microtome, Thermo Fisher Scientific, Waltham, Massachusetts, USA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' The cut sections are then placed on poly-L-lysine coated Si3N4 waveguide chips, and deparaffinized in xylene (3 × 5 min), followed by rehydration in descendent series of ethanol: 100% (2 × 10 min), 96% (2 × 10 min) and 70% (10 min).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Experimental particulars The following spectral filters are used in this work: Table 1: Sl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Filter Name Spectral range (LP: LongPass, BP: BandPass) 1 FITC 515 nm LP + 535\\30  nm BP 2 TRITC 585 nm LP \\ 630\\75 nm BP 3 CY5 655 nm LP \\ 690\\50 nm BP  Table 2:  Figure #  Sample  λill  Spectral  filter \\  MO2  Exposure  Reconstruction  Algorithm  # Images  Comments  3a  195 nm  Polystyrene  beads  488 nm  TRITC \\  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45 NA  100 ms  SACD [4]  500  Order 2 used  for  reconstruction  3b  150 nm Gold  nanoparticles  640 nm  CY5 \\ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45  NA  1 sec  SACD  100  Order 2 used  for  reconstruction  3c  200 nm Gold  nanoparticles  640 nm  CY5 \\ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2  NA  100 ms  FairSIM [5]  3  4  (75 –250) nm  Extracellular  vesicles  488 nm  for PL  TRITC \\  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45 NA  1 sec  SACD  50  Order 2 used  for  reconstruction  640 nm  for TIRF  CY5 \\ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45  NA, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='2  NA  100 ms  50  5  Human Placenta  Tissue  488 nm  TRITC\\  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='25 NA  (PL  image) and  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='45 NA  (Ground  truth)  50 ms  SACD  20  Order 2 used  for  reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  Each image is  acquired for  50 ms and 20  images are  averaged to  create (50  ms 20 = 1  sec) to create  one input  image for  SACD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Prieto, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Sepúlveda, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Calle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Llobera, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Domínguez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Abad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Montoya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Lechuga, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' An integrated optical interferometric nanodevice based on silicon technology for biosensor applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nanotechnology, 14(8), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Ramirez-Garrastacho, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Berge, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Linē, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Llorente, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Potential of miRNAs in urinary extracellular vesicles for management of active surveillance in prostate cancer patients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' British journal of cancer, 126(3), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='492-501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Slaoui, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Fiette, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Histopathology procedures: from tissue sampling to histopathological evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' In Drug safety evaluation (pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 69-82).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Humana Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Müller, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Mönkemöller, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hennig, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hübner, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Huser, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Open-source image reconstruction of super-resolution structured illumination microscopy data in ImageJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Nature communications, 7(1), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content='1-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Zhao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Han, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Ding, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Mao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Jiu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', Tan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' and Ding, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=', 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' Enhancing detectable fluorescence fluctuation for high-throughput and four-dimensional live-cell super-resolution imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
+page_content=' bioRxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jdE1T4oBgHgl3EQf0AWa/content/2301.03451v1.pdf'}
diff --git a/kdE3T4oBgHgl3EQfhgpA/content/tmp_files/2301.04571v1.pdf.txt b/kdE3T4oBgHgl3EQfhgpA/content/tmp_files/2301.04571v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fdc1334d12569c1a5104d8616176e2ae461a7c1d
--- /dev/null
+++ b/kdE3T4oBgHgl3EQfhgpA/content/tmp_files/2301.04571v1.pdf.txt
@@ -0,0 +1,716 @@
+IMPROVING AND ANALYZING NEURAL SPEAKER EMBEDDINGS FOR ASR
+Christoph L¨uscher∗1,2, Jingjing Xu∗1, Mohammad Zeineldeen1,2, Ralf Schl¨uter1,2, Hermann Ney1,2
+1Human Language Technology and Pattern Recognition Group,
+Computer Science Department, RWTH Aachen University, 52074 Aachen, Germany
+2AppTek GmbH, 52062 Aachen, Germany
+{luescher,zeineldeen}@cs.rwth-aachen.de
+ABSTRACT
+Neural speaker embeddings encode the speaker’s speech
+characteristics through a DNN model and are prevalent for
+speaker verification tasks. However, few studies have inves-
+tigated the usage of neural speaker embeddings for an ASR
+system. In this work, we present our efforts w.r.t integrating
+neural speaker embeddings into a conformer based hybrid
+HMM ASR system. For ASR, our improved embedding ex-
+traction pipeline in combination with the Weighted-Simple-
+Add integration method results in x-vector and c-vector reach-
+ing on par performance with i-vectors. We further compare
+and analyze different speaker embeddings. We present our
+acoustic model improvements obtained by switching from
+newbob learning rate schedule to one cycle learning schedule
+resulting in a ∼3% relative WER reduction on Switchboard,
+additionally reducing the overall training time by 17%. By
+further adding neural speaker embeddings, we gain additional
+∼3% relative WER improvement on Hub5’00. Our best Con-
+former-based hybrid ASR system with speaker embeddings
+achieves 9.0% WER on Hub5’00 and Hub5’01 with training
+on SWB 300h.
+Index Terms— automatic speech recognition, neural
+speaker embeddings, I-vector
+1. INTRODUCTION & RELATED WORK
+For quite some time, speaker adaptation methods have been
+used to build robust automatic speech recognition (ASR) sys-
+tems [1], aiming at reducing the divergence of distribution
+caused by various speakers in the train and test datasets, com-
+pensating for differing vocal tracts, gender, accents, dialects,
+and further general speaker characteristics.
+Methodically,
+speaker adaptation is sub-divided into different types of ap-
+proaches, namely model space and feature space approaches.
+Model space approaches accommodate speaker-specific
+representations within the acoustic model (AM) [2–8] or
+add additional auxiliary losses in a multitask or adversar-
+ial training fashion, while feature space approaches focus
+on the input to the AM. For feature space approaches, two
+∗Equal contribution
+common methods exist. Firstly, transforming the input fea-
+ture vectors to be speaker normalized or speaker-dependent,
+for example with Vocal Tract Length Normalization [9] and
+Maximum Likelihood Linear Regression [10, 11]. Secondly,
+by augmenting the model with speaker embeddings [12, 13].
+The specific integration method for a chosen speaker em-
+bedding depends on the AM architecture. Concatenating the
+i-vector to the network input gives performance gains for a bi-
+directional long-short term memory (BLSTM) recurrent neu-
+ral network (RNN) AM in a hybrid modeling approach [14].
+The identical integration method leads to performance degra-
+dation when utilizing a Conformer AM [15]. In our previous
+work [16], we proposed an integration method suited to the
+Conformer AM: Weighted-Simple-Add, in which we add the
+weighted speaker embeddings to the input of the multi-head
+self-attention (MHSA) module. However, that approach only
+works well for i-vectors but not for neural speaker embed-
+dings, in our case x-vectors. This trend can also be observed
+throughout the research literature, as i-vectors are widely
+used for ASR [1,14,16,17], but x-vectors are not. To the best
+of our knowledge, there has only been very limited research
+on neural speaker embeddings for ASR. In [18, 19], (neural)
+speaker embeddings have been applied to different ASR sys-
+tems, but no clear statement on which neural or non-neural
+speaker embedding to favour can be made. Besides, [18, 19]
+have the drawback that the models utilized are not state-
+of-the-art anymore, namely deep neural network (DNN) or
+BLSTM based. In this work, we focus on understanding the
+short-comings of current neural speaker embeddings for ASR
+and investigate methods to extract more suitable speaker em-
+beddings for ASR.
+The main contributions of this paper are: 1. proposing an
+improved extraction pipeline for neural speaker embeddings,
+which are performant in an ASR system. The resulting x-
+vector and c-vector from our improved extraction pipeline
+improve our ASR system by ∼3% relative word error rate
+(WER) on Hub5’00. 2. improving our Switchboard baseline
+by using one cycle learning rate (OCLR), leading to a relative
+WER improvement of ∼3% relative and a 17% reduction in
+overall training time. 3. verifying the Weighted-Simple-Add
+arXiv:2301.04571v1  [cs.CL]  11 Jan 2023
+
+method on the LibriSpeech dataset, resulting in a relative
+WER reduction of 5.6% on test-other.
+2. SPEAKER EMBEDDINGS
+Every speaker’s speech has unique characteristics due to gen-
+der, age, vocal tract variations, personal speaking style, into-
+nation, pronunciation pattern, etc. Speaker embeddings cap-
+ture these speaker characteristics from the speech signal in
+the form of a learnable low-dimensional fixed size vector.
+The classical technique is based on a Gaussian mixture model
+(GMM)-universal background model (UBM) system which
+extracts an i-vector [12] as a feature vector.
+2.1. Neural speaker embedding
+Neural speaker embeddings are extracted from the bottle-
+neck layer of a DNN, which given speech data as input
+is trained in a supervised manner to discriminate between
+speakers. Given the strong representation capability of DNNs
+in learning highly abstract features, neural embeddings have
+outperformed i-vectors in speaker verification and speaker
+identification tasks [13, 20, 21].
+However, when applying
+neural speaker embeddings as a speaker adaptation method
+for ASR, in general i-vectors still outperform neural speaker
+embeddings [16, 19]. In this work, we propose an improved
+extraction pipeline for neural speaker embeddings which is
+more suitable for speaker adaptation in ASR tasks.
+2.1.1. Neural extraction model
+Choosing an appropriate neural network (NN) for the neural
+speaker embeddings is vital. In this work, two neural archi-
+tectures are chosen: the time delay neural network (TDNN)
+based x-vector [13] and the Multi-scale Feature Aggrega-
+tion (MFA)-Conformer based c-vector [21]. The well-known
+x-vector captures the speaker characteristics locally via the
+TDNN structures in the bottom layers. The newly proposed
+MFA-Conformer model captures speaker characteristics lo-
+cally AND globally via a self-attention mechanism and ag-
+gregates hidden representations from multiple layers within
+the NN. Since the lower layers are more significant for learn-
+ing speaker discriminative information [22], such multi-level
+aggregation can make the speaker representation more ro-
+bust. Both models apply a temporal pooling layer to aggre-
+gate frame-level speaker features to obtain an utterance-level
+speaker embedding. This aggregation across the time dimen-
+sion is crucial for extracting speaker embeddings for ASR.
+In this work, we compare four different temporal pooling
+methods within the NN: average pooling, statistics pool-
+ing [23], attention-based pooling [24], and attentive statistics
+pooling [25].
+2.1.2. Post-processing methods
+After extracting the embeddings from the NN, post-processing
+is applied to boost the quality of the speaker representations.
+We apply three standard post-processing procedures. Firstly,
+subtract global mean to center the representations. Secondly,
+use linear discriminant analysis (LDA) to maximize the vari-
+Fig. 1: The speaker embedding model with auxiliary recon-
+struction loss.
+ance between the speaker embeddings of different speak-
+ers clusters and minimizes intra-speaker variance caused by
+channel effects [12]. Thirdly, apply length (L2) normaliza-
+tion to normalize the euclidean length of each embedding
+to unit length [19].
+Besides, in order to generate embed-
+dings on a recording- or speaker-level, we simply average the
+embeddings corresponding to the same recording or speaker.
+2.1.3. Improved extraction pipeline
+An i-vector is designed to capture the highest mode from the
+total variability space, and can therefore encode both speaker
+and channel characteristics. However, the neural speaker em-
+bedding is trained to discriminate between speakers and thus
+focuses on speaker-specific information. As a result, the neu-
+ral speaker embeddings capture less information, which might
+be helpful for speaker adaptation, namely channel and other
+acoustic characteristics, compared to the i-vector. This infor-
+mation loss could be a cause of the performance degradation
+of neural speaker embeddings [16,18].
+To let the neural speaker embeddings encode additional
+channel and acoustic information, on the layer below the tem-
+poral pooling layer, we add an auxiliary branch. It consists
+of a linear layer with dropout on the input, followed by an
+auxiliary mean squared error (MSE) loss to reconstruct the
+acoustic inputs, which can be seen in Figure 1. Suppose the
+layer representation is ht and the acoustic inputs are xt. The
+reconstruction loss can be formulated as
+L = 1
+2
+T
+�
+t=1
+C
+�
+c=1
+(ht,c − xt,c)2
+where C is the corresponding feature dimension. Overall, we
+propose a better extraction pipeline: 1. train speaker embed-
+ding extractor with additional reconstruction loss 2. extract
+speaker embeddings from bottleneck layer 3. average over
+recordings 4. subtract the global mean
+3. EXPERIMENTAL SETUP
+The experiments are conducted on Switchboard 300h dataset
+[26] and LibriSpeech 960h dataset [27].
+For Switchboard
+300h dataset, we use Hub5’00 as the development set and
+Hub5’01 as test set. For LibriSpeech, we use the dev and
+test sets accordingly.
+3.1. Baseline
+We use the same Conformer architecture and experimen-
+tal setting as in our previous work [16]. However, we re-
+
+temporal
+bottleneck
+linear&
+pooling
+layer
+softmax
+shared
+bottomlayers
+dropout
+linearplace the newbob learning rate (LR) schedule with OCLR
+schedule [28].
+OCLR can improve neural network train-
+ing time without hurting performance, i.e. so-called super-
+convergence phenomenon. Our OCLR schedule consists of
+three phases, in the same manner as in [29]. Firstly, the LR
+linearly increases from 2e − 3 to 2e − 2 for 16 full epochs.
+Secondly, the LR linearly decreases from 2e − 2 to 2e − 3 for
+another 16 full epochs. Finally, 10 more epochs are used to
+further decrease the learning rate to 1e − 7. For LibriSpeech,
+we apply the same training recipe with two changes. First, we
+increase the dimension of feed-forward module to 2048 and
+attention dimension to 512 with 8 heads. Second, we extend
+the LR schedule to fully utilize the larger amount of training
+data.
+We use the lattice-based version of state-level minimum
+Bayes risk criterion [30]. The lattices are generated using
+the best Conformer AM and a bigram language model (LM).
+A small constant learning rate 4e-5 is used. We use 4-gram
+count-based LM and long-short term memory (LSTM) LM
+in first pass decoding [31] and Transformer LM for lattice
+rescoring. For Switchboard, the LSTM and Transformer LMs
+have perplexity 51.3 and 48.1 on Hub5’00 respectively. More
+details of LM for LibriSpeech can refer to [32]. If not further
+specified, we use the count-based LM.
+3.2. Speaker embeddings extraction
+All speaker embeddings are trained on either Switchboard
+300h or LibriSpeech 960h dataset.
+The total number of
+speakers is 520 or 2338, accordingly. Our i-vector extraction
+pipeline follows the recipe described in [14]. Empirically,
+we observe that 200-dim i-vectors works best for us, while
+experimenting with 100-dim, 200-dim and 300-dim. Our x-
+vector TDNN system follows the same architecture described
+in [13]. The structure of the c-vector MFA-Conformer frame-
+work is based on [21]. We use 6 conformer blocks for the
+embedding extractor. The attention dimension of each MHSA
+module is 384 with 6 attention heads. The dimension of the
+feed-forward module is set to 1536. The bottleneck feature
+dimension is set to 512 for both embedding models.
+For
+training the neural speaker embeddings, we split the train-
+ing data into a train and cross-validation set. The speaker
+identification is reported on cross-validation set.
+4. RESULTS
+4.1. Improved baseline
+In Table 1, we present our results using different LR sched-
+ules and applying our Weighted-Simple-Add method on the
+Switchboard dataset. We observe that switching from new-
+bob LR to OCLR schedule greatly enhances training effec-
+tiveness, allowing a reduction from 50 training epochs to 43,
+while improving WER from 10.7% to 10.4% on Hub5’00.
+One possible explanation of this phenomenon is that larger
+learning rate helps regularize the training. We also show that
+using integrating i-vectors using Weighted-Simple-Add out-
+performs basic concatenation of the i-vector to the model in-
+put and improves WER from 10.4% to 10.1% on Hub5’00. A
+comparison experiment using the same hyper-parameters but
+without i-vector integration proves that the improvement does
+not stem from simply training longer.
+Table 1: WERs [%] of improved baseline using one cycle
+learning rate schedule on Switchboard 300h dataset
+LR schedule
+I-vec
+integration
+method
+WER [%]
+full
+epochs
+Hub5’00
+SWB CH Total
+newbob
+-
+7.1 14.3 10.7
+50
+OCLR
+-
+6.8 13.9 10.4
+43
++ longer train
+-
+6.6 14.1 10.4
+68
++ i-vec
+append to input
+6.7 13.8 10.3
+68
+Weighted-Simple-Add 6.7 13.5 10.1
+To show the transferability of the Weighted-Simple-
+Add method, we perform experiments on LibriSpeech 960h
+dataset, shown in Table 2. The results show around 6% rel-
+ative improvement in terms of WER on all sub-sets with the
+4-gram LM. However, the improvement gets smaller when
+we recognize with an LSTM LM.
+Table 2: WERs [%] speaker adaptive training by integrating
+i-vectors with Weighted-Simple-Add method on LibriSpeech
+960h dataset
+Model
+LM
+dev[%]
+test[%]
+full
+epochs
+clean other clean other
+baseline
+4-gram
+2.9
+6.7
+3.2
+7.1
+15
+LSTM
+2.1
+4.7
+2.4
+5.2
++ longer train 4-gram
+2.8
+6.6
+3.0
+6.9
+25
++ i-vec
+4-gram
+2.7
+6.3
+3.0
+6.7
+25
+LSTM
+2.0
+4.7
+2.3
+5.0
+4.2. Temporal pooling comparison
+In order to extract speaker embeddings optimized for ASR,
+we study the impacts of temporal pooling in embedding ex-
+tractor layer.
+The speaker embeddings are averaged over
+recordings and global mean is subtracted.
+Table 3: Speaker identification accuracy [%] of speaker em-
+beddings extractor on dev set and WERs [%] of SAT using
+x-vectors that are aggregated with different temporal pooling
+methods.
+Temporal
+Pooling Method
+SpkId
+Accuracy [%]
+WER [%]
+Hub5’00
+SWB CH Total
+average pooling
+93.8
+6.8
+14.0 10.4
+statistics pooling
+89.9
+6.7
+14.0 10.3
+attention-based pooling
+94.3
+6.8
+14.0 10.4
+attentive statistics pooling
+90.5
+6.6
+13.7 10.2
+Table 3 shows that the speaker identification accuracy
+
+and ASR performance, measured in WER, do not correlate
+highly. Both statistics pooling and attentive statistics pool-
+ing outperform average pooling and attention-based pooling
+respectively regarding WER, but show weaker performance
+for speaker identification accuracy.
+This indicates that in-
+cluding the standard deviation gives some additional useful
+information for ASR task.
+4.3. Neural speaker embedding post processing
+In Table 4, we compare methods for improving the neural
+speaker embeddings for ASR.
+Table 4: WERs [%] of SAT using DNN-based speaker em-
+beddings that are different in aspects of speaker recognizer
+model and post processing level.
+Post
+Processing
+Level
+Subtract
+mean LDA
+With
+reconst
+loss
+X-vec
+C-vec
+Hub5’00
+Hub5’00
+SWB CH Total SWB CH Total
+utterance
+no
+no
+no
+6.9 14.1 10.5
+6.7 14.1 10.4
+recording
+6.6 13.9 10.2
+6.7 13.8 10.2
+speaker
+6.7 13.9 10.3
+6.6 13.8 10.2
+recording
+yes
+6.6 13.7 10.2
+6.6 13.8 10.2
+yes
+6.6 13.8 10.2
+6.7 13.7 10.2
+no
+yes
+6.7 13.5 10.1
+6.6 13.7 10.1
+We observe that the Conformer AM only improves with
+recording-wise or speaker-wise embeddings. This could be
+due to the increased context embedded into the speaker em-
+beddings. Furthermore, we also notice that x-vector and c-
+vector have similar performance. Subtracting global gives no
+improvement to the overall Hub5’00 WER, but only minor
+improvement in the subsets. Applying LDA has almost no
+effects on performance. The reconstruction loss scale is set
+to 5. With the reconstruction loss, the speaker identification
+accuracy of the TDNN embedding model would drop from
+90.5% to 85.8%. On the contrary, the WER of SAT improves
+from 10.2% to 10.1% on Hub5’00.
+4.4. Speaker embeddings comparison
+The comparison between i-vectors and neural speaker em-
+beddings is reported in Table 5. With our proposed extrac-
+tion pipeline, the WER when integrating x-vectors is reduced
+by 3.8% relative, i.e., from 10.5% to 10.1%, reaching the
+same performance as with i-vector integration. Combining
+i-vectors with neural embeddings by concatenation did not
+show any further improvement.
+Hinting that the different
+speaker embeddings contain the same information. As a con-
+trol experiment we replaced the learned speaker embeddings
+with Gaussian noise to verify the concern that the speaker em-
+beddings only had an effect due to a form of noise regulariza-
+tion. The control experiments has the same performance as
+the baseline, showing that the AM utilizes the speaker em-
+beddings in the correct way.
+4.5. Overall result
+In Table 6, we present a highly competitive and efficient Con-
+former hybrid ASR system with 58M parameters and trained
+Table 5: WERs [%] of SAT using different types of speaker
+embeddings.
+Speaker embedding
+With
+reconst.
+loss
+WER [%]
+Hub5’00
+Hub
+5’01
+SWB CH Total
+none
+-
+6.8 13.9 10.4 10.7
+Gaussian noise
+-
+6.7 14.1 10.4 10.6
+i-vec
+-
+6.7 13.5 10.1 10.3
+x-vec
+no
+6.9 14.1 10.5 10.6
+yes
+6.7 13.5 10.1 10.4
+c-vec
+no
+6.7 14.1 10.4 10.6
+yes
+6.6 13.7 10.1 10.5
+i-vec + x-vec
+yes
+6.7 13.6 10.1 10.3
+i-vec + x-vec + c-vec
+yes
+6.6 13.6 10.1 10.3
+with 74 epochs. We outperform the well-trained Conformer
+transducer system [29] and our previous work [16] with less
+epochs and shorter training time. Our best Conformer ASR
+system does not reach the state-of-the-art results by [17].
+However, two important methods applied in [17], speed per-
+turbation and a cross-utterance LM, are not used in this work,
+but could lead to further improvements.
+Table 6: Overall WER [%] comparison with literature.
+Work ASR
+Arch.
+AM
+LM
+seq
+disc ivec num
+param
+full
+epochs
+WER [%]
+Hub5’00
+Hub
+5’01
+SWB CH Total
+[29] RNNT Conf. Trafo yes no
+75
+86
+-
+-
+9.2
+9.3
+[17]
+LAS
+Conf. Trafo no yes
+68
+250
+5.5 11.2 8.4
+8.5
+[33]
+Hybrid
+TDNN RNN yes yes
+19
+-
+7.2 13.6 10.4
+-
+[16]
+Conf.
+Trafo yes yes
+58
+90
+6.3 12.1 9.2
+9.3
+ours
+4-gr
+no
+no
+58
+43
+6.8 13.9 10.4 10.7
+yes
+68
+6.7 13.5 10.1 10.3
+yes
+74
+6.7 13.3 10.0 10.1
+LSTM
+6.1 12.2 9.2
+9.3
+Trafo
+6.1 11.9 9.0
+9.0
+5. CONCLUSION
+In this work, we improve neural speaker embeddings for
+ASR. We focus on the shortcomings of neural speaker em-
+beddings compared to the conventional i-vectors and propose
+an improved extraction pipeline. With our proposed pipeline,
+the integration of x-vector or c-vector improves the ASR
+system performance by ∼3% relative, reaching on-par per-
+formance with i-vectors. So far, we do not see improvements
+beyond i-vectors. Moreover, we tried to combine the i-vector
+with neural speaker embeddings but gained no further im-
+provement.
+Overall, we present a highly competitive and
+efficient Conformer hybrid ASR system, approaching the
+state-of-the-art results but with a much smaller model and
+less training time.
+6. ACKNOWLEDGEMENTS
+This work was partially supported by the project HYKIST funded by the
+German Federal Ministry of Health on the basis of a decision of the German
+Federal Parliament (Bundestag) under funding ID ZMVI1-2520DAT04A.
+
+7. REFERENCES
+[1] G. Saon, H. Soltau, D. Nahamoo, and M. Picheny, “Speaker
+adaptation of neural network acoustic models using i-vectors,”
+in 2013 IEEE Workshop on Automatic Speech Recognition and
+Understanding, Olomouc, Czech Republic, Dec. 2013, pp.
+55–59.
+[2] H. Liao, “Speaker adaptation of context dependent deep neural
+networks,”
+in ICASSP, Vancouver, Canada, May 2013, pp.
+7947–7951.
+[3] D. Yu, K. Yao, H. Su, G. Li, and F. Seide, “Kl-divergence regu-
+larized deep neural network adaptation for improved large vo-
+cabulary speech recognition,” in ICASSP, Vancouver, Canada,
+May 2013, pp. 7893–7897.
+[4] F. Seide, G. Li, X. Chen, and D. Yu, “Feature engineering
+in context-dependent deep neural networks for conversational
+speech transcription,”
+in ASRU, Waikoloa, HI, USA, april
+2011, IEEE, pp. 24–29.
+[5] P. Swietojanski and S. Renals, “Learning hidden unit contri-
+butions for unsupervised speaker adaptation of neural network
+acoustic models,” in SLT, 2014, pp. 171–176.
+[6] P. Swietojanski, J. Li, and S. Renals, “Learning hidden unit
+contributions for unsupervised acoustic model adaptation,”
+IEEE ACM Trans. Audio Speech Lang. Process., vol. 24, no.
+8, pp. 1450–1463, 2016.
+[7] R. Gemello, F. Mana, S. Scanzio, P. Laface, and R. De Mori,
+“Adaptation of hybrid ann/hmm models using linear hid-
+den transformations and conservative training,” in ICASSP,
+Toubouse, France, May 2006, IEEE, pp. 1189–1192.
+[8] Bo L. and Khe Chai S., “Comparison of discriminative input
+and output transformations for speaker adaptation in the hy-
+brid nn/hmm systems,” in Eleventh Annual Conference of the
+International Speech Communication Association, Makuhari,
+Chiba, Japan, 2010.
+[9] L. Welling, S. Kanthak, and H. Ney, “Improved methods for
+vocal tract normalization,” in ICASSP, Phoenix, AZ, USA,
+march 1999, vol. 2, pp. 761–764 vol.2.
+[10] C.J. Leggetter and P.C. Woodland,
+“Maximum Likelihood
+Linear Regression for Speaker Adaptation of Continuous Den-
+sity Hidden Markov Models,” Computer Speech & Language,
+vol. 9, no. 2, pp. 171–185, 1995.
+[11] S. H. Ghalehjegh and R. C. Rose, “Regularized constrained
+maximum likelihood linear regression for speech recognition,”
+in ICASSP, 05 2014, pp. 6319–6323.
+[12] N. Dehak, P. J. Kenny, R. Dehak, P. Dumouchel, and P. Ouel-
+let, “Front-end factor analysis for speaker verification,” IEEE
+Transactions on Audio, Speech, and Language Processing,
+vol. 19, no. 4, pp. 788–798, 2011.
+[13] D. Snyder, D. Garcia-Romero, G. Sell, D. Povey, and S. Khu-
+danpur, “X-Vectors: Robust DNN Embeddings for Speaker
+Recognition,”
+in ICASSP, Calgary, Alberta, Canada, april
+2018, IEEE, pp. 5329–5333.
+[14] M. Kitza, P. Golik, R. Schl¨uter, and H. Ney,
+“Cumula-
+tive Adaptation for BLSTM Acoustic Models,”
+in INTER-
+SPEECH, Graz, Austria, sep 2019, pp. 754–758.
+[15] J. Deng, X. Xie, T. Wang, M. Cui, B. Xue, Z. Jin, M. Geng,
+G. Li, X. Liu, and H. Meng, “Confidence score based con-
+former speaker adaptation for speech recognition,” CoRR, vol.
+abs/2206.12045, 2022.
+[16] M. Zeineldeen, J. Xu, C. L¨uscher, R. Schl¨uter, and H. Ney,
+“Improving the training recipe for a robust conformer-based
+hybrid model,” in INTERSPEECH, Incheon, Korea, sep 2022.
+[17] Z. T¨uske, G. Saon, and B. Kingsbury, “On the limit of en-
+glish conversational speech recognition,” in Interspeech, Brno,
+Czech, Sept. 2021, pp. 2062–2066.
+[18] Joanna Rownicka, Peter Bell, and Steve Renals, “Embeddings
+for dnn speaker adaptive training,” in ASRU, Sentosa, Singa-
+pore, December 2019, pp. 479–486.
+[19] A. Rouhe, T. Kaseva, and M. Kurimo, “Speaker-aware Train-
+ing of Attention-based End-to-end Speech Recognition Using
+Neural Speaker Embeddings,” in ICASSP, Barcelona, Spain,
+may 2020, pp. 7064–7068.
+[20] J. Jung, H. Heo, J. Kim, H. Shim, and H. Yu, “Rawnet: Ad-
+vanced end-to-end deep neural network using raw waveforms
+for text-independent speaker verification,” in INTERSPEECH,
+Graz, Austria, September 2019, pp. 1268–1272.
+[21] Y. Zhang, Z. Lv, H. Wu, S. Zhang, P. Hu, Z. Wu, H. Lee, and
+H. Meng, “MFA-Conformer: Multi-scale Feature Aggrega-
+tion Conformer for Automatic Speaker Verification,” in Proc.
+Interspeech 2022, 2022, pp. 306–310.
+[22] Y. Tang, G. Ding, J. Huang, X. He, and B. Zhou,
+“Deep
+speaker embedding learning with multi-level pooling for text-
+independent speaker verification,” in ICASSP. 2019, pp. 6116–
+6120, IEEE.
+[23] D. Snyder, D. Garcia-Romero, D. Povey, and S. Khudan-
+pur, “Deep neural network embeddings for text-independent
+speaker verification,” in INTERSPEECH, Stockholm, Sweden,
+Aug. 2017, pp. 999–1003.
+[24] FA R. rahman Chowdhury, Q. Wang, I. L. Moreno, and Li W.,
+“Attention-based models for text-dependent speaker verifica-
+tion,”
+in ICASSP, Calgary, Alberta, April 2018, pp. 5359–
+5363.
+[25] K. Okabe, T. Koshinaka, and K. Shinoda, “Attentive Statistics
+Pooling for Deep Speaker Embedding,” in INTERSPEECH,
+Hyderabad, India, Sept. 2018, pp. 2252–2256.
+[26] J.J. Godfrey, E.C. Holliman, and J. McDaniel, “Switchboard:
+Telephone Speech Corpus for Research and Development,” in
+ICASSP, San Francisco,USA, Mar. 1992, vol. 1, pp. 517–520.
+[27] V. Panayotov, G. Chen, D. Povey, and S. Khudanpur, “Lib-
+riSpeech: An ASR Corpus Based on Public Domain Audio
+Books,” in ICASSP, South Brisbane, Australia, Apr. 2015, pp.
+5206–5210.
+[28] L. N. Smith and Nicholay T., “Super-convergence: Very fast
+training of neural networks using large learning rates,”
+in
+Artificial intelligence and machine learning for multi-domain
+operations applications. International Society for Optics and
+Photonics, 2019, vol. 11006, p. 1100612.
+[29] W. Zhou, W. Michel, R. Schl¨uter, and H. Ney, “Efficient train-
+ing of neural transducer for speech recognition,” in INTER-
+SPEECH, Incheon, Korea, September 2022.
+[30] M. Gibson and T. Hain, “Hypothesis Spaces for Minimum
+Bayes Risk Training in Large Vocabulary Speech Recogni-
+tion,” in INTERSPEECH, Pittsburgh, USA, Sept. 2006.
+[31] E. Beck, W. Zhou, R. Schl¨uter, and H. Ney,
+“LSTM Lan-
+guage Models for LVCSR in First-Pass Decoding and Lattice-
+Rescoring,” CoRR, vol. abs/1907.01030, 2019.
+[32] C. L¨uscher, E. Beck, K. Irie, M. Kitza, W. Michel, A. Zeyer,
+R. Schl¨uter, and H. Ney,
+“RWTH ASR Systems for Lib-
+riSpeech: Hybrid vs Attention,”
+in INTERSPEECH, Graz,
+Austria, Sept. 2019, pp. 231–235.
+[33] S. Hu, X. Xie, S. Liu, J. Yu, Z. Ye, M. Geng, X. Liu, and
+H. Meng,
+“Bayesian learning of lf-mmi trained time delay
+neural networks for speech recognition,” IEEE/ACM Transac-
+tions on Audio, Speech, and Language Processing, vol. 29, pp.
+1514–1529, 2021.
+
diff --git a/kdE3T4oBgHgl3EQfhgpA/content/tmp_files/load_file.txt b/kdE3T4oBgHgl3EQfhgpA/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..731ca7e0fc717f609c201250c91f17fd0d94da66
--- /dev/null
+++ b/kdE3T4oBgHgl3EQfhgpA/content/tmp_files/load_file.txt
@@ -0,0 +1,590 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf,len=589
+page_content='IMPROVING AND ANALYZING NEURAL SPEAKER EMBEDDINGS FOR ASR  Christoph L¨uscher∗1,2, Jingjing Xu∗1, Mohammad Zeineldeen1,2, Ralf Schl¨uter1,2, Hermann Ney1,2  1Human Language Technology and Pattern Recognition Group,  Computer Science Department, RWTH Aachen University, 52074 Aachen, Germany  2AppTek GmbH, 52062 Aachen, Germany  {luescher,zeineldeen}@cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='rwth-aachen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='de  ABSTRACT  Neural speaker embeddings encode the speaker’s speech  characteristics through a DNN model and are prevalent for  speaker verification tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' However, few studies have inves-  tigated the usage of neural speaker embeddings for an ASR  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' In this work, we present our efforts w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='t integrating  neural speaker embeddings into a conformer based hybrid  HMM ASR system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' For ASR, our improved embedding ex-  traction pipeline in combination with the Weighted-Simple-  Add integration method results in x-vector and c-vector reach-  ing on par performance with i-vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' We further compare  and analyze different speaker embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' We present our  acoustic model improvements obtained by switching from  newbob learning rate schedule to one cycle learning schedule  resulting in a ∼3% relative WER reduction on Switchboard,  additionally reducing the overall training time by 17%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' By  further adding neural speaker embeddings, we gain additional  ∼3% relative WER improvement on Hub5’00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Our best Con-  former-based hybrid ASR system with speaker embeddings  achieves 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0% WER on Hub5’00 and Hub5’01 with training  on SWB 300h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Index Terms— automatic speech recognition, neural  speaker embeddings, I-vector  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' INTRODUCTION & RELATED WORK  For quite some time, speaker adaptation methods have been  used to build robust automatic speech recognition (ASR) sys-  tems [1], aiming at reducing the divergence of distribution  caused by various speakers in the train and test datasets, com-  pensating for differing vocal tracts, gender, accents, dialects,  and further general speaker characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Methodically,  speaker adaptation is sub-divided into different types of ap-  proaches, namely model space and feature space approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Model space approaches accommodate speaker-specific  representations within the acoustic model (AM) [2–8] or  add additional auxiliary losses in a multitask or adversar-  ial training fashion, while feature space approaches focus  on the input to the AM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' For feature space approaches, two  ∗Equal contribution  common methods exist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Firstly, transforming the input fea-  ture vectors to be speaker normalized or speaker-dependent,  for example with Vocal Tract Length Normalization [9] and  Maximum Likelihood Linear Regression [10, 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Secondly,  by augmenting the model with speaker embeddings [12, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  The specific integration method for a chosen speaker em-  bedding depends on the AM architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Concatenating the  i-vector to the network input gives performance gains for a bi-  directional long-short term memory (BLSTM) recurrent neu-  ral network (RNN) AM in a hybrid modeling approach [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  The identical integration method leads to performance degra-  dation when utilizing a Conformer AM [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' In our previous  work [16], we proposed an integration method suited to the  Conformer AM: Weighted-Simple-Add, in which we add the  weighted speaker embeddings to the input of the multi-head  self-attention (MHSA) module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' However, that approach only  works well for i-vectors but not for neural speaker embed-  dings, in our case x-vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' This trend can also be observed  throughout the research literature, as i-vectors are widely  used for ASR [1,14,16,17], but x-vectors are not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' To the best  of our knowledge, there has only been very limited research  on neural speaker embeddings for ASR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' In [18, 19], (neural)  speaker embeddings have been applied to different ASR sys-  tems, but no clear statement on which neural or non-neural  speaker embedding to favour can be made.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Besides, [18, 19]  have the drawback that the models utilized are not state-  of-the-art anymore, namely deep neural network (DNN) or  BLSTM based.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' In this work, we focus on understanding the  short-comings of current neural speaker embeddings for ASR  and investigate methods to extract more suitable speaker em-  beddings for ASR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  The main contributions of this paper are: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' proposing an  improved extraction pipeline for neural speaker embeddings,  which are performant in an ASR system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The resulting x-  vector and c-vector from our improved extraction pipeline  improve our ASR system by ∼3% relative word error rate  (WER) on Hub5’00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' improving our Switchboard baseline  by using one cycle learning rate (OCLR), leading to a relative  WER improvement of ∼3% relative and a 17% reduction in  overall training time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' verifying the Weighted-Simple-Add  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='04571v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='CL]  11 Jan 2023  method on the LibriSpeech dataset, resulting in a relative  WER reduction of 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6% on test-other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' SPEAKER EMBEDDINGS  Every speaker’s speech has unique characteristics due to gen-  der, age, vocal tract variations, personal speaking style, into-  nation, pronunciation pattern, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Speaker embeddings cap-  ture these speaker characteristics from the speech signal in  the form of a learnable low-dimensional fixed size vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  The classical technique is based on a Gaussian mixture model  (GMM)-universal background model (UBM) system which  extracts an i-vector [12] as a feature vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Neural speaker embedding  Neural speaker embeddings are extracted from the bottle-  neck layer of a DNN, which given speech data as input  is trained in a supervised manner to discriminate between  speakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Given the strong representation capability of DNNs  in learning highly abstract features, neural embeddings have  outperformed i-vectors in speaker verification and speaker  identification tasks [13, 20, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  However, when applying  neural speaker embeddings as a speaker adaptation method  for ASR, in general i-vectors still outperform neural speaker  embeddings [16, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' In this work, we propose an improved  extraction pipeline for neural speaker embeddings which is  more suitable for speaker adaptation in ASR tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Neural extraction model  Choosing an appropriate neural network (NN) for the neural  speaker embeddings is vital.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' In this work, two neural archi-  tectures are chosen: the time delay neural network (TDNN)  based x-vector [13] and the Multi-scale Feature Aggrega-  tion (MFA)-Conformer based c-vector [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The well-known  x-vector captures the speaker characteristics locally via the  TDNN structures in the bottom layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The newly proposed  MFA-Conformer model captures speaker characteristics lo-  cally AND globally via a self-attention mechanism and ag-  gregates hidden representations from multiple layers within  the NN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Since the lower layers are more significant for learn-  ing speaker discriminative information [22], such multi-level  aggregation can make the speaker representation more ro-  bust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Both models apply a temporal pooling layer to aggre-  gate frame-level speaker features to obtain an utterance-level  speaker embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' This aggregation across the time dimen-  sion is crucial for extracting speaker embeddings for ASR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  In this work, we compare four different temporal pooling  methods within the NN: average pooling, statistics pool-  ing [23], attention-based pooling [24], and attentive statistics  pooling [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Post-processing methods  After extracting the embeddings from the NN, post-processing  is applied to boost the quality of the speaker representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  We apply three standard post-processing procedures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Firstly,  subtract global mean to center the representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Secondly,  use linear discriminant analysis (LDA) to maximize the vari-  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 1: The speaker embedding model with auxiliary recon-  struction loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  ance between the speaker embeddings of different speak-  ers clusters and minimizes intra-speaker variance caused by  channel effects [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Thirdly, apply length (L2) normaliza-  tion to normalize the euclidean length of each embedding  to unit length [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Besides, in order to generate embed-  dings on a recording- or speaker-level, we simply average the  embeddings corresponding to the same recording or speaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Improved extraction pipeline  An i-vector is designed to capture the highest mode from the  total variability space, and can therefore encode both speaker  and channel characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' However, the neural speaker em-  bedding is trained to discriminate between speakers and thus  focuses on speaker-specific information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' As a result, the neu-  ral speaker embeddings capture less information, which might  be helpful for speaker adaptation, namely channel and other  acoustic characteristics, compared to the i-vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' This infor-  mation loss could be a cause of the performance degradation  of neural speaker embeddings [16,18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  To let the neural speaker embeddings encode additional  channel and acoustic information, on the layer below the tem-  poral pooling layer, we add an auxiliary branch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' It consists  of a linear layer with dropout on the input, followed by an  auxiliary mean squared error (MSE) loss to reconstruct the  acoustic inputs, which can be seen in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Suppose the  layer representation is ht and the acoustic inputs are xt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The  reconstruction loss can be formulated as  L = 1  2  T  �  t=1  C  �  c=1  (ht,c − xt,c)2  where C is the corresponding feature dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Overall, we  propose a better extraction pipeline: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' train speaker embed-  ding extractor with additional reconstruction loss 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' extract  speaker embeddings from bottleneck layer 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' average over  recordings 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' subtract the global mean  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' EXPERIMENTAL SETUP  The experiments are conducted on Switchboard 300h dataset  [26] and LibriSpeech 960h dataset [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  For Switchboard  300h dataset, we use Hub5’00 as the development set and  Hub5’01 as test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' For LibriSpeech, we use the dev and  test sets accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Baseline  We use the same Conformer architecture and experimen-  tal setting as in our previous work [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' However, we re-  temporal  bottleneck  linear&  pooling  layer  softmax  shared  bottomlayers  dropout  linearplace the newbob learning rate (LR) schedule with OCLR  schedule [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  OCLR can improve neural network train-  ing time without hurting performance, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' so-called super-  convergence phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Our OCLR schedule consists of  three phases, in the same manner as in [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Firstly, the LR  linearly increases from 2e − 3 to 2e − 2 for 16 full epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Secondly, the LR linearly decreases from 2e − 2 to 2e − 3 for  another 16 full epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Finally, 10 more epochs are used to  further decrease the learning rate to 1e − 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' For LibriSpeech,  we apply the same training recipe with two changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' First, we  increase the dimension of feed-forward module to 2048 and  attention dimension to 512 with 8 heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Second, we extend  the LR schedule to fully utilize the larger amount of training  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  We use the lattice-based version of state-level minimum  Bayes risk criterion [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The lattices are generated using  the best Conformer AM and a bigram language model (LM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  A small constant learning rate 4e-5 is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' We use 4-gram  count-based LM and long-short term memory (LSTM) LM  in first pass decoding [31] and Transformer LM for lattice  rescoring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' For Switchboard, the LSTM and Transformer LMs  have perplexity 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3 and 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 on Hub5’00 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' More  details of LM for LibriSpeech can refer to [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' If not further  specified, we use the count-based LM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Speaker embeddings extraction  All speaker embeddings are trained on either Switchboard  300h or LibriSpeech 960h dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  The total number of  speakers is 520 or 2338, accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Our i-vector extraction  pipeline follows the recipe described in [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Empirically,  we observe that 200-dim i-vectors works best for us, while  experimenting with 100-dim, 200-dim and 300-dim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Our x-  vector TDNN system follows the same architecture described  in [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The structure of the c-vector MFA-Conformer frame-  work is based on [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' We use 6 conformer blocks for the  embedding extractor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The attention dimension of each MHSA  module is 384 with 6 attention heads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The dimension of the  feed-forward module is set to 1536.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The bottleneck feature  dimension is set to 512 for both embedding models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  For  training the neural speaker embeddings, we split the train-  ing data into a train and cross-validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The speaker  identification is reported on cross-validation set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' RESULTS  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Improved baseline  In Table 1, we present our results using different LR sched-  ules and applying our Weighted-Simple-Add method on the  Switchboard dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' We observe that switching from new-  bob LR to OCLR schedule greatly enhances training effec-  tiveness, allowing a reduction from 50 training epochs to 43,  while improving WER from 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7% to 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4% on Hub5’00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  One possible explanation of this phenomenon is that larger  learning rate helps regularize the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' We also show that  using integrating i-vectors using Weighted-Simple-Add out-  performs basic concatenation of the i-vector to the model in-  put and improves WER from 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4% to 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1% on Hub5’00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' A  comparison experiment using the same hyper-parameters but  without i-vector integration proves that the improvement does  not stem from simply training longer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Table 1: WERs [%] of improved baseline using one cycle  learning rate schedule on Switchboard 300h dataset  LR schedule  I-vec  integration  method  WER [%]  full  epochs  Hub5’00  SWB CH Total  newbob 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7  50  OCLR 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4  43  + longer train 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4  68  + i-vec  append to input  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  68  Weighted-Simple-Add 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1  To show the transferability of the Weighted-Simple-  Add method, we perform experiments on LibriSpeech 960h  dataset, shown in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The results show around 6% rel-  ative improvement in terms of WER on all sub-sets with the  4-gram LM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' However, the improvement gets smaller when  we recognize with an LSTM LM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Table 2: WERs [%] speaker adaptive training by integrating  i-vectors with Weighted-Simple-Add method on LibriSpeech  960h dataset  Model  LM  dev[%]  test[%]  full  epochs  clean other clean other  baseline  4-gram  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1  15  LSTM  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  + longer train 4-gram  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9  25  + i-vec  4-gram  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7  25  LSTM  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Temporal pooling comparison  In order to extract speaker embeddings optimized for ASR,  we study the impacts of temporal pooling in embedding ex-  tractor layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  The speaker embeddings are averaged over  recordings and global mean is subtracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Table 3: Speaker identification accuracy [%] of speaker em-  beddings extractor on dev set and WERs [%] of SAT using  x-vectors that are aggregated with different temporal pooling  methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Temporal  Pooling Method  SpkId  Accuracy [%]  WER [%]  Hub5’00  SWB CH Total  average pooling  93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4  statistics pooling  89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  attention-based pooling  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4  attentive statistics pooling  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  Table 3 shows that the speaker identification accuracy  and ASR performance, measured in WER, do not correlate  highly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Both statistics pooling and attentive statistics pool-  ing outperform average pooling and attention-based pooling  respectively regarding WER, but show weaker performance  for speaker identification accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  This indicates that in-  cluding the standard deviation gives some additional useful  information for ASR task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Neural speaker embedding post processing  In Table 4, we compare methods for improving the neural  speaker embeddings for ASR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Table 4: WERs [%] of SAT using DNN-based speaker em-  beddings that are different in aspects of speaker recognizer  model and post processing level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Post  Processing  Level  Subtract  mean LDA  With  reconst  loss  X-vec  C-vec  Hub5’00  Hub5’00  SWB CH Total SWB CH Total  utterance  no  no  no  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4  recording  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  speaker  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  recording  yes  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  yes  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  no  yes  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1  We observe that the Conformer AM only improves with  recording-wise or speaker-wise embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' This could be  due to the increased context embedded into the speaker em-  beddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Furthermore, we also notice that x-vector and c-  vector have similar performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Subtracting global gives no  improvement to the overall Hub5’00 WER, but only minor  improvement in the subsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Applying LDA has almost no  effects on performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The reconstruction loss scale is set  to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' With the reconstruction loss, the speaker identification  accuracy of the TDNN embedding model would drop from  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5% to 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' On the contrary, the WER of SAT improves  from 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2% to 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1% on Hub5’00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Speaker embeddings comparison  The comparison between i-vectors and neural speaker em-  beddings is reported in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' With our proposed extrac-  tion pipeline, the WER when integrating x-vectors is reduced  by 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8% relative, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=', from 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5% to 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1%, reaching the  same performance as with i-vector integration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Combining  i-vectors with neural embeddings by concatenation did not  show any further improvement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Hinting that the different  speaker embeddings contain the same information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' As a con-  trol experiment we replaced the learned speaker embeddings  with Gaussian noise to verify the concern that the speaker em-  beddings only had an effect due to a form of noise regulariza-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' The control experiments has the same performance as  the baseline, showing that the AM utilizes the speaker em-  beddings in the correct way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Overall result  In Table 6, we present a highly competitive and efficient Con-  former hybrid ASR system with 58M parameters and trained  Table 5: WERs [%] of SAT using different types of speaker  embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Speaker embedding  With  reconst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  loss  WER [%]  Hub5’00  Hub  5’01  SWB CH Total  none 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7  Gaussian noise 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6  i-vec 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  x-vec  no  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6  yes  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4  c-vec  no  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6  yes  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5  i-vec + x-vec  yes  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  i-vec + x-vec + c-vec  yes  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  with 74 epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' We outperform the well-trained Conformer  transducer system [29] and our previous work [16] with less  epochs and shorter training time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Our best Conformer ASR  system does not reach the state-of-the-art results by [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  However, two important methods applied in [17], speed per-  turbation and a cross-utterance LM, are not used in this work,  but could lead to further improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Table 6: Overall WER [%] comparison with literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Work ASR  Arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  AM  LM  seq  disc ivec num  param  full  epochs  WER [%]  Hub5’00  Hub  5’01  SWB CH Total  [29] RNNT Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Trafo yes no  75  86 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  [17]  LAS  Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Trafo no yes  68  250  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5  [33]  Hybrid  TDNN RNN yes yes  19 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='6 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4 [16]  Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Trafo yes yes  58  90  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  ours  4-gr  no  no  58  43  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='8 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='4 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7  yes  68  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  yes  74  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1  LSTM  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='3  Trafo  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='1 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='9 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='0  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' CONCLUSION  In this work, we improve neural speaker embeddings for  ASR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' We focus on the shortcomings of neural speaker em-  beddings compared to the conventional i-vectors and propose  an improved extraction pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' With our proposed pipeline,  the integration of x-vector or c-vector improves the ASR  system performance by ∼3% relative, reaching on-par per-  formance with i-vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' So far, we do not see improvements  beyond i-vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Moreover, we tried to combine the i-vector  with neural speaker embeddings but gained no further im-  provement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Overall, we present a highly competitive and  efficient Conformer hybrid ASR system, approaching the  state-of-the-art results but with a much smaller model and  less training time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' ACKNOWLEDGEMENTS  This work was partially supported by the project HYKIST funded by the  German Federal Ministry of Health on the basis of a decision of the German  Federal Parliament (Bundestag) under funding ID ZMVI1-2520DAT04A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' REFERENCES  [1] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Saon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Soltau, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Nahamoo, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Picheny, “Speaker  adaptation of neural network acoustic models using i-vectors,”  in 2013 IEEE Workshop on Automatic Speech Recognition and  Understanding, Olomouc, Czech Republic, Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  55–59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [2] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Liao, “Speaker adaptation of context dependent deep neural  networks,”  in ICASSP, Vancouver, Canada, May 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  7947–7951.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [3] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Yu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Yao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Su, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Li, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Seide, “Kl-divergence regu-  larized deep neural network adaptation for improved large vo-  cabulary speech recognition,” in ICASSP, Vancouver, Canada,  May 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 7893–7897.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [4] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Seide, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Chen, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Yu, “Feature engineering  in context-dependent deep neural networks for conversational  speech transcription,”  in ASRU, Waikoloa, HI, USA, april  2011, IEEE, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 24–29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [5] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Swietojanski and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Renals, “Learning hidden unit contri-  butions for unsupervised speaker adaptation of neural network  acoustic models,” in SLT, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 171–176.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [6] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Swietojanski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Li, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Renals, “Learning hidden unit  contributions for unsupervised acoustic model adaptation,”  IEEE ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Audio Speech Lang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 24, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 1450–1463, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [7] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Gemello, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Mana, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Scanzio, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Laface, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' De Mori,  “Adaptation of hybrid ann/hmm models using linear hid-  den transformations and conservative training,” in ICASSP,  Toubouse, France, May 2006, IEEE, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 1189–1192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [8] Bo L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' and Khe Chai S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=', “Comparison of discriminative input  and output transformations for speaker adaptation in the hy-  brid nn/hmm systems,” in Eleventh Annual Conference of the  International Speech Communication Association, Makuhari,  Chiba, Japan, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [9] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Welling, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Kanthak, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ney, “Improved methods for  vocal tract normalization,” in ICASSP, Phoenix, AZ, USA,  march 1999, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 761–764 vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [10] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Leggetter and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Woodland,  “Maximum Likelihood  Linear Regression for Speaker Adaptation of Continuous Den-  sity Hidden Markov Models,” Computer Speech & Language,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 171–185, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ghalehjegh and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Rose, “Regularized constrained  maximum likelihood linear regression for speech recognition,”  in ICASSP, 05 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 6319–6323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [12] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Dehak, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Kenny, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Dehak, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Dumouchel, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ouel-  let, “Front-end factor analysis for speaker verification,” IEEE  Transactions on Audio, Speech, and Language Processing,  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 788–798, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Snyder, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Garcia-Romero, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Sell, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Povey, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Khu-  danpur, “X-Vectors: Robust DNN Embeddings for Speaker  Recognition,”  in ICASSP, Calgary, Alberta, Canada, april  2018, IEEE, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 5329–5333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Kitza, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Golik, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Schl¨uter, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ney,  “Cumula-  tive Adaptation for BLSTM Acoustic Models,”  in INTER-  SPEECH, Graz, Austria, sep 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 754–758.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Deng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Xie, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Cui, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Xue, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Jin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Geng,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Liu, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Meng, “Confidence score based con-  former speaker adaptation for speech recognition,” CoRR, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  abs/2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='12045, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Zeineldeen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Xu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' L¨uscher, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Schl¨uter, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ney,  “Improving the training recipe for a robust conformer-based  hybrid model,” in INTERSPEECH, Incheon, Korea, sep 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [17] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' T¨uske, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Saon, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Kingsbury, “On the limit of en-  glish conversational speech recognition,” in Interspeech, Brno,  Czech, Sept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2062–2066.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [18] Joanna Rownicka, Peter Bell, and Steve Renals, “Embeddings  for dnn speaker adaptive training,” in ASRU, Sentosa, Singa-  pore, December 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 479–486.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Rouhe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Kaseva, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Kurimo, “Speaker-aware Train-  ing of Attention-based End-to-end Speech Recognition Using  Neural Speaker Embeddings,” in ICASSP, Barcelona, Spain,  may 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 7064–7068.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Jung, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Heo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Kim, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Shim, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Yu, “Rawnet: Ad-  vanced end-to-end deep neural network using raw waveforms  for text-independent speaker verification,” in INTERSPEECH,  Graz, Austria, September 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 1268–1272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [21] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Lv, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Hu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Wu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Lee, and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Meng, “MFA-Conformer: Multi-scale Feature Aggrega-  tion Conformer for Automatic Speaker Verification,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  Interspeech 2022, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 306–310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [22] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Tang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ding, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Huang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' He, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Zhou,  “Deep  speaker embedding learning with multi-level pooling for text-  independent speaker verification,” in ICASSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 6116–  6120, IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [23] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Snyder, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Garcia-Romero, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Povey, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Khudan-  pur, “Deep neural network embeddings for text-independent  speaker verification,” in INTERSPEECH, Stockholm, Sweden,  Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 999–1003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [24] FA R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' rahman Chowdhury, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Wang, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Moreno, and Li W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=',  “Attention-based models for text-dependent speaker verifica-  tion,”  in ICASSP, Calgary, Alberta, April 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 5359–  5363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [25] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Okabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Koshinaka, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Shinoda, “Attentive Statistics  Pooling for Deep Speaker Embedding,” in INTERSPEECH,  Hyderabad, India, Sept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2252–2256.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Godfrey, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Holliman, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' McDaniel, “Switchboard:  Telephone Speech Corpus for Research and Development,” in  ICASSP, San Francisco,USA, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 1992, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 517–520.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [27] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Panayotov, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Povey, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Khudanpur, “Lib-  riSpeech: An ASR Corpus Based on Public Domain Audio  Books,” in ICASSP, South Brisbane, Australia, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  5206–5210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [28] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Smith and Nicholay T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=', “Super-convergence: Very fast  training of neural networks using large learning rates,”  in  Artificial intelligence and machine learning for multi-domain  operations applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' International Society for Optics and  Photonics, 2019, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 11006, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 1100612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [29] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Zhou, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Michel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Schl¨uter, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ney, “Efficient train-  ing of neural transducer for speech recognition,” in INTER-  SPEECH, Incheon, Korea, September 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Gibson and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Hain, “Hypothesis Spaces for Minimum  Bayes Risk Training in Large Vocabulary Speech Recogni-  tion,” in INTERSPEECH, Pittsburgh, USA, Sept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [31] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Beck, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Zhou, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Schl¨uter, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ney,  “LSTM Lan-  guage Models for LVCSR in First-Pass Decoding and Lattice-  Rescoring,” CoRR, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' abs/1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='01030, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [32] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' L¨uscher, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Beck, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Irie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Kitza, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Michel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Zeyer,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Schl¨uter, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ney,  “RWTH ASR Systems for Lib-  riSpeech: Hybrid vs Attention,”  in INTERSPEECH, Graz,  Austria, Sept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 231–235.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  [33] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Hu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Xie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Yu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Ye, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Geng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Liu, and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' Meng,  “Bayesian learning of lf-mmi trained time delay  neural networks for speech recognition,” IEEE/ACM Transac-  tions on Audio, Speech, and Language Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content=' 29, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
+page_content='  1514–1529, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/kdE3T4oBgHgl3EQfhgpA/content/2301.04571v1.pdf'}
diff --git a/ldFST4oBgHgl3EQfJTg8/content/tmp_files/2301.13732v1.pdf.txt b/ldFST4oBgHgl3EQfJTg8/content/tmp_files/2301.13732v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..54d5b8239a97af4f0e6f3794e0ec9c55f47020a7
--- /dev/null
+++ b/ldFST4oBgHgl3EQfJTg8/content/tmp_files/2301.13732v1.pdf.txt
@@ -0,0 +1,1641 @@
+Preserving local densities in low-dimensional embeddings
+Jonas Fischer 1 Rebekka Burkholz 2 Jilles Vreeken 2
+Abstract
+Low-dimensional embeddings and visualizations
+are an indispensable tool for analysis of high-
+dimensional data. State-of-the-art methods, such
+as TSNE and UMAP, excel in unveiling local
+structures hidden in high-dimensional data and
+are therefore routinely applied in standard analy-
+sis pipelines in biology. We show, however, that
+these methods fail to reconstruct local properties,
+such as relative differences in densities (Fig. 1)
+and that apparent differences in cluster size can
+arise from computational artifact caused by differ-
+ing sample sizes (Fig. 2). Providing a theoretical
+analysis of this issue, we then suggest DTSNE,
+which approximately conserves local densities. In
+an extensive study on synthetic benchmark and
+real world data comparing against five state-of-
+the-art methods, we empirically show that DT-
+SNE provides similar global reconstruction, but
+yields much more accurate depictions of local
+distances and relative densities.
+1. Introduction
+Low-dimensional embeddings are an essential tool of data
+analysis allowing exploration of the structure and relation-
+ships encoded in the data. Given the high-dimensional
+datasets that are gathered on a daily basis, such low-
+dimensional embeddings have been shown to be especially
+fruitful in aiding experts to identify general trends, clusters
+and inter-cluster relationships, as well as extreme-valued
+samples and outliers. In natural sciences, such as genomics,
+they are routinely applied as a first step in data exploration,
+in core machine learning they are frequently used as a tool
+for understanding neural embeddings, such as given by
+word or sentence encoders. The property of most high-
+dimensional data that allows for such a reduction of dimen-
+sions is that samples live in a lower dimensional subspace
+1Department of Biostatistics, Harvard T.H. Chan School of
+Public Health, Boston MA, USA 2CISPA Helmholtz Center for
+Information Security, Saarbr¨ucken, Germany. Correspondence to:
+Jonas Fischer <jfischer@hsph.harvard.edu>.
+or manifold, which low-dimensional embeddings aim to
+approximate.
+While a classical projection onto the first two principal com-
+ponents can be insightful and a valuable first step of anal-
+ysis, the interesting regularities are often non-linear and
+are, hence, not approximated well by principal components.
+Different solutions have been suggested for this problem,
+with most successful advances using a similarity measure
+for the high-dimensional data to be reconstructed in the
+low-dimensional embedding. Moreover, it is inherently
+hard to correctly reconstruct relationships at all distance
+scales. Instead, state-of-the-art methods focus on recon-
+structing local structures correctly, in exchange allowing
+to distort long-range distances, as this arguably preserves
+the more interesting regularities in the data. The most
+widely used are TSNE (van der Maaten & Hinton, 2008) and
+UMAP (McInnes et al., 2018), as well as their recent adap-
+atations LARGEVIS (Tang et al., 2016) and NCVIS (Arte-
+menkov & Panov, 2020), which are by now an indispensable
+part in standard data analysis pipelines in, e.g., biology.
+While these methods yield arguably good overall recon-
+structions and visualizations of the data, their embeddings
+share an often neglected problem. Most experts are well
+aware that inter-cluster distances are distorted and argue
+about those with care. In contrast, individual clusters are (at
+least relative to each other) often assumed to be faithfully
+reconstructed locally.
+This, however, turns out not to be true: Cluster sizes and den-
+sities in the embedding do not model variances respectively
+densities of the high-dimensional data. Two clusters with
+the same number of points, as diverse as one stretched over
+vasts amount of space and the other one extremely compact,
+both appear equally sized for current embedding techniques,
+which we visualize in a simple example in Fig. 1. In ex-
+periments on real world data, these methods often yield
+embeddings with different cluster sizes, which, however,
+turn out to be not due to differently sized clusters in high di-
+mensions, but to be different numbers of samples per cluster
+artificially bloating clusters in the embedding (see Fig. 2).
+These relative differences in local densities, which state-
+of-the-art methods fail to model correctly, however, could
+provide crucial information about the data at hand, such
+as a cell types, which are evident as clusters, being more
+arXiv:2301.13732v1  [cs.LG]  31 Jan 2023
+
+Preserving local densities in low-dimensional embeddings
+1
+2
+3
+X1
+X2
+2
+1
+3
+LARGEVIS1
+LARGEVIS2
+2
+3
+1
+NCVIS1
+NCVIS2
+1
+2
+3
+TSNE1
+TSNE2
+1
+2
+3
+UMAP1
+UMAP2
+1
+2
+3
+DTSNE1
+DTSNE2
+Figure 1. Preservation of relative densities. For data of 3 Gaussians with different densities in 2 dimensional space, we give the original
+data, LARGEVIS, NCVIS, TSNE, UMAP, and DTSNE embeddings (from left to right). The state-of-the-art does not preserve the relative
+densities nor the relative local distances. Our method DTSNE reflects the relative densities and local distances across clusters. The results
+are consistent for higher dimensional data and we provide more information on data generation in the Appendix.
+1
+2
+3
+X1
+X2
+1
+3
+2
+LARGEVIS1
+LARGEVIS2
+1
+3
+2
+NCVIS1
+NCVIS2
+1
+3
+2
+TSNE1
+TSNE2
+1
+2
+3
+UMAP1
+UMAP2
+1
+3
+2
+DTSNE1
+DTSNE2
+Figure 2. Robustness to sample sizes. For data of 3 Gaussians in 2 dimensional space with different number of samples per cluster, we
+give (from left to right) the original data, LARGEVIS, NCVIS, TSNE, UMAP, and DTSNE embeddings. The state-of-the-art artificially
+blows up, respectively shrinks clusters based on number of samples in a cluster. Our method reflects the differences in local densities per
+clusters. The results are consistent for higher dimensional data and we provide more information on data generation in the Appendix.
+heterogeneous than others in a biological dataset. Here,
+we provide a theoretical argument why current methods
+fail to reconstruct relative densities and suggest a domain-
+independent and entirely unsupervised approach to properly
+account for relative local densities. In extensive experiments
+on synthetic and real world data, we show that our solution
+better recovers the relative differences of cluster densities
+hidden in the high dimensional data, while yielding overall
+performance that is on par with state-of-the-art approaches
+in terms of overall reconstruction quality.
+In summary, our main contributions are
+• a theoretical analysis of why current methods do not
+reflect local densities correctly,
+• an unsupervised embedding approach preserving rela-
+tive densities (DTSNE),
+• a theoretical analysis of DTSNE proving its ability to
+preserve densities for local neighbourhoods, and
+• an extensive evaluation on synthetic and real-world
+data against six state-of-the-art methods.
+2. Related Work
+Embeddings of high dimensional data into a low dimen-
+sional space, in particular to 2 or 3 dimensions, have in
+recent years become an essential tool of unsupervised anal-
+ysis of high dimensional data in modern science. Clas-
+sical methods of principal component analysis (Pearson,
+1901), multidimensional scaling (Torgerson, 1952), lapla-
+cian eigenmaps (Belkin & Niyogi, 2001), and self orga-
+nizing maps (Kohonen, 1982) focus on keeping all, and in
+particular the large distances intact. As high dimensional
+data typically lies on a manifold (Silva & Tenenbaum, 2003),
+resembling euclidean space only locally, research attention
+shifted on modeling geodesic distances (Tenenbaum et al.,
+2000), or focusing only on local distances trough locally lin-
+ear embeddings (LLE) (Roweis & Saul, 2000) or stochastic
+neighbour embeddings (SNE) (Hinton & Roweis, 2003).
+The current state-of-the-art in low-dimensional embeddings
+for visualizations t-distributed SNE (TSNE) by van der
+Maaten & Hinton (2008) and Uniform Manifold Approx-
+imation (UMAP) by McInnes et al. (2018) also focus on
+modeling local distances correctly, allowing to distort long-
+range distances. They successfully reveal intrinsic structures
+of high dimensional data and, hence, have been adapted as
+standard exploration and pre-processing tools in, e.g., ge-
+nomics (Becht et al., 2019; Kobak & Berens, 2019) and
+embeddings through natural language processing (Coenen
+et al., 2019). As they usually yield highly similar embed-
+dings when properly initialized (Kobak & Linderman, 2021),
+it is a matter of taste which one to use, especially after re-
+cent algorithmic improvements (Linderman et al., 2019)
+also resulted in similar runtimes. Recent theoretical works
+confirmed that the clustering revealed by TSNE is prov-
+ably correct under simple assumptions about the data (Arora
+et al., 2018; Linderman & Steinerberger, 2019) and unified
+the theory behind both TSNE and UMAP through the lens
+of contrastive learning (Damrich et al., 2023).
+
+Preserving local densities in low-dimensional embeddings
+Building on the successful application of low dimensional
+embeddings to real world problems, Kobak et al. (2019) ex-
+tended TSNE to reveal more pronounced and fine-grained
+cluster structures. To emphasize user-specified structures,
+several works proposed supervised and interactive ap-
+proaches (De Ridder et al., 2003; Alipanahi & Ghodsi, 2011;
+Barshan et al., 2011). Similarly, supervised approaches were
+designed to account for unwanted or known variations – re-
+vealing knowledge beyond what is already known – based
+on user interaction (Puolam¨aki et al., 2018) or by removing
+information given by a prior (Kang et al., 2016; 2021; Heiter
+et al., 2021). To extend low-dimensional embeddings to ex-
+tremely large-scale datasets in terms of samples, such as
+given by huge web-crawls of newspapers, recent advances
+focused on improving the runtime of different embedding
+techniques (Tang et al., 2016; Artemenkov & Panov, 2020).
+We are specifically interested in unsupervised low dimen-
+sional embeddings and hence compare to the state-of-the-art
+methods TSNE, UMAP, LLE, LARGEVIS, and NCVIS.
+3. Theory
+In this section, we first provide a description of the gen-
+eral problem statement for low dimensional embeddings.
+We then revisit the formulation of t-distributed stochastic
+neighbour embedding (TSNE) thereby analyzing its inher-
+ent limitations with regard to preserving (relative) local
+densities. Subsequently, we propose DTSNE, an adaptation
+which properly addresses modeling local densities.
+3.1. Low-dimensional embeddings
+Given data, X = (x1, x2, . . . , xn) of n samples, where
+xi ∈ Rm is usually of large dimension m, our aim is to
+find an embedding Y = (y1, y2, . . . , yn), yi ∈ Rm′ where
+m′ ∈ {2, 3}, such that the important structure in X is pre-
+served in Y . To model the structure in Y , first approaches
+suggested to preserve the relative pairwise distances, i.e.
+λ ∥yi − yj∥ ≈ ∥xi − xj∥, over a norm based on euclidean
+or geodesic distances for some algorithm dependent scal-
+ing factor λ, which could be e.g. based on normalizing X.
+Preserving all (relative) distances, however, is usually not
+possible and leads to poor results on complex data (van der
+Maaten & Hinton, 2008) as a lower dimensional space can
+encode less information. Consider the simple example of 4
+clusters living in some higher dimensional space, all equidis-
+tant to each other, then modeling all distances between clus-
+ters correctly becomes infeasible in 2 dimensions.1 With
+the typically used pairwise Euclidean distance, which em-
+phasize modeling large distances correctly, the clusters get
+distorted to maintain the inter-cluster distances.
+Preserving relative local distances and only crudely approx-
+1This can be immediately seen from Pythagoras’ theorem.
+imating global distances offers a remedy, as it shows to
+preserve the relevant structure of the data despite the loss
+of information (van der Maaten & Hinton, 2008; McInnes
+et al., 2018). In the example before, this would mean to
+only approximating the inter-cluster distances, but keeping
+the important local distances – the within-cluster distances –
+intact. Next, we revisit TSNE, which is considered state-of-
+the-art for low-dimensional embeddings.
+3.2. TSNE
+The t-distributed stochastic neighbour embedding models
+the relationship between points i and j in the high dimen-
+sional space X and embedding Y in terms of a similarity
+metric that emphasizes local structure. In particular, sim-
+ilarity of i, j in X is modeled by a normalized Gaussian
+centered at xi
+pj|i =
+exp(− ∥xi − xj∥2
+2 /(2σ2
+i ))
+�
+k̸=i exp(− ∥xi − xk∥2
+2 /(2σ2
+i ))
+.
+Through the normalization in the denominator it can be
+interpreted as the conditional probability that i would pick
+j as its neighbour, if neighbours were picked in proportion
+to their probability density under a Gaussian centered at xi.
+The conditional probabilites over all j given an i yield the
+probability distribution Pi.
+The deviation σi of sample i is fitted to account for the
+differences in local densities across the data, i.e., for dense
+regions smaller values of σi suffice to capture local struc-
+ture, whereas we need large σi for sparser regions to cap-
+ture enough of the local structure. In practice, TSNE em-
+ploys a binary search to find the σi that produces a Pi
+for fixed perplexity. The perplexity of a distribution Pi
+is defined as perplexity(Pi) = 2H(Pi), where H(Pi) =
+− �
+j pj|i log pj|i is the Shannon entropy. In practice, it
+is a user-set hyperparameter and can be seen as a smooth
+measure of effective number of neighbours, for which we
+can solve above equation for σi. For more information, we
+refer to van der Maaten & Hinton (2008). Plugging the σi
+into the definition of pj|i above, we obtain a probability
+distribution for each point Pi = �
+j̸=i pj|i .
+To ease computation, probabilities are symmetrized to ob-
+tain one joint probability P, where for n samples we get
+pij = pj|i + pi|j
+2n
+.
+The corresponding low dimensional probabilities are mod-
+eled by a t-distribution with one degree of freedom
+qij =
+(1 + ∥xi − xj∥2
+2)−1
+�
+k̸=l(1 + ∥xk − xl∥2
+2)−1 ,
+which – in contrast to the Gaussian distribution – allows to
+model large distances more flexible due to its heavy tails,
+
+Preserving local densities in low-dimensional embeddings
+thus avoiding the crowding problem2 in the embedding
+space (van der Maaten & Hinton, 2008).
+With representations of similarities for the given high dimen-
+sional data, and the (unknown) embedding, both in terms
+of probability distributions, we can now optimize for the
+probability distribution Q to model P. In TSNE, this is
+done by optimizing the Kullback-Leibler (KL) divergence
+KL(P || Q) =
+�
+i
+�
+j
+pij log
+�pij
+qij
+�
+.
+The KL divergence measures the number of additional bits
+needed to encode P using a code optimal for encoding Q
+and thus models how well Q approximates P. It is differ-
+entiable with respect to yi and thus allows for optimization
+via gradient descent approaches. A common problem of
+state-of-the-art embedding techniques, including TSNE, is,
+however, that relative densities in the data X, such as dif-
+ferently sized clusters or different point densities within
+clusters, are not captured in the embedding Y .
+3.3. One size does not fit all
+The state-of-the-art methods for low-dimensional embed-
+dings, such as TSNE, NCVIS, LARGEVIS, and UMAP,
+usually model low-dimensional distances locally as we have
+seen before, using the same representation of those dis-
+tances for different regions in the space, regardless of local
+densities. As an example, consider TSNE, which maps
+distances represented as pij, which reflects neighbourhood
+density through the learned σi, σj, to qij, which is scale-
+less. Hence, no matter how far stretched, or how compact a
+cluster is, it will be assigned the same amount of space in
+low dimensions. This is what we see happening in Fig. 1.
+Why, however, do we see differently sized clusters in em-
+beddings of TSNE and UMAP? For data of clusters with
+same density (or variance), but varying number of samples
+per cluster, we observe that TSNE and UMAP embed these
+clusters as vastly differently sized in the embedding space
+(see Fig. 2). What happens is that in high dimensions when
+the local variance σi is very small, the resulting Gaussian Pi
+is hence very narrow. The more points we have in a cluster,
+the more likely it is that we have kNNs that are very close
+to i and hence the neighbourhood distribution Pi becomes
+narrow. Points from the same cluster, but which are further
+away than the kNNs of i, hence fall into the tail of Pi and
+have to be matched with a similar probability mass in Q.
+This also means that they are modeled further away than
+their counterparts in clusters with fewer points, where the
+kNNs are further apart.
+2The crowding problem is the phenomenon of assembling all
+points in the center of the map, due to the accumulation of many
+small attractive forces as moderate distances are not accurately
+modelled.
+While in these arguments we discussed the formulation
+of TSNE, the same applies for NCVIS, LARGEVIS, and
+UMAP. NCVIS and LARGEVIS follow a analogous formu-
+lation of neighbourhood probabilities as TSNE. Although
+UMAP has solid theoretical foundations in Riemannian ge-
+ometry and fuzzy simplicial sets, its practical implementa-
+tion has a one-to-one correspondence to TSNE as discussed
+by the original authors (McInnes et al., 2018, Appendix
+C). In particular, the low dimensional distribution also has
+the same shape for each data point, which is why UMAP
+suffers from the same issues as TSNE.
+Next, we provide a theoretical argument that TSNE fails to
+capture variations of local densities.
+3.4. Reflecting local densities in embeddings
+Theoretical insights into TSNE are rare, as the method and
+the solutions to the related optimization problem do not need
+to be unique. Gradient descent, which is usually employed
+in this context, only seeks for a local minimum that has zero
+gradient. To still be able to reason about our method we
+instead argue about those solutions that best support the in-
+tuition behind the design of TSNE, which is to approximate
+local distances well, and that we would prefer to find with
+our optimization approach. Those solutions should fulfill
+the zero gradient condition by qin ≈ pin.
+Let us consider two sufficiently small distances ∥xi − xj∥
+and ∥xk − xl∥ so that ∥xi − xj∥2 < ϵ and ∥xk − xl∥2 < ϵ
+for a small ϵ > 0. All involved points xp for p ∈ {i, j, k, l}
+have lower dimensional representations yi,
+yj,
+yk,
+yl that are obtained from an embedding method.
+A
+good
+local
+distance
+preserving
+method
+would
+ful-
+fill
+∥xi − xj∥ / ∥xk − xl∥
+≈
+∥yi − yj∥ / ∥yk − yl∥
+or,
+equivalently,
+∥xi − xj∥2 / ∥xk − xl∥2
+≈
+∥yi − yj∥2 / ∥yk − yl∥2. How does this quantity look for
+TSNE? Let us assume that ϵ is small enough so that we can
+approximate exp(−x2) ≈ 1 − x2 + O(x4). We, thus, get
+pij = 1
+2n
+�
+1
+Zi
+exp
+�
+−∥xi − xj∥2
+2σ2
+i
+�
++ 1
+Zj
+exp
+�
+−∥xi − xj∥2
+2σ2
+j
+��
+≈ 1
+2n
+� 1
+Zi
++ 1
+Zj
+� �
+1 −
+�
+1
+2σ2
+i
++
+1
+2σ2
+j
+�
+∥xi − xj∥2
+�
+,
+where Zi := �
+k̸=i exp(− ∥xi − xk∥2
+2 /(2σ2
+i )) denotes the
+corresponding normalization constant. The same arguments
+also apply to the distance ∥xk − xl∥. Similarly, for q we
+
+Preserving local densities in low-dimensional embeddings
+can approximate
+qij = 1
+Zq
+�
+1 + ∥yi − yj∥2�−1
+≈ 1
+Zq
+�
+1 − ∥yi − yj∥2�
+,
+with Zq = �
+m̸=p(1 + ∥xm − xp∥2
+2)−1. Next, we will fur-
+ther employ the assumption that the TSNE optimization was
+successful so that qij ≈ pij and qkl ≈ pkl. In combination
+with our above approximations, this leads to the relation
+∥xi − xj∥2 ≈ 2�σ2
+ij
+�
+(1 − cij) + cij ∥yi − yj∥2�
+,
+with cij :=
+2nZiZj
+(Zi+Zj)Zq and �σ2
+ij :=
+σ2
+i σ2
+j
+σ2
+i +σ2
+j . This already
+highlights the general problem with TSNE: The constant
+and scaling factor of small distances depends on the neigh-
+bourhood of i and j. To make the problem more explicit let
+us study our quantity of interest, the preservation of relative
+distances:
+∥xi − xj∥2
+∥xk − xl∥2 = �σ2
+ijcij
+�σ2
+klckl
+1
+cij − 1 + ∥yi − yj∥2
+1
+ckl − 1 + ∥yk − yl∥2 .
+To simplify the expression note that since ∥xi − xj∥ is
+small, the local neighbourhood is similar, thus σi ≈ σj
+and therefore Zi ≈ Zj. We get
+∥xi − xj∥2
+∥xk − xl∥2 = σ2
+i Zi
+σ2
+kZk
+Zq
+nZi − 1 + ∥yi − yj∥2
+Zq
+nZk − 1 + ∥yk − yl∥2 .
+Intuitively, this means that unless the clusters are similar
+in density or size, i.e., σi ≈ σk and Zi ≈ Zk, we can not
+preserve relative distances. Distances are scaled by a quan-
+tity that is inversely proportional to the high-dimensional
+variances. A natural fix to these issues would therefore be
+to scale ∥yi − yj∥2 proportional to this inverse of �σ2
+ij (or
+any form of mean of σ2
+i and σ2
+j ) and to choose σ2
+i so that
+cij ≈ 1 or at least Zin ≈ Zq.
+3.5. Preserving densities with DTSNE
+As discussed above, to properly model relative densities, we
+need a distribution for our low-dimensional point pairs that
+properly reflect the density of their neighbourhood. Concep-
+tually, we want to map the distances of close neighbours of
+points in differently dense regions in X to regions in Y that
+show a similar relative difference in scale.
+Based on the above insights, for a pair of points i, j we
+define the scaling factor for low-dimensional distances as
+γij =
+�
+(σi + σj)2�−1
+maxk,l ((σk + σl)2)−1 ,
+which is a scaling factor that is inverse proportional to the
+squared average deviation of i, j, 1/(σi + σj)2, and normal-
+ized to have maximum value of 1.
+By incorporating the scaling into low-dimensional probabil-
+ities qij, we enable learning of relative densities as
+qij =
+(1 + γij ∥xi − xj∥2
+2)−1
+�
+k̸=l(1 + γkl ∥xk − xl∥2
+2)−1 .
+We further adapt the high-dimensional probabilities to be
+defined analogous to our low-dimensional probabilities
+in terms of the symmetry of the scaling factor.
+That
+is, we make the distribution pj|i and, hence, pij depen-
+dent on the neighbourhood of both i and j, by using
+σ2
+ij = (1/2(σi + σj))2. This not only makes the distri-
+butions more comparable, but also allows us to analyze the
+behaviour of this method theoretically. We thus get
+pj|i =
+exp(− ∥xi − xj∥2
+2 /(2σ2
+ij))
+�
+k̸=i exp(− ∥xi − xk∥2
+2 /(2σ2
+ik))
+,
+and symmetrize the distributions as in vanilla TSNE
+pij = pj|i + pi|j
+2n
+.
+Deriving the KL-divergence on this new probability distri-
+butions with respect to Y , we get
+∂KL(P || Q)
+∂yi
+=
+4 �
+j(pij − qij)(yi − yj)γij
+(1 + γij ∥yi − yj∥2
+2)
+.
+We give the derivation in App. A. Based on this gradient, we
+can optimize for an embedding Y by gradient descent. We
+call this method DTSNE for density preserving TSNE, and
+give pseudocode in Alg. 1. By design, it closely resembles
+TSNE and comes with the same computational costs of
+O(n2T) for data of n samples and descent for T iterations.
+In practice, we can make use of established ways to speed
+up and improve the optimization, such as early exaggeration
+and PCA initialization, both improving formation of natural
+clusters of the data in the embedding, and hence speeding
+up the overall computations. We refer to van der Maaten &
+Hinton (2008) and Kobak & Berens (2019) for details.
+THEORETICAL DENSITY PRESERVATION
+DTSNE is able to address the outlined issues of preserving
+relative densities approximately just by rescaling the dis-
+tances in q with a variance γij that is proportional to σ2
+ij.
+Recall that pij = wij exp
+�
+− ∥xi − xj∥2 /(2σ2
+ij)
+�
+, where
+wij =
+1
+Zp
+�
+1
+Zi +
+1
+Zj
+�
+with a modified definition of Zi :=
+�
+k̸=i exp(− ∥xi − xk∥2
+2 /(2σ2
+ik)) and a global normaliza-
+tion constant Zp. Furthermore, qij = (1+γij∥yi−yj∥2)
+−1
+Zq
+,
+with Zq = �
+k̸=l(1 + γkl ∥xk − xl∥2
+2)−1.
+
+Preserving local densities in low-dimensional embeddings
+Algorithm 1 DTSNE
+Input:
+Data X, perplexity k, iterations T, learning rate µ,
+momentum δ
+Output:
+Embedding Y
+1: compute P
+// Use symmetrized σij
+2: compute γij
+// Scaling factor γij
+3: Y (0) ← PCA(X, 2)
+// Initialization of embedding
+4: Y (0) ← .0001
+Y (0)
+std(Y (0)) // (Kobak & Linderman, 2021)
+5: for t = 1 . . . T do
+6:
+compute Q
+// Use scaling γij
+7:
+compute ∂KL(P || Q)
+∂Y
+8:
+Y (t) ← Y (t−1)+γ ∂KL(P || Q)
+∂Y
++δ(Y (t−1)−Y (t−2))
+9: end for
+10: return Y (T )
+Considering close points i, j and that pij ≈ qij, we can
+solve pij for the distance
+∥xi − xj∥2
+≈ 2σ2
+ij
+�
+log (wijZq) + log
+�
+1 + γij ∥yi − yj∥2��
+= 2σ2
+ij
+γ−1
+ij
+�
+log (wijZq) γ−1
+ij + γ−1
+ij log
+�
+1 + γij ∥yi − yj∥2��
+≈ 2σ2
+ij
+γ−1
+ij
+�
+log (wijZq) γ−1
+ij + ∥yi − yj∥2�
+,
+where the last approximation holds for sufficiently small
+γij ∥yi − yj∥2. DTSNE sets γij = λ(σ2
+ij)−1 for a λ > 0 so
+that we receive
+∥xi − xj∥2
+≈ 2σ2
+ij
+γ−1
+ij
+�
+log (wijZq) γ−1
+ij + γ−1
+ij log
+�
+1 + γij ∥yi − yj∥2��
+≈ 2λ
+�
+log (wijZq) λ−1σ2
+ij
++ λ−1σ2
+ij log
+�
+1 + λ(σ2
+ij)−1 ∥yi − yj∥2� �
+≈ 2λ
+�
+log (wijZq) λ−1σ2
+ij + ∥yi − yj∥2�
+,
+where the last approximation applies solely to small dis-
+tances. Note that the choice of λ does not affect the embed-
+ding yp or the normalization constant Zq, as the optimization
+could just return λyp instead of yp, thus yielding the same
+probability distribution q with the same Zq for any λ > 0.
+λ also does not influence the scaling factor of relative local
+distances, as it cancels out:
+∥xi − xj∥2
+∥xk − xl∥2 ≈ log (wijZq) λ−1σ2
+ij + ∥yi − yj∥2
+log (wklZq) λ−1σ2
+klλ + ∥yk − yl∥2 .
+We are thus free to choose λ such that the contribution of
+log (wijZq) λ−1σ2
+ij or log (wklZq) λ−1σ2
+kl becomes irrele-
+vant in comparison with ∥yi − yj∥2 or ∥yk − yl∥2. We con-
+clude that for small enough λ, DTSNE succeeds in preserv-
+ing relative local distances, as ∥xi−xj∥2
+∥xk−xl∥2 ≈ ∥yi−yj∥2
+∥yk−yl∥2 holds
+for any pair of small distances ∥xi − xj∥ and ∥xk − xl∥.
+Next, we show that DTSNE also empirically preserves rela-
+tive local distances.
+4. Experiments
+To evaluate DTSNE, we compare on both synthetic as well
+as real world data against the state-of-the-art in unsupervised
+low-dimensional embedding approaches UMAP (McInnes
+et al., 2018), TSNE (van der Maaten & Hinton, 2008),
+LLE (Roweis & Saul, 2000), LARGEVIS (Tang et al., 2016),
+and NCVIS (Artemenkov & Panov, 2020). We consider
+benchmarks of gaussian and uniform mixtures, the (vector-
+ized) MNIST dataset of handwritten digits (Lecun et al.,
+1998), two biological single-cell datasets (Wong et al., 2016;
+Samusik et al., 2016), and neural sentence embeddings of
+Amazon reviews (He & McAuley, 2016).
+For DTSNE and TSNE, we set the learning rate as µ =
+n/12 (Belkina et al., 2019), the momentum to δ = .5 in
+the first 20 iterations and to δ = .8 afterwards (van der
+Maaten & Hinton, 2008), and set the perplexity to k = 100
+in all experiments, which showed consistently good per-
+formance across all data. For all other methods, we use
+the recommended parameter settings from the respective
+original publications. Before embedding a given dataset,
+we project it to its first 50 principal components, a com-
+mon practice to improve low-dimensional embeddings. We
+use the OpenTSNE3 implementation for TSNE embeddings
+and use the original publicly available implementations for
+other methods. An implementation of DTSNE and bench-
+mark data generation is publicly available.4 On all datasets,
+all methods take less than an hour to finish, with UMAP,
+TSNE, LARGEVIS, and NCVIS taking seconds to a few
+minutes and DTSNE showing a slightly slower computation
+with 10-30 minutes depending on the data, which is due
+to a less-optimized code. In particular, we stick to stan-
+dard learning rates, use no fine-tuned learning rate schedule,
+or early stopping, leaving this in combination with other
+methods, such as FFT-based acceleration, for future work.
+We compare all methods based on Pearson correlation ρ
+between high- and low-dimensional distances, a common
+measure of embedding quality. Any correlation measures
+across all distances, however, places more importance on
+reconstruction of the global arrangement of data, and much
+3https://opentsne.readthedocs.io/en/
+latest/
+4http://eda.rg.cispa.io/dtsne/
+
+Preserving local densities in low-dimensional embeddings
+ρ
+ρknn
+ρr
+-.25
+0
+.25
+.5
+.75
+1
+Correlation
+(a) G3-s
+ρ
+ρknn
+ρr
+(b) G3-d
+ρ
+ρknn
+ρr
+(c) G10-d
+ρ
+ρknn
+ρr
+(d) U5-d
+ρ
+ρknn
+ρr
+-.25
+0
+.25
+.5
+.75
+1
+Correlation
+DTSNE
+LARGEVIS
+LLE
+NCVIS
+TSNE
+UMAP
+(e) Amazon reviews
+ρ
+ρknn
+ρr
+(f) MNIST
+ρ
+ρknn
+ρr
+(g) Samusik
+ρ
+ρknn
+ρr
+(h) Wong
+Figure 3. Experimental results. Comparison on 4 synthetic benchmark (top) and 4 real data sets (bottom). We report Pearson correlation
+between all high- and low-dimensional distances as ρ (global reconstruction), correlation between high- and low-dimensional distances of
+each point with its 100 closest neighbours as ρknn (local reconstruction), and correlation between radii of smallest balls enclosing the 100
+neighbours of each point in high- and low-dimensional space as ρr (relative density reconstruction). We provide all numerical results in
+App. Tab. 1.
+less on the reconstruction of local structures, that we are
+usually interested in. To evaluate how well such short-range
+(local) distances are preserved we compute the Pearson cor-
+relation ρknn of distances of each point to its k = 100 clos-
+est neighbours between high- and low-dimensional space.
+Not only short-range distances but also the relative sizes
+and densities between different structures capture crucial
+information. We, hence, also evaluate how good relative
+densities are reconstructed in the embedding. For that we
+take for each point i the radius ri of the (smallest) ball en-
+closing its 100 neighbours, i.e., the distance to its 100th
+neighbour. The ball serves as a proxy of how far neighbour-
+ing points are spread out in the space. As we are interested
+in reconstructing relative densities, we then take fractions of
+each pair of radii, ri
+rj , and measure the Pearson correlation
+ρr between them in high- and low-dimensional space.
+4.1. Embeddings on synthetic benchmark data
+We first benchmark all methods on synthetic data with
+known cluster structure, providing more details in the
+App. B. Overall, we generate 6 datasets varying different
+properties, such as number of samples per cluster, cluster
+variances, and generating distributions. We first generate
+two 2D datasets with 3 Gaussian clusters each, one where
+each Gaussian has a different variance but we keep the
+number of samples per cluster fixed, and one where each
+Gaussian has same variance but the number of samples per
+cluster is different. These two datasets serve as the basis
+for Fig 1 and Fig 2, as they visually show the underlying
+problem of current low-dimensional embedding algorithms.
+To evaluate all methods quantitatively, we generate more
+complex datasets in a 50 dimensional space. The first dataset
+is made of 3 Gaussian clusters with same scale but varying
+number of samples in each (G3-s). The second dataset has
+3 Gaussian clusters with differing scale but same number of
+samples per cluster (G3-d). The third dataset contains 10
+clusters with a different scale (G10-d) and the last dataset
+has 150 dimensions in which we place 5 clusters, each
+drawn from a Uniform distribution with a different scale
+(U5-d). The results are visualized in Fig. 3a-d.
+When it comes to global reconstruction, DTSNE performs
+on par with the best other methods. More interestingly, when
+looking at quality of local reconstruction ρknn, which tells
+how well the actual local structures that we are interested
+in are preserved, we get a different picture. LLE still per-
+forms worst, yet all other competitors also show comparably
+bad performance, for example achieving only single-figure
+correlations on G3-d. Only DTSNE achieves consistently
+high quality when it comes to local reconstruction. This
+trend is even more extreme when looking at preservation
+of relative densities ρr, showing that all except DTSNE fail
+to recover densities. While these datasets were challenging
+and also DTSNE does not achieve perfect reconstruction,
+for example for G3-s, the state-of-the-art does not maintain
+any difference in cluster size at all. This becomes also evi-
+dent when looking at the visualization of the embeddings,
+for example for G10-d given in Fig. 4.
+
+Preserving local densities in low-dimensional embeddings
+DTSNE1
+DTSNE2
+(a) DTSNE
+LARGEVIS1
+LARGEVIS2
+(b) LARGEVIS
+LLE1
+LLE2
+(c) LLE
+NCVIS1
+NCVIS2
+(d) NCVIS
+TSNE1
+TSNE2
+(e) TSNE
+UMAP1
+UMAP2
+(f) UMAP
+Figure 4. G10-d embeddings. For data of 10 Gaussian clusters with different scale in a 50 dimensional space, we provide the embeddings
+produced by all methods. DTSNE is the only method able to correctly reflect variation in cluster densities.
+4.2. Embeddings of real world data
+Among our real world datasets, Amazon reviews is the most
+challenging to embed, as the reviews contain colloquial
+language and abbreviations and have frequent grammatical
+or spelling mistakes. This challenging problem also re-
+flects in the performances, regardless of tool or metric (see
+Fig. 3e). Surprisingly, TSNE performs best. DTSNE shows
+almost similar performance when it comes to reconstructing
+neigbourhoods and is the only other tool with decent per-
+formance when it comes to reconstructing relative densities.
+Intriguingly, even though TSNE performs so well, it at the
+same time gives the least informative clusters – only Luxury
+and Beauty products are clearly separated from the rest –
+whereas other methods such as DTSNE provide slightly bet-
+ter separation of individual clusters (see App. Fig. 8). These
+clusters reveal informative sub-classes of products, such as
+knitting and crocheting, or shooting.
+For MNIST embeddings, DTSNE consistently performs
+best across all measures (see Fig. 3f). Except for LLE,
+which has overall bad performance, the other methods per-
+form decently in terms of reconstructing global distances
+and neighbourhoods, with TSNE being the best of the com-
+petitors. Yet, consistent with our findings on synthetic data,
+we see that the state-of-the-art is not able to reconstruct
+relative densities well. Out of those competitors TSNE per-
+forms decently with ρr = .38, yet has a wide gap to the .67
+achieved by DTSNE. For the interested reader, we provide
+visualizations of the embeddings in App. Fig. 6.
+On Samusik and Wong data, we see a similar trend for
+global and neighbourhood reconstruction, with DTSNE the
+best and competitors performing well, with a larger gap
+to DTSNE in terms of neighbourhood reconstruction (see
+Fig. 3g,h). Consistent with the literature (Kobak & Lin-
+derman, 2021), we see that neither UMAP nor TSNE is
+consistently better than the other. When it comes to the
+reconstruction of relative densities, all methods fare better
+than on the MNIST data, yet have a substantially worse den-
+sity reconstruction than DTSNE. We provide a visualization
+of Samusik embeddings in App. Fig. 7, where we observe
+that certain cell type clusters, such as pDCs and different
+T-cell types, are compacted in state-of-the-art embeddings,
+likely due to their small relative proportion in the overall
+data. In DTSNE we see that those clusters are not that small
+in comparison to others once corrected for density – these
+cell types likely have similar heterogeneity than others and
+are not as specialized as UMAP or TSNE suggest.
+5. Discussion & Conclusion
+We considered the problem of finding low-dimensional
+embeddings that capture the main regularities of high-
+dimensional data. On a simple benchmark, we showed
+that the state-of-the-art methods fail to capture local densi-
+ties at all and provided theoretical arguments on why this
+is the case. Based on our findings, we proposed DTSNE,
+a stochastic neighbourhood embedding approach that over-
+comes these issues by accounting for local variations in
+data.
+As opposed to the state-of-the-art, DTSNE not only theoreti-
+cally preserves relative density differences. In extensive em-
+pirical experiments including synthetic benchmark as well
+as real world data, we also showed that DTSNE faithfully
+reconstructs relative differences in local distributions, such
+as differently sized clusters. DTSNE also quantitatively pre-
+serves local distances better than the state-of-the-art while
+yielding similar overall reconstruction performance.
+Our approach easily scales to data of thousands of sam-
+ples and is, thus, ready to be used in the applications of
+standard genomics or natural language processing datasets.
+For exceptionally large datasets, it would be an interesting
+avenue for future research to explore how we can com-
+bine DTSNE with recent advances in improving runtime
+for low-dimensional embeddings, such as those based on
+FFTs (Linderman et al., 2019).
+DTSNE represents a first solution to low-dimensional em-
+beddings that preserves relative local densities. We, hence,
+open up the analysis of low-dimensional embeddings and
+their visualizations with respect to cluster differences and
+densities. This could, for example, be used by experts as
+an indicator of heterogeneity or specialization of cell types,
+which are evident as clusters in embeddings of single-cell
+transcriptomics data.
+
+Preserving local densities in low-dimensional embeddings
+Acknowledgements
+The authors thank Daniel Kindler for the insightful discus-
+sions and running preliminary experiments.
+References
+Alipanahi, B. and Ghodsi, A. Guided Locally Linear Em-
+bedding. Pattern recognition letters, 32(7):1029–1035,
+2011.
+Arora, S., Hu, W., and Kothari, P. K. An analysis of the
+t-sne algorithm for data visualization. In Conference On
+Learning Theory, pp. 1455–1462, 2018.
+Artemenkov, A. and Panov, M. Ncvis: Noise contrastive ap-
+proach for scalable visualization. In International World
+Wide Web Conference, pp. 2941–2947, 2020.
+Barshan, E., Ghodsi, A., Azimifar, Z., and Jahromi, M. Z.
+Supervised Principal Component Analysis: Visualization,
+Classification and Regression on Subspaces and Subman-
+ifolds. Pattern Recognition, 44(7):1357–1371, 2011.
+Becht, E., McInnes, L., Healy, J., Dutertre, C.-A., Kwok,
+I. W., Ng, L. G., Ginhoux, F., and Newell, E. W. Dimen-
+sionality reduction for visualizing single-cell data using
+umap. Nature biotechnology, 37(1):38–44, 2019.
+Belkin, M. and Niyogi, P. Laplacian eigenmaps and spectral
+techniques for embedding and clustering. In Advances in
+Neural Information Processing Systems, 2001.
+Belkina, A. C., Ciccolella, C. O., Anno, R., Halpert, R.,
+Spidlen, J., and Snyder-Cappione, J. E. Automated op-
+timized parameters for t-distributed stochastic neighbor
+embedding improve visualization and analysis of large
+datasets. Nature Communications, 10(1):5415, 2019.
+Coenen, A., Reif, E., Yuan, A., Kim, B., Pearce, A., Vi´egas,
+F., and Wattenberg, M. Visualizing and measuring the
+geometry of bert. arXiv preprint arXiv:1906.02715, 2019.
+Damrich, S., B¨ohm, J. N., Hamprecht, F. A., and Kobak,
+D. Contrastive learning unifies t-SNE and UMAP. In
+International Conference on Learning Representations,
+2023.
+De Ridder, D., Kouropteva, O., Okun, O., Pietik¨ainen, M.,
+and Duin, R. P. Supervised locally linear embedding.
+In Artificial Neural Networks and Neural Information
+Processing, pp. 333–341. Springer, 2003.
+He, R. and McAuley, J. Ups and downs: Modeling the visual
+evolution of fashion trends with one-class collaborative
+filtering. In International World Wide Web Conference,
+pp. 507––517, 2016.
+Heiter, E., Fischer, J., and Vreeken, J. Factoring out prior
+knowledge from low-dimensional embeddings. arXiv
+preprint arXiv:2103.01828, 2021.
+Hinton, G. E. and Roweis, S. T. Stochastic neighbor em-
+bedding. In Advances in neural information processing
+systems, pp. 857–864, 2003.
+Kang, B., Lijffijt, J., Santos-Rodr´ıguez, R., and De Bie,
+T. Subjectively Interesting Component Analysis: Data
+Projections that Contrast with Prior Expectations. In Pro-
+ceedings of the International Conference on Knowledge
+Discovery and Data Mining, pp. 1615–1624, 2016.
+Kang, B., a, D., Lijffijt, J., guez, R., and De Bie, T. Condi-
+tional t-SNE: more informative t-SNE embeddings. Ma-
+chine Learning, 110(10):2905–2940, 2021.
+Kobak, D. and Berens, P. The art of using t-sne for single-
+cell transcriptomics. Nature communications, 10(1):1–14,
+2019.
+Kobak, D. and Linderman, G. C. Initialization is critical
+for preserving global data structure in both t-SNE and
+UMAP. Nature Biotechnology, 39(2):156–157, 02 2021.
+Kobak, D., Linderman, G., Steinerberger, S., Kluger, Y.,
+and Berens, P. Heavy-tailed kernels reveal a finer cluster
+structure in t-sne visualisations. In Joint European Con-
+ference on Machine Learning and Knowledge Discovery
+in Databases, pp. 124–139. Springer, 2019.
+Kohonen, T. Self-organized formation of topologically cor-
+rect feature maps. Biological cybernetics, 43(1):59–69,
+1982.
+Lecun, Y., Bottou, L., Bengio, Y., and Haffner, P. Gradient-
+based learning applied to document recognition. Proceed-
+ings of the IEEE, 86(11):2278–2324, 1998.
+Linderman, G., Rachh, M., Hoskins, J., Steinerberger, S.,
+and Kluger, Y. Fast interpolation-based t-SNE for im-
+proved visualization of single-cell RNA-seq data. Nature
+Methods, 16:1, 03 2019.
+Linderman, G. C. and Steinerberger, S. Clustering with
+t-SNE, provably. SIAM J Math Data Sci, 1(2):313–332,
+2019.
+McInnes, L., Healy, J., and Melville, J. Umap: Uniform
+Manifold Approximation and Projection for Dimension
+Reduction. arXiv preprint arXiv:1802.03426, 2018.
+Pearson, K. On lines and planes of closest fit to systems
+of points in space. The London, Edinburgh, and Dublin
+Philosophical Magazine and Journal of Science, 2(11):
+559–572, 1901.
+
+Preserving local densities in low-dimensional embeddings
+Puolam¨aki, K., Oikarinen, E., Kang, B., Lijffijt, J., and
+De Bie, T. Interactive Visual Data Exploration with Sub-
+jective Feedback: An Information-Theoretic Approach.
+In International Conference on Data Engineering, pp.
+1208–1211. IEEE, 2018.
+Roweis, S. T. and Saul, L. K. Nonlinear dimensionality
+reduction by locally linear embedding.
+Science, 290
+(5500):2323–2326, 2000.
+Samusik, N., Good, Z., Spitzer, M. H., Davis, K. L., and
+Nolan, G. P. Automated mapping of phenotype space
+with single-cell data. Nature Methods, 13(6):493–496,
+2016.
+Silva, V. D. and Tenenbaum, J. B. Global Versus Local Meth-
+ods in Nonlinear Dimensionality Reduction. In Advances
+in neural information processing systems, pp. 721–728,
+2003.
+Tang, J., Liu, J., Zhang, M., and Mei, Q. Visualizing large-
+scale and high-dimensional data. In International World
+Wide Web Conference, pp. 287–297, 2016.
+Tenenbaum, J. B., De Silva, V., and Langford, J. C. A
+Global Geometric Framework for Nonlinear Dimension-
+ality Reduction. Science, 290(5500):2319–2323, 2000.
+Torgerson, W. S. Multidimensional scaling: I. Theory and
+method. Psychometrika, 17(4):401–419, 1952.
+van der Maaten, L. and Hinton, G. Viualizing data using
+t-SNE. Journal of Machine Learning Research, 9:2579–
+2605, 2008.
+Wong, M. T., Ong, D. E. H., Lim, F. S. H., Teng, K. W. W.,
+McGovern, N., Narayanan, S., Ho, W. Q., Cerny, D., Tan,
+H. K. K., Anicete, R., Tan, B. K., Lim, T. K. H., Chan,
+C. Y., Cheow, P. C., Lee, S. Y., Takano, A., Tan, E.-H.,
+Tam, J. K. C., Tan, E. Y., Chan, J. K. Y., Fink, K., Berto-
+letti, A., Ginhoux, F., Curotto de Lafaille, M. A., and
+Newell, E. W. A high-dimensional atlas of human t cell
+diversity reveals tissue-specific trafficking and cytokine
+signatures. Immunity, 45(2):442–456, 2016.
+
+Preserving local densities in low-dimensional embeddings
+A. DTSNE gradient
+In the following, we derive the gradient for DTSNE. In particular, we compute the derivative of the Kullback-Leibler (KL)
+divergence of the high and low dimensional probability distributions P, Q with respect to the embedding Y . For ease of
+notation, let
+T −1
+ij
+= (1 + γij ∥xi − xj∥2
+2)−1 and
+Zq =
+�
+k̸=l
+(1 + γkl ∥xk − xl∥2
+2)−1 , then
+qij =
+T −1
+ij
+Zq
+and note that T −1
+ij
+= T −1
+ji . Recall the loss function is given by the KL-divergence
+C = KL(P || Q) =
+�
+i
+�
+j
+pij log
+�pij
+qij
+�
+,
+where pij is only determined by the high-dimensional data X and thus fixed throughout optimization. Reorganizing the
+KL-divergence, we obtain
+C =
+�
+i
+�
+j
+pij log (pij) − pij log (qij) =
+�
+i
+�
+j
+pij log (pij) − pij log
+�
+T −1
+ij
+�
++ pij log (Zq) .
+Deriving with respect to one sample l, we get
+∂C
+∂yl
+=
+�
+i
+�
+j
+∂pij log (pij)
+∂yl
+−
+∂pij log
+�
+T −1
+ij
+�
+∂yl
++ ∂pij log (Zq)
+∂yl
+=
+�
+i
+�
+j
+−
+∂pij log
+�
+T −1
+ij
+�
+∂yl
++ ∂pij log (Zq)
+∂yl
+.
+In the following, we will analyze the left and right term separately. Starting with the left term, we can simplify by only
+looking at the terms of the sum dependent on l and use basic rules of derivation
+�
+i
+�
+j
+−
+∂pij log
+�
+T −1
+ij
+�
+∂yl
+=
+�
+k̸=l
+−2pkl
+∂ log
+�
+T −1
+kl
+�
+∂yl
+=
+�
+k̸=l
+−2pklTkl
+T −1
+kl
+∂yl
+=
+�
+k̸=l
+−2pklT −1
+kl (−2γkl(yk − yl))
+= 4
+�
+k̸=l
+pklT −1
+kl γkl(yk − yl) .
+For the right term, we get
+�
+i
+�
+j
+∂pij log (Zq)
+∂yl
+=
+�
+k̸=l
+Z−1
+q
+2T −1
+kl
+∂yl
+=
+�
+k̸=l
+2Z−1
+q T −2
+kl (−2γkl(yk − yl))
+= −4
+�
+k̸=l
+qklT −1
+kl γkl(yk − yl) ,
+
+Preserving local densities in low-dimensional embeddings
+DTSNE1
+DTSNE2
+(a) DTSNE
+LARGEVIS1
+LARGEVIS2
+(b) LARGEVIS
+LLE1
+LLE2
+(c) LLE
+NCVIS1
+NCVIS2
+(d) NCVIS
+TSNE1
+TSNE2
+(e) TSNE
+UMAP1
+UMAP2
+(f) UMAP
+Figure 5. U5-d embeddings. For data of 5 Uniform clusters with different scales in a 150 dimensional space, we provide the embeddings
+produced by all methods. DTSNE is the only method able to reflect variation in cluster densities.
+where we used that �
+k̸=l pkl = 1 the derivative of Zq can be split in the outer derivative Z−1
+q
+and the inner derivative, for
+which only the two index combinations kl and lk are non-zero.
+Combining the above, we arrive at
+∂C
+∂yl
+= −4
+�
+k̸=l
+(pkl − qkl)T −1
+kl γkl(yk − yl) .
+B. Experiments
+In this section we provide additional information on the data generation and resulting embeddings. Numerical results are
+reported in Tab. 1. Additional visualizations for U5-d, which is the other more challenging synthetic benchmark dataset (i.e.,
+where clusters can not be placed in a 2D plane) are given in Fig. 5. Visualizations of real world data are given further below.
+B.1. Synthetic data
+We produced two different types of data, one where of the clusters are each distributed uniformly, and one where each
+cluster follows a Gaussian distribution. We varied the number of clusters k the dimensionality of the data d, as well as the
+number of samples s in each cluster or the spread of each cluster d.
+2D DATA
+We generated two 2-dimensional dataset with 3 Gaussian clusters each. The Gaussian clusters had unit variance and were
+centered at (10, 0), (0, 15), and (−10, 0), respectively. For the first dataset, we drew 300 points from each Gaussian and
+scaled the spread of the clusters by 1, 2, 4 (i.e., multiply the centered data by this number), respectively. For the second
+dataset we drew 100, 200, 500, samples from the Gaussians, respectively, keeping the scale the same across clusters.
+G3-S
+For this dataset we generated 3 Gaussian clusters living in 50 dimensions, each cluster distribution ci with mean drawn
+from U(0, 50) (each dimension iid from this uniform) and unit variance. We then draw 200, 400, 600 points from c1, c2, c3,
+respectively, and scale the spread of the cluster by 2 (i.e., multiply the centered data by 2).
+G3-D
+For this dataset we generated 3 Gaussian clusters living in 50 dimensions, each cluster distribution ci with mean drawn
+from U(0, 50) and unit variance. We then draw 300 points from each of the cluster distributions and scale the spread of the
+c1, c2, c3 by 2, 4, 8, respectively.
+G10-D
+To look at data that is not easily projectable, i.e., the inter-cluster distances can be correctly modeled in 2D, for this dataset
+we generated 10 Gaussian clusters living in 50 dimensions, each cluster distribution ci again with mean drawn from U(0, 50)
+and unit variance. We then draw 200 points from each of the cluster distributions and scale the spread of the c1, . . . , c10 by
+1, . . . , 10, respectively.
+
+Preserving local densities in low-dimensional embeddings
+Synthetic benchmark data
+Real world data
+Metric
+Method
+G3-s
+G3-d
+G10-d
+U5-d
+Amazon
+MNIST
+Samusik
+Wong
+ρ
+DTSNE
+.99
+.95
+.62
+.79
+.27
+.49
+.80
+.60
+LARGEVIS
+.98
+.95
+.59
+.85
+.35
+.42
+.78
+.43
+LLE
+.92
+.93
+.16
+.56
+.0
+−.18
+.64
+.22
+NCVIS
+.95
+.92
+.45
+.80
+.35
+.36
+.63
+.45
+TSNE
+.100
+.95
+.65
+.86
+.38
+.48
+.77
+.60
+UMAP
+.98
+.95
+.57
+.85
+.33
+.44
+.79
+.46
+ρknn
+DTSNE
+.74
+.81
+.71
+.82
+.54
+.68
+.85
+.78
+LARGEVIS
+.56
+.08
+.39
+.13
+.52
+.47
+.67
+.68
+LLE
+.15
+−.08
+.21
+−.28
+−.28
+−.40
+.64
+.52
+NCVIS
+.59
+.09
+.40
+.10
+.44
+.49
+.74
+.64
+TSNE
+.70
+.12
+.40
+.12
+.62
+.61
+.76
+.69
+UMAP
+.56
+.06
+.39
+.11
+.45
+.44
+.65
+.66
+ρr
+DTSNE
+.31
+.88
+.91
+.89
+.22
+.67
+.66
+.70
+LARGEVIS
+.02
+−.01
+−.01
+−.01
+.15
+.08
+.31
+.42
+LLE
+−.06
+−.02
+.08
+−.11
+−.16
+−.24
+.34
+.22
+NCVIS
+.16
+−.07
+−.08
+−.08
+.01
+−.01
+.45
+.33
+TSNE
+.20
+−.11
+.01
+−.09
+.34
+.38
+.31
+.44
+UMAP
+−.02
+−.05
+−.02
+−.01
+.04
+.02
+.40
+.38
+Table 1. Results for synthetic and real-world data. Synthetic data are generated as k Gaussian or Uniform clusters and with varying
+sample-sizes or varying densities across clusters. We report Spearman rank correlation between all high- and low-dimensional distances ρ
+(global reconstruction), correlation between high- and low-dimensional distances of each point with its 100 closest neighbours (local
+reconstruction), and correlation between radii of balls enclosing the 100 neighbours of each point in high- and low-dimensional space
+(relative density reconstruction).
+U5-D
+To look at a different distribution and higher dimensional data, we generated 10 Uniform clusters living in 150 dimensions,
+each cluster distribution ci again with mean drawn from U(0, 50) and unit variance. We then draw 200 points from each of
+the cluster distributions and scale the spread of the c1, . . . , c10 by 1, . . . , 10, respectively.
+B.2. Real data
+For our comparison on real data, we considered 4 datasets, a simple image benchmark, two biological single-cell datasets,
+and a neural sentence embedding of Amazon reviews. For the image benchmark MNIST (Fig. 6) and both single-cell
+datasets we took a random subset of 5000 samples from the original publications as referenced in the main manuscript, for
+MNIST we additionally vectorized the images. We provide the visualizations of embeddings for the Samusik et al. data in
+Fig. 7, Wong et al. did not have informative labels available for these embeddings.
+For the Amazon Review dataset, we downloaded reviews for 8 categories from https://nijianmo.github.io/
+amazon/index.html that are closely related: ”Patio Lawn and Garden”, ”Tools and Home Improvement”, ”Industrial
+and Scientific”, ”Sports and Outdoors”,”Amazon fashion”, ”Arts and Crafts”,”Clothing, Shoes, Jewelry”, and ”Luxury
+Beauty”. We then sampled 5000 reviews that had at least 15 words in it, keeping original proportions of the categories intact.
+We set the threshold of 15 words to keep only reviews that are more likely to be informative about a product, as there are
+many reviews that just read ”Great product!!!” or ”Can highly recommend!”. We then use the Universal Sentence Encoder
+(https://tfhub.dev/google/universal-sentence-encoder/4) to obtain a 512-dimensional embedding
+of each review, resulting in the input data for our experiments. We give embeddings for the top 4 methods only, to be able to
+fit on one page, in Fig. 8.
+
+Preserving local densities in low-dimensional embeddings
+(a) DTSNE
+(b) LARGEVIS
+(c) LLE
+(d) NCVIS
+(e) TSNE
+(f) UMAP
+Figure 6. MNIST embeddings. Embedding of a random subset of 5000 samples from the MNIST dataset. Each sample is visualized as the
+original image stripped off its background, which allows to see inter-cluster dependencies such as curvatures and writing styles of digits.
+
+11
+11
+11
+..It
+119
++
+1
+t
+1,15
+1
+11
+1
+[1
+11Preserving local densities in low-dimensional embeddings
+(a) DTSNE
+(b) LARGEVIS
+(c) LLE
+(d) NCVIS
+(e) TSNE
+(f) UMAP
+Figure 7. Samusik et al. single-cell data embeddings. Embedding of a random subset of 5000 samples from the Samusik dataset. Samples
+are colored by cell type annotation from the original study. Cluster arrangement in all except LLE reflect hematopoiesis.
+
+B-cell Frac A-C (pro-B cells)
+GMP
+MPP
+Classical Monocytes
+Intermediate Monocytes
+pDCs
+Basophils
+IgD- IgMpos B cells
+NK cells
+CLP
+Macrophages
+Plasma Cells
+CD4 T cells
+IgDpos IgMpos B cells
+NKT cells
+CMP
+mDCs
+CD8 T cells
+IgM- IgD- B-cells
+Non-Classical Monocytes *
+Eosinophils
+MEPPreserving local densities in low-dimensional embeddings
+DTSNE1
+DTSNE2
+LARGEVIS1
+LARGEVIS2
+Amazon Fashion
+Arts & Crafts
+Clothing, Shoes, Jewelry
+Industrial & Scientific
+Luxury Beauty
+Patio, Lawn & Garden
+Sports & Outdoors
+Tools & Home Improv.
+TSNE1
+TSNE2
+UMAP1
+UMAP2
+Figure 8. Structure in amazon reviews. Embeddings of Universal Sentence Encoded Amazon reviews. Comparison of clusters retrieved by
+DTSNE and the best performing competitors LARGEVIS, TSNE, and UMAP. Clusters are annotated by examining the review texts.
+
diff --git a/ldFST4oBgHgl3EQfJTg8/content/tmp_files/load_file.txt b/ldFST4oBgHgl3EQfJTg8/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6c2313c6550776a4c81a83f9e4cd51466501e65c
--- /dev/null
+++ b/ldFST4oBgHgl3EQfJTg8/content/tmp_files/load_file.txt
@@ -0,0 +1,852 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf,len=851
+page_content='Preserving local densities in low-dimensional embeddings  Jonas Fischer 1 Rebekka Burkholz 2 Jilles Vreeken 2  Abstract  Low-dimensional embeddings and visualizations  are an indispensable tool for analysis of high-  dimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' State-of-the-art methods, such  as TSNE and UMAP, excel in unveiling local  structures hidden in high-dimensional data and  are therefore routinely applied in standard analy-  sis pipelines in biology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We show, however, that  these methods fail to reconstruct local properties,  such as relative differences in densities (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 1)  and that apparent differences in cluster size can  arise from computational artifact caused by differ-  ing sample sizes (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Providing a theoretical  analysis of this issue, we then suggest DTSNE,  which approximately conserves local densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In  an extensive study on synthetic benchmark and  real world data comparing against five state-of-  the-art methods, we empirically show that DT-  SNE provides similar global reconstruction, but  yields much more accurate depictions of local  distances and relative densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Introduction  Low-dimensional embeddings are an essential tool of data  analysis allowing exploration of the structure and relation-  ships encoded in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Given the high-dimensional  datasets that are gathered on a daily basis, such low-  dimensional embeddings have been shown to be especially  fruitful in aiding experts to identify general trends, clusters  and inter-cluster relationships, as well as extreme-valued  samples and outliers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In natural sciences, such as genomics,  they are routinely applied as a first step in data exploration,  in core machine learning they are frequently used as a tool  for understanding neural embeddings, such as given by  word or sentence encoders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The property of most high-  dimensional data that allows for such a reduction of dimen-  sions is that samples live in a lower dimensional subspace  1Department of Biostatistics, Harvard T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Chan School of  Public Health, Boston MA, USA 2CISPA Helmholtz Center for  Information Security, Saarbr¨ucken, Germany.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Correspondence to:  Jonas Fischer <jfischer@hsph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='harvard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='edu>.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  or manifold, which low-dimensional embeddings aim to  approximate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  While a classical projection onto the first two principal com-  ponents can be insightful and a valuable first step of anal-  ysis, the interesting regularities are often non-linear and  are, hence, not approximated well by principal components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Different solutions have been suggested for this problem,  with most successful advances using a similarity measure  for the high-dimensional data to be reconstructed in the  low-dimensional embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Moreover, it is inherently  hard to correctly reconstruct relationships at all distance  scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Instead, state-of-the-art methods focus on recon-  structing local structures correctly, in exchange allowing  to distort long-range distances, as this arguably preserves  the more interesting regularities in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The most  widely used are TSNE (van der Maaten & Hinton, 2008) and  UMAP (McInnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2018), as well as their recent adap-  atations LARGEVIS (Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2016) and NCVIS (Arte-  menkov & Panov, 2020), which are by now an indispensable  part in standard data analysis pipelines in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', biology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  While these methods yield arguably good overall recon-  structions and visualizations of the data, their embeddings  share an often neglected problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Most experts are well  aware that inter-cluster distances are distorted and argue  about those with care.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In contrast, individual clusters are (at  least relative to each other) often assumed to be faithfully  reconstructed locally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  This, however, turns out not to be true: Cluster sizes and den-  sities in the embedding do not model variances respectively  densities of the high-dimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Two clusters with  the same number of points, as diverse as one stretched over  vasts amount of space and the other one extremely compact,  both appear equally sized for current embedding techniques,  which we visualize in a simple example in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In ex-  periments on real world data, these methods often yield  embeddings with different cluster sizes, which, however,  turn out to be not due to differently sized clusters in high di-  mensions, but to be different numbers of samples per cluster  artificially bloating clusters in the embedding (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  These relative differences in local densities, which state-  of-the-art methods fail to model correctly, however, could  provide crucial information about the data at hand, such  as a cell types, which are evident as clusters, being more  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='13732v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='LG]  31 Jan 2023  Preserving local densities in low-dimensional embeddings  1  2  3  X1  X2  2  1  3  LARGEVIS1  LARGEVIS2  2  3  1  NCVIS1  NCVIS2  1  2  3  TSNE1  TSNE2  1  2  3  UMAP1  UMAP2  1  2  3  DTSNE1  DTSNE2  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Preservation of relative densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For data of 3 Gaussians with different densities in 2 dimensional space, we give the original  data, LARGEVIS, NCVIS, TSNE, UMAP, and DTSNE embeddings (from left to right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The state-of-the-art does not preserve the relative  densities nor the relative local distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Our method DTSNE reflects the relative densities and local distances across clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The results  are consistent for higher dimensional data and we provide more information on data generation in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  1  2  3  X1  X2  1  3  2  LARGEVIS1  LARGEVIS2  1  3  2  NCVIS1  NCVIS2  1  3  2  TSNE1  TSNE2  1  2  3  UMAP1  UMAP2  1  3  2  DTSNE1  DTSNE2  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Robustness to sample sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For data of 3 Gaussians in 2 dimensional space with different number of samples per cluster, we  give (from left to right) the original data, LARGEVIS, NCVIS, TSNE, UMAP, and DTSNE embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The state-of-the-art artificially  blows up, respectively shrinks clusters based on number of samples in a cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Our method reflects the differences in local densities per  clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The results are consistent for higher dimensional data and we provide more information on data generation in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  heterogeneous than others in a biological dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Here,  we provide a theoretical argument why current methods  fail to reconstruct relative densities and suggest a domain-  independent and entirely unsupervised approach to properly  account for relative local densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In extensive experiments  on synthetic and real world data, we show that our solution  better recovers the relative differences of cluster densities  hidden in the high dimensional data, while yielding overall  performance that is on par with state-of-the-art approaches  in terms of overall reconstruction quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  In summary, our main contributions are  a theoretical analysis of why current methods do not  reflect local densities correctly,  an unsupervised embedding approach preserving rela-  tive densities (DTSNE),  a theoretical analysis of DTSNE proving its ability to  preserve densities for local neighbourhoods, and  an extensive evaluation on synthetic and real-world  data against six state-of-the-art methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Related Work  Embeddings of high dimensional data into a low dimen-  sional space, in particular to 2 or 3 dimensions, have in  recent years become an essential tool of unsupervised anal-  ysis of high dimensional data in modern science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Clas-  sical methods of principal component analysis (Pearson,  1901), multidimensional scaling (Torgerson, 1952), lapla-  cian eigenmaps (Belkin & Niyogi, 2001), and self orga-  nizing maps (Kohonen, 1982) focus on keeping all, and in  particular the large distances intact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' As high dimensional  data typically lies on a manifold (Silva & Tenenbaum, 2003),  resembling euclidean space only locally, research attention  shifted on modeling geodesic distances (Tenenbaum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=',  2000), or focusing only on local distances trough locally lin-  ear embeddings (LLE) (Roweis & Saul, 2000) or stochastic  neighbour embeddings (SNE) (Hinton & Roweis, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  The current state-of-the-art in low-dimensional embeddings  for visualizations t-distributed SNE (TSNE) by van der  Maaten & Hinton (2008) and Uniform Manifold Approx-  imation (UMAP) by McInnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' (2018) also focus on  modeling local distances correctly, allowing to distort long-  range distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' They successfully reveal intrinsic structures  of high dimensional data and, hence, have been adapted as  standard exploration and pre-processing tools in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', ge-  nomics (Becht et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Kobak & Berens, 2019) and  embeddings through natural language processing (Coenen  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' As they usually yield highly similar embed-  dings when properly initialized (Kobak & Linderman, 2021),  it is a matter of taste which one to use, especially after re-  cent algorithmic improvements (Linderman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2019)  also resulted in similar runtimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Recent theoretical works  confirmed that the clustering revealed by TSNE is prov-  ably correct under simple assumptions about the data (Arora  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Linderman & Steinerberger, 2019) and unified  the theory behind both TSNE and UMAP through the lens  of contrastive learning (Damrich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving local densities in low-dimensional embeddings  Building on the successful application of low dimensional  embeddings to real world problems, Kobak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' (2019) ex-  tended TSNE to reveal more pronounced and fine-grained  cluster structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' To emphasize user-specified structures,  several works proposed supervised and interactive ap-  proaches (De Ridder et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Alipanahi & Ghodsi, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Barshan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Similarly, supervised approaches were  designed to account for unwanted or known variations – re-  vealing knowledge beyond what is already known – based  on user interaction (Puolam¨aki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2018) or by removing  information given by a prior (Kang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Heiter  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' To extend low-dimensional embeddings to ex-  tremely large-scale datasets in terms of samples, such as  given by huge web-crawls of newspapers, recent advances  focused on improving the runtime of different embedding  techniques (Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Artemenkov & Panov, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  We are specifically interested in unsupervised low dimen-  sional embeddings and hence compare to the state-of-the-art  methods TSNE, UMAP, LLE, LARGEVIS, and NCVIS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Theory  In this section, we first provide a description of the gen-  eral problem statement for low dimensional embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  We then revisit the formulation of t-distributed stochastic  neighbour embedding (TSNE) thereby analyzing its inher-  ent limitations with regard to preserving (relative) local  densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Subsequently, we propose DTSNE, an adaptation  which properly addresses modeling local densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Low-dimensional embeddings  Given data, X = (x1, x2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' , xn) of n samples, where  xi ∈ Rm is usually of large dimension m, our aim is to  find an embedding Y = (y1, y2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' , yn), yi ∈ Rm′ where  m′ ∈ {2, 3}, such that the important structure in X is pre-  served in Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' To model the structure in Y , first approaches  suggested to preserve the relative pairwise distances, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  λ ∥yi − yj∥ ≈ ∥xi − xj∥, over a norm based on euclidean  or geodesic distances for some algorithm dependent scal-  ing factor λ, which could be e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' based on normalizing X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving all (relative) distances, however, is usually not  possible and leads to poor results on complex data (van der  Maaten & Hinton, 2008) as a lower dimensional space can  encode less information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Consider the simple example of 4  clusters living in some higher dimensional space, all equidis-  tant to each other, then modeling all distances between clus-  ters correctly becomes infeasible in 2 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='1 With  the typically used pairwise Euclidean distance, which em-  phasize modeling large distances correctly, the clusters get  distorted to maintain the inter-cluster distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving relative local distances and only crudely approx-  1This can be immediately seen from Pythagoras’ theorem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  imating global distances offers a remedy, as it shows to  preserve the relevant structure of the data despite the loss  of information (van der Maaten & Hinton, 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' McInnes  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In the example before, this would mean to  only approximating the inter-cluster distances, but keeping  the important local distances – the within-cluster distances –  intact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Next, we revisit TSNE, which is considered state-of-  the-art for low-dimensional embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' TSNE  The t-distributed stochastic neighbour embedding models  the relationship between points i and j in the high dimen-  sional space X and embedding Y in terms of a similarity  metric that emphasizes local structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In particular, sim-  ilarity of i, j in X is modeled by a normalized Gaussian  centered at xi  pj|i =  exp(− ∥xi − xj∥2  2 /(2σ2  i ))  �  k̸=i exp(− ∥xi − xk∥2  2 /(2σ2  i ))  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Through the normalization in the denominator it can be  interpreted as the conditional probability that i would pick  j as its neighbour, if neighbours were picked in proportion  to their probability density under a Gaussian centered at xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  The conditional probabilites over all j given an i yield the  probability distribution Pi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  The deviation σi of sample i is fitted to account for the  differences in local densities across the data, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', for dense  regions smaller values of σi suffice to capture local struc-  ture, whereas we need large σi for sparser regions to cap-  ture enough of the local structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In practice, TSNE em-  ploys a binary search to find the σi that produces a Pi  for fixed perplexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The perplexity of a distribution Pi  is defined as perplexity(Pi) = 2H(Pi), where H(Pi) =  − �  j pj|i log pj|i is the Shannon entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In practice, it  is a user-set hyperparameter and can be seen as a smooth  measure of effective number of neighbours, for which we  can solve above equation for σi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For more information, we  refer to van der Maaten & Hinton (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Plugging the σi  into the definition of pj|i above, we obtain a probability  distribution for each point Pi = �  j̸=i pj|i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  To ease computation, probabilities are symmetrized to ob-  tain one joint probability P, where for n samples we get  pij = pj|i + pi|j  2n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  The corresponding low dimensional probabilities are mod-  eled by a t-distribution with one degree of freedom  qij =  (1 + ∥xi − xj∥2  2)−1  �  k̸=l(1 + ∥xk − xl∥2  2)−1 ,  which – in contrast to the Gaussian distribution – allows to  model large distances more flexible due to its heavy tails,  Preserving local densities in low-dimensional embeddings  thus avoiding the crowding problem2 in the embedding  space (van der Maaten & Hinton, 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  With representations of similarities for the given high dimen-  sional data, and the (unknown) embedding, both in terms  of probability distributions, we can now optimize for the  probability distribution Q to model P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In TSNE, this is  done by optimizing the Kullback-Leibler (KL) divergence  KL(P || Q) =  �  i  �  j  pij log  �pij  qij  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  The KL divergence measures the number of additional bits  needed to encode P using a code optimal for encoding Q  and thus models how well Q approximates P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' It is differ-  entiable with respect to yi and thus allows for optimization  via gradient descent approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' A common problem of  state-of-the-art embedding techniques, including TSNE, is,  however, that relative densities in the data X, such as dif-  ferently sized clusters or different point densities within  clusters, are not captured in the embedding Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' One size does not fit all  The state-of-the-art methods for low-dimensional embed-  dings, such as TSNE, NCVIS, LARGEVIS, and UMAP,  usually model low-dimensional distances locally as we have  seen before, using the same representation of those dis-  tances for different regions in the space, regardless of local  densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' As an example, consider TSNE, which maps  distances represented as pij, which reflects neighbourhood  density through the learned σi, σj, to qij, which is scale-  less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Hence, no matter how far stretched, or how compact a  cluster is, it will be assigned the same amount of space in  low dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' This is what we see happening in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Why, however, do we see differently sized clusters in em-  beddings of TSNE and UMAP?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For data of clusters with  same density (or variance), but varying number of samples  per cluster, we observe that TSNE and UMAP embed these  clusters as vastly differently sized in the embedding space  (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' What happens is that in high dimensions when  the local variance σi is very small, the resulting Gaussian Pi  is hence very narrow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The more points we have in a cluster,  the more likely it is that we have kNNs that are very close  to i and hence the neighbourhood distribution Pi becomes  narrow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Points from the same cluster, but which are further  away than the kNNs of i, hence fall into the tail of Pi and  have to be matched with a similar probability mass in Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  This also means that they are modeled further away than  their counterparts in clusters with fewer points, where the  kNNs are further apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  2The crowding problem is the phenomenon of assembling all  points in the center of the map, due to the accumulation of many  small attractive forces as moderate distances are not accurately  modelled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  While in these arguments we discussed the formulation  of TSNE, the same applies for NCVIS, LARGEVIS, and  UMAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' NCVIS and LARGEVIS follow a analogous formu-  lation of neighbourhood probabilities as TSNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Although  UMAP has solid theoretical foundations in Riemannian ge-  ometry and fuzzy simplicial sets, its practical implementa-  tion has a one-to-one correspondence to TSNE as discussed  by the original authors (McInnes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2018, Appendix  C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In particular, the low dimensional distribution also has  the same shape for each data point, which is why UMAP  suffers from the same issues as TSNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Next, we provide a theoretical argument that TSNE fails to  capture variations of local densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Reflecting local densities in embeddings  Theoretical insights into TSNE are rare, as the method and  the solutions to the related optimization problem do not need  to be unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Gradient descent, which is usually employed  in this context, only seeks for a local minimum that has zero  gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' To still be able to reason about our method we  instead argue about those solutions that best support the in-  tuition behind the design of TSNE, which is to approximate  local distances well, and that we would prefer to find with  our optimization approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Those solutions should fulfill  the zero gradient condition by qin ≈ pin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Let us consider two sufficiently small distances ∥xi − xj∥  and ∥xk − xl∥ so that ∥xi − xj∥2 < ϵ and ∥xk − xl∥2 < ϵ  for a small ϵ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' All involved points xp for p ∈ {i, j, k, l}  have lower dimensional representations yi,  yj,  yk,  yl that are obtained from an embedding method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  A  good  local  distance  preserving  method  would  ful-  fill  ∥xi − xj∥ / ∥xk − xl∥  ≈  ∥yi − yj∥ / ∥yk − yl∥  or,  equivalently,  ∥xi − xj∥2 / ∥xk − xl∥2  ≈  ∥yi − yj∥2 / ∥yk − yl∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' How does this quantity look for  TSNE?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Let us assume that ϵ is small enough so that we can  approximate exp(−x2) ≈ 1 − x2 + O(x4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We, thus, get  pij = 1  2n  �  1  Zi  exp  �  −∥xi − xj∥2  2σ2  i  �  + 1  Zj  exp  �  −∥xi − xj∥2  2σ2  j  ��  ≈ 1  2n  � 1  Zi  + 1  Zj  � �  1 −  �  1  2σ2  i  +  1  2σ2  j  �  ∥xi − xj∥2  �  ,  where Zi := �  k̸=i exp(− ∥xi − xk∥2  2 /(2σ2  i )) denotes the  corresponding normalization constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The same arguments  also apply to the distance ∥xk − xl∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Similarly, for q we  Preserving local densities in low-dimensional embeddings  can approximate  qij = 1  Zq  �  1 + ∥yi − yj∥2�−1  ≈ 1  Zq  �  1 − ∥yi − yj∥2�  ,  with Zq = �  m̸=p(1 + ∥xm − xp∥2  2)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Next, we will fur-  ther employ the assumption that the TSNE optimization was  successful so that qij ≈ pij and qkl ≈ pkl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In combination  with our above approximations, this leads to the relation  ∥xi − xj∥2 ≈ 2�σ2  ij  �  (1 − cij) + cij ∥yi − yj∥2�  ,  with cij :=  2nZiZj  (Zi+Zj)Zq and �σ2  ij :=  σ2  i σ2  j  σ2  i +σ2  j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' This already  highlights the general problem with TSNE: The constant  and scaling factor of small distances depends on the neigh-  bourhood of i and j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' To make the problem more explicit let  us study our quantity of interest, the preservation of relative  distances:  ∥xi − xj∥2  ∥xk − xl∥2 = �σ2  ijcij  �σ2  klckl  1  cij − 1 + ∥yi − yj∥2  1  ckl − 1 + ∥yk − yl∥2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  To simplify the expression note that since ∥xi − xj∥ is  small, the local neighbourhood is similar, thus σi ≈ σj  and therefore Zi ≈ Zj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We get  ∥xi − xj∥2  ∥xk − xl∥2 = σ2  i Zi  σ2  kZk  Zq  nZi − 1 + ∥yi − yj∥2  Zq  nZk − 1 + ∥yk − yl∥2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Intuitively, this means that unless the clusters are similar  in density or size, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', σi ≈ σk and Zi ≈ Zk, we can not  preserve relative distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Distances are scaled by a quan-  tity that is inversely proportional to the high-dimensional  variances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' A natural fix to these issues would therefore be  to scale ∥yi − yj∥2 proportional to this inverse of �σ2  ij (or  any form of mean of σ2  i and σ2  j ) and to choose σ2  i so that  cij ≈ 1 or at least Zin ≈ Zq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Preserving densities with DTSNE  As discussed above, to properly model relative densities, we  need a distribution for our low-dimensional point pairs that  properly reflect the density of their neighbourhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Concep-  tually, we want to map the distances of close neighbours of  points in differently dense regions in X to regions in Y that  show a similar relative difference in scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Based on the above insights, for a pair of points i, j we  define the scaling factor for low-dimensional distances as  γij =  �  (σi + σj)2�−1  maxk,l ((σk + σl)2)−1 ,  which is a scaling factor that is inverse proportional to the  squared average deviation of i, j, 1/(σi + σj)2, and normal-  ized to have maximum value of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  By incorporating the scaling into low-dimensional probabil-  ities qij, we enable learning of relative densities as  qij =  (1 + γij ∥xi − xj∥2  2)−1  �  k̸=l(1 + γkl ∥xk − xl∥2  2)−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  We further adapt the high-dimensional probabilities to be  defined analogous to our low-dimensional probabilities  in terms of the symmetry of the scaling factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  That  is, we make the distribution pj|i and, hence, pij depen-  dent on the neighbourhood of both i and j, by using  σ2  ij = (1/2(σi + σj))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' This not only makes the distri-  butions more comparable, but also allows us to analyze the  behaviour of this method theoretically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We thus get  pj|i =  exp(− ∥xi − xj∥2  2 /(2σ2  ij))  �  k̸=i exp(− ∥xi − xk∥2  2 /(2σ2  ik))  ,  and symmetrize the distributions as in vanilla TSNE  pij = pj|i + pi|j  2n  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Deriving the KL-divergence on this new probability distri-  butions with respect to Y , we get  ∂KL(P || Q)  ∂yi  =  4 �  j(pij − qij)(yi − yj)γij  (1 + γij ∥yi − yj∥2  2)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  We give the derivation in App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Based on this gradient, we  can optimize for an embedding Y by gradient descent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We  call this method DTSNE for density preserving TSNE, and  give pseudocode in Alg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' By design, it closely resembles  TSNE and comes with the same computational costs of  O(n2T) for data of n samples and descent for T iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  In practice, we can make use of established ways to speed  up and improve the optimization, such as early exaggeration  and PCA initialization, both improving formation of natural  clusters of the data in the embedding, and hence speeding  up the overall computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We refer to van der Maaten &  Hinton (2008) and Kobak & Berens (2019) for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  THEORETICAL DENSITY PRESERVATION  DTSNE is able to address the outlined issues of preserving  relative densities approximately just by rescaling the dis-  tances in q with a variance γij that is proportional to σ2  ij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Recall that pij = wij exp  �  − ∥xi − xj∥2 /(2σ2  ij)  �  , where  wij =  1  Zp  �  1  Zi +  1  Zj  �  with a modified definition of Zi :=  �  k̸=i exp(− ∥xi − xk∥2  2 /(2σ2  ik)) and a global normaliza-  tion constant Zp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Furthermore, qij = (1+γij∥yi−yj∥2)  −1  Zq  ,  with Zq = �  k̸=l(1 + γkl ∥xk − xl∥2  2)−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving local densities in low-dimensional embeddings  Algorithm 1 DTSNE  Input:  Data X, perplexity k, iterations T, learning rate µ,  momentum δ  Output:  Embedding Y  1: compute P  // Use symmetrized σij  2: compute γij  // Scaling factor γij  3: Y (0) ← PCA(X, 2)  // Initialization of embedding  4: Y (0) ← .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='0001  Y (0)  std(Y (0)) // (Kobak & Linderman, 2021)  5: for t = 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' T do  6:  compute Q  // Use scaling γij  7:  compute ∂KL(P || Q)  ∂Y  8:  Y (t) ← Y (t−1)+γ ∂KL(P || Q)  ∂Y  +δ(Y (t−1)−Y (t−2))  9: end for  10: return Y (T )  Considering close points i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' j and that pij ≈ qij,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' we can  solve pij for the distance  ∥xi − xj∥2  ≈ 2σ2  ij  �  log (wijZq) + log  �  1 + γij ∥yi − yj∥2��  = 2σ2  ij  γ−1  ij  �  log (wijZq) γ−1  ij + γ−1  ij log  �  1 + γij ∥yi − yj∥2��  ≈ 2σ2  ij  γ−1  ij  �  log (wijZq) γ−1  ij + ∥yi − yj∥2�  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  where the last approximation holds for sufficiently small  γij ∥yi − yj∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' DTSNE sets γij = λ(σ2  ij)−1 for a λ > 0 so  that we receive  ∥xi − xj∥2  ≈ 2σ2  ij  γ−1  ij  �  log (wijZq) γ−1  ij + γ−1  ij log  �  1 + γij ∥yi − yj∥2��  ≈ 2λ  �  log (wijZq) λ−1σ2  ij  + λ−1σ2  ij log  �  1 + λ(σ2  ij)−1 ∥yi − yj∥2� �  ≈ 2λ  �  log (wijZq) λ−1σ2  ij + ∥yi − yj∥2�  ,  where the last approximation applies solely to small dis-  tances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Note that the choice of λ does not affect the embed-  ding yp or the normalization constant Zq, as the optimization  could just return λyp instead of yp, thus yielding the same  probability distribution q with the same Zq for any λ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  λ also does not influence the scaling factor of relative local  distances, as it cancels out:  ∥xi − xj∥2  ∥xk − xl∥2 ≈ log (wijZq) λ−1σ2  ij + ∥yi − yj∥2  log (wklZq) λ−1σ2  klλ + ∥yk − yl∥2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  We are thus free to choose λ such that the contribution of  log (wijZq) λ−1σ2  ij or log (wklZq) λ−1σ2  kl becomes irrele-  vant in comparison with ∥yi − yj∥2 or ∥yk − yl∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We con-  clude that for small enough λ, DTSNE succeeds in preserv-  ing relative local distances, as ∥xi−xj∥2  ∥xk−xl∥2 ≈ ∥yi−yj∥2  ∥yk−yl∥2 holds  for any pair of small distances ∥xi − xj∥ and ∥xk − xl∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Next, we show that DTSNE also empirically preserves rela-  tive local distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Experiments  To evaluate DTSNE, we compare on both synthetic as well  as real world data against the state-of-the-art in unsupervised  low-dimensional embedding approaches UMAP (McInnes  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2018), TSNE (van der Maaten & Hinton, 2008),  LLE (Roweis & Saul, 2000), LARGEVIS (Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2016),  and NCVIS (Artemenkov & Panov, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We consider  benchmarks of gaussian and uniform mixtures, the (vector-  ized) MNIST dataset of handwritten digits (Lecun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=',  1998), two biological single-cell datasets (Wong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Samusik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2016), and neural sentence embeddings of  Amazon reviews (He & McAuley, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  For DTSNE and TSNE, we set the learning rate as µ =  n/12 (Belkina et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2019), the momentum to δ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='5 in  the first 20 iterations and to δ = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='8 afterwards (van der  Maaten & Hinton, 2008), and set the perplexity to k = 100  in all experiments, which showed consistently good per-  formance across all data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For all other methods, we use  the recommended parameter settings from the respective  original publications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Before embedding a given dataset,  we project it to its first 50 principal components, a com-  mon practice to improve low-dimensional embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We  use the OpenTSNE3 implementation for TSNE embeddings  and use the original publicly available implementations for  other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' An implementation of DTSNE and bench-  mark data generation is publicly available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='4 On all datasets,  all methods take less than an hour to finish, with UMAP,  TSNE, LARGEVIS, and NCVIS taking seconds to a few  minutes and DTSNE showing a slightly slower computation  with 10-30 minutes depending on the data, which is due  to a less-optimized code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In particular, we stick to stan-  dard learning rates, use no fine-tuned learning rate schedule,  or early stopping, leaving this in combination with other  methods, such as FFT-based acceleration, for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  We compare all methods based on Pearson correlation ρ  between high- and low-dimensional distances, a common  measure of embedding quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Any correlation measures  across all distances, however, places more importance on  reconstruction of the global arrangement of data, and much  3https://opentsne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='io/en/  latest/  4http://eda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='rg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='cispa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='io/dtsne/  Preserving local densities in low-dimensional embeddings  ρ  ρknn  ρr  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='25  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='25  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='75  1  Correlation  (a) G3-s  ρ  ρknn  ρr  (b) G3-d  ρ  ρknn  ρr  (c) G10-d  ρ  ρknn  ρr  (d) U5-d  ρ  ρknn  ρr  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='25  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='25  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='5  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='75  1  Correlation  DTSNE  LARGEVIS  LLE  NCVIS  TSNE  UMAP  (e) Amazon reviews  ρ  ρknn  ρr  (f) MNIST  ρ  ρknn  ρr  (g) Samusik  ρ  ρknn  ρr  (h) Wong  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Comparison on 4 synthetic benchmark (top) and 4 real data sets (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We report Pearson correlation  between all high- and low-dimensional distances as ρ (global reconstruction), correlation between high- and low-dimensional distances of  each point with its 100 closest neighbours as ρknn (local reconstruction), and correlation between radii of smallest balls enclosing the 100  neighbours of each point in high- and low-dimensional space as ρr (relative density reconstruction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We provide all numerical results in  App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  less on the reconstruction of local structures, that we are  usually interested in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' To evaluate how well such short-range  (local) distances are preserved we compute the Pearson cor-  relation ρknn of distances of each point to its k = 100 clos-  est neighbours between high- and low-dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Not only short-range distances but also the relative sizes  and densities between different structures capture crucial  information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We, hence, also evaluate how good relative  densities are reconstructed in the embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For that we  take for each point i the radius ri of the (smallest) ball en-  closing its 100 neighbours, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', the distance to its 100th  neighbour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The ball serves as a proxy of how far neighbour-  ing points are spread out in the space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' As we are interested  in reconstructing relative densities, we then take fractions of  each pair of radii, ri  rj , and measure the Pearson correlation  ρr between them in high- and low-dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Embeddings on synthetic benchmark data  We first benchmark all methods on synthetic data with  known cluster structure, providing more details in the  App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Overall, we generate 6 datasets varying different  properties, such as number of samples per cluster, cluster  variances, and generating distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We first generate  two 2D datasets with 3 Gaussian clusters each, one where  each Gaussian has a different variance but we keep the  number of samples per cluster fixed, and one where each  Gaussian has same variance but the number of samples per  cluster is different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' These two datasets serve as the basis  for Fig 1 and Fig 2, as they visually show the underlying  problem of current low-dimensional embedding algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  To evaluate all methods quantitatively, we generate more  complex datasets in a 50 dimensional space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The first dataset  is made of 3 Gaussian clusters with same scale but varying  number of samples in each (G3-s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The second dataset has  3 Gaussian clusters with differing scale but same number of  samples per cluster (G3-d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The third dataset contains 10  clusters with a different scale (G10-d) and the last dataset  has 150 dimensions in which we place 5 clusters, each  drawn from a Uniform distribution with a different scale  (U5-d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The results are visualized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 3a-d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  When it comes to global reconstruction, DTSNE performs  on par with the best other methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' More interestingly, when  looking at quality of local reconstruction ρknn, which tells  how well the actual local structures that we are interested  in are preserved, we get a different picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' LLE still per-  forms worst, yet all other competitors also show comparably  bad performance, for example achieving only single-figure  correlations on G3-d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Only DTSNE achieves consistently  high quality when it comes to local reconstruction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' This  trend is even more extreme when looking at preservation  of relative densities ρr, showing that all except DTSNE fail  to recover densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' While these datasets were challenging  and also DTSNE does not achieve perfect reconstruction,  for example for G3-s, the state-of-the-art does not maintain  any difference in cluster size at all.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' This becomes also evi-  dent when looking at the visualization of the embeddings,  for example for G10-d given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving local densities in low-dimensional embeddings  DTSNE1  DTSNE2  (a) DTSNE  LARGEVIS1  LARGEVIS2  (b) LARGEVIS  LLE1  LLE2  (c) LLE  NCVIS1  NCVIS2  (d) NCVIS  TSNE1  TSNE2  (e) TSNE  UMAP1  UMAP2  (f) UMAP  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' G10-d embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For data of 10 Gaussian clusters with different scale in a 50 dimensional space, we provide the embeddings  produced by all methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' DTSNE is the only method able to correctly reflect variation in cluster densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Embeddings of real world data  Among our real world datasets, Amazon reviews is the most  challenging to embed, as the reviews contain colloquial  language and abbreviations and have frequent grammatical  or spelling mistakes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' This challenging problem also re-  flects in the performances, regardless of tool or metric (see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 3e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Surprisingly, TSNE performs best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' DTSNE shows  almost similar performance when it comes to reconstructing  neigbourhoods and is the only other tool with decent per-  formance when it comes to reconstructing relative densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Intriguingly, even though TSNE performs so well, it at the  same time gives the least informative clusters – only Luxury  and Beauty products are clearly separated from the rest –  whereas other methods such as DTSNE provide slightly bet-  ter separation of individual clusters (see App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' These  clusters reveal informative sub-classes of products, such as  knitting and crocheting, or shooting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  For MNIST embeddings, DTSNE consistently performs  best across all measures (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 3f).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Except for LLE,  which has overall bad performance, the other methods per-  form decently in terms of reconstructing global distances  and neighbourhoods, with TSNE being the best of the com-  petitors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Yet, consistent with our findings on synthetic data,  we see that the state-of-the-art is not able to reconstruct  relative densities well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Out of those competitors TSNE per-  forms decently with ρr = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='38, yet has a wide gap to the .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='67  achieved by DTSNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For the interested reader, we provide  visualizations of the embeddings in App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  On Samusik and Wong data, we see a similar trend for  global and neighbourhood reconstruction, with DTSNE the  best and competitors performing well, with a larger gap  to DTSNE in terms of neighbourhood reconstruction (see  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 3g,h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Consistent with the literature (Kobak & Lin-  derman, 2021), we see that neither UMAP nor TSNE is  consistently better than the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' When it comes to the  reconstruction of relative densities, all methods fare better  than on the MNIST data, yet have a substantially worse den-  sity reconstruction than DTSNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We provide a visualization  of Samusik embeddings in App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 7, where we observe  that certain cell type clusters, such as pDCs and different  T-cell types, are compacted in state-of-the-art embeddings,  likely due to their small relative proportion in the overall  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In DTSNE we see that those clusters are not that small  in comparison to others once corrected for density – these  cell types likely have similar heterogeneity than others and  are not as specialized as UMAP or TSNE suggest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Discussion & Conclusion  We considered the problem of finding low-dimensional  embeddings that capture the main regularities of high-  dimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' On a simple benchmark, we showed  that the state-of-the-art methods fail to capture local densi-  ties at all and provided theoretical arguments on why this  is the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Based on our findings, we proposed DTSNE,  a stochastic neighbourhood embedding approach that over-  comes these issues by accounting for local variations in  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  As opposed to the state-of-the-art, DTSNE not only theoreti-  cally preserves relative density differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In extensive em-  pirical experiments including synthetic benchmark as well  as real world data, we also showed that DTSNE faithfully  reconstructs relative differences in local distributions, such  as differently sized clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' DTSNE also quantitatively pre-  serves local distances better than the state-of-the-art while  yielding similar overall reconstruction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Our approach easily scales to data of thousands of sam-  ples and is, thus, ready to be used in the applications of  standard genomics or natural language processing datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  For exceptionally large datasets, it would be an interesting  avenue for future research to explore how we can com-  bine DTSNE with recent advances in improving runtime  for low-dimensional embeddings, such as those based on  FFTs (Linderman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  DTSNE represents a first solution to low-dimensional em-  beddings that preserves relative local densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We, hence,  open up the analysis of low-dimensional embeddings and  their visualizations with respect to cluster differences and  densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' This could, for example, be used by experts as  an indicator of heterogeneity or specialization of cell types,  which are evident as clusters in embeddings of single-cell  transcriptomics data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving local densities in low-dimensional embeddings  Acknowledgements  The authors thank Daniel Kindler for the insightful discus-  sions and running preliminary experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  References  Alipanahi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Ghodsi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Guided Locally Linear Em-  bedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Pattern recognition letters, 32(7):1029–1035,  2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Arora, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Hu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Kothari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' An analysis of the  t-sne algorithm for data visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In Conference On  Learning Theory, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 1455–1462, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Artemenkov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Panov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Ncvis: Noise contrastive ap-  proach for scalable visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In International World  Wide Web Conference, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 2941–2947, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Barshan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Ghodsi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Azimifar, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Jahromi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Supervised Principal Component Analysis: Visualization,  Classification and Regression on Subspaces and Subman-  ifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Pattern Recognition, 44(7):1357–1371, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Becht, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', McInnes, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Healy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Dutertre, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Kwok,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Ng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Ginhoux, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Newell, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Dimen-  sionality reduction for visualizing single-cell data using  umap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Nature biotechnology, 37(1):38–44, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Belkin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Niyogi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Laplacian eigenmaps and spectral  techniques for embedding and clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In Advances in  Neural Information Processing Systems, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Belkina, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Ciccolella, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Anno, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Halpert, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=',  Spidlen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Snyder-Cappione, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Automated op-  timized parameters for t-distributed stochastic neighbor  embedding improve visualization and analysis of large  datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Nature Communications, 10(1):5415, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Coenen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Reif, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Yuan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Kim, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Pearce, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Vi´egas,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Wattenberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Visualizing and measuring the  geometry of bert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' arXiv preprint arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='02715, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Damrich, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', B¨ohm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Hamprecht, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Kobak,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Contrastive learning unifies t-SNE and UMAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In  International Conference on Learning Representations,  2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  De Ridder, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Kouropteva, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Okun, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Pietik¨ainen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=',  and Duin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Supervised locally linear embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  In Artificial Neural Networks and Neural Information  Processing, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 333–341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Springer, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  He, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and McAuley, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Ups and downs: Modeling the visual  evolution of fashion trends with one-class collaborative  filtering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In International World Wide Web Conference,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 507––517, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Heiter, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Fischer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Vreeken, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Factoring out prior  knowledge from low-dimensional embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' arXiv  preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='01828, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Hinton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Roweis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Stochastic neighbor em-  bedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In Advances in neural information processing  systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 857–864, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Kang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Lijffijt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Santos-Rodr´ıguez, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and De Bie,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Subjectively Interesting Component Analysis: Data  Projections that Contrast with Prior Expectations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In Pro-  ceedings of the International Conference on Knowledge  Discovery and Data Mining, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 1615–1624, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Kang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', a, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Lijffijt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', guez, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and De Bie, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Condi-  tional t-SNE: more informative t-SNE embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Ma-  chine Learning, 110(10):2905–2940, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Kobak, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Berens, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The art of using t-sne for single-  cell transcriptomics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Nature communications, 10(1):1–14,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Kobak, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Linderman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Initialization is critical  for preserving global data structure in both t-SNE and  UMAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Nature Biotechnology, 39(2):156–157, 02 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Kobak, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Linderman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Steinerberger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Kluger, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=',  and Berens, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Heavy-tailed kernels reveal a finer cluster  structure in t-sne visualisations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In Joint European Con-  ference on Machine Learning and Knowledge Discovery  in Databases, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 124–139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Springer, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Kohonen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Self-organized formation of topologically cor-  rect feature maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Biological cybernetics, 43(1):59–69,  1982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Lecun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Bottou, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Bengio, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Haffner, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Gradient-  based learning applied to document recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Proceed-  ings of the IEEE, 86(11):2278–2324, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Linderman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Rachh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Hoskins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Steinerberger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=',  and Kluger, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Fast interpolation-based t-SNE for im-  proved visualization of single-cell RNA-seq data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Nature  Methods, 16:1, 03 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Linderman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Steinerberger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Clustering with  t-SNE, provably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' SIAM J Math Data Sci, 1(2):313–332,  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  McInnes, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Healy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Melville, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Umap: Uniform  Manifold Approximation and Projection for Dimension  Reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' arXiv preprint arXiv:1802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='03426, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Pearson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' On lines and planes of closest fit to systems  of points in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The London, Edinburgh, and Dublin  Philosophical Magazine and Journal of Science, 2(11):  559–572, 1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving local densities in low-dimensional embeddings  Puolam¨aki, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Oikarinen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Kang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Lijffijt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and  De Bie, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Interactive Visual Data Exploration with Sub-  jective Feedback: An Information-Theoretic Approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  In International Conference on Data Engineering, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  1208–1211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' IEEE, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Roweis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Saul, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Nonlinear dimensionality  reduction by locally linear embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Science, 290  (5500):2323–2326, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Samusik, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Good, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Spitzer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Davis, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and  Nolan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Automated mapping of phenotype space  with single-cell data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Nature Methods, 13(6):493–496,  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Silva, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Tenenbaum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Global Versus Local Meth-  ods in Nonlinear Dimensionality Reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In Advances  in neural information processing systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 721–728,  2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Tang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Mei, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Visualizing large-  scale and high-dimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In International World  Wide Web Conference, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 287–297, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Tenenbaum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', De Silva, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and Langford, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' A  Global Geometric Framework for Nonlinear Dimension-  ality Reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Science, 290(5500):2319–2323, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Torgerson, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Multidimensional scaling: I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Theory and  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Psychometrika, 17(4):401–419, 1952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  van der Maaten, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' and Hinton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Viualizing data using  t-SNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Journal of Machine Learning Research, 9:2579–  2605, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Wong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Ong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Lim, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Teng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=',  McGovern, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Narayanan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Ho, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Cerny, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Tan,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Anicete, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Tan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Lim, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Chan,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Cheow, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Takano, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Tan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=',  Tam, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Tan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Chan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Fink, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Berto-  letti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Ginhoux, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', Curotto de Lafaille, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', and  Newell, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' A high-dimensional atlas of human t cell  diversity reveals tissue-specific trafficking and cytokine  signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Immunity, 45(2):442–456, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving local densities in low-dimensional embeddings  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' DTSNE gradient  In the following, we derive the gradient for DTSNE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' In particular, we compute the derivative of the Kullback-Leibler (KL)  divergence of the high and low dimensional probability distributions P, Q with respect to the embedding Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For ease of  notation, let  T −1  ij  = (1 + γij ∥xi − xj∥2  2)−1 and  Zq =  �  k̸=l  (1 + γkl ∥xk − xl∥2  2)−1 , then  qij =  T −1  ij  Zq  and note that T −1  ij  = T −1  ji .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Recall the loss function is given by the KL-divergence  C = KL(P || Q) =  �  i  �  j  pij log  �pij  qij  �  ,  where pij is only determined by the high-dimensional data X and thus fixed throughout optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Reorganizing the  KL-divergence, we obtain  C =  �  i  �  j  pij log (pij) − pij log (qij) =  �  i  �  j  pij log (pij) − pij log  �  T −1  ij  �  + pij log (Zq) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Deriving with respect to one sample l, we get  ∂C  ∂yl  =  �  i  �  j  ∂pij log (pij)  ∂yl  −  ∂pij log  �  T −1  ij  �  ∂yl  + ∂pij log (Zq)  ∂yl  =  �  i  �  j  −  ∂pij log  �  T −1  ij  �  ∂yl  + ∂pij log (Zq)  ∂yl  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  In the following, we will analyze the left and right term separately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Starting with the left term, we can simplify by only  looking at the terms of the sum dependent on l and use basic rules of derivation  �  i  �  j  −  ∂pij log  �  T −1  ij  �  ∂yl  =  �  k̸=l  −2pkl  ∂ log  �  T −1  kl  �  ∂yl  =  �  k̸=l  −2pklTkl  T −1  kl  ∂yl  =  �  k̸=l  −2pklT −1  kl (−2γkl(yk − yl))  = 4  �  k̸=l  pklT −1  kl γkl(yk − yl) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  For the right term, we get  �  i  �  j  ∂pij log (Zq)  ∂yl  =  �  k̸=l  Z−1  q  2T −1  kl  ∂yl  =  �  k̸=l  2Z−1  q T −2  kl (−2γkl(yk − yl))  = −4  �  k̸=l  qklT −1  kl γkl(yk − yl) ,  Preserving local densities in low-dimensional embeddings  DTSNE1  DTSNE2  (a) DTSNE  LARGEVIS1  LARGEVIS2  (b) LARGEVIS  LLE1  LLE2  (c) LLE  NCVIS1  NCVIS2  (d) NCVIS  TSNE1  TSNE2  (e) TSNE  UMAP1  UMAP2  (f) UMAP  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' U5-d embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For data of 5 Uniform clusters with different scales in a 150 dimensional space, we provide the embeddings  produced by all methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' DTSNE is the only method able to reflect variation in cluster densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  where we used that �  k̸=l pkl = 1 the derivative of Zq can be split in the outer derivative Z−1  q  and the inner derivative, for  which only the two index combinations kl and lk are non-zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Combining the above, we arrive at  ∂C  ∂yl  = −4  �  k̸=l  (pkl − qkl)T −1  kl γkl(yk − yl) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Experiments  In this section we provide additional information on the data generation and resulting embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Numerical results are  reported in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Additional visualizations for U5-d, which is the other more challenging synthetic benchmark dataset (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=',  where clusters can not be placed in a 2D plane) are given in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Visualizations of real world data are given further below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Synthetic data  We produced two different types of data, one where of the clusters are each distributed uniformly, and one where each  cluster follows a Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We varied the number of clusters k the dimensionality of the data d, as well as the  number of samples s in each cluster or the spread of each cluster d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  2D DATA  We generated two 2-dimensional dataset with 3 Gaussian clusters each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' The Gaussian clusters had unit variance and were  centered at (10, 0), (0, 15), and (−10, 0), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For the first dataset, we drew 300 points from each Gaussian and  scaled the spread of the clusters by 1, 2, 4 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', multiply the centered data by this number), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For the second  dataset we drew 100, 200, 500, samples from the Gaussians, respectively, keeping the scale the same across clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  G3-S  For this dataset we generated 3 Gaussian clusters living in 50 dimensions, each cluster distribution ci with mean drawn  from U(0, 50) (each dimension iid from this uniform) and unit variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We then draw 200, 400, 600 points from c1, c2, c3,  respectively, and scale the spread of the cluster by 2 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', multiply the centered data by 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  G3-D  For this dataset we generated 3 Gaussian clusters living in 50 dimensions, each cluster distribution ci with mean drawn  from U(0, 50) and unit variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We then draw 300 points from each of the cluster distributions and scale the spread of the  c1, c2, c3 by 2, 4, 8, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  G10-D  To look at data that is not easily projectable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=', the inter-cluster distances can be correctly modeled in 2D, for this dataset  we generated 10 Gaussian clusters living in 50 dimensions, each cluster distribution ci again with mean drawn from U(0, 50)  and unit variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We then draw 200 points from each of the cluster distributions and scale the spread of the c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' , c10 by  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' , 10, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving local densities in low-dimensional embeddings  Synthetic benchmark data  Real world data  Metric  Method  G3-s  G3-d  G10-d  U5-d  Amazon  MNIST  Samusik  Wong  ρ  DTSNE  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='99  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='95  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='62  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='79  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='27  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='49  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='80  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='60  LARGEVIS  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='98  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='95  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='59  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='85  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='35  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='42  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='78  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='43  LLE  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='92  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='93  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='16  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='56  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='0  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='18  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='64  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='22  NCVIS  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='95  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='92  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='45  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='80  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='35  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='36  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='63  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='45  TSNE  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='100  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='95  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='65  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='86  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='38  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='48  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='77  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='60  UMAP  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='98  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='95  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='57  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='85  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='33  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='44  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='79  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='46  ρknn  DTSNE  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='74  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='81  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='71  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='82  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='54  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='68  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='85  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='78  LARGEVIS  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='56  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='08  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='39  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='13  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='52  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='47  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='67  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='68  LLE  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='15  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='08  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='21  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='28  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='28  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='40  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='64  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='52  NCVIS  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='59  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='09  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='40  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='10  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='44  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='49  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='74  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='64  TSNE  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='70  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='12  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='40  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='12  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='62  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='61  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='76  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='69  UMAP  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='56  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='06  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='39  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='11  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='45  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='44  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='65  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='66  ρr  DTSNE  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='31  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='88  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='91  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='89  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='22  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='67  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='66  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='70  LARGEVIS  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='02  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='01  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='01  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='01  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='15  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='08  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='31  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='42  LLE  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='06  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='02  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='08  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='11  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='16  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='24  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='34  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='22  NCVIS  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='16  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='07  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='08  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='08  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='01  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='01  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='45  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='33  TSNE  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='20  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='11  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='01  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='09  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='34  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='38  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='31  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='44  UMAP  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='02  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='05  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='02  −.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='01  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='04  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='02  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='40  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='38  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Results for synthetic and real-world data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Synthetic data are generated as k Gaussian or Uniform clusters and with varying  sample-sizes or varying densities across clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We report Spearman rank correlation between all high- and low-dimensional distances ρ  (global reconstruction), correlation between high- and low-dimensional distances of each point with its 100 closest neighbours (local  reconstruction), and correlation between radii of balls enclosing the 100 neighbours of each point in high- and low-dimensional space  (relative density reconstruction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  U5-D  To look at a different distribution and higher dimensional data, we generated 10 Uniform clusters living in 150 dimensions,  each cluster distribution ci again with mean drawn from U(0, 50) and unit variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We then draw 200 points from each of  the cluster distributions and scale the spread of the c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' , c10 by 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' , 10, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Real data  For our comparison on real data, we considered 4 datasets, a simple image benchmark, two biological single-cell datasets,  and a neural sentence embedding of Amazon reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' For the image benchmark MNIST (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 6) and both single-cell  datasets we took a random subset of 5000 samples from the original publications as referenced in the main manuscript, for  MNIST we additionally vectorized the images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We provide the visualizations of embeddings for the Samusik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' data in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 7, Wong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' did not have informative labels available for these embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  For the Amazon Review dataset, we downloaded reviews for 8 categories from https://nijianmo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='io/  amazon/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='html that are closely related: ”Patio Lawn and Garden”, ”Tools and Home Improvement”, ”Industrial  and Scientific”, ”Sports and Outdoors”,”Amazon fashion”, ”Arts and Crafts”,”Clothing, Shoes, Jewelry”, and ”Luxury  Beauty”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We then sampled 5000 reviews that had at least 15 words in it, keeping original proportions of the categories intact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  We set the threshold of 15 words to keep only reviews that are more likely to be informative about a product, as there are  many reviews that just read ”Great product!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' !”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' or ”Can highly recommend!”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We then use the Universal Sentence Encoder  (https://tfhub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='dev/google/universal-sentence-encoder/4) to obtain a 512-dimensional embedding  of each review, resulting in the input data for our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' We give embeddings for the top 4 methods only, to be able to  fit on one page, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  Preserving local densities in low-dimensional embeddings  (a) DTSNE  (b) LARGEVIS  (c) LLE  (d) NCVIS  (e) TSNE  (f) UMAP  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' MNIST embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Embedding of a random subset of 5000 samples from the MNIST dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Each sample is visualized as the  original image stripped off its background, which allows to see inter-cluster dependencies such as curvatures and writing styles of digits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  11  11  11  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='.It  119  +  1  t  1,15  1  11  1  [1  11Preserving local densities in low-dimensional embeddings  (a) DTSNE  (b) LARGEVIS  (c) LLE  (d) NCVIS  (e) TSNE  (f) UMAP  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Samusik et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' single-cell data embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Embedding of a random subset of 5000 samples from the Samusik dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Samples  are colored by cell type annotation from the original study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Cluster arrangement in all except LLE reflect hematopoiesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  B-cell Frac A-C (pro-B cells)  GMP  MPP  Classical Monocytes  Intermediate Monocytes  pDCs  Basophils  IgD- IgMpos B cells  NK cells  CLP  Macrophages  Plasma Cells  CD4 T cells  IgDpos IgMpos B cells  NKT cells  CMP  mDCs  CD8 T cells  IgM- IgD- B-cells  Non-Classical Monocytes *  Eosinophils  MEPPreserving local densities in low-dimensional embeddings  DTSNE1  DTSNE2  LARGEVIS1  LARGEVIS2  Amazon Fashion  Arts & Crafts  Clothing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Shoes,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Jewelry  Industrial & Scientific  Luxury Beauty  Patio,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Lawn & Garden  Sports & Outdoors  Tools & Home Improv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content='  TSNE1  TSNE2  UMAP1  UMAP2  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Structure in amazon reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Embeddings of Universal Sentence Encoded Amazon reviews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Comparison of clusters retrieved by  DTSNE and the best performing competitors LARGEVIS, TSNE, and UMAP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
+page_content=' Clusters are annotated by examining the review texts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ldFST4oBgHgl3EQfJTg8/content/2301.13732v1.pdf'}
diff --git a/mtE3T4oBgHgl3EQf6gu4/vector_store/index.pkl b/mtE3T4oBgHgl3EQf6gu4/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..72dc46fd1e2c17c693a4e837ca5655ec3d126e9d
--- /dev/null
+++ b/mtE3T4oBgHgl3EQf6gu4/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:93b9a6cb943f65c1ab5d6a211d2c4716f74ba4706b86b1937ef5d74965297901
+size 215287
diff --git a/ntE0T4oBgHgl3EQfqAHb/content/tmp_files/2301.02548v1.pdf.txt b/ntE0T4oBgHgl3EQfqAHb/content/tmp_files/2301.02548v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d5070f453efafdbddd2c72c83dfed6f085c90a1a
--- /dev/null
+++ b/ntE0T4oBgHgl3EQfqAHb/content/tmp_files/2301.02548v1.pdf.txt
@@ -0,0 +1,1076 @@
+Lattice Distortions and Magnetic Interactions in Single-Layer VOCl
+Mohammad Amirabbasi
+Independent Research Center, Shahrood, Iran
+Marcus Ekholm∗
+Link¨oping University, SE-581 83 Link¨oping, Sweden
+(Dated: January 9, 2023)
+Atomically thin layers exfoliated from magnetic van der Waals layered materials are currently of
+high interest in solid state physics. VOCl is a quasi-two-dimensional layered antiferromagnet which
+was recently synthesized in monolayer form. Previous theoretical studies have assumed the high-
+temperature orthorhombic lattice symmetry also in the low temperature range, where the bulk
+system is known to be monoclinic due to a strong magnetoelastic coupling. We demonstrate from
+ab-initio calulations that this monoclinic distortion is prevalent also in monolayers, which is in
+line with recent experimental indications of monoclinic symmetry. Our calculations also show that
+competing ferromagnetic and antiferromagnetic interactions give rise a frustrated two-fold magnetic
+superstructure where higher-order magnetic interactions play a key role to stabilize the observed
+magnetic ground state.
+I.
+INTRODUCTION
+The recent discovery of spontaneous long-range fer-
+romagnetic order in the two-dimensional (2D) material
+CrI3 [1] has lead to a surge in the search for such
+materials by experiments and theoretical calculations
+alike. Stable long-range ordering in low dimension that
+prospectively could be combined with various tunable
+properties make them appealing for next generation spin-
+tronics devices and functional materials [2–8]. Yet, the
+fundamental understanding of magnetic interactions in
+such 2D magnets is still a developing field in solid state
+theory [9, 10], as ferro- or antiferromagnetic order in a
+2D spin array with isotropic interactions is forbidden at
+non-zero temperature by the Mermin-Wagner theorem
+[11]. The observed long-range ordering is commonly at-
+tributed to magnetic anisotropy introducing a spin-wave
+excitation gap [12].
+In this pursuit, the magnetic van
+der Waals (vdW) layered materials receive considerable
+attention, as the weakly bonded layers may be easily ex-
+foliated, and they can be expected to retain the magnetic
+properties of the bulk material [12–14].
+VOCl is a layered vdW material consisting of V–O
+bilayers connected by Cl ions on each side, as illustrated
+in Fig. 1. In its bulk form, these bilayers are separated by
+a large vdW gap, taking orthorhombic Pmmn symmetry
+(space group No. 58) at ambient conditions [15].
+The
+crystal structure is common to all the so-called transition
+metal oxychlorides, MOCl, where M ∈ {Ti, V, Cr, Fe}.
+At room temperature, bulk VOCl is a paramagnetic
+insulator, but a twofold antiferromagnetic (AFM) super-
+structure develops below the N´eel temperature, TN ≈ 80
+K [16, 17].
+The large vdW gap makes VOCl suitable
+for intercalation applications, and it is currently being
+considered for novel transistors [18] and battery archi-
+∗ marcus.ekholm@liu.se
+tectures, with a demonstrated stability to air exposure
+and cyclic ion shuttling [19–21].
+Single crystals of VOCl with a thickness of only a few
+atomic layers were first synthesized by Wang et al. [22],
+and were shown to retain the crystal symmetry of the
+bulk form at room temperature. However, detailed mea-
+surements of the magnetic order of single-layers are chal-
+lenging and scant. An ab-initio study by Marouche et al.
+[23] found ferromagnetic ordering to be the most favor-
+able configuration on a single bilayer with orthorhom-
+bic symmetry.
+Subsequent theoretical studies [24, 25]
+suggested that the corresponding AFM configuration ob-
+served in bulk VOCl (see Fig. 1) would constitute the
+magnetic ground state of the single-layers.
+Theoretical studies have so far assumed the orthorhom-
+bic lattice structure experimentally observed at room
+temperature [23, 25] The system is then highly frustrated,
+as each V ion is connected to two V↑ and two V↓ ions.
+Nevertheless, in bulk VOCl, the development of magnetic
+order below TN is accompanied by a monoclinic distor-
+tion of the crystal structure, lowering the symmetry to
+P2/n (space group No. 13)[16, 17]. Ab-initio calculations
+have shown that this distortion is related to magnetoe-
+lastic coupling, reducing the V↑–V↓ distance [26]. This
+monoclinic distortion appears to lift the apparent mag-
+netic frustration that would prevail for the orthorhom-
+bic lattice, as the bonds, and the exchange interactions,
+would be equivalent by symmetry [16]. Indeed, recent low
+temperature measurements on VOCl single-layers have
+inferred a monoclinic lattice symmetry, although the de-
+tailed lattice geometry and magnetic properties require
+further investigation [27].
+In this study, we perform structural relaxation of VOCl
+monolayers by density functional theory (DFT) [28, 29]
+calculations to show that the AFM configuration leads to
+a distortion of the lattice that is completely analogous to
+the monoclinic distortion of bulk VOCl. Assuming this
+lower lattice symmetry, we derive a magnetic Hamilto-
+nian to study the role of exchange interactions, single-ion
+arXiv:2301.02548v1  [cond-mat.mtrl-sci]  6 Jan 2023
+
+2
+(a)
+(b)
+(c)
+(d)
+FIG. 1.
+(a)–(c) Geometry of a single VOCl bilayer viewed
+along the c-, a-, and b-axes. The green, blue and red spheres
+denote Cl, V, and O, respectively. The AFM magnetic order
+corresponding to bulk VOCl is indicated. (d) The distorted
+VO4Cl2 octahedron and the local (x, y, z) coordinate system,
+where ˆx = −ˆa, ˆy = ˆc, and ˆz = ˆb.
+anisotropy and the Dzyaloshinskii–Moriya (DM) [30, 31]
+interaction in the monoclinic phase. Monte Carlo simu-
+lations recover a TN comparable to the bulk form. Our
+study shows that, counterintuitively, the non-equivalent
+nearest and next-nearest neighbor interactions are both
+ferromagnetic; the AFM configuration is due to more
+long-ranged exchange interactions. This shows that the
+system remains frustrated even in the monoclinic phase.
+The paper is structured as follows. In Section II we
+provide details of the electronic structure calculations
+and Monte Carlo simulations. In Section III we first re-
+port on the structural optimization and magnetic order.
+We then describe the electronic structure before detailing
+the magnetic interactions. Finally, in Section IV we dis-
+cuss the implications of our results for VOCl single-layers
+and in the broader context of magnetic vdW layered ma-
+terials.
+II.
+COMPUTATIONAL DETAILS
+Calculations
+were
+performed
+with
+the
+Quantum
+Espresso [32, 33] code using the GBRV ultra-soft pseudo-
+potentials [34], and the all-electron FLEUR [35] code.
+In Quantum Espresso calculations, we used the cutoffs
+50 Ry and 550 Ry when expanding wave functions and
+charge density in plane waves, respectively.
+In FLEUR-based calculations, the wave function ex-
+pansion cut-off in the interstitial region was set to kmax =
+4.2 a.u.−1. The muffin-tin radius of V, Cl, and O atoms
+were set to 2.28, 2.13, and 1.29 a.u., respectively. We
+have included the 3s and 3p V-orbitals as semicore states.
+For the exchange-correlation energy functional, we
+have
+employed
+the
+Perdew-Burke-Ernzerhof
+(PBE)
+parametrization of the generalized gradient approxima-
+tion (GGA) [36] with the on-site Coulomb repulsion
+(DFT+U) [37, 38] applied to the V-3d orbitals.
+In
+FLEUR calculations, the on-site Hund’s exchange J-
+parameter was set to J = 1 eV [39], and the on-site
+Coulomb repulsion, U, was varied. In Quantum Espresso
+calculations we used the Dudarev parametrization, which
+requires only the on-site effective Coulomb repulsion,
+Ueff= U − J [40].
+Magnetic interactions were obtained by fitting a model
+Hamiltonian to total energy calculations for various mag-
+netic configurations, as described in the Supplemental
+Material [15].
+To simulate an isolated bilayer, we in-
+creased the c lattice parameter to over 30 ˚A. For primitive
+cell calculations (6 atoms), we used a 20×20×1 optimized
+Monkhorst-Pack [41] k-mesh. The AFM structures re-
+quire a 2×2×1 cell, and we used a 10×10×1 Monkhorst-
+Pack k-point mesh.
+Monte Carlo simulations were performed for a simu-
+lation cell containing 12800 spins, using the replica ex-
+change method [42]. We performed 2×106 steps for each
+spin at each temperature. To reduce correlation between
+successive data, statistics were collected every 10 Monte
+Carlo steps. Figures of the crystal structures were cre-
+ated with the VESTA software [43].
+
+bC3
+III.
+RESULTS AND DISCUSSION
+A.
+Crystal structure and magnetic order
+Using the DFT+U method we have optimized the crys-
+tal structure while adopting the AFM order previously
+established for the bulk (see Fig. 1), for various values of
+the parameter Ueff= U−J. As a first step, we constrained
+the lattice symmetry to orthorhombic, which yields the
+lattice constants in Table I. These values are in agreement
+with previous calculations [24, 25]. Ref. 23 reported sim-
+ilar lattice constants for FM ordering.
+TABLE I. Optimized lattice constants for a single VOCl layer
+with enforced orthorhombic symmetry, obtained with various
+Ueff-values, along with theoretical literature values.
+Ueff
+a
+b
+eV
+˚A
+˚A
+This work
+1.0
+3.31
+3.80
+”
+2.0
+3.33
+3.81
+”
+5.0
+3.38
+3.88
+Ref. 24
+4
+3.38
+3.89
+Ref. 25
+3.25
+3.36
+3.86
+Ref. 23
+2
+3.341
+3.843
+Lifting the orthorhombic symmetry constraint of the
+unit cell we find a monoclinic distortion of the crystal lat-
+tice for all considered values of the Ueff-parameter. This
+is in agreement with the recent experimental results by
+Villalpando et al. [27], who reported a monoclinic lattice
+symmetry. The distortion is due to magnetoelastic cou-
+pling and is induced by the two-fold AFM superstructure,
+which breaks the translational symmetry of FM order. It
+is completely analogous to what is seen in the bulk; the
+V↑–V↓ distance is decreased at the expense of the V↑–V↑
+distance.
+Table II accounts for the monoclinic angle γ and the
+lattice parameters obtained with various Ueff-values. A
+larger Ueff-value will reduce the monoclinic angle, while
+expanding the lattice.
+In the bulk, the value Ueff= 2
+eV has been shown to simultaneously reproduce struc-
+tural, electronic and magnetic properties reasonably well
+[20, 26]. We have calculated the Ueff-parameter with den-
+sity functional perturbation theory (DFPT) [44], which
+resulted in the value Ueff=5.67 eV for both monolayers
+as well as the bulk. Consequently, we have taken Ueff= 5
+eV as an upper limit while considering Ueff= 2.0 eV a
+reasonable value.
+For Ueff= 2 eV, the distortion lowers total energy by
+2.2 meV / atom, and the difference in V↑–V↓ and V↑–
+V↑ distances is 0.019 ˚A. The values of a and b more or
+less the same, and they are within ∼ 0.02 ˚A of what
+was previously found for bulk VOCl for the same Ueff-
+value [26]. These values may in turn be compared to the
+experimental a = 3.30 ˚A and b = 3.78 ˚A reported in Ref.
+22 for single crystal results at room temperature.
+TABLE II. Optimized lattice constants and monoclinic angle,
+γ, for a VOCl single-layer, obtained with various Ueff-values.
+Ueff
+a
+b
+γ
+eV
+˚A
+˚A
+◦
+1.0
+3.31
+3.80
+90.68
+2.0
+3.33
+3.81
+90.53
+5.0
+3.38
+3.88
+90.32
+The local V spin magnetic moment is 1.5µB and the
+orbital moment is −0.079µB, which is quite insensitive
+to the particular choice of Ueff. We find the magnetic
+easy axis to be along b, which is agreement with the
+orthorhombic structure, [16, 22, 23, 25], and is also anal-
+ogous to the bulk [26].
+These results clearly demonstrate that the magnetoe-
+lastic properties seen in bulk VOCl carry over to isolated
+single-layers as well. All calculations indicate a mono-
+clinic ground state, which is induced by the AFM mag-
+netic order.
+An orthorhombic lattice symmetry would
+indicate magnetic disorder.
+Nevertheless, by expanding the lattice we may recover
+an AFM orthorhombic structure. Fig. 2 shows the re-
+sulting γ-angle as a function of the a lattice constant.
+At each point, the basis coordinates and the b/a-ratio
+3.18
+3.24
+3.30
+3.36
+3.42
+3.48
+a(Å)
+90.0
+90.1
+90.2
+90.3
+90.4
+γ(∘)
+a=3.33∘Å
+FIG. 2. The monoclinic γ-angle as a function of the lattice
+constant a. At each point, the b/a has been optimized.
+has been optimized with Ueff= 2 eV. Above a = 3.37
+˚A (b = 3.85 ˚A) the lattice symmetry abruptly changes
+from monoclinic to orthorhombic, with γ = 90.0◦. As
+the interionic distances are increased, the magnetic in-
+teractions are diminished until there is no elastic energy
+gain in the distortion, whereupon the lattice changes its
+symmetry accordingly. Compressing the lattice has the
+effect of slightly decreasing the γ-angle, but no transition
+is seen in the examined range.
+
+4
+Before discussing further details of the magnetic inter-
+actions in Sec. III C, we will outline how the electronic
+structure of the single-layers compare to the bulk in Sec.
+III B.
+B.
+Electronic structure
+Fig. 3(a) shows the total density of states (DOS) for
+a VOCl single-layer compared with that of the bulk, cal-
+culated with Ueff= 2 eV and the AFM order shown in
+Fig. 1. The electronic structure is very similar in the two
+cases, with an insulating gap of 1.2 eV. The similarity
+underlines the two-dimensional aspects of bulk VOCl, as
+the single-layers are seen to be quite independent. Con-
+sequently, VOCl single-layers can be expected to retain
+the electronic and magnetic properties of the bulk.
+8
+6
+4
+2
+0
+2
+4
+E-EF(eV)
+0.00
+0.50
+1.00
+1.50
+2.00
+DOS(a.u.)
+Ueff=2.0 eV
+Monolayer
+Bulk
+(a)
+8
+6
+4
+2
+0
+2
+4
+E-EF(eV)
+0.00
+0.50
+1.00
+1.50
+2.00
+DOS(a.u.)
+Ueff=2.0 eV
+Total DOS
+Cl-2p
+O-2p
+V-3d
+(b)
+FIG. 3.
+(a) Total DOS of bulk and monolayer VOCl.
+(b)
+Site-projected DOS.
+In Fig. 3(b) we show the site-projected DOS, indicat-
+ing that the V-3d electrons dominate the valence states.
+These are in turn separated by a gap of 1.05 eV from a
+manifold of Cl and O states hybridizing with a single V
+electron.
+The character of the valence V states are seen in Fig.
+4(a) to be of dzx and dx2−y2 character. The lowest unoc-
+cupied orbital is of dzy character. Thus, the degeneracy
+of the 3d-levels is completely lifted by the crystal field of
+the strongly distorted VO4Cl2 octahedron. Referring to
+Fig. 1(d), the dx2−y2 lobes are directed along the a and c
+axes, between the V–O and V–Cl bonds of the ac-plane.
+The dzx lobes would be most pronounced in the ab-plane
+pointing towards V next-nearest neighbors.
+The band structure, shown in Fig. 4(b), reveals several
+indirect band gaps of approximately the same size. How-
+ever, this is highly dependent on the Ueff-value. At the
+large value of Ueff= 5 eV, shown in Fig. 4(c) and 4(d), the
+conduction bands hybridize with the high-binding energy
+manifold, and the delicate balance between the top and
+bottom of the conduction and valence bands will shift.
+In Ref. [24] it was reported an indirect Γ–X gap, which
+we cannot reproduce.
+Having established the crystal symmetry, magnetic or-
+der and electronic structure, we will detail the magnetic
+interactions in the following section.
+C.
+Magnetic interactions
+We have derived the coefficients of the following mag-
+netic Hamiltonian [15]:
+H = −1
+2
+�
+i̸=j
+Jij(ˆSi · ˆSj) + 1
+2B
+�
+i,j∈nn
+(ˆSi · ˆSj)2
+(1)
++ 1
+2D
+�
+i,j∈nn
+ˆDij · (ˆSi × ˆSj) + 1
+2∆
+�
+i
+(ˆSi · ˆd)2 ,
+where the unit vector ˆSi denotes the magnetic spin at
+site i. Jij and B are the bilinear exchange and the near-
+est neighbor (nn) biquadratic [47] exchange couplings,
+respectively. ∆ denotes the single-ion anisotropy, which
+is responsible for aligning the spins along the easy axis,
+ˆd.
+As the monoclinic distortion removes inversion sym-
+metry, the nearest neighbor DM interaction, D, may be
+nonzero. According to the Moriya rules [30], ˆD should
+lie in the ab-plane. Our calculations indeed show that
+ˆD is directed along the easy axis, b. For orthorhombic
+symmetry, we recover D = 0.
+The bilinear Heisenberg exchange interactions, Jij, de-
+serve particular attention and will be discussed in detail
+in Sec. III C 1 below. In Sec. III C 2 we will present results
+from Monte Carlo simulations based on the Hamiltonian
+(1) and discuss the impact of higher order magnetic in-
+teractions.
+
+5
+3.0
+1.5
+0.0
+1.5
+3.0
+E-EF(eV)
+-2.50
+0.00
+2.50
+5.00
+PDOS
+Ueff=2.0 eV
+dz2
+dzx
+dzy
+dx2-y2
+dxy
+(a)
+(b)
+5.0
+2.5
+0.0
+2.5
+E-EF(eV)
+-2.50
+0.00
+2.50
+5.00
+PDOS
+Ueff=5.0 eV
+dz2
+dzx
+dzy
+dx2-y2
+dxy
+(c)
+(d)
+FIG. 4.
+Orbital-resolved partial DOS (PDOS) and band structure obtained with Ueff=2 eV and Ueff=5 eV. In (b) and (d),
+the indirect band gaps are shown by dotted lines. The path are selected based on crystallography [45, 46].
+1.
+Bilinear exchange interactions
+In Fig. 5(a) we highlight the most relevant Heisenberg
+exchange-couplings on the VOCl lattice. We denote the
+nearest neighbor interaction by J1 and the second near-
+est neighbor J′
+1. In the orthorhombic case, J1 and J′
+1 are
+equivalent by symmetry as discussed in Sec. III A. This
+means that the spin configuration in Fig. 5(b) is degen-
+erate with that of Fig. 5(a). For monoclinic symmetry,
+this degeneracy has been lifted, and the configuration in
+Fig. 5(a) is the ground state.
+The J2 and J3 interactions act between ions separated
+by a and b (note that a > b), while the J4 and J5 act
+along ±a ± b.
+The obtained magnetic interactions are summarized
+in Table III, which shows that J4 and J5 are negligible,
+and will therefore not be discussed further. The nearest
+neighbor interactions, J1 and J′
+1 are both seen to favor
+FM order, while the J2 and J3 interactions are AFM,
+regardless of the Ueff-parameter. This means that it is
+not primarily the nearest neighbor interactions which are
+responsible for the magnetic ordering, as anticipated in
+the literature [16], but the more distant J2 and J3 inter-
+actions. It also means that the the monoclinic phase is
+frustrated: each V↑/↓ ion has two V↑ and two V↓ nearest
+neighbors, although all four nearest neighbor exchange
+interactions actually favor FM alignment.
+The nearest-neigbor exchange interactions in bulk
+VOCl have previously been discussed in terms of a com-
+bination of direct exchange mediated by the V dzx or-
+bitals and superexchange involving dx2−y2 electrons [51].
+Indeed, the former indeed point approximately along a
+line connecting the V–V nearest neighbors, while the
+latter involves two V–O–V paths.
+The sign of the
+
+3.00
+1.50
+Eg = 2.56 eV
+E-Ef(eV)
+U=5.0 eV
+0.00
+Af
+-1.50
+-3.00
+X
+Z
+R2
+T2
+U2
+V23.00
+1.50
+E-Ef(eV)
+0.00
+= 1.22 eV
+U=2.0 eV
+eff
+-1.50
+-3.00
+x
+Y
+rz
+R2
+T2
+U2
+r
+V26
+J2
+J1
+!!
+"
+J3
+J4
+J5
+J2
+J3
+J5
+J4
+J1
+(a)
+(b)
+FIG. 5. (a) Exchange couplings in a VOCl bilayer. The J1 and J′
+1 interactions act between V↑–V↓ and V↑–V↑ ions, respectively.
+The J2 and J3 interactions are between nearest neighbors along a and b.
+The magnetic configuration in (a) and (b) are
+degenerate for orthorhombic symmetry, where J1 = J′
+1. A monoclinic distortion of the lattice reduces the J′
+1 distance.
+TABLE III. Calculated Heisenberg couplings (J1–J6), biquadratic exchange (B), single-ion anisotropy ∆, and DM interaction
+(D) for different Ueff-parameters in the monoclinic structure. Positive (negative) values denote (anti-)ferromagnetic coupling.
+TN is the N´eel temperature obtained from Monte Carlo simulations [48–50].
+Ueff
+J1
+J′
+1
+J2
+J3
+J4
+J5
+B
+∆
+D
+TN
+eV
+meV
+K
+1.0
+4.34
+6.43
+-9.84
+-7.94
+-0.09
+-0.09
+-3.58
+-0.13
+-0.60
+98.67
+2.0
+3.62
+4.96
+-6.10
+-6.42
+-0.07
+-0.07
+-3.55
+-0.15
+-0.66
+73.33
+5.0
+2.79
+3.32
+-1.31
+-3.68
+-0.00
+-0.00
+-2.88
+-0.11
+-0.65
+32.16
+J1 and J′
+1 interactions are consistent with the Goode-
+nough–Kanamori–Anderson (GKA) rule [52] for superex-
+change, applied to the two V–O–V paths: the bond an-
+gles are close to 90◦ (99.5◦ and 100.4◦) with the same
+total bond length, which would favor FM ordering.
+The V–O–V bond angle along b is 147.5◦, closer to
+180◦ which would favor AFM order for the J2 interaction,
+as observed. As noted in Sec. III B the lobes of the dx2−y2
+orbitals point along a and b, which indeed would support
+the V–O–V hopping path. However, the J3 interaction
+along a is mediated by a V–Cl–V bond, which forms a
+97.3◦ angle, together with the V–O–V 103◦ bond, yet the
+J3 interaction is AFM, contradicting the GKA rule.
+It remains an open question how the superexchange
+mechanism would work in polyvalent materials, such as
+VOCl, although attempts have been made to construct
+a theory for CrOCl and FeOCl [53].
+Although direct
+overlap may seem unlikely, it cannot be ruled out that
+the exchange interactions are mediated by a combination
+of direct and indirect exchange. Most likely, there is a
+competition between Pauli exchange, Hund’s coupling,
+and dynamical electron correlation [54, 55].
+Varying the Ueff-parameter, we also find that interac-
+tions are reduced. The nearest neighbor interaction J1
+is always smaller than J′
+1, although it has a shorter V–V
+distance and also corresponds to the smaller 99.5◦ V–O–
+V bond. It seems as if the forced AFM order between
+the V–V nearest neighbors leads to a reduction of the
+FM exchange interactions.
+However, the ratio between the AFM J2,3 and the FM
+J1/J′
+1 will vary with Ueff. In particular, the J2 interaction
+which connects V -spins along a is affected most strongly.
+For Ueff= 1 eV, the J2,3 interactions dominate J1 and
+J′
+1, and J2 is by far the strongest. For Ueff= 5 eV, J2 is
+instead the weakest interaction, and J3 is comparable to
+the J1/J′
+1 interactions.
+In the orbital-resolved DOS of Fig. 4, the t2g and eg
+orbitals are seen to be well separated from the high en-
+ergy manifold for Ueff= 2 eV. But for Ueff= 5 eV, the
+hybridization of these orbitals is significant. The band
+gap has also been effectively doubled, which reduces the
+hopping tendency to the unoccupied dzy states along V–
+
+7
+V bonds in the bc-plane. The dominating effect seems
+to be the latter, which reduces the hopping of the large-
+angle V–O–V bond along b responsible for J2.
+It is interesting to compare the exchange interactions
+on the monoclinic lattice with those of the orthorhom-
+bic lattice. Our calculations [15] (for Ueff= 2 eV) yield
+a smaller FM J1 parameter of 1.27 meV, with compara-
+ble AFM J2,3. These results are in qualitative agreement
+with Ref. [25], although those interactions were derived
+from a smaller set of magnetic configurations, and the
+implications of the results were never discussed. Allow-
+ing the lattice to we thus observe an increase in the FM
+nearest neighbor interactions.
+Glawion et al. [51] considered exchange interactions for
+the orthorhombic bulk system and also reported AFM
+interactions along a and b, but found the sign of J1 to
+depend on the assumed Ueff-value. We do not see this
+effect in the single-layers, which may be due to an as-
+sumed FM state in Ref. 51. In any case, all theoretical
+work agrees on competing FM and AFM interactions in
+the VOCl system, giving rise to frustration.
+2.
+Spin texture
+As a test of the calculated magnetic interactions, we
+have performed Heisenberg Monte Carlo simulations on
+the monoclinic lattice. We define an AFM order param-
+eter as m =
+1
+N
+�N
+i=1 ˆSi · ˆdi, where ˆdi = ±ˆb is the ideal
+direction of the spin at site i, and N is the total number
+of spins. m = 1 thus corresponds to the AFM ground
+state and m = 0 indicates complete disorder. Fig. 6(a)
+shows the order parameter as a function of temperature
+for various values of Ueff, which reaches m = 0.98 at
+T = 0.5 K. The magnetic heat capacity is plotted in Fig.
+6(b) and is seen to reach a finite value in the T → 0 limit.
+The N´eel temperature, TN, is taken from the divergence
+of the heat capacity, and is listed in Table III. For Ueff= 2
+eV, we obtain TN = 70 K, which is comparable to the
+experimental value of 80 K for bulk VOCl [16, 56].
+TN is mostly determined by the size of the isotropic
+Jij-parameters. However, the biquadratic exchange in-
+teraction, B, is comparable with the Jij-values and gives
+a non-negligible contribution to TN. Neglecting the bi-
+quadratic exchange would lower TN by 13 K for Ueff= 2
+eV.
+The DM-interaction parameter, D, is seen in Table III
+to be quite small and only weakly dependent on Ueff. It
+does not give any appreciable contribution to TN. The
+negative values of D indicate that the DM interaction
+tends to make the spins collinear to each other [57, 58].
+Fig. 7(a) shows a snapshot of the spin texture at 0.5
+K on the monoclinic lattice. Although the correct AFM
+ground state is reached, we observe slight deviations from
+collinearity.
+Averaging the deviation angle, θ, of the
+local spin moments from the global quantization axis
+over all atoms in 100 individual simulation cells, we find
+⟨θ⟩ = 2.8◦. The corresponding distribution is shown in
+0
+25
+50
+75
+100
+125
+150
+T (K)
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+Order parameter
+Ueff=5.0 eV
+Ueff=2.0 eV
+Ueff=1.0 eV
+(a)
+0
+25
+50
+75
+100
+125
+150
+T (K)
+0
+1
+2
+3
+4
+5
+6
+Specific Heat (a.u.)
+TN=98.67 K
+TN=73.33 K
+TN=32.16 K
+Ueff=5.0 eV
+Ueff=2.0 eV
+Ueff=1.0 eV
+(b)
+FIG. 6. (a) AFM order parameter, m, and (b) magnetic (spe-
+cific) heat capacity as a function of temperature, T, for dif-
+ferent Ueff parameters.
+Fig. 7(b). Apart from Jij, the most important term for
+the alignment of the spins seems to be the biquadratic
+interaction, B. Removing the biquadratic term by set-
+ting B = 0 leads to ⟨θ⟩ = 3.9◦ with a larger variation of
+θ.
+Ref. [48] reported the much smaller value of TN = 23 K
+from Monte Carlo simulations on the orthorhombic lat-
+tice. In the orthorhombic case we find that the system
+jumps between the two degenerate magnetic solutions be-
+low TN (see Fig. 5) leading to a non-monotonic depen-
+dence of the order parameter with temperature. This is
+interesting, as the monoclinic angle is temperature de-
+pendent, pointing at the importance of the spin-lattice
+coupling, that ideally should be taken into account. How-
+ever, this is beyond the scope of this study, which targets
+the magnetic ground state.
+
+8
+(a)
+full Hamiltonian
+B = 0
+0
+2
+4
+6
+8
+10
+12
+3 ( ° )
+3
+3
+(b)
+FIG. 7. (a) Spin snapshot from Monte Carlo simulations at
+T = 0.5 K. The black rectangle indicates a 2 × 2 magnetic
+unit cell. Yellow lines highlight nearest-neighbors and blue
+lines next-nearest neighbors. (b) Histogram of the angle be-
+tween the spins and the global quantization axis, θ, obtained
+with the full Hamiltonian of Eq. (1) (blue), and setting the
+biquadratic term B = 0 (red).
+IV.
+SUMMARY AND CONCLUSIONS
+In summary, using DFT+U calculations we have de-
+termined structural and magnetic properties of the sin-
+gle VOCl bilayer. Our PBE+U calculations show that
+the system undergoes the same monoclinic distortion as
+previously observed in bulk VOCl [16, 17, 26]. The mono-
+clinic AFM phase is magnetically frustrated, as the near-
+est neighbor interactions are all FM, and the observed
+AFM order is in fact enforced by longer ranged AFM
+interactions. Thus, the monoclinic distortion does not
+remove the magnetic frustration. These conclusions are
+independent of the particular value of the Ueff-parameter
+and are in line with recent experimental reports of a
+monolinic lattice symmetry [27].
+Together with our calculations of the electronic struc-
+ture, we conclude that the physical properties of the in-
+dividual layers of bulk VOCl carry over to single-layers.
+Nevertheless, it should be remembered that the layers
+of bulk VOCl are not completely magnetically indepen-
+dent, as they do form a well ordered two-fold magnetic
+superstructure along c as well.
+By means of Monte Carlo simulations we have calcu-
+lated the N´eel temperature, which will depend on the
+Ueff-value. With Ueff = 2 eV we obtain results in good
+agreement with the experimental transition temperature
+for the bulk. In addition, our results underline the im-
+portance of higher-order exchange-interactions, such as
+biquadratic exchange, in line with previous theoretical
+predictions for layered vdW materials [47]. Nevertheless,
+the spin-phonon coupling is most likely more pronounced
+in the single layer systems [59] and our calculations also
+do not include the contribution of low-energy excitations,
+such as magnons.
+We hope that our results can aid in the interpretation
+of future experiments on atomically thin VOCl layers,
+as well as the other members of the MOCl family, which
+also become distorted at low temperature, and which cur-
+rently receive increasing attention [53–55, 60, 61].
+ACKNOWLEDGMENTS
+We gratefully acknowledge financial support from Olle
+Engkvists stiftelse, grant 207-0582, and the Swedish e-
+Science Research Centre (SeRC). All calculations were
+carried out using the facilities of the Swedish National
+Infrastructure of Computing (SNIC) at the National Su-
+percomputer Centre (NSC), and the High Performance
+Computing Center North (HPC2N). We thank Dr. L.
+Schoop for useful discussions. The guidance provided by
+Dr. G. Bhilmayer, especially for the FLEUR calculations
+is gratefully acknowledged by the authors.
+[1] B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein,
+R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A.
+McGuire, D. H. Cobden, et al., Nature 546, 270 (2017).
+
+个9
+[2] W. Han, R. K. Kawakami, M. Gmitra,
+and J. Fabian,
+Nature nanotechnology 9, 794 (2014).
+[3] Z. Wang, I. Guti´errez-Lezama, N. Ubrig, M. Kroner,
+M. Gibertini, T. Taniguchi, K. Watanabe, A. Imamo˘glu,
+E. Giannini, and A. F. Morpurgo, Nature Communica-
+tions 9, 2516 (2018).
+[4] T. Song, Z. Fei, M. Yankowitz, Z. Lin, Q. Jiang,
+K. Hwangbo, Q. Zhang, B. Sun, T. Taniguchi, K. Watan-
+abe, M. A. McGuire, D. Graf, T. Cao, J.-H. Chu, D. H.
+Cobden, C. R. Dean, D. Xiao, and X. Xu, Nature Ma-
+terials 18, 1298 (2019).
+[5] T. Li, S. Jiang, N. Sivadas, Z. Wang, Y. Xu, D. Weber,
+J. E. Goldberger, K. Watanabe, T. Taniguchi, C. J. Fen-
+nie, K. Fai Mak, and J. Shan, Nature Materials 18, 1303
+(2019).
+[6] E. C. Ahn, npj 2D Materials and Applications 4, 17
+(2020).
+[7] J. F. Sierra, J. Fabian, R. K. Kawakami, S. Roche, and
+S. O. Valenzuela, Nature Nanotechnology 16, 856 (2021).
+[8] H. Kurebayashi, J. H. Garcia, S. Khan, J. Sinova, and
+S. Roche, Nature Reviews Physics 4, 150 (2022).
+[9] K. S. Burch, D. Mandrus, and J.-G. Park, Nature 563,
+47 (2018).
+[10] L. Ke and M. I. Katsnelson, npj Computational Materials
+7, 4 (2021).
+[11] N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1307
+(1966).
+[12] C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao,
+W. Bao, C. Wang, Y. Wang, et al., Nature 546, 265
+(2017).
+[13] N. Mounet, M. Gibertini, P. Schwaller, D. Campi,
+A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Ce-
+pellotti, G. Pizzi, and N. Marzari, Nature Nanotechnol-
+ogy 13, 246 (2018).
+[14] X. Chen, Y.-T. Shao, R. Chen, S. Susarla, T. Hogan,
+Y. He, H. Zhang, S. Wang, J. Yao, P. Ercius, D. A.
+Muller, R. Ramesh,
+and R. J. Birgeneau, Phys. Rev.
+Lett. 128, 217203 (2022).
+[15] See Supplemental Material at [URL will be inserted by
+publisher] for details of the bulk structure, interatomic
+distances and further computational details of the mag-
+netic interactions.
+[16] A. C. Komarek, T. Taetz, M. T. Fern´andez-D´ıaz, D. M.
+Trots, A. M¨oller,
+and M. Braden, Phys. Rev. B 79,
+104425 (2009).
+[17] A. Sch¨onleber, J. Angelkort, S. van Smaalen, L. c. v.
+Palatinus, A. Senyshyn, and W. Morgenroth, Phys. Rev.
+B 80, 064426 (2009).
+[18] W. Zhu, Q. Cui, M. L. Adam, Z. Liu, L. Zhang, Z. Dai,
+Y. Yin, S. Chen, and L. Song, 2D Materials 8, 025010
+(2020).
+[19] X. Zhao, Z. Zhao-Karger, D. Wang,
+and M. Ficht-
+ner,
+Angewandte
+Chemie
+International
+Edition
+52,
+13621–13624 (2013).
+[20] D. Gao, J. Dong, Y. Yuan, R. Xiao, Y. Liu, D. Yu,
+C. Chen, A. Tang, D. Zhang,
+and F. Pan, Journal of
+The Electrochemical Society 169, 040566 (2022).
+[21] P. Gao, M. A. Reddy, X. Mu, T. Diemant, L. Zhang,
+Z. Zhao-Karger, V. S. K. Chakravadhanula, O. Clemens,
+R. J. Behm, and M. Fichtner, Angewandte Chemie 128,
+4357 (2016).
+[22] W. Wang, R. Sun, S. He, Z. Jia, C. Su, Y. Li,
+and
+Z. Wang, 2D Materials 8, 015027 (2020).
+[23] F. Mahrouche, K. Rezouali, Z. Wang, J. Fern´andez-
+Rossier, and A. Molina-S´anchez, 2D Materials 8, 045008
+(2021).
+[24] Y. Feng, R. Peng, Y. Dai, B. Huang, L. Duan,
+and
+Y. Ma, Applied Physics Letters 119, 173103 (2021).
+[25] Y. Li, Y.-F. Zhang, J. Deng, W.-H. Dong, J.-T. Sun,
+J. Pan, and S. Du, The Journal of Physical Chemistry
+Letters 13, 3594 (2022).
+[26] M. Ekholm, A. Sch¨onleber, and S. van Smaalen, Journal
+of Physics: Condensed Matter 31, 325502 (2019).
+[27] G. Villalpando, A. M. Ferrenti, R. Singha, X. Song,
+G. Cheng, N. Yao,
+and L. M. Schoop, ACS Nano 16,
+13814 (2022).
+[28] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864
+(1964).
+[29] W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
+[30] T. Moriya, Phys. Rev. 120, 91 (1960).
+[31] I. Dzyaloshinsky, Journal of Physics and Chemistry of
+Solids 4, 241 (1958).
+[32] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car,
+C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococ-
+cioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris,
+G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis,
+A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari,
+F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello,
+L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P.
+Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcov-
+itch, Journal of Physics: Condensed Matter 21, 395502
+(2009).
+[33] P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau,
+M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni,
+D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo,
+A. D. Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio,
+A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer,
+U. Gerstmann, F. Giustino, T. Gorni, J. Jia, M. Kawa-
+mura, H.-Y. Ko, A. Kokalj, E. K¨u¸c¨ukbenli, M. Lazzeri,
+M. Marsili, N. Marzari, F. Mauri, N. L. Nguyen, H.-
+V. Nguyen, A. O. de-la Roza, L. Paulatto, S. Ponc´e,
+D. Rocca, R. Sabatini, B. Santra, M. Schlipf, A. P. Seitso-
+nen, A. Smogunov, I. Timrov, T. Thonhauser, P. Umari,
+N. Vast, X. Wu, and S. Baroni, Journal of Physics: Con-
+densed Matter 29, 465901 (2017).
+[34] K. F. Garrity, J. W. Bennett, K. M. Rabe, and D. Van-
+derbilt, Computational Materials Science 81, 446 (2014).
+[35] FLEURgroup, “http://www.flapw.de/,” .
+[36] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.
+Lett. 77, 3865 (1996).
+[37] V. I. Anisimov, J. Zaanen, and O. K. Andersen, Phys.
+Rev. B 44, 943 (1991).
+[38] M. Cococcioni and S. de Gironcoli, Phys. Rev. B 71,
+035105 (2005).
+[39] L. Vaugier, H. Jiang,
+and S. Biermann, Phys. Rev. B
+86, 165105 (2012).
+[40] S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J.
+Humphreys,
+and A. P. Sutton, Phys. Rev. B 57, 1505
+(1998).
+[41] H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188
+(1976).
+[42] K. Hukushima and K. Nemoto, Journal of the Physical
+Society of Japan 65, 1604 (1996).
+[43] K. Momma and F. Izumi, Journal of Applied Crystallog-
+raphy 44, 1272–1276 (2011).
+[44] I. Timrov, N. Marzari,
+and M. Cococcioni, Phys. Rev.
+B 98, 085127 (2018).
+[45] Y. Hinuma, G. Pizzi, Y. Kumagai, F. Oba,
+and
+
+10
+I. Tanaka, Computational Materials Science 128, 140
+(2017).
+[46] A. Togo and I. Tanaka, arXiv preprint arXiv:1808.01590
+(2018).
+[47] A. Kartsev,
+M. Augustin,
+R. F. L. Evans,
+K. S.
+Novoselov, and E. J. G. Santos, npj Computational Ma-
+terials 6, 150 (2020).
+[48] X. Li, H. Yu, F. Lou, J. Feng, M.-H. Whangbo,
+and
+H. Xiang, Molecules 26, 803 (2021).
+[49] K. Wang, K. Ren, Y. Cheng, S. Chen,
+and G. Zhang,
+Materials Horizons 9, 2384 (2022).
+[50] F. Illas, I. P. Moreira, C. De Graaf,
+and V. Barone,
+Theoretical Chemistry Accounts 104, 265 (2000).
+[51] S. Glawion, M. R. Scholz, Y.-Z. Zhang, R. Valent´ı,
+T. Saha-Dasgupta, M. Klemm, J. Hemberger, S. Horn,
+M. Sing,
+and R. Claessen, Phys. Rev. B 80, 155119
+(2009).
+[52] W. Geertsma and D. Khomskii, Phys. Rev. B 54, 3011
+(1996).
+[53] F. Zhang, Y.-C. Kong, R. Pang, L. Hu, P.-L. Gong, X.-Q.
+Shi, and Z.-K. Tang, New Journal of Physics 21, 053033
+(2019).
+[54] X. Qing, H. Li, C. Zhong, P. Zhou, Z. Dong, and J. Liu,
+Physical Chemistry Chemical Physics 22, 17255 (2020).
+[55] S. W. Jang, D. H. Kiem, J. Lee, Y.-G. Kang, H. Yoon,
+and M. J. Han, Physical Review Materials 5, 034409
+(2021).
+[56] A. Wiedenmann, J. Rossat-Mignod, J. V´enien,
+and
+P. Palvadeau, Journal of Magnetism and Magnetic Ma-
+terials 45, 275–278 (1984).
+[57] B. Canals, M. Elhajal, and C. Lacroix, Physical Review
+B 78, 214431 (2008).
+[58] M. Elhajal, B. Canals, R. Sunyer, and C. Lacroix, Phys-
+ical Review B 71, 094420 (2005).
+[59] B. Sadhukhan, A. Bergman, Y. O. Kvashnin, J. Hellsvik,
+and A. Delin, Phys. Rev. B 105, 104418 (2022).
+[60] N. Miao, B. Xu, L. Zhu, J. Zhou, and Z. Sun, Journal
+of the American Chemical Society 140, 2417 (2018).
+[61] A. M. Schaller, M. Bykov, E. Bykova, K. Glazyrin, and
+S. van Smaalen, Physical Review B 105, 184109 (2022).
+
diff --git a/ntE0T4oBgHgl3EQfqAHb/content/tmp_files/load_file.txt b/ntE0T4oBgHgl3EQfqAHb/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2861a8c26123d551a24c1cc0f48bfae3a71d4ebb
--- /dev/null
+++ b/ntE0T4oBgHgl3EQfqAHb/content/tmp_files/load_file.txt
@@ -0,0 +1,1036 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf,len=1035
+page_content='Lattice Distortions and Magnetic Interactions in Single-Layer VOCl  Mohammad Amirabbasi  Independent Research Center, Shahrood, Iran  Marcus Ekholm∗  Link¨oping University, SE-581 83 Link¨oping, Sweden  (Dated: January 9, 2023)  Atomically thin layers exfoliated from magnetic van der Waals layered materials are currently of  high interest in solid state physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' VOCl is a quasi-two-dimensional layered antiferromagnet which  was recently synthesized in monolayer form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Previous theoretical studies have assumed the high-  temperature orthorhombic lattice symmetry also in the low temperature range, where the bulk  system is known to be monoclinic due to a strong magnetoelastic coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' We demonstrate from  ab-initio calulations that this monoclinic distortion is prevalent also in monolayers, which is in  line with recent experimental indications of monoclinic symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Our calculations also show that  competing ferromagnetic and antiferromagnetic interactions give rise a frustrated two-fold magnetic  superstructure where higher-order magnetic interactions play a key role to stabilize the observed  magnetic ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  INTRODUCTION  The recent discovery of spontaneous long-range fer-  romagnetic order in the two-dimensional (2D) material  CrI3 [1] has lead to a surge in the search for such  materials by experiments and theoretical calculations  alike.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Stable long-range ordering in low dimension that  prospectively could be combined with various tunable  properties make them appealing for next generation spin-  tronics devices and functional materials [2–8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yet, the  fundamental understanding of magnetic interactions in  such 2D magnets is still a developing field in solid state  theory [9, 10], as ferro- or antiferromagnetic order in a  2D spin array with isotropic interactions is forbidden at  non-zero temperature by the Mermin-Wagner theorem  [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The observed long-range ordering is commonly at-  tributed to magnetic anisotropy introducing a spin-wave  excitation gap [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  In this pursuit, the magnetic van  der Waals (vdW) layered materials receive considerable  attention, as the weakly bonded layers may be easily ex-  foliated, and they can be expected to retain the magnetic  properties of the bulk material [12–14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  VOCl is a layered vdW material consisting of V–O  bilayers connected by Cl ions on each side, as illustrated  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In its bulk form, these bilayers are separated by  a large vdW gap, taking orthorhombic Pmmn symmetry  (space group No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 58) at ambient conditions [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The  crystal structure is common to all the so-called transition  metal oxychlorides, MOCl, where M ∈ {Ti, V, Cr, Fe}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  At room temperature, bulk VOCl is a paramagnetic  insulator, but a twofold antiferromagnetic (AFM) super-  structure develops below the N´eel temperature, TN ≈ 80  K [16, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The large vdW gap makes VOCl suitable  for intercalation applications, and it is currently being  considered for novel transistors [18] and battery archi-  ∗ marcus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='ekholm@liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='se  tectures, with a demonstrated stability to air exposure  and cyclic ion shuttling [19–21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Single crystals of VOCl with a thickness of only a few  atomic layers were first synthesized by Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' [22],  and were shown to retain the crystal symmetry of the  bulk form at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' However, detailed mea-  surements of the magnetic order of single-layers are chal-  lenging and scant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' An ab-initio study by Marouche et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [23] found ferromagnetic ordering to be the most favor-  able configuration on a single bilayer with orthorhom-  bic symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Subsequent theoretical studies [24, 25]  suggested that the corresponding AFM configuration ob-  served in bulk VOCl (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 1) would constitute the  magnetic ground state of the single-layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Theoretical studies have so far assumed the orthorhom-  bic lattice structure experimentally observed at room  temperature [23, 25] The system is then highly frustrated,  as each V ion is connected to two V↑ and two V↓ ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Nevertheless, in bulk VOCl, the development of magnetic  order below TN is accompanied by a monoclinic distor-  tion of the crystal structure, lowering the symmetry to  P2/n (space group No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 13)[16, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ab-initio calculations  have shown that this distortion is related to magnetoe-  lastic coupling, reducing the V↑–V↓ distance [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' This  monoclinic distortion appears to lift the apparent mag-  netic frustration that would prevail for the orthorhom-  bic lattice, as the bonds, and the exchange interactions,  would be equivalent by symmetry [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Indeed, recent low  temperature measurements on VOCl single-layers have  inferred a monoclinic lattice symmetry, although the de-  tailed lattice geometry and magnetic properties require  further investigation [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  In this study, we perform structural relaxation of VOCl  monolayers by density functional theory (DFT) [28, 29]  calculations to show that the AFM configuration leads to  a distortion of the lattice that is completely analogous to  the monoclinic distortion of bulk VOCl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Assuming this  lower lattice symmetry, we derive a magnetic Hamilto-  nian to study the role of exchange interactions, single-ion  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='02548v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='mtrl-sci]  6 Jan 2023  2  (a)  (b)  (c)  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  (a)–(c) Geometry of a single VOCl bilayer viewed  along the c-, a-, and b-axes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The green, blue and red spheres  denote Cl, V, and O, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The AFM magnetic order  corresponding to bulk VOCl is indicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' (d) The distorted  VO4Cl2 octahedron and the local (x, y, z) coordinate system,  where ˆx = −ˆa, ˆy = ˆc, and ˆz = ˆb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  anisotropy and the Dzyaloshinskii–Moriya (DM) [30, 31]  interaction in the monoclinic phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Monte Carlo simu-  lations recover a TN comparable to the bulk form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Our  study shows that, counterintuitively, the non-equivalent  nearest and next-nearest neighbor interactions are both  ferromagnetic;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' the AFM configuration is due to more  long-ranged exchange interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' This shows that the  system remains frustrated even in the monoclinic phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The paper is structured as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In Section II we  provide details of the electronic structure calculations  and Monte Carlo simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In Section III we first re-  port on the structural optimization and magnetic order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  We then describe the electronic structure before detailing  the magnetic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Finally, in Section IV we dis-  cuss the implications of our results for VOCl single-layers  and in the broader context of magnetic vdW layered ma-  terials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  COMPUTATIONAL DETAILS  Calculations  were  performed  with  the  Quantum  Espresso [32, 33] code using the GBRV ultra-soft pseudo-  potentials [34], and the all-electron FLEUR [35] code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  In Quantum Espresso calculations, we used the cutoffs  50 Ry and 550 Ry when expanding wave functions and  charge density in plane waves, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  In FLEUR-based calculations, the wave function ex-  pansion cut-off in the interstitial region was set to kmax =  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='2 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The muffin-tin radius of V, Cl, and O atoms  were set to 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='28, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='13, and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='29 a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=', respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' We  have included the 3s and 3p V-orbitals as semicore states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  For the exchange-correlation energy functional, we  have  employed  the  Perdew-Burke-Ernzerhof  (PBE)  parametrization of the generalized gradient approxima-  tion (GGA) [36] with the on-site Coulomb repulsion  (DFT+U) [37, 38] applied to the V-3d orbitals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  In  FLEUR calculations, the on-site Hund’s exchange J-  parameter was set to J = 1 eV [39], and the on-site  Coulomb repulsion, U, was varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In Quantum Espresso  calculations we used the Dudarev parametrization, which  requires only the on-site effective Coulomb repulsion,  Ueff= U − J [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Magnetic interactions were obtained by fitting a model  Hamiltonian to total energy calculations for various mag-  netic configurations, as described in the Supplemental  Material [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  To simulate an isolated bilayer, we in-  creased the c lattice parameter to over 30 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' For primitive  cell calculations (6 atoms), we used a 20×20×1 optimized  Monkhorst-Pack [41] k-mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The AFM structures re-  quire a 2×2×1 cell, and we used a 10×10×1 Monkhorst-  Pack k-point mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Monte Carlo simulations were performed for a simu-  lation cell containing 12800 spins, using the replica ex-  change method [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' We performed 2×106 steps for each  spin at each temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' To reduce correlation between  successive data, statistics were collected every 10 Monte  Carlo steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Figures of the crystal structures were cre-  ated with the VESTA software [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  bC3  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  RESULTS AND DISCUSSION  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Crystal structure and magnetic order  Using the DFT+U method we have optimized the crys-  tal structure while adopting the AFM order previously  established for the bulk (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 1), for various values of  the parameter Ueff= U−J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' As a first step, we constrained  the lattice symmetry to orthorhombic, which yields the  lattice constants in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' These values are in agreement  with previous calculations [24, 25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 23 reported sim-  ilar lattice constants for FM ordering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Optimized lattice constants for a single VOCl layer  with enforced orthorhombic symmetry, obtained with various  Ueff-values, along with theoretical literature values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Ueff  a  b  eV  ˚A  ˚A  This work  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='31  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='80  ”  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='33  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='81  ”  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='38  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='88  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 24  4  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='38  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='89  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='36  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='86  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 23  2  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='341  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='843  Lifting the orthorhombic symmetry constraint of the  unit cell we find a monoclinic distortion of the crystal lat-  tice for all considered values of the Ueff-parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' This  is in agreement with the recent experimental results by  Villalpando et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' [27], who reported a monoclinic lattice  symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The distortion is due to magnetoelastic cou-  pling and is induced by the two-fold AFM superstructure,  which breaks the translational symmetry of FM order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' It  is completely analogous to what is seen in the bulk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' the  V↑–V↓ distance is decreased at the expense of the V↑–V↑  distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Table II accounts for the monoclinic angle γ and the  lattice parameters obtained with various Ueff-values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' A  larger Ueff-value will reduce the monoclinic angle, while  expanding the lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  In the bulk, the value Ueff= 2  eV has been shown to simultaneously reproduce struc-  tural, electronic and magnetic properties reasonably well  [20, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' We have calculated the Ueff-parameter with den-  sity functional perturbation theory (DFPT) [44], which  resulted in the value Ueff=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='67 eV for both monolayers  as well as the bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Consequently, we have taken Ueff= 5  eV as an upper limit while considering Ueff= 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV a  reasonable value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  For Ueff= 2 eV, the distortion lowers total energy by  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='2 meV / atom, and the difference in V↑–V↓ and V↑–  V↑ distances is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='019 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The values of a and b more or  less the same, and they are within ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='02 ˚A of what  was previously found for bulk VOCl for the same Ueff-  value [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' These values may in turn be compared to the  experimental a = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='30 ˚A and b = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='78 ˚A reported in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  22 for single crystal results at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  TABLE II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Optimized lattice constants and monoclinic angle,  γ, for a VOCl single-layer, obtained with various Ueff-values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Ueff  a  b  γ  eV  ˚A  ˚A 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='31  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='80  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='68  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='33  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='81  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='53  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='38  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='88  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='32  The local V spin magnetic moment is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5µB and the  orbital moment is −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='079µB, which is quite insensitive  to the particular choice of Ueff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' We find the magnetic  easy axis to be along b, which is agreement with the  orthorhombic structure, [16, 22, 23, 25], and is also anal-  ogous to the bulk [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  These results clearly demonstrate that the magnetoe-  lastic properties seen in bulk VOCl carry over to isolated  single-layers as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' All calculations indicate a mono-  clinic ground state, which is induced by the AFM mag-  netic order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  An orthorhombic lattice symmetry would  indicate magnetic disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Nevertheless, by expanding the lattice we may recover  an AFM orthorhombic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 2 shows the re-  sulting γ-angle as a function of the a lattice constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  At each point, the basis coordinates and the b/a-ratio  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='18  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='24  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='30  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='36  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='42  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='48  a(Å)  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='1  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='2  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='3  90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='4  γ(∘)  a=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='33∘Å  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The monoclinic γ-angle as a function of the lattice  constant a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' At each point, the b/a has been optimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  has been optimized with Ueff= 2 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Above a = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='37  ˚A (b = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='85 ˚A) the lattice symmetry abruptly changes  from monoclinic to orthorhombic, with γ = 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' As  the interionic distances are increased, the magnetic in-  teractions are diminished until there is no elastic energy  gain in the distortion, whereupon the lattice changes its  symmetry accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Compressing the lattice has the  effect of slightly decreasing the γ-angle, but no transition  is seen in the examined range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  4  Before discussing further details of the magnetic inter-  actions in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' III C, we will outline how the electronic  structure of the single-layers compare to the bulk in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  III B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Electronic structure  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 3(a) shows the total density of states (DOS) for  a VOCl single-layer compared with that of the bulk, cal-  culated with Ueff= 2 eV and the AFM order shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The electronic structure is very similar in the two  cases, with an insulating gap of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='2 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The similarity  underlines the two-dimensional aspects of bulk VOCl, as  the single-layers are seen to be quite independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Con-  sequently, VOCl single-layers can be expected to retain  the electronic and magnetic properties of the bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  8  6  4  2  0  2  4  E-EF(eV)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  DOS(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=')  Ueff=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  Monolayer  Bulk  (a)  8  6  4  2  0  2  4  E-EF(eV)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  DOS(a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=')  Ueff=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  Total DOS  Cl-2p  O-2p  V-3d  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  (a) Total DOS of bulk and monolayer VOCl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  (b)  Site-projected DOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 3(b) we show the site-projected DOS, indicat-  ing that the V-3d electrons dominate the valence states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  These are in turn separated by a gap of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='05 eV from a  manifold of Cl and O states hybridizing with a single V  electron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The character of the valence V states are seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  4(a) to be of dzx and dx2−y2 character.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The lowest unoc-  cupied orbital is of dzy character.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Thus, the degeneracy  of the 3d-levels is completely lifted by the crystal field of  the strongly distorted VO4Cl2 octahedron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Referring to  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 1(d), the dx2−y2 lobes are directed along the a and c  axes, between the V–O and V–Cl bonds of the ac-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The dzx lobes would be most pronounced in the ab-plane  pointing towards V next-nearest neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The band structure, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 4(b), reveals several  indirect band gaps of approximately the same size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' How-  ever, this is highly dependent on the Ueff-value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' At the  large value of Ueff= 5 eV, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 4(c) and 4(d), the  conduction bands hybridize with the high-binding energy  manifold, and the delicate balance between the top and  bottom of the conduction and valence bands will shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  In Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' [24] it was reported an indirect Γ–X gap, which  we cannot reproduce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Having established the crystal symmetry, magnetic or-  der and electronic structure, we will detail the magnetic  interactions in the following section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Magnetic interactions  We have derived the coefficients of the following mag-  netic Hamiltonian [15]:  H = −1  2  �  i̸=j  Jij(ˆSi · ˆSj) + 1  2B  �  i,j∈nn  (ˆSi · ˆSj)2  (1)  + 1  2D  �  i,j∈nn  ˆDij · (ˆSi × ˆSj) + 1  2∆  �  i  (ˆSi · ˆd)2 ,  where the unit vector ˆSi denotes the magnetic spin at  site i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Jij and B are the bilinear exchange and the near-  est neighbor (nn) biquadratic [47] exchange couplings,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' ∆ denotes the single-ion anisotropy, which  is responsible for aligning the spins along the easy axis,  ˆd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  As the monoclinic distortion removes inversion sym-  metry, the nearest neighbor DM interaction, D, may be  nonzero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' According to the Moriya rules [30], ˆD should  lie in the ab-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Our calculations indeed show that  ˆD is directed along the easy axis, b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' For orthorhombic  symmetry, we recover D = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The bilinear Heisenberg exchange interactions, Jij, de-  serve particular attention and will be discussed in detail  in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' III C 1 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' III C 2 we will present results  from Monte Carlo simulations based on the Hamiltonian  (1) and discuss the impact of higher order magnetic in-  teractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  E-EF(eV)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  PDOS  Ueff=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  dz2  dzx  dzy  dx2-y2  dxy  (a)  (b)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5  E-EF(eV)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  PDOS  Ueff=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  dz2  dzx  dzy  dx2-y2  dxy  (c)  (d)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Orbital-resolved partial DOS (PDOS) and band structure obtained with Ueff=2 eV and Ueff=5 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In (b) and (d),  the indirect band gaps are shown by dotted lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The path are selected based on crystallography [45, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Bilinear exchange interactions  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 5(a) we highlight the most relevant Heisenberg  exchange-couplings on the VOCl lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' We denote the  nearest neighbor interaction by J1 and the second near-  est neighbor J′  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In the orthorhombic case, J1 and J′  1 are  equivalent by symmetry as discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' III A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' This  means that the spin configuration in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 5(b) is degen-  erate with that of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 5(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' For monoclinic symmetry,  this degeneracy has been lifted, and the configuration in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 5(a) is the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The J2 and J3 interactions act between ions separated  by a and b (note that a > b), while the J4 and J5 act  along ±a ± b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The obtained magnetic interactions are summarized  in Table III, which shows that J4 and J5 are negligible,  and will therefore not be discussed further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The nearest  neighbor interactions, J1 and J′  1 are both seen to favor  FM order, while the J2 and J3 interactions are AFM,  regardless of the Ueff-parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' This means that it is  not primarily the nearest neighbor interactions which are  responsible for the magnetic ordering, as anticipated in  the literature [16], but the more distant J2 and J3 inter-  actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' It also means that the the monoclinic phase is  frustrated: each V↑/↓ ion has two V↑ and two V↓ nearest  neighbors, although all four nearest neighbor exchange  interactions actually favor FM alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The nearest-neigbor exchange interactions in bulk  VOCl have previously been discussed in terms of a com-  bination of direct exchange mediated by the V dzx or-  bitals and superexchange involving dx2−y2 electrons [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Indeed, the former indeed point approximately along a  line connecting the V–V nearest neighbors, while the  latter involves two V–O–V paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The sign of the  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  Eg = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='56 eV  E-Ef(eV)  U=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  Af  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  X  Z  R2  T2  U2  V23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  E-Ef(eV)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='22 eV  U=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  eff  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='50  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  x  Y  rz  R2  T2  U2  r  V26  J2  J1  !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  "  J3  J4  J5  J2  J3  J5  J4  J1  (a)  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' (a) Exchange couplings in a VOCl bilayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The J1 and J′  1 interactions act between V↑–V↓ and V↑–V↑ ions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The J2 and J3 interactions are between nearest neighbors along a and b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The magnetic configuration in (a) and (b) are  degenerate for orthorhombic symmetry, where J1 = J′  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' A monoclinic distortion of the lattice reduces the J′  1 distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  TABLE III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Calculated Heisenberg couplings (J1–J6), biquadratic exchange (B), single-ion anisotropy ∆, and DM interaction  (D) for different Ueff-parameters in the monoclinic structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Positive (negative) values denote (anti-)ferromagnetic coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  TN is the N´eel temperature obtained from Monte Carlo simulations [48–50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Ueff  J1  J′  1  J2  J3  J4  J5  B  ∆  D  TN  eV  meV  K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='34  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='43  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='84  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='94  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='09  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='09  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='58  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='13  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='60  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='67  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='62  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='96  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='10  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='42  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='07  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='55  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='66  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='33  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='79  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='32  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='31  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='68  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='00  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='88  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='65  32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='16  J1 and J′  1 interactions are consistent with the Goode-  nough–Kanamori–Anderson (GKA) rule [52] for superex-  change, applied to the two V–O–V paths: the bond an-  gles are close to 90◦ (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5◦ and 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='4◦) with the same  total bond length, which would favor FM ordering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The V–O–V bond angle along b is 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5◦, closer to  180◦ which would favor AFM order for the J2 interaction,  as observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' As noted in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' III B the lobes of the dx2−y2  orbitals point along a and b, which indeed would support  the V–O–V hopping path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' However, the J3 interaction  along a is mediated by a V–Cl–V bond, which forms a  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='3◦ angle, together with the V–O–V 103◦ bond, yet the  J3 interaction is AFM, contradicting the GKA rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  It remains an open question how the superexchange  mechanism would work in polyvalent materials, such as  VOCl, although attempts have been made to construct  a theory for CrOCl and FeOCl [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Although direct  overlap may seem unlikely, it cannot be ruled out that  the exchange interactions are mediated by a combination  of direct and indirect exchange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Most likely, there is a  competition between Pauli exchange, Hund’s coupling,  and dynamical electron correlation [54, 55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Varying the Ueff-parameter, we also find that interac-  tions are reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The nearest neighbor interaction J1  is always smaller than J′  1, although it has a shorter V–V  distance and also corresponds to the smaller 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5◦ V–O–  V bond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' It seems as if the forced AFM order between  the V–V nearest neighbors leads to a reduction of the  FM exchange interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  However, the ratio between the AFM J2,3 and the FM  J1/J′  1 will vary with Ueff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In particular, the J2 interaction  which connects V -spins along a is affected most strongly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  For Ueff= 1 eV, the J2,3 interactions dominate J1 and  J′  1, and J2 is by far the strongest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' For Ueff= 5 eV, J2 is  instead the weakest interaction, and J3 is comparable to  the J1/J′  1 interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  In the orbital-resolved DOS of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 4, the t2g and eg  orbitals are seen to be well separated from the high en-  ergy manifold for Ueff= 2 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' But for Ueff= 5 eV, the  hybridization of these orbitals is significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The band  gap has also been effectively doubled, which reduces the  hopping tendency to the unoccupied dzy states along V–  7  V bonds in the bc-plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The dominating effect seems  to be the latter, which reduces the hopping of the large-  angle V–O–V bond along b responsible for J2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  It is interesting to compare the exchange interactions  on the monoclinic lattice with those of the orthorhom-  bic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Our calculations [15] (for Ueff= 2 eV) yield  a smaller FM J1 parameter of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='27 meV, with compara-  ble AFM J2,3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' These results are in qualitative agreement  with Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' [25], although those interactions were derived  from a smaller set of magnetic configurations, and the  implications of the results were never discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Allow-  ing the lattice to we thus observe an increase in the FM  nearest neighbor interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Glawion et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' [51] considered exchange interactions for  the orthorhombic bulk system and also reported AFM  interactions along a and b, but found the sign of J1 to  depend on the assumed Ueff-value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' We do not see this  effect in the single-layers, which may be due to an as-  sumed FM state in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In any case, all theoretical  work agrees on competing FM and AFM interactions in  the VOCl system, giving rise to frustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Spin texture  As a test of the calculated magnetic interactions, we  have performed Heisenberg Monte Carlo simulations on  the monoclinic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' We define an AFM order param-  eter as m =  1  N  �N  i=1 ˆSi · ˆdi, where ˆdi = ±ˆb is the ideal  direction of the spin at site i, and N is the total number  of spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' m = 1 thus corresponds to the AFM ground  state and m = 0 indicates complete disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 6(a)  shows the order parameter as a function of temperature  for various values of Ueff, which reaches m = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='98 at  T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The magnetic heat capacity is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  6(b) and is seen to reach a finite value in the T → 0 limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The N´eel temperature, TN, is taken from the divergence  of the heat capacity, and is listed in Table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' For Ueff= 2  eV, we obtain TN = 70 K, which is comparable to the  experimental value of 80 K for bulk VOCl [16, 56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  TN is mostly determined by the size of the isotropic  Jij-parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' However, the biquadratic exchange in-  teraction, B, is comparable with the Jij-values and gives  a non-negligible contribution to TN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Neglecting the bi-  quadratic exchange would lower TN by 13 K for Ueff= 2  eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  The DM-interaction parameter, D, is seen in Table III  to be quite small and only weakly dependent on Ueff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' It  does not give any appreciable contribution to TN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The  negative values of D indicate that the DM interaction  tends to make the spins collinear to each other [57, 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 7(a) shows a snapshot of the spin texture at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5  K on the monoclinic lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Although the correct AFM  ground state is reached, we observe slight deviations from  collinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Averaging the deviation angle, θ, of the  local spin moments from the global quantization axis  over all atoms in 100 individual simulation cells, we find  ⟨θ⟩ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='8◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The corresponding distribution is shown in  0  25  50  75  100  125  150  T (K)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0  Order parameter  Ueff=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  Ueff=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  Ueff=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  (a)  0  25  50  75  100  125  150  T (K)  0  1  2  3  4  5  6  Specific Heat (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=')  TN=98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='67 K  TN=73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='33 K  TN=32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='16 K  Ueff=5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  Ueff=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  Ueff=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='0 eV  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' (a) AFM order parameter, m, and (b) magnetic (spe-  cific) heat capacity as a function of temperature, T, for dif-  ferent Ueff parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 7(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Apart from Jij, the most important term for  the alignment of the spins seems to be the biquadratic  interaction, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Removing the biquadratic term by set-  ting B = 0 leads to ⟨θ⟩ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='9◦ with a larger variation of  θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' [48] reported the much smaller value of TN = 23 K  from Monte Carlo simulations on the orthorhombic lat-  tice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In the orthorhombic case we find that the system  jumps between the two degenerate magnetic solutions be-  low TN (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 5) leading to a non-monotonic depen-  dence of the order parameter with temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' This is  interesting, as the monoclinic angle is temperature de-  pendent, pointing at the importance of the spin-lattice  coupling, that ideally should be taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' How-  ever, this is beyond the scope of this study, which targets  the magnetic ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  8  (a)  full Hamiltonian  B = 0  0  2  4  6  8  10  12  3 ( ° )  3  3  (b)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' (a) Spin snapshot from Monte Carlo simulations at  T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='5 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The black rectangle indicates a 2 × 2 magnetic  unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yellow lines highlight nearest-neighbors and blue  lines next-nearest neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' (b) Histogram of the angle be-  tween the spins and the global quantization axis, θ, obtained  with the full Hamiltonian of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' (1) (blue), and setting the  biquadratic term B = 0 (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  SUMMARY AND CONCLUSIONS  In summary, using DFT+U calculations we have de-  termined structural and magnetic properties of the sin-  gle VOCl bilayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Our PBE+U calculations show that  the system undergoes the same monoclinic distortion as  previously observed in bulk VOCl [16, 17, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The mono-  clinic AFM phase is magnetically frustrated, as the near-  est neighbor interactions are all FM, and the observed  AFM order is in fact enforced by longer ranged AFM  interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Thus, the monoclinic distortion does not  remove the magnetic frustration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' These conclusions are  independent of the particular value of the Ueff-parameter  and are in line with recent experimental reports of a  monolinic lattice symmetry [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Together with our calculations of the electronic struc-  ture, we conclude that the physical properties of the in-  dividual layers of bulk VOCl carry over to single-layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Nevertheless, it should be remembered that the layers  of bulk VOCl are not completely magnetically indepen-  dent, as they do form a well ordered two-fold magnetic  superstructure along c as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  By means of Monte Carlo simulations we have calcu-  lated the N´eel temperature, which will depend on the  Ueff-value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' With Ueff = 2 eV we obtain results in good  agreement with the experimental transition temperature  for the bulk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' In addition, our results underline the im-  portance of higher-order exchange-interactions, such as  biquadratic exchange, in line with previous theoretical  predictions for layered vdW materials [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Nevertheless,  the spin-phonon coupling is most likely more pronounced  in the single layer systems [59] and our calculations also  do not include the contribution of low-energy excitations,  such as magnons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  We hope that our results can aid in the interpretation  of future experiments on atomically thin VOCl layers,  as well as the other members of the MOCl family, which  also become distorted at low temperature, and which cur-  rently receive increasing attention [53–55, 60, 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  We gratefully acknowledge financial support from Olle  Engkvists stiftelse, grant 207-0582, and the Swedish e-  Science Research Centre (SeRC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' All calculations were  carried out using the facilities of the Swedish National  Infrastructure of Computing (SNIC) at the National Su-  percomputer Centre (NSC), and the High Performance  Computing Center North (HPC2N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' We thank Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Schoop for useful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' The guidance provided by  Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Bhilmayer, especially for the FLEUR calculations  is gratefully acknowledged by the authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Huang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Clark, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Navarro-Moratalla, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Klein,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cheng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Seyler, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhong, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Schmidgall, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  McGuire, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cobden, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=', Nature 546, 270 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  个9  [2] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Han, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kawakami, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gmitra,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fabian,  Nature nanotechnology 9, 794 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [3] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Guti´errez-Lezama, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ubrig, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kroner,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gibertini, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Taniguchi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Watanabe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Imamo˘glu,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Giannini, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Morpurgo, Nature Communica-  tions 9, 2516 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [4] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Song, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fei, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yankowitz, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Lin, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Jiang,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Hwangbo, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sun, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Taniguchi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Watan-  abe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' McGuire, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Graf, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Chu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Cobden, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Dean, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Xiao, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Xu, Nature Ma-  terials 18, 1298 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Jiang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sivadas, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Xu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Weber,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Goldberger, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Watanabe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Taniguchi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fen-  nie, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fai Mak, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Shan, Nature Materials 18, 1303  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [6] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ahn, npj 2D Materials and Applications 4, 17  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sierra, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fabian, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kawakami, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Roche, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Valenzuela, Nature Nanotechnology 16, 856 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [8] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kurebayashi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Garcia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Khan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sinova, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Roche, Nature Reviews Physics 4, 150 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [9] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Burch, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Mandrus, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Park, Nature 563,  47 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ke and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Katsnelson, npj Computational Materials  7, 4 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [11] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Mermin and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wagner, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 17, 1307  (1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [12] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ji, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Stern, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Xia, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cao,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Bao, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=', Nature 546, 265  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [13] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Mounet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gibertini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Schwaller, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Campi,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Merkys, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Marrazzo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sohier, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Castelli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ce-  pellotti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Pizzi, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Marzari, Nature Nanotechnol-  ogy 13, 246 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [14] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Shao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Susarla, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Hogan,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' He, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yao, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ercius, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Muller, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ramesh,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Birgeneau, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 128, 217203 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [15] See Supplemental Material at [URL will be inserted by  publisher] for details of the bulk structure, interatomic  distances and further computational details of the mag-  netic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Komarek, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Taetz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fern´andez-D´ıaz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Trots, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' M¨oller,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Braden, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B 79,  104425 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sch¨onleber, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Angelkort, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' van Smaalen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Palatinus, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Senyshyn, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Morgenroth, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  B 80, 064426 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [18] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cui, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Adam, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Dai,  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Chen, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Song, 2D Materials 8, 025010  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [19] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhao-Karger, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ficht-  ner,  Angewandte  Chemie  International  Edition  52,  13621–13624 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [20] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Dong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yuan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Xiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yu,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Tang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhang,  and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Pan, Journal of  The Electrochemical Society 169, 040566 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [21] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Reddy, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Mu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Diemant, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhang,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhao-Karger, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Chakravadhanula, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Clemens,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Behm, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fichtner, Angewandte Chemie 128,  4357 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [22] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sun, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' He, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Jia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Su, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Li,  and  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang, 2D Materials 8, 015027 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [23] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Mahrouche, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rezouali, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fern´andez-  Rossier, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Molina-S´anchez, 2D Materials 8, 045008  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [24] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Feng, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Peng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Dai, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Huang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Duan,  and  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ma, Applied Physics Letters 119, 173103 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [25] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Deng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Dong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sun,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Pan, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Du, The Journal of Physical Chemistry  Letters 13, 3594 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ekholm, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sch¨onleber, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' van Smaalen, Journal  of Physics: Condensed Matter 31, 325502 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [27] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Villalpando, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ferrenti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Singha, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Song,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cheng, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yao,  and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Schoop, ACS Nano 16,  13814 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [28] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Hohenberg and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kohn, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 136, B864  (1964).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [29] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kohn and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sham, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 140, A1133 (1965).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [30] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Moriya, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 120, 91 (1960).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [31] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Dzyaloshinsky, Journal of Physics and Chemistry of  Solids 4, 241 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [32] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Giannozzi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Baroni, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Bonini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Calandra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Car,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cavazzoni, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ceresoli, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Chiarotti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cococ-  cioni, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Dabo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Corso, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' de Gironcoli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fabris,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fratesi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gebauer, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gerstmann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gougoussis,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kokalj, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Lazzeri, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Martin-Samos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Marzari,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Mauri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Mazzarello, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Paolini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Pasquarello,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Paulatto, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sbraccia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Scandolo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sclauzero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Seitsonen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Smogunov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Umari, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wentzcov-  itch, Journal of Physics: Condensed Matter 21, 395502  (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [33] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Giannozzi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Andreussi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Brumme, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Bunau,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Nardelli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Calandra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Car, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cavazzoni,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ceresoli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cococcioni, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Colonna, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Carnimeo,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Corso, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' de Gironcoli, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Delugas, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' DiStasio,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ferretti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Floris, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fratesi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Fugallo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gebauer,  U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gerstmann, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Giustino, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gorni, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Jia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kawa-  mura, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kokalj, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' K¨u¸c¨ukbenli, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Lazzeri,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Marsili, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Marzari, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Mauri, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Nguyen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Nguyen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' de-la Roza, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Paulatto, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ponc´e,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rocca, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sabatini, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Santra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Schlipf, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Seitso-  nen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Smogunov, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Timrov, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Thonhauser, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Umari,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Vast, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wu, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Baroni, Journal of Physics: Con-  densed Matter 29, 465901 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [34] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Garrity, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Bennett, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rabe, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Van-  derbilt, Computational Materials Science 81, 446 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [35] FLEURgroup, “http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='flapw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='de/,” .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [36] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Perdew, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Burke, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ernzerhof, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' 77, 3865 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [37] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Anisimov, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zaanen, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Andersen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B 44, 943 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [38] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cococcioni and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' de Gironcoli, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B 71,  035105 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [39] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Vaugier, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Jiang,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Biermann, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B  86, 165105 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [40] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Dudarev, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Botton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Savrasov, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Humphreys,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sutton, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B 57, 1505  (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [41] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Monkhorst and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Pack, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B 13, 5188  (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [42] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Hukushima and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Nemoto, Journal of the Physical  Society of Japan 65, 1604 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [43] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Momma and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Izumi, Journal of Applied Crystallog-  raphy 44, 1272–1276 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [44] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Timrov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Marzari,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cococcioni, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  B 98, 085127 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [45] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Hinuma, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Pizzi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kumagai, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Oba,  and  10  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Tanaka, Computational Materials Science 128, 140  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [46] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Togo and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Tanaka, arXiv preprint arXiv:1808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='01590  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [47] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kartsev,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Augustin,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Evans,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Novoselov, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Santos, npj Computational Ma-  terials 6, 150 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [48] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Lou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Feng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Whangbo,  and  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Xiang, Molecules 26, 803 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [49] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Ren, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Cheng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Chen,  and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhang,  Materials Horizons 9, 2384 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [50] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Illas, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Moreira, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' De Graaf,  and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Barone,  Theoretical Chemistry Accounts 104, 265 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [51] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Glawion, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Scholz, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Valent´ı,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Saha-Dasgupta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Klemm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Hemberger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Horn,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sing,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Claessen, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B 80, 155119  (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [52] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Geertsma and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Khomskii, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B 54, 3011  (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [53] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Pang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Hu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Gong, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  Shi, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Tang, New Journal of Physics 21, 053033  (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [54] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Qing, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhong, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhou, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Dong, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Liu,  Physical Chemistry Chemical Physics 22, 17255 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [55] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Jang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kiem, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Lee, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Yoon,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Han, Physical Review Materials 5, 034409  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [56] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Wiedenmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rossat-Mignod, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' V´enien,  and  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Palvadeau, Journal of Magnetism and Magnetic Ma-  terials 45, 275–278 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [57] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Canals, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Elhajal, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Lacroix, Physical Review  B 78, 214431 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [58] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Elhajal, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Canals, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sunyer, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Lacroix, Phys-  ical Review B 71, 094420 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [59] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sadhukhan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Bergman, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Kvashnin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Hellsvik,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Delin, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' B 105, 104418 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [60] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Miao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Xu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Zhou, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Sun, Journal  of the American Chemical Society 140, 2417 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content='  [61] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Schaller, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Bykov, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Bykova, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' Glazyrin, and  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
+page_content=' van Smaalen, Physical Review B 105, 184109 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ntE0T4oBgHgl3EQfqAHb/content/2301.02548v1.pdf'}
diff --git a/o9E5T4oBgHgl3EQfIw4s/content/tmp_files/2301.05451v1.pdf.txt b/o9E5T4oBgHgl3EQfIw4s/content/tmp_files/2301.05451v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8d2da5d97df3510ae19704e04c141db88f11f9be
--- /dev/null
+++ b/o9E5T4oBgHgl3EQfIw4s/content/tmp_files/2301.05451v1.pdf.txt
@@ -0,0 +1,2504 @@
+TeD-Q: a tensor network enhanced distributed hybrid quantum machine learning
+framework
+Yaocheng Chen,1, 2, 3, ∗ Xingyao Wu ∗,3, † Chung-Yun Kuo,1, 2, 3 Yuxuan Du,3, ‡ and Dacheng Tao3, §
+1Department of Physics, National Taiwan University, Taipei, Taiwan
+2Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, Taiwan
+3JD Explore Academy, Beijing, China
+(Dated: January 16, 2023)
+TeD-Q is an open-source software framework for quantum machine learning, variational quan-
+tum algorithm (VQA), and simulation of quantum computing. It seamlessly integrates classical
+machine learning libraries with quantum simulators, giving users the ability to leverage the power
+of classical machine learning while training quantum machine learning models. TeD-Q supports
+auto-differentiation that provides backpropagation, parameters shift, and finite difference methods
+to obtain gradients. With tensor contraction, simulation of quantum circuits with large number of
+qubits is possible. TeD-Q also provides a graphical mode in which the quantum circuit and the
+training progress can be visualized in real-time.
+I.
+INTRODUCTION
+Quantum computing is one of the most promising di-
+rections that may save us from Moore’s law. Recent re-
+sults show that quantum computing is indeed advanta-
+geous over classical computing in certain problems [1–3].
+With the progress in quantum hardware, quantum soft-
+ware and research in algorithms are also catching up.
+Quantum software plays a crucial role in bridging quan-
+tum hardware and real-world applications.
+There has
+been a decent amount of work in quantum software plat-
+forms in recent years. Some of these already allow users
+to access real quantum hardware [4–6], while others fo-
+cus more on building a complete software environment
+for better quantum algorithm development [7].
+TeD-Q is a Python-based quantum programming
+framework that has differentiable functionality. It is op-
+timized particularly for quantum machine learning prob-
+lems [8–11] and variational quantum algorithms [12–14],
+which constitute the majority of contemporary Noisy
+Intermediate-Scale Quantum (NISQ) algorithms [15, 16].
+TeD-Q provides a universal framework for program-
+ming on different backends, including quantum hardware,
+quantum simulator, and distributed GPU accelerators.
+In terms of top-level applications, users could enjoy the
+convenience of using TeD-Q without worrying about how
+to deal with different backends. One could simply treat
+a quantum neural network (QNN) training as in classical
+machine learning.
+With TeD-Q, the quantum circuit is treated as a
+Python function. It is free to choose either PyTorch or
+JAX as the interface with the execution backends. Due
+to this systematic integration, one could also leverage the
+rich features provided by the well-developed AI-oriented
+∗ These two authors contributed equally
+† wu.x.yao@gmail.com
+‡ duyuxuan123@gmail.com
+§ dacheng.tao@gmail.com
+libraries [17] to help the implementation of quantum algo-
+rithms better. Specific benefits include batch execution,
+Just In Time compilation (JIT) [18], parallel GPU opti-
+mization, and auto-differentiation for backpropagation.
+TeD-Q has both full amplitude quantum simulation
+and a tensor network enhanced multi-amplitude simula-
+tion. TeD-Q will estimate the complexity of both modes,
+and users could choose on their own which mode to exe-
+cute the code.
+TeD-Q is also equipped with a built-in tensor network
+module and contraction path optimizer JDtensorPath,
+which could provide additional improvements on the per-
+formance in the tensor network simulation mode. This
+is achieved by optimizing the tensor network contraction
+order.
+Besides, TeD-Q provides a graphical circuit composer
+that makes it user-friendly to beginners with intuitive
+visualization.
+Table I shows the comparison among TeD-Q and three
+major general-purpose quantum machine learning plat-
+forms – PennyLane [4], Qiskit [5] and Paddle Quan-
+tum [19].
+PennyLane is a cross-platform Python package for pro-
+gramming quantum and hybrid quantum-classical algo-
+rithms. It builds upon the idea of auto differentiable pro-
+gramming and integrates mainstream classical machine
+learning libraries with quantum algorithms to provide an
+easy-to-use interface[4]. Qiskit is an open source quan-
+tum software development framework of IBM. It inte-
+grates PyTorch and can be executed with IBMQ on real
+quantum hardware[5]. Paddle Quantum is developed by
+Baidu, it is based on the PaddlePaddle deep learning
+platform and can access real quantum computers Quan-
+tum Leaf[19].
+The main distinct features of TeD-Q are hypergraph-
+based tensor network contraction (TNC) and paralleling
+via index slicing.
+Simulation of quantum circuits nor-
+mally can be carried out by matrix multiplication and
+tensor network contraction. Current quantum software
+platforms generally support only matrix multiplication
+arXiv:2301.05451v1  [quant-ph]  13 Jan 2023
+
+2
+Table I: A summary of features of existing quantum
+simulation frameworks.
+TeD-Q
+Pennylane Qiskit
+Paddle
+Quantum
+Backpropagation
+v
+v
+-
+v
+Hypergraph-based TNC
+v
+-
+-
+-
+Slicing paralleling
+v
+-
+-
+-
+PyTorch interface
+v
+v
+v
+-
+Noise model
+future release
+v
+v
+v
+Hardware compatibility
+via Qiskit
+v
+v
+v
+Circuit composer
+v
+-
+v
+-
+mode [4, 5, 19], which is enough while the number of
+qubits is below roughly 38.
+However, when the num-
+ber of qubits exceeds 38, the time cost and storage cost
+surge exponentially. The TNC mode of TeD-Q could eas-
+ily handle quantum circuit simulation with qubit number
+larger than 38. Hypergraph-based TNC method can pro-
+vide several orders of magnitude improvement in both
+computation and memory complexity while paralleling
+via index slicing delivers advantages in GPU device com-
+munication. Since the order of tensor network contrac-
+tion will affect the time cost a lot, TeD-Q also provides
+a dedicated tensor network contraction optimizer, called
+JDTensorPath. These new features are designed to im-
+prove the efficiency of large-scale quantum circuit simu-
+lation.
+Compared to Qiskit, Pennylane and Paddle Quantum,
+TeD-Q also featured a reusable mechanism. In most of
+the quantum algorithms including NISQ algorithms, the
+parameterized quantum circuit will be evaluated multiple
+times without changing the circuit structure. In TeD-Q,
+the quantum state and quantum gate objects inside a
+quantum circuit will be reused in every evaluation. This
+feature can save a considerable amount of time for class
+instantiation in small quantum circuits. This advantage
+could be easily seen in the performance comparison of
+multiple qubits rotation example in Section VI.
+II.
+ARCHITECTURE OF TED-Q
+TeD-Q is designed for fast and efficient implementation
+of quantum algorithms.
+For this purpose, the compo-
+nents of application design, computation backends, and
+the interface in between are packed into relatively inde-
+pendent modules. TeD-Q is composed of four main mod-
+ules, QInterpreter, Backends, Interface, and Optimizer,
+as shown in Fig. 1.
+Any quantum algorithm will eventually be passed
+through and processed as classical codes. This is where
+the QInterpreter plays its role, transforming quantum
+algorithms into executable codes.
+Quantum state and
+quantum gate classes are the basic building blocks of
+QInterpreter. A series of quantum gates applied to the
+quantum state will make up a quantum circuit.
+The quantum circuit object in TeD-Q is agnostic with
+respect to simulation and hardware backends.
+It is
+an abstraction of user-defined quantum function, that
+FIG. 1: The design of TeD-Q architecture. The part in
+yellow is quantum while the rest is classical processing.
+bridges the high-level quantum algorithms and low-level
+backend-specific instructions.
+QInterpreter of TeD-Q
+provides tools for obtaining and manipulating represen-
+tations of quantum operators and measurements. These
+tools and representations are useful for generating a
+quantum circuit. The user needs to provide a quantum
+function, the number of qubits, and the parameters or the
+shape of the parameters (in this case, random parame-
+ters will be generated and used) to construct a quantum
+circuit.
+A quantum function is defined as a normal Python
+function. It accepts classical input parameters and uses
+their elements for quantum gate parameters. The user
+needs to put quantum operations inside the quantum
+function in the order that matches how they are applied.
+A keyword argument ”qubit”, which is a list of integers,
+need to be specified to denote which qubit each quantum
+operation applies on. After all the quantum operations,
+a single or a list of measurements must be placed as part
+of the return statement. Code Listing 1 shows a simple
+example of defining a quantum function and constructing
+a quantum circuit from it.
+1
+import
+tedq
+2
+3 # Define
+quantum
+circuit
+4 def
+circuitDef (params):
+5
+tedq.RX(params [0],
+qubits =[0])
+6
+tedq.RY(params [1],
+qubits =[1])
+7
+tedq.CNOT(qubits =[0, 1])
+8
+return [tedq.expval(tedq.PauliZ(qubits =[0]))
+9
+tedq.expval(tedq.PauliZ(qubits =[1]))]
+10
+11
+number_of_qubits = 2
+12
+parameter_shapes = [(2 ,)]
+13
+14 # Quantum
+circuit
+construction
+15
+circuit = tedq.Circuit(circuitDef , number_of_qubits ,
+parameter_shapes = parameter_shapes )
+Code Listing 1: How to construct a quantum circuit.
+Line 4-9 define a quantum circuit function while line 15
+constructs a TeD-Q quantum circuit object.
+The quantum circuit is not yet executable since the
+computation mode and backend have not been chosen.
+After specifying these, it can be compiled into an exe-
+
+QInterpreter
+Quantum function
+Tools
+Circuit
+Gates
+Observables
+Visualization
+QNN
+Measurements
+Template
+circuit to
+execute
+Backends
+Hardware
+Optimizer
+Simulator
+Training
+Tensor network
+State vector
+1/O
+JDTensorPath
+Interface
+Input/output data3
+cutable compiled circuit.
+The compiled circuit can be
+used like a standard Python function to compute the re-
+sult. The order of input parameters must be the same as
+the order of the corresponding quantum gates. A quan-
+tum circuit can be run on different backends by manu-
+ally compiling it with different specifications, as shown
+in Code Listing 2.
+This is why it is called a reusable
+quantum circuit.
+1 # compile
+quantum
+circuit
+with "jax" backend
+2
+compileCir1 = circuit. compilecircuit (backend="jax")
+3
+4 # compile
+quantum
+circuit
+with "pytorch" backend
+5
+compileCir2 = circuit. compilecircuit (backend="pytorch")
+Code Listing 2: Compile quantum circuit with different
+backends.
+III.
+SIMULATION MODES
+A.
+State vector propagation mode
+In quantum theory, the wave function is used as a
+mathematical description of the quantum state of a sys-
+tem. A state vector is denoted by a complex ket vector
+|ψ⟩. In this mode, quantum gates act on the state vector
+as a sequence of matrix operators, so that the resulting
+state after each operation is:
+|ψ⟩ = U|ψ0⟩,
+(1)
+where U is the matrix operator. The state vector prop-
+agation mode is the default simulation backend of TeD-
+Q. A user-defined initial quantum state can be used by
+putting tedq.InitStateVector() as the first line of the
+quantum circuit definition function as shown in Code
+Listing 3. Notice that the length of the initial state vec-
+tor must match 2n, where n is the number of qubits. If no
+initial state is specified, TeD-Q will set it to the ground
+state |0⟩⊗n by default. With TeD-Q, this mode allows a
+normal laptop to deal with a non-trival quantum circuit
+of up to 20 qubits.
+1 # Prepare
+quantum
+state
+vector
+2
+init_state = np.array ([1./ np.sqrt (2.) , 1./np.sqrt (2.) ])
+3
+4 # Define
+the
+quantum
+circuit
+with a specific
+initial
+quantum
+state
+5 def
+circuitDef(parameters):
+6
+tedq. InitStateVector (init_state)
+7
+# other
+circuit
+definition
+Code Listing 3: Define quantum circuit with user-defined
+initial quantum state.
+B.
+Tensor network contraction mode
+In the state vector propagation mode, the number
+of amplitudes grows exponentially with the number of
+qubits, 2n complex numbers are needed to describe the
+quantum state for an n-qubit system [20]. Therefor, it is
+extremely difficult for classical state vector-based simu-
+lator to handle NISQ devices with more than 50 qubits.
+TeD-Q integrates the tensor network contraction method
+and mainstream deep learning frameworks – PyTorch and
+JAX, providing an efficient built-in tensor network-based
+quantum simulator. This mode can easily simulate cer-
+tain quantum circuits of 50 ∼ 100 qubits on a single CPU
+or GPU.
+The workflow of the tensor contraction mode in TeD-
+Q consists of the following steps: (a) manipulating the
+quantum circuit according to its output type and con-
+verting it into a tensor network by the built-in Tensor-
+Network module; (b) applying structural simplification
+on the tensor network; (c) searching for best contraction
+sequences for the simplified tensor network; (d) slicing
+the contractions down to memory limit; (e) carrying out
+the actual contraction with the backend library accord-
+ing to sliced contraction sequences. The computational
+complexity of steps (a) and (b) are very low, which can be
+done by a single CPU thread. Step (b) is optional, how-
+ever, it will generally reduce the size of the tensor network
+significantly.
+Except for the default trivial pathfinder,
+two cutting-edge hyper-graph partition-based packages
+– CoTenGra[21] & JDtensorPath can also be chosen for
+step (c). JDtensorPath was originally a built-in module
+in TeD-Q and was separated into an independent soft-
+ware for better code structure management. It perfectly
+matches TeD-Q’s design paradigm and will be introduced
+in the Section III B 2. Step (d) can also be carried out
+with CoTenGra or JDtensorPath libraries. This is also
+an optional step and will cost some extra overhead of
+the total contraction floating point operations (FLOPs).
+In JDtensorPath, step (c) and (d) are done parallelly in
+CPUs. The path found in step (c) or (d) can be re-used in
+step (e) to obtain the result of the same quantum circuit
+but with different input parameters. Step (e) is the most
+time-consuming part, which will be executed repeatedly
+in the machine learning training loop. Step (e) can be
+run on a single CPU, single GPU, or a cluster of GPUs.
+1.
+Tensor network and simplification
+A quantum circuit can be simulated in various ways,
+of which tensor network method is increasingly popular
+recently years. TeD-Q can represent a quantum circuit
+with the corresponding graphical tensor network. Both
+the quantum state and any quantum gate can be rep-
+resented as tensors while the tensor network preserves
+the topological structure of them. The resulting graph
+G = (V, E) thus contains vertexes associated with the
+tensors, while the edges are labeled by their indices. The
+rank of a tensor is given by the number of edges connect-
+ing to it. Since a single qubit lives in a 2D Hilbert space,
+meaning each index takes value from {0, 1}, a rank-k ten-
+sor will require O(2k) storage space.
+To calculate the
+probability of finding certain final state |φout⟩ from the
+output of the quantum circuit U |φin⟩, i.e. ⟨φin| U |φout⟩,
+
+4
+the tensor network needs to be contracted, meaning
+shared indices between vertices will be summed up; while
+open edges remains. Fig. 2 gives an example of a trivial
+two qubits quantum circuit and its graphical tensor net-
+work representation in TeD-Q. Each vertex in the tensor
+network is associated with a tensor representing either
+the quantum state or one quantum gate. Aa and Bb are
+tensors corresponding to state |0⟩s of the two qubits while
+Cca and Ddb are representing single qubit Pauli X and
+rotational Ry quantum gates respectively; the two qubits
+CNOT gate corresponds to Eefcd and the measurement
+in the z direction is presented by Fgf. Since the expecta-
+tion value is derived by ⟨I⊗Z⟩ = ⟨00|U †(θ)I⊗ZU(θ)|00⟩,
+to calculate it with tensor network, we must append the
+tensor network corresponding to the complex conjugate
+of the original quantum circuit, which is ⟨00| U †(θ). The
+Ry(θ) gate could then be represented by Ddb which in
+tensor form will be:
+Ddb =
+�
+cos(θ/2) − sin(θ/2)
+sin(θ/2)
+cos(θ/2)
+�
+;
+(2)
+while the tensor form of the CNOT gate is:
+E00cd =
+�
+1 0
+0 1
+�
+, E11cd =
+�
+0 1
+1 0
+�
+,
+E01cd = E10cd =
+�
+0 0
+0 0
+�
+.
+(3)
+FIG. 2: A quantum circuit and its graphical tensor
+network representation in TeD-Q. (a) A two qubits
+quantum circuit with expectation value measurement
+on second qubit. (b) The corresponding graphical
+tensor network representation, each vertex is associated
+with a tensor given by quantum state or operator (gate,
+state or observable).
+Thus, the expectation value can be calculated by the
+summation:
+T =
+�
+a,...,k
+AaBbCcaDdbEefcdFgfE∗
+hiegC∗
+jhD∗
+kiA∗
+jB∗
+k
+= sin2(θ/2) − cos2(θ/2),
+which can be verified with the traditional vector mode
+calculation. It is shown that the actual order of carry-
+ing these summation (for instance, whether to sum a or k
+first) does matter a lot and finding a good contraction or-
+der composes most part of the tensor network algorithm.
+TeD-Q supports an efficient local processing of the ten-
+sor network prior to the searching of the contraction or-
+der by a set of simplifications based on its structure and
+sparsity of the tensors. The simplifications include ten-
+sor shape squeezing, diagonal and anti-diagonal reduc-
+tion, and rank simplification, which are designed to de-
+crease the complexity and the rank of the tensor [21].
+After the local pre-procession, the tensor network will be
+transferred from a line graph into a hyper-graph (a gen-
+eralization of the graph that allows an edge connecting
+any number of vertices).
+An illustration of the tensor network and its hyper-
+graph representation is shown in Fig. 3 (a). Notice that
+the red hyper-edge (corresponding to index c) is con-
+nected with three vertices (tensors). The original tensor
+network is defined as:
+Tde :=
+�
+a,c,b,f
+AacBabfCbceDcdEef,
+(4)
+where the upper-case and lower-case letters denote ten-
+sors and its indices respectively.
+FIG. 3: An illustration of tensor network and its
+hypergraph representation, binary contraction tree, and
+index slicing. (a) An example of a tensor network and
+its hypergraph representation, edge c is a hyper-edge
+connecting three vertices. Dashed lines represent open
+edges while solid lines correspond to closed edges. (b) A
+binary contraction tree, each node represents a pairwise
+contraction of two tensors as well as a bi-partitioning of
+its hyper-graph. The upward edges indicate the indices
+of the intermediate tensor. (c) Slicing the green edge
+(index a), generating simpler tensor networks with the
+same structure labeled by all possible values of a. Each
+individual contraction is to be carried out independently
+and the summed of them gives the final result.
+
+(a)
+<0ol
+X
+<ol
+Z
+(b)
+e
+h
+E
+Et
+BH
+DtBt(a)
+a
+B
+AacBabfCbceDcdEef
+C
+a,c,b,f
+E
+(b)
+[de}
+C
+[ace}
+[acd)
+C
+(abe)
+d
+D
+E
+B5
+2.
+hyper-graph-based tensor contraction path optimizer
+The time and memory complexity of tensor network
+contraction depend on its tensor ranks and contraction
+order. Despite finding optimal contraction sequences is
+theoretically a non-deterministic polynomial-time (NP)-
+hard task for general cases, efficient heuristic algo-
+rithms [22] exist in practice for obtaining ’good enough’
+sequences. Several established algorithms are supported
+by TeD-Q from third party libraries, including brute-
+force search, branching strategy, greedy and random-
+greedy path, dynamic programming approach, line-graph
+tree decomposition via QuickBB or FlowCutter, commu-
+nity detection, Boltzmann-greedy agglomerative contrac-
+tion trees, and hypergraph partitioning method [21, 23].
+The default basic pathfinder of TeD-Q supports the first
+four methods.
+For better performance, we adopt the
+hyper-graph partitioning method which is original pro-
+posed in CoTenGra and develop our own hypergraph
+based pathfinder library – JDtensorPath.
+The key idea of this algorithm is to recursively divide
+the hypergraph of a given tensor network, and explicitly
+build an incomplete binary contraction tree in a ’top-
+down’ fashion as shown in Fig. 3b. The root node of the
+tree corresponds to the initial whole graph of the tensor
+network and the effective tensor of the final result. Bi-
+partitioning the hypergraph of the parent node will create
+two child nodes that represent the effective intermediate
+tensors. The contraction tree can be generated in this re-
+cursively divisive manner. The contraction sequences are
+obtained by ascending the tree from the bottom up, and
+combining two child nodes to a parent node corresponds
+to a pair contraction of two intermediate tensors.
+The FLOPs for an individual contraction (node bi-
+partitioning) is given by:
+FLOPs = p ∗ (2 ∗ q − 1),
+(5)
+where p is the product of the dimensions of the outer in-
+dices (indices that are not contracted) and q is that of the
+contracted indices (which equals to 1 if no index is con-
+tracted). For each node bi-partitioning, p is fixed; there-
+fore, the cost of the corresponding pairwise contraction
+can be minimized by minimizing the sum of the weighted
+edges (indices) cut by the partition. This method is like a
+greedy approach from top to down since it only considers
+the cost of every single contraction. Furthermore, JDten-
+sorPath not only requires partitioning of the current node
+to be optimal, but also takes the partitioning of its child
+nodes into consideration, so that the overall tree size and
+total contraction FLOPs could be minimized.
+Specifi-
+cally, it is required that the outer indices of the parent
+node must be distributed as evenly as possible on two
+child nodes. This requirement can reduce p in the parti-
+tioning of the child nodes and thus affects the FLOPs of
+their contractions. The memory usage of a pairwise con-
+traction is given by the sum of the sizes of all the related
+tensors. Since the parent node tensor of each contraction
+is fixed, evenly distributing its indices on children node
+tensors can also reduce the memory usage. This is due
+to the fact that, supposing p is fixed and defining m, n
+to be the product of the dimensions of remaining indices
+of children node tensors respectively during contraction,
+the memory cost of the contraction m ∗ q + n ∗ q will be
+minimized when m = n given m ∗ n = p.
+Advanced multilevel hypergraph partitioning frame-
+work KaHyPar[24, 25] is employed to construct the con-
+traction tree, modern parallel and distributed Python
+package–Ray is used to generating multiple trials in par-
+allel. JDtensorPath can provide high-quality contraction
+sequences to TeD-Q and enables tensor network contrac-
+tion mode to achieve orders of magnitude speedup for
+various quantum circuits simulation.
+3.
+Slicing
+Slicing is an optional step. It is designed to solve the
+memory limit problem and provides an efficient way for
+parallel computing[26]. Even with an excellent contrac-
+tion path, contraction of a large tensor network is still
+limited by its intrinsic memory complexity. In addition,
+the elaborated data dependency between the tensors be-
+comes a bottleneck for contraction with multiple com-
+putational units since it needs a lot of inter-processor
+communication. Slicing the indices can split the original
+tensor network into multiple tensor networks with iden-
+tical structures (same hypergraph), each with a memory
+cost small enough to fit into a single processing unit. The
+simulator can execute these sub-tasks in parallel without
+dependencies or sequentially depending on the computa-
+tional resources. The value of the original tensor network
+is given by summing up the partial results obtained from
+the contractions of each sub-tasks, in which the assign-
+ment of the selected sliced indices is fixed[27]. Take Fig. 3
+as an example, after slicing, the original tensor network
+can be further represented as:
+Tde :=
+�
+i=a
+(
+�
+c,b,f
+A(i)
+c B(i)
+bf CbceDcdEef).
+(6)
+Finding the optimal subset of indices to slice is also an
+NP-hard task with complexity O(mn), where m and n are
+the number of all and sliced indices, respectively. The
+strategy here is to use a heuristically greedy algorithm
+described as the following:
+(a) find out all intermediate tensors that are larger than
+the target size;
+(b) pick up one index shared by the largest tensors or
+appears most frequently among step (a) tensors random;
+(c) repeat the above steps until the contraction width is
+low enough.
+Finding slicing indices is strongly entangled with
+searching for the best contraction path. Slicing is based
+on an existing contraction path, but the optimal path
+for the original tensor network is not guaranteed to be
+suitable for slicing. Therefore, JDtensorPath proposes a
+two-phase indices-slicing-incorporated contraction path
+
+6
+finding heuristic. The first phase generates contraction
+tree trials followed by 128 pseudo-slicing trials, which
+only calculate the FLOPs without actually slicing indices
+on contraction trees. In the second phase, apply “real”
+slicing trials (default is 1024 times) on the contraction
+tree with the lowest FLOPs after pseudo-slicing. Then,
+the simulator can obtain a “good enough” slicing indices
+and contraction path for sub-tasks in a reasonable search-
+ing time. The implementation of the slicing heuristic is
+based on set operations, and the simulator will store only
+the best-sliced contraction tree. By doing so, it becomes
+a very efficient and memory-saving algorithm. Besides,
+this slicing subroutine can also be carried out in parallel
+in the CPU computation using the Ray framework.
+4.
+Users API
+TeD-Q enables users to customize their control of the
+tensor network contraction process. Code Listing 4 shows
+an example of compiling a quantum circuit with tensor
+network contraction mode using JDtensorPath.
+1 def
+circuitDef(parameters):
+2
+# Circuit
+definition
+3 # parse
+and
+construct
+the
+circuit
+4
+circuit = tedq.circuit(circuitDef , n_qubits , parameters
+)
+5 # compile
+the
+quantum
+with
+tensor
+network
+contraction
+mode by using
+JDtensorPath
+6 from
+jdtensorpath
+import
+JDOptTN
+as
+jdopttn
+7
+slicing_opts = {’target_size ’:2**28 ,
+8
+’repeats ’:512 ,
+9
+’target_num_slices ’:None ,
+10
+’contract_parallel ’:True}
+11
+12
+hyper_opts = {’max_time ’:120 ,
+13
+’max_repeats ’:128 ,
+14
+’search_parallel ’:8,
+15
+’slicing_opts ’: slicing_opts }
+16
+17
+compileCir = circuit. compilecircuit (
+18
+backend = "pytorch",
+19
+use_jdopttn = jdopttn ,
+20
+hyper_opt = hyper_opts ,
+21
+tn_simplify = False)
+Code Listing 4: How to use tensor network contraction
+mode.
+To enable the tensor contraction mode, user needs to
+specify the options for slicing and hypergraph-based op-
+timizer, shown as “slicing opts” and “hyper opts”, and
+pass these options and a contraction path optimizer,
+shown as “jdopttn”, into the circuit compiler. The com-
+piled circuit would be constructed in tensor contraction
+mode. The detailed description of each option and ar-
+gument can be found in the github repository and the
+documentation of TeD-Q.
+IV.
+VARIATIONAL QUANTUM CIRCUIT
+Optimization is an important common factor of most
+NISQ algorithms, including quantum machine learning
+and quantum chemistry simulation.
+It relies on a hy-
+brid quantum-classical optimization process on the pa-
+rameterized quantum circuit, or the so-called variational
+quantum circuit (VQC). For instance, quantum neural
+network (QNN) can be regarded as a VQC. In quantum
+machine learning tasks, a VQC could work as a com-
+ponent together with some pre- and post-processing like
+feature extraction and prediction.
+Typically, the cost
+function of a task can be taken as the expectation value
+of a VQC:
+f(x; θ) = ⟨ ˆO⟩ = ⟨0|U †(x; θ) ˆOU(x; θ)|0⟩.
+(7)
+The optimization process relies on the gradient of the cir-
+cuit output with respect to the parameters of the quan-
+tum gates.
+The parameter shift and finite differential
+methods are the common methods to obtain gradients
+of a quantum circuit for both quantum hardware and
+simulation, which are the built-in methods of TeD-Q.
+However, the simulation with such methods usually takes
+a very long time due to the computational complexity.
+Meanwhile, the demand for fast simulation of circuits
+with large number of qubits has become urgent due to
+recent development of large-scale quantum devices. To
+this end, TeD-Q provides an efficient method to com-
+pute the gradient of a circuit in the simulation via the
+conventional backpropagation technique and the newly-
+developed tensor-network engine of TeD-Q.
+A.
+Backpropagation method
+The backpropagation method in TeD-Q is based on the
+well-developed automatic differentiation libraries, such
+as PyTorch[28] and JAX[29], which have been widely
+used in classical machine learning.
+These libraries are
+integrated into TeD-Q as simulation backends.
+When
+the backend is specified, TeD-Q will convert the matrix
+data of the quantum circuit to the corresponding format.
+While evaluating the quantum circuit, known as the ”for-
+ward” computation, the backend will store all of the in-
+termediate results. The backend will use the chain rule
+to obtain the gradient of the gate parameters from the
+circuit output, known as backpropagation. This function
+will store the gradient of each intermediate result so that
+the gradient of all of the parameters can be evaluated at
+one time. Although the backpropagation method cannot
+be applied to real quantum devices, this is the fastest
+method to obtain the gradient in quantum simulations.
+Thus, this is the default method for the simulation back-
+ends.
+1 def
+circuitDef ( parameters):
+2
+# Circuit
+definition
+3 # parse
+and
+compile
+the
+circuit
+4 cir = tedq.circuit(circuitDef , n_qubits , parameters )
+5
+myCompileCir = cir. compilecircuit (
+6
+backend="pytorch")
+Code Listing 5: How to use backpropagation method to
+get the gradient of parameters.
+
+7
+B.
+Parameter shift and finite differential method
+In real quantum devices, the gradients of the variables
+can only be obtained by the parameter shift method or
+finite differential method. The parameter shift method
+can provide the analytical derivatives, while the finite-
+differential method provides only numerical derivatives.
+In TeD-Q, we implement the parameter shift method
+based on the theoretical paper [30, 31] and recent devel-
+opments by [32]. This method can be applied to quantum
+gates with the form eiµH, where H is a Hermitian opera-
+tor with two or four eigenvalues, and µ is the parameter
+of the gate. For a single gate parameter, the analytical
+derivative can be calculated by evaluating the expecta-
+tion value of the circuit twice with the parameter value
+being µ + s and µ − s[30], as shown in Equation 8, where
+s is the shift and k is the shift constant. TeD-Q’s back-
+end will shift the parameters automatically with proper
+spacing for each gate. For the simulation backend, like
+PyTorch or JAX, the user can use the parameter shift
+method to obtain the gradient by specifying it in the dif-
+ferential option while compiling the circuit, as shown in
+Code Listing 6. For the hardware backend, the param-
+eter shift is the default and only method to obtain the
+gradient.
+∂f
+∂µ =
+�
+�
+�
+k[f(µ + s) − f(µ − s)]
+parameter shift
+f(µ+∆µ)−f(µ)
+∆µ
+finite differential
+(8)
+1 def
+circuitDef(parameters):
+2
+# Circuit
+definition
+3 # parse
+and
+compile
+the
+circuit
+4 cir = tedq.circuit(circuitDef , n_qubits , parameters )
+5
+compileCir = cir. compilecircuit (
+6
+backend="pytorch",
+7
+diff_method = " param_shift ")
+Code Listing 6: How to use parameter shift method to
+get the gradient of parameters.
+C.
+Quantum to classical computing interface
+The design paradigm of TeD-Q provides seamless inte-
+gration of quantum and classical processing. In this hy-
+brid algorithm, a quantum circuit that is parameterized
+by tunable variables is seen as a normal Python function
+with a specific interface. It can be inserted into a classical
+optimization function or wrapped in a layer of a machine
+learning framework module.
+TeD-Q supports two interfaces – JAX array and Py-
+Torch tensor. For the JAX simulation backend, the JAX
+array is the default one, but the PyTorch tensor inter-
+face can also be used via the interface keyword argument
+(interface=”pytorch”) while compiling the quantum cir-
+cuit. As for the PyTorch simulation backend and hard-
+ware backend, TeD-Q only supports the PyTorch back-
+end at the time of writing.
+The interfaces provide a
+seamless connection to the classical part in ”forward”
+calculation and in ”backward” gradient extraction. For
+simulation backends with their own interface and de-
+fault backpropagation gradient method, the integration
+is straightforward, relying on built-in data structure and
+automatic differentiation algorithm of JAX or PyTorch.
+For other cases (JAX backend with PyTorch tensor in-
+terface, hardware backend, parameter shift method), the
+classical backpropagation algorithm cannot process the
+quantum information inside the quantum circuit.
+For
+this situation, the quantum circuit is treated as a black
+box. TeD-Q implements custom autograd functions and
+will compute and provide the gradient (one output) or
+Jacobian (multiple inputs and multiple outputs) of the
+quantum circuit with respect to its classical inputs and
+variables. Code Listing 7 shows an example of connecting
+the JAX backend quantum circuit to the classical calcu-
+lation by the PyTorch tensor interface.
+More detailed
+examples can refer to Section V A 3. The integration is
+imperceptible to the user, via JAX or PyTorch, with the
+flexibility to run the hybrid quantum-classical algorithms
+code on CPUs, GPUs, and TPUs.
+1 # Quantum
+circuit
+construction
+2
+# Neglect
+here
+3
+4 # Compile
+quantum
+circuit
+with
+JAX
+quantum
+simulation
+backend
+and
+PyTorch
+interface
+5
+compileCirJAX = circuit. compilecircuit (
+6
+backend="jax",
+7
+interface="pytorch")
+8
+9 # Connect
+quantum
+systems
+to
+classical
+cost
+function
+by
+PyTorch
+interface
+10 def
+cost(weight , params):
+11
+return
+weight * compileCirJAX (params)
+12
+13 # PyTorch
+tensor is used as input
+14
+weight = torch.tensor (0.5)
+15
+params = torch.tensor ([0.12])
+16 cost(weight , params)
+Code
+Listing
+7:
+Quantum
+to
+classical
+computing
+interface.
+A quantum circuit is compiled into an
+executable quantum object by using JAX simulation
+backend and PyTorch tensor interface. The executable
+quantum circuit is then integrated with classical cost
+function.
+V.
+USE CASE
+The detailed introduction and manual of the user in-
+terface can be found in the online documentation. It in-
+cludes step-by-step examples demonstrating the feature
+of Ted-Q. In the following section, We briefly go through
+the main features and its use cases.
+A.
+Basic quantum circuits
+Quantum circuit evaluation is the basic function of
+TeD-Q. It provides a universal set of quantum gates so
+
+8
+all kinds of quantum circuits can be constructed and sim-
+ulated. With the tensor network engine described in Sec-
+tion III B, TeD-Q can process the simulation faster than
+the conventional quantum simulators. Besides, TeD-Q is
+equipped with an easy-to-use graphical circuit composer
+and circuit drawer. These tools are well integrated with
+TeD-Q’s simulator. Users can use it for quick prototyping
+of the quantum circuit. Moreover, the hardware backend
+in Ted-Q provides an interface to the real quantum de-
+vices like Qiskit[5]. Users Can switch the simulation to a
+real experiment with a simple command. The following
+sections demonstrate these features via TeD-Q API.
+1.
+Fast simulation
+Consider a simple two-qubit quantum circuit with a
+Hadamard gate on qubit 0, a CNOT gate on qubits 0
+and 1, and a rotation gate Rot on qubit 1 apply to the ini-
+tial zero state. And we want to obtain its quantum state
+with some input rotation angles. TeD-Q can implement
+the simulation as code block 8. Qubits are counted from
+0 and multiqubit registers labeled with the first (zeroth)
+qubit on the left. Measurement of a quantum state is only
+available by the simulation backend, while both simula-
+tion and hardware backend enables expectation values
+and probability measurements. Keyword argument “re-
+quires grad” can disable the gradient feature and improve
+the simulation speed since the backend doesn’t need to
+store the intermediate state for backpropagation.
+1
+import
+tedq
+2
+import
+torch
+3
+n_qubits =2
+4
+5 # Circuit
+definition
+6 def
+circuitDef(phi , theta , omega):
+7
+tedq.Hadamard(qubits =[0])
+8
+tedq.CNOT(qubits =[0, 1])
+9
+tedq.Rot(phi , theta , omega , qubits =[1])
+10
+# Return
+quantum
+state
+11
+return
+tedq. measurement.state ()
+12
+13 phi = torch.tensor ([0.4])
+14
+theta = torch.tensor ([0.5])
+15
+omega = torch.tensor ([0.6])
+16
+circuit = tedq.Circuit(circuitDef , n_qubits , phi , theta
+, omega)
+17 # Parse
+and
+compile
+the
+circuit
+18
+compileCir = circuit. compilecircuit (backend="pytorch",
+requires_grad =False)
+19
+20 # Obtain
+the
+quantum
+state
+21
+quantum_state = compileCir ()
+Code Listing 8:
+An example of a simple two-qubits
+quantum circuit.
+Hadamard and CNOT gates are
+used to generate a entangled state, Rot gate is used for
+adding some rotation angle and the final quantum state
+is measured at the end.
+2.
+Intuitive prototyping
+Circuit composer in TeD-Q is a WYSIWYG (what you
+see is what you get) editor for a quantum circuit. The
+graphical composer can be initialized with a single line
+command, as shown in Code Listing 9.
+It consists of
+a panel for the template quantum gates and the several
+qubits indicated by lines, as shown in Figure 4. Users can
+construct the circuit by dragging the icon of the quantum
+gate to a specific qubit line or remove one quantum gate
+by dragging it away from the qubit line. Users can also
+adjust the sequence of the operations by pulling the icons
+to the desired location.
+1 # Enable
+circuit
+composer
+2
+composer = tedq. circuit_composer (4, figsize =(11 ,5))
+Code Listing 9: Usage of circuit composer
+FIG. 4: Circuit composer
+The composing result can be converted and fed into
+TeD-Q’s tensor network engine. The user can obtain the
+simulation result using the same method mentioned in
+the previous section, as shown in the Code Listing 10.
+Users can also get the circuit definition from the com-
+posing result for further development with TeD-Q API.
+1 # Convert
+to
+circuit
+class
+2
+circuit = composer.toCircuit ()
+3
+compiledCircuit = circuit. compilecircuit ()
+4
+5 # Evaluating
+the
+circuit
+6 prob = compiledCircuit ()
+7
+8 # Print
+the
+circuit
+definition
+9
+print(circuit)
+Code Listing 10: Converting the composing result to a
+TeD-Q circuit and obtaining the circuit definition
+Besides the circuit composer, the circuit initialized by
+the script can also be visualized with the circuit drawer,
+as shown in the Code Listing 11.
+It follows the same
+drawing style as the circuit composer.
+Moreover, the
+function will automatically fit the circuit to the correct
+size of the plot.
+1 # Init a circuit
+2
+circuit = tedq.circuit(circuitDef ())
+3 # Draw a circuit
+4 tedq. draw_circuit (circuit)
+Code Listing 11: Usage of circuit drawer
+3.
+Hardware compatibility
+Aside from simulation, the circuit can also be adopted
+to real quantum devices with the hardware backend. At
+the time of writing, TeD-Q only supports IBM-Q quan-
+tum devices, and more quantum hardware devices will be
+
+Del
+X
+Z
+S
+H
+RX
+Y
+RZ
+CNOT
+x9
+available soon. The built-in parameter shift method is re-
+sponsible for obtaining gradients of the quantum circuit,
+and the PyTorch tensor interface is provided for com-
+munication with other functions. Code Listing 12 shows
+an example of compiling a quantum circuit into two exe-
+cutable quantum objects with both simulation and hard-
+ware backends and tries to minimize their difference by
+tuning input parameters with a built-in gradient-descent
+optimizer.
+1 # Quantum
+circuit
+construction
+2
+# Neglect
+here
+3
+4 # Compile
+quantum
+circuit
+with
+hardware
+backend ,
+default
+PyTorch
+interface
+5 from
+qiskit
+import
+IBMQ
+6 IBMQ. enable_account (’your
+IBMQ
+token ’)
+7
+compileCirHardware = circuit. compilecircuit (backend="
+IBMQ_hardware ")
+8
+9 # Compile
+quantum
+circuit
+with
+JAX
+quantum
+simulation
+backend
+and
+PyTorch
+interface
+10
+compileCirJAX = circuit. compilecircuit (backend="jax",
+interface="pytorch")
+11
+12 # Connect
+two
+quantum
+systems
+to
+classical
+cost
+function
+by
+PyTorch
+interface
+13 def
+cost(params):
+14
+results = ( compileCirHardware (params) -
+compileCirJAX (params))**2
+15
+return
+results
+16
+17 # Tuning
+variables
+with built -in
+optimizer
+18
+Optimizer = tedq. GradientDescentOptimizer (
+19
+objective_fn =cost ,
+20
+trainable_params =[0, 1],
+21
+interface="pytorch")
+22
+params = (torch.tensor ([0.12] ,
+requires_grad =True),
+23
+torch.tensor ([0.75] ,
+requires_grad =True))
+24
+new_variables = Optimizer.step (* params)
+Code Listing 12: Hardware compatibility example.
+A
+quantum circuit is compiled into two executable quantum
+objects with JAX simulation backend and hardware
+backend.
+And these two executable quantum circuit
+are connected to classical cost function with PyTorch
+interface.
+B.
+Variational quantum algorithm
+A variation quantum algorithm consists of a variational
+quantum circuit and a classical optimizer. The method
+to obtain the gradient of a gate parameter in a quantum
+circuit is described in Section IV. Recursively updating
+the gate parameters allows the circuit to be optimized
+according to a certain cost function. It’s widely used in
+current NISQ devices and quantum simulations. With
+TeD-Q’s tensor engine, simulation can be processed at a
+very high speed compared to other simulation packages.
+Besides, with the hardware backend, the variational al-
+gorithm can also be adapted to a real quantum device.
+The following example shows a simple circuit based on
+the variational quantum algorithm to demonstrate how
+to construct a VQA circuit by TeD-Q API.
+1
+import
+tedq
+2
+import
+torch
+3
+n_qubits =3
+4
+5 # Circuit
+definition
+6 def
+circuitDef (theta):
+7
+# Circuit
+8
+tedq.RX(theta [0], qubits =[0])
+9
+tedq.RY(theta [1], qubits =[1])
+10
+tedq.RZ(theta [2], qubits =[2])
+11
+12
+tedq.CNOT(qubits =[0, 1])
+13
+tedq.CNOT(qubits =[1, 2])
+14
+tedq.CNOT(qubits =[2, 0])
+15
+16
+# Measurement
+17
+for idx in range(n_qubits):
+18
+tedq. measurement .expval(tedq.PauliZ(qubits =[ idx
+]))
+19
+20 # Parse
+and
+compile
+the
+circuit
+21
+circuit = tedq.Circuit(circuitDef , n_qubits , torch.rand
+(n_qubits))
+22
+my_compilecircuit = circuit. compilecircuit (backend="
+pytorch" )
+23
+24 # Init
+the
+parameters
+by the
+torch
+library
+25
+params = torch.rand(n_qubits , requires_grad =True)
+26
+27 # Forward
+computation
+of the
+expectation
+value
+28
+exp_val = my_compilecircuit (params)
+29
+30 # Define
+the
+loss
+function
+31
+optimizer = torch.optim.Adam ([ params], lr =0.5)
+32 loss = torch.nn.MSELoss(reduction=’mean ’)
+33 l = loss(exp_val , torch.Tensor ([0, 1, 1]))
+34
+35 # Backward
+computation
+for the
+gradient
+of the
+parameters
+36 l.backward ()
+37
+38 # Output
+the
+result
+39
+print("Expected
+value
+from
+circuit: ", exp_val)
+40
+print("Gradient
+of
+parameters ", params.grad)
+Code Listing 13:
+Example of variational quantum
+algorithm.
+C.
+Quantum machine learning
+Machine learning deals with the problem of generaliza-
+tion from finite data in high-dimensional Hilbert spaces.
+It is a very appealing application for quantum compu-
+tation since both of them involve statistics theories at
+a fundamental level. Users can transform classical fea-
+ture information into the quantum state through encod-
+ing schemes (basis encoding, amplitude encoding, angle
+encoding, etc.):
+|ψ(x)⟩ =
+�
+�
+�
+�
+�
+�
+�
+�
+�
+|ix⟩
+basis encoding
+�n
+i xi|i⟩
+amplitude encoding
+⊗n
+i R(xi)|0n⟩
+angle encoding
+(9)
+VQA can be designed as a linear model to classify data
+explicitly in Hilbert space. With a nice performance of
+TeD-Q’s tensor engine, a more complex VQA circuit can
+be constructed and simulated, which allows testing of a
+large-scale quantum and hybrid quantum-classical ma-
+chine learning algorithm with the simulator.
+
+10
+1.
+Templates
+TeD-Q equips several pre-defined quantum circuit tem-
+plates, or ansatz, commonly used in the quantum ma-
+chine learning field to enable the fast development of
+the circuit for quantum machine learning. The following
+briefly introduces three templates in TeD-Q – Random-
+generated layer, Fully-connected layer, and Hardware-
+efficient layer.
+The randomly-generated layer can provide a circuit
+with a single- and two-qubits gate while their locations
+and parameters are random (Fig. 5). It’s suitable for sim-
+ulating a non-linear transformation, as shown in TeD-Q’s
+Quanvolution Neural Network example.
+FIG. 5: Randomly-generated circuit
+The fully-connected layer is a parameterized circuit
+to provide maximum entanglement among each qubit.
+The number of layers is called depth, which the user
+can customize.
+Each qubit is connected to the other
+qubits in each layer by a CNOT gate followed by a two-
+parameterized rotation gate (Fig. 6). This template is
+usually used to simulate a classical fully-connected layer
+in quantum machine learning.
+FIG. 6: Fully-connected circuit
+The hardware-efficient layer is a practical implemen-
+tation of a fully-connected circuit. In the real quantum
+device, a two-qubit operation is only efficient between the
+qubit nearby the qubit. Therefore, the CNOT gates in
+this template are only placed between the qubits nearby
+a selected qubit (Fig. 7).
+2.
+Quantum layer wrapping
+Users can easily exploit quantum machine learning by
+replacing some layers of a well-developed classical ma-
+chine learning model with a wrapped quantum layer.
+FIG. 7: Hardware efficient circuit
+Code Listing 14 illustrates how to build the pipeline in
+TeD-Q.
+1 # Global
+variable
+2
+n_qubits = 8
+# Number of
+qubits
+3
+q_depth = 12
+# Number
+of
+variational
+layers
+4
+n_classes = 10
+# Number of image
+classes
+5
+6 # Angle
+encoding
+7 def
+features_encoding (nqubits , w):
+8
+for idx in range(nqubits):
+9
+tedq.Hadamard(qubits =[ idx ])
+10
+for idx , element
+in
+enumerate(w):
+11
+tedq.RX(element , qubits =[ idx ])
+12
+13 # Define a variational
+quantum
+circuit
+14 def
+circuitDef (q_input_features , q_weights_flat ):
+15
+# Reshape
+weights
+16
+q_weights = q_weights_flat .reshape (( q_depth +1)*2,
+n_qubits)
+17
+18
+# Encode
+classical
+features
+into
+quantum
+state
+19
+features_encoding (n_qubits , q_input_features )
+20
+21
+# Built -in
+template
+circuit
+22
+tedq.templates. HardwareEfficient (n_qubits , q_depth ,
+q_weights)
+23
+24
+# Expectation
+values
+measurement
+25
+exp_vals = [tedq.expval(tedq.PauliZ(qubits =[
+position ])) for
+position
+in range(n_qubits)]
+26
+return
+tuple(exp_vals)
+27
+28 # Quantum
+circuit
+construction
+29
+circuit = tedq.Circuit(circuitDef , n_qubits , torch.
+zeros(n_qubits), torch.zeros (( q_depth +1)*2,
+n_qubits))
+30
+compiledCircuit = circuit. compilecircuit (backend="
+pytorch")
+31
+32 # Quantum
+layer
+with
+PyTorch
+NN
+interface
+33
+class
+DressedQuantumNet (nn.Module):
+34
+def
+__init__(self):
+35
+super ().__init__ ()
+36
+self.pre_net = nn.Linear (2048 ,
+n_qubits)
+37
+self.q_params = nn.Parameter(q_delta * torch.
+randn (( q_depth +1) * n_qubits *2))
+38
+self.post_net = nn.Linear(n_qubits , n_classes)
+39
+def
+q_func( q_input_features ):
+40
+return
+compiledCircuit (q_input_features ,
+self.q_params)
+41
+from
+functorch
+import
+vmap
+42
+# for
+batch
+executation
+43
+self. batched_q_func = vmap(q_func)
+44
+45
+# Tensors
+moves
+through
+quantum
+circuit
+46
+def
+forward(self , input_features ):
+47
+pre_out = self.pre_net( input_features )
+48
+q_in = torch.tanh(pre_out) * np.pi / 2.0
+49
+q_out = self. batched_q_func (q_in).float ()
+50
+return
+self.post_net(q_out)
+51
+52 # Replacing
+classical
+machine
+learning
+model
+ResNet -50
+fully -connected
+layer
+with
+quantum
+layer
+53
+model_hybrid = torchvision .models.resnet50 ()
+
+x
+Rx
+Rz 
+Rx
+RyRy
+Ry
+Rz
+Ry
+Rz
+Ry
+Ry
+Rz
+X
+Ry
+Rz
+Ry
+Ry
+Rz
+X
++
+Ry
+Rz
+Ry
+Ry
+Rz
+X
+X
+Ry
+Rz
+Z
+XRy
+Ry
+Rz
+Ry
+Rz
+Ry
+Ry
+Rz
+X
+Ry
+Rz
+Ry
+Ry
+Rz
+X
+Ry
+Rz
+Ry
+Ry
+Rz
+X
+Ry
+Rz11
+54
+model_hybrid .fc = DressedQuantumNet ()
+Code Listing 14: Code snippet for creating a hybrid-
+quantum-classical machine learning model for image
+recognition.
+The quantum circuit is wrapped into a
+quantum layer and used to replace the fully-connected
+layer of the classical deep learning model ResNet-50. The
+main structure of this example follows the PennyLane
+tutorial on quantum transfer learning[32]
+The above example shows a way of constructing a hy-
+brid quantum-classical machine learning model. TeD-Q
+can straightforwardly integrate quantum algorithms with
+various well-established machine learning practices. The
+quantum circuit model behaves as if it was a pure classi-
+cal one. All the following processes, like cost function or
+optimization, can be seamlessly adopted. In the next ,
+a pure quantum machine learning example is introduced
+and used as a benchmark to compare the performance of
+TeD-Q and other software.
+VI.
+PERFORMANCE
+We benchmark TeD-Q’s performance with other quan-
+tum software through two examples – multiple qubits ro-
+tation (MQR) and many body localization (MBL) [33].
+MQR is a very simple algorithm which uses hardware-
+efficient network to flip the quantum state from all ze-
+ros state |0⟩⊗n to all ones state |1⟩⊗n. It is suitable for
+evaluating TeD-Q’s performance on small and simple cir-
+cuit which can be run on personal computer. MBL is
+a relatively complex problem of great significance both
+theoretically and practically. It is used to demonstrate
+the great advantage of TeD-Q tensor network contraction
+mode. The source code of the comparison can be found
+on TeD-Q’s Github.
+A.
+Multiple qubits rotation
+In this simulation, the initial quantum state is set to be
+all zeros state |0⟩⊗n followed by a variational hardware-
+efficient network and expectation value measurement on
+Pauli-Z basis for each qubit. The learning is done by min-
+imizing sum of the measurements through tuning param-
+eters via gradient descent method. And the performance
+of platforms are evaluated by the time cost for finishing
+500 iterations of training. Since there is a great demand
+for user to develop and learn quantum algorithm through
+simple circuit on their personal computer, the evaluation
+is done with single AMD RyzenT M 5 3500U mobile pro-
+cessor CPU. Fig. 8 shows the advantage of TeD-Q in this
+application.
+FIG. 8: Performance comparison among TeD-Q,
+PennyLane, Paddle Quantum and Qiskit for small
+simple circuit on single laptop CPU. TeD-Q result uses
+the PyTorch backend with backpropagation gradient
+method.
+B.
+VQE of Hydrogen Molecule
+Variational quantum eigensolver (VQE) method is one
+of the popular applications of quantum computing in the
+NISQ era [15].
+It is a concrete example of variational
+quantum algorithm (VQA) used for solving quantum
+chemistry problems, specifically, the eigenstate problem.
+In a VQE algorithm, a parameterized quantum circuit
+would prepare a quantum state, dubbed as the ansatz
+state, which is supposed to be the ground state of the
+Hamiltonian of the molecule. By repeatedly measuring
+the ansatz state with different measurement settings, the
+expectation value of the Hamiltonian could be evaluated.
+An optimization process could be applied to the parame-
+ters of the quantum circuit so that the expectation value
+could be minimized.
+Here we use the VQE of Hydrogen molecule to illus-
+trate the performance of TeD-Q versus other platforms.
+In this experiment, there are totally four qubits and the
+quantum circuit contains 12 freely changing parameters.
+(The problem can in principle be simplified to use just
+one qubit, but we did not do this since we only want to
+compare the speed on the same ground.)
+We run the experiment on a Macbook Air with Intel
+CoreT M i5-1030NG7 CPU. As we could see from Fig. 9,
+TeD-Q converges to an error of 10−6 Hartree about 3
+times faster than Pennylane and around 15 times faster
+than Qiskit. With a limited time of execution, for in-
+stance, within 5 seconds as shown in Fig. 10a, TeD-Q
+can correctly plot the energy curve of the ground state
+with different H-O distances, while Pennylane can almost
+do it and Qiskit being far away from that. When the time
+limit is set to 30 seconds Pennylane can converge to the
+correct energy curve but Qiskit still cannot, as shown
+in Fig. 10b. From this comparison, we can see TeD-Q
+indeed has advantages in simulating traditional VQE al-
+gorithm over the compared platforms.
+
+102
+time (s)
+101
+TeD-Q State Vector Propagation Mode
+PennyLane
+Paddle Quantum
+100
+Qiskit
+2
+4
+6
+8
+10
+Number of qubits12
+FIG. 9: Error between the VQE result and the FCI
+reference energy.
+(a) Execution time limited to 5 seconds.
+(b) Execution time limited to 30 seconds.
+FIG. 10: Energy curve of the Hydrogen atom from VQE
+with limited execution time and FCI methods.
+C.
+Quantum GAN
+Classical generative adversarial network (GAN) has
+found its position in artificial intelligence via rapid grow-
+ing applications recent years [34]. The idea is to utilize a
+generative network to create new data that resembles the
+(a) QGAN patch
+(b) QGAN non-patch
+FIG. 11: Performance comparison between TeD-Q and
+PennyLane for quantum GAN training on single laptop
+CPU. TeD-Q result uses the PyTorch backend with
+backpropagation gradient method.
+original data, while a discriminative network tries to eval-
+uate the distance. The two networks contest with each
+other to play a zero-sum game, which leads to improved
+quality of the newly generated data.
+Quantum GAN borrowed this idea and wishes to boost
+the performance by quantum computing [35, 36]. While
+it is possible to use QNN in both the generative and
+discriminative networks, here, we adopt both the patch
+and non-patch quantum GAN methods where only the
+generative part is made quantum.
+In this example, the generator tries to mimic the hand-
+written zeros from a small set of grayscale samples im-
+ages with size 8 × 8. Please see [36] for details of the
+QGAN example. Similar to the multiple qubits rotation
+example, we run the experiment with an AMD RyzenT M
+5 3500U mobile processor CPU. As we can see from the
+result Fig. 11, in either patch or non-patch scenario, TeD-
+Q outperforms Pennylane in the training of the quantum
+GAN model.
+
+15
+TeD-Q
+Pennylane
+1.0
+Qiskit
+Energy(Hartree) 
+FCI reference energy
+0.5
+0.0
+0.5
+1.0
+0.5
+1.0
+1.5
+2.0
+25
+3.0
+3.5
+Distance(ao)0.75
+TeD-Q
+0.50
+Pennylane
+Qiskit
+nergy(Hartree]
+0.25
+FCI reference energy
+0.00
+0.25
+0.50
+6
+0.75
+1.00
+0.5
+10
+15
+20
+25
+3.0
+3.5
+Distance(ao)1.6
+TeD-Q State Vector Propagation Mode
+PennyLane
+1.4
+1.2
+1.0
+S
+0.8
+0.6
+0.4
+0.2
+0.0
+0
+200
+400
+600
+800
+1000
+1200
+1400
+time (s)1.4
+TeD-Q State Vector Propagation Mode
+PennyLane
+1.2
+1.0
+0.8
+S
+oss
+0.6
+0.4
+0.2
+0.0
+0
+200
+400
+600
+800
+1000
+1200
+1400
+time (s)100
+TeD-Q
+Pennylane
+10~1
+Qiskit
+10~2
+W
+Jau
+E-OT
+10-4
+105
+10~6
+0
+20
+40
+60
+80
+100
+120
+140
+Time(s)13
+D.
+Quantum Architecture Search
+Quantum architecture search (QAS) was recently pro-
+posed to generate better variational ansatz circuits for
+given VQA tasks [37, 38].
+By constructing an ansatz
+pool, QAS iteratively samples a new ansatz at every step
+of the optimization in the VQA. It can be shown that
+by doing this, the resulting ansatz improves the perfor-
+mance of the VQA in terms of both circuit output and
+learnability in learning tasks.
+In the training of the QAS task, the ansatz circuit is
+replaced by new sample from the pool at every step of
+the optimization, which requires the backend to compile
+the new ansatz circuit at every step. Thus, the differ-
+ence of the performance mainly depends on the speed of
+implementing each circuit. We run the experiment on a
+Macbook Air with Intel CoreT M i5-1030NG7 CPU. The
+result in Fig. 12 shows the time the training takes with
+increasing iteration numbers. TeD-Q is more than 2 time
+faster than Pennylane when performing QAS tasks.
+FIG. 12: QAS performance comparison between TeD-Q
+and Pennylane
+E.
+Many body localization
+Many body localization (MBL) is a phase of an iso-
+lated many-body quantum system that prevents it from
+thermalization; that is, a system in this phase can pre-
+serve the initial information as time evolves. It provides
+a possibility to hold the quantum effect for a long time.
+The experimental and theoretical research in this field
+has been dramatically progressing in recent years due to
+the rapid development of quantum technology. In this
+section, we demonstrate that TeD-Q can process a sim-
+ulation of a 1-D MBL along with a quantum neural net-
+work with more than 50 qubits at a reasonable speed,
+which is not achievable by conventional quantum simu-
+lators.
+For an isolated many-body quantum system, it evolves
+under its intrinsic Hamiltonian. The interaction between
+the particles exchanges information and energy so that
+the close system reaches thermal equilibrium as the whole
+system is the thermal bath of its subsystem[39]. The in-
+formation of its initial state is eventually washed out.
+However, in the presence of sufficient disorder poten-
+tial, the system can reach the many-body localization
+phase and prevent it from falling into thermal states even
+though the particles in the system still interact.
+Ergodic state
+Localized state
+FIG. 13: Many body localization. The shade of the
+circles represents probability to be |1⟩ state. The
+system is initially prepared in the Neel state. After the
+evolution under its intrinsic Hamiltonian and a
+controllable disorder potential, the system can fall into
+either ergodic state, as shown in the bottom left, or
+localized state as shown in the bottom right.
+The system would fall into thermalization with a small
+disorder potential, known as the ergodic state. On the
+other hand, with sufficient disorder power, the system
+would be in the MBL phase and stay in its initial state,
+known as the localized state. However, multiple measure-
+ments are required to distinguish a localized state from
+an ergodic state for a many-body system. Following the
+circuit architecture shown in [40], we develop and train
+a quantum neural network for classifying the states of a
+1-D many-body system. With this QNN circuit, we can
+identify whether the circuit is either an ergodic state or
+a localized state with a single measurement on the first
+qubit.
+1.
+Simulation setup
+In our simulation, the qubits are placed in a chain and
+prepared in the Neel state. It is followed by a simulated
+Hamiltonian Hd includes the interactions between the
+nearest qubits and a controllable random disorder di for
+each qubit, which is
+Hd = ℏ
+�
+i,j
+diσi
+z + gi,j(σi
+xσj
+x + σi
+yσj
+y)/2,
+(10)
+and the system is evolving under this Hamiltonian for a
+period of time td. For the state classification, the cir-
+cuit is then connected to a classifier built in a digital-
+analog quantum neural network, proposed by [40].
+It
+is consist of Nq + 1 single-qubit operation R(θi, φi) =
+
+350
+TeD-Q
+Pennylane
+300
+250
+200
+150
+100
+50
+0
+0
+100
+300
+400
+500
+Iteratian [#)U=e
+-Hdtd14
+Z(θi)X(φi)Z(−θi), which is the digital part, and an uni-
+tary operation H0, which is the analog part, on each
+qubit.
+H0 = gi,j(σi
+xσj
+x + σi
+yσj
+y)/2,
+(11)
+Finally, the only measurement was placed on one of the
+qubits. The parameters of QNN would be trained so that
+the measurement of it can classify the state of the system.
+The circuit diagram is shown in Figure 14.
+…
+State preparation
+Quantum neural network
+BCE loss 
+Gradient
+Truth
+Classical optimizer
+Localized state
+Ergodic state
+Recursively update the parameters
+…
+FIG. 14: The quantum circuit and the classical
+optimizer used in MBL simulation. The diagram can be
+separated into three stages – state preparation,
+quantum neural network (QNN), and classical
+optimizer. The state preparation stage generates the
+state in either ergodic or localized state. The QNN
+stage is trained to distinguish ergodic states from
+localized states. The optimizer stage evaluates the
+result and optimizes the QNN based on the loss
+function.
+The simulation parameters, like gi,j and td, follow the
+setting used in [40], which are the properties of a 64-qubit
+quantum computer. The parameters in the classifier are
+then trained with the binary cross entropy loss so that
+the expected value of the the selected qubit can be 1
+when the system is in an ergodic state and 0 when the
+system is in a localized state.
+2.
+Speed comparison
+The performance of TeD-Q is evaluated by the time
+cost for finishing 50 epochs of 1D-MBL training.
+The
+circuit depth is about 89, and each epoch consists of 40
+training iterations of the circuit. For the comparison, we
+also set up the same simulation using Qiskit and Penny-
+lane. CPU simulations use Intel(R) Xeon(R) Processor
+E5-2680 v4 @ 2.4GHz CPU while GPU simulations use
+Nvidia Tesla P40 24 GB GPU.
+Figure 15 compares these three quantum simulation
+methods on CPU and GPU. TeD-Q can provide similar
+behavior as PennyLane while using state vector propaga-
+tion mode. This method becomes computationally infea-
+sible while the simulation involves more than 20 qubits.
+However, TeD-Q, using tensor network contraction mode,
+can process the same simulation with up to 50 qubits
+within a comparable time.
+(a) Single CPU mode
+(b) Single GPU mode
+FIG. 15: Performance comparison among TeD-Q,
+PennyLane and Qiskit for the MBL task.
+F.
+Discussion
+Generally, the state vector propagation mode of TeD-
+Q and PennyLane have similar performance both in CPU
+and GPU. This is with-in our expectation since both of
+them calculate the full amplitude and use backpropaga-
+tion method for obtaining gradient. TeD-Q has a slight
+advantage (20 ∼ 30%) over Pennylane on CPU for qubits
+less than 11, this can be explained by the reusable mech-
+anism that saves the time for state and gate class instan-
+tiation.
+Tensor network contraction mode shows its power on
+large qubit systems. It can reduce the computation and
+memory complexity substantially. But currently its per-
+formance is constrained by inefficient use of GPU. Most
+pair contractions in the contraction path involve small
+tensors, they contribute very small portions of the over-
+all computation and memory complexity. But the trans-
+mission of these small tensors to GPU will cost sizable
+overhead. This overhead problem can be improved by
+pre-computing contractions with small sizes on CPU and
+only performing the large ones on GPU[26], which will
+be included in the future release of TeD-Q.
+
+104
+time (s)
+103
+TeD-Q State Vector Propagation Mode
+TeD-Q Tensor Network Contraction Mode
+PennyLane
+102
+Qiskit
+5
+10
+15
+20
+25
+30
+3540 45 50
+Number of qubits104
+time (s)
+103
+TeD-Q State Vector Propagation Mode
+TeD-Q Tensor Network Contraction Mode
+PennyLane
+Qiskit
+5
+10
+15
+20
+25
+30
+35 40 45 50
+Number of qubitsR(0,Φ-Hoto
+U=e0U=e
+-HdtdR(0o, Φ0R(ON, ΦNR(01. 01R(02, Φ215
+VII.
+SUMMARY
+In this work, we introduced TeD-Q, an open-source
+software framework for quantum machine learning, varia-
+tional quantum algorithm, and quantum computing sim-
+ulation. With tensor contraction, simulation of quantum
+circuit with large number of qubits is possible. TeD-Q
+seamlessly integrates classical machine learning libraries
+with quantum simulators, allowing users to leverage the
+power of classical machine learning while training quan-
+tum machine learning models. TeD-Q is also empowered
+with the capability of training quantum machine learn-
+ing models in a distributed manner. This is an important
+feature considering that most NISQ quantum algorithms
+require results from multiple instances of the same quan-
+tum circuit. In TeD-Q, the quantum circuit is seen as a
+Python function, which makes it easy to use. TeD-Q is
+device independent so that users can run the circuits on
+different backends, including software simulators (JAX
+and PyTorch) and quantum hardwares.
+To better facilitate the implementation of quantum
+machine learning, TeD-Q supports automatic differen-
+tiation, for instance, backpropagation, parameters shift,
+and finite difference methods, to obtain gradient. It also
+has a flexible interface that bridges quantum circuits
+to powerful machine learning libraries (like PyTorch).
+In addition, TeD-Q supports visualization functionality,
+where users can visualize quantum circuits and training
+progress in real-time.
+There are still challenges in future works of TeD-Q.
+One crucial aspect is how to leverage distributed com-
+putation’s ability to solve real quantum machine learn-
+ing problems. Even though TeD-Q supports distributed
+computation, algorithms, and applications that make the
+most use of it are still lacking. Another aspect that TeD-
+Q can improve is to work completely compatible with
+different kinds of quantum hardwares on the cloud. We
+have demonstrated how TeD-Q can access the hardware
+resources on the IBM cloud in Section V A 3 and in later
+releases support for other platforms, e.g. Pennylane and
+Amazon, will be introduced. In principle, TeD-Q is ready
+to connect with any device; however, due to the lack of
+quantum hardware resources, this has not been tested.
+It would be exciting to see TeD-Q working with differ-
+ent hardware backends and implementing real distributed
+quantum algorithms, especially QML algorithms, in the
+future.
+ACKNOWLEDGMENTS
+We appreciate the helpful discussion with Juhua Liu.
+Author contributions. X.-Y. W., Y.-X. D., and D.-
+C. T. conceived the project. X.-Y. W. and Y.-C. C. de-
+signed the architecture of the software. Y.-C. C., X.-Y.
+W., and C.-Y. K. did the coding and carried out the
+numerical simulation. X.-Y. W., Y.-X. D., Y.-C. C., C.-
+Y. K. and D.-C. T. analyzed the results.
+All authors
+contributed to discussions of the results and the develop-
+ment of the manuscript. Y.-C. C., C.-Y. K., and X.-Y.
+W. wrote the manuscript with input from all co-authors.
+X.-Y. W., Y.-X. D., and D.-C. T. supervised the whole
+project.
+[1] F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin,
+R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A.
+Buell, et al., Nature 574, 505 (2019).
+[2] L. S. Madsen, F. Laudenbach, M. F. Askarani, F. Rortais,
+T. Vincent, J. F. Bulmer, F. M. Miatto, L. Neuhaus,
+L. G. Helt, M. J. Collins, et al., Nature 606, 75 (2022).
+[3] Y. Wu, W.-S. Bao, S. Cao, F. Chen, M.-C. Chen,
+X. Chen, T.-H. Chung, H. Deng, Y. Du, D. Fan, et al.,
+Physical review letters 127, 180501 (2021).
+[4] V. Bergholm, J. Izaac, M. Schuld, C. Gogolin, M. S.
+Alam, S. Ahmed, J. M. Arrazola, C. Blank, A. Delgado,
+S. Jahangiri, et al., arXiv preprint arXiv:1811.04968
+(2018).
+[5] A. tA v, M. S. ANIS, Abby-Mitchell, H. Abraham,
+AduOffei, R. Agarwal, G. Agliardi, M. Aharoni, V. Ajith,
+I. Y. Akhalwaya, G. Aleksandrowicz, T. Alexander,
+M. Amy, S. Anagolum, Anthony-Gandon, I. F. Araujo,
+E. Arbel, A. Asfaw, A. Athalye, A. Avkhadiev, C. Azaus-
+tre, P. BHOLE, V. Bajpe, A. Banerjee, S. Banerjee,
+W. Bang, A. Bansal, P. Barkoutsos, A. Barnawal, G. Bar-
+ron, G. S. Barron, L. Bello, Y. Ben-Haim, M. C. Bennett,
+D. Bevenius, D. Bhatnagar, P. Bhatnagar, A. Bhobe,
+P. Bianchini, L. S. Bishop, C. Blank, S. Bolos, S. Bopar-
+dikar, S. Bosch, S. Brandhofer, Brandon, S. Bravyi,
+Bryce-Fuller,
+D. Bucher,
+L. Burgholzer,
+A. Burov,
+F. Cabrera, P. Calpin, L. Capelluto, J. Carballo, G. Car-
+rascal, A. Carriker, I. Carvalho, R. Chakrabarti, A. Chen,
+C.-F. Chen, E. Chen, J. C. Chen, R. Chen, F. Cheval-
+lier, K. Chinda, R. Cholarajan, J. M. Chow, S. Churchill,
+CisterMoke, C. Claus, C. Clauss, C. Clothier, R. Cock-
+ing, R. Cocuzzo, J. Connor, F. Correa, Z. Crockett,
+A. J. Cross, A. W. Cross, S. Cross, J. Cruz-Benito,
+C. Culver, A. D. C´orcoles-Gonzales, N. D, S. Dague,
+T. E. Dandachi, A. N. Dangwal, J. Daniel, M. Daniels,
+M. Dartiailh, A. R. Davila, F. Debouni, A. Dekusar,
+A. Deshmukh, M. Deshpande, D. Ding, J. Doi, E. M.
+Dow, P. Downing, E. Drechsler, M. S. Drudis, E. Du-
+mitrescu, K. Dumon, I. Duran, K. EL-Safty, E. East-
+man, G. Eberle, A. Ebrahimi, P. Eendebak, D. Egger,
+ElePT, I. Elsayed, Emilio, A. Espiricueta, M. Everitt,
+D. Facoetti, Farida, P. M. Fern´andez, S. Ferracin, D. Fer-
+rari, A. H. Ferrera, R. Fouilland, A. Frisch, A. Fuhrer,
+B. Fuller, M. GEORGE, J. Gacon, B. G. Gago, C. Gam-
+bella, J. M. Gambetta, A. Gammanpila, L. Garcia,
+T. Garg, S. Garion, J. R. Garrison, J. Garrison, T. Gates,
+N. Gavrielov,
+G. Gentinetta,
+H. Georgiev,
+L. Gil,
+A. Gilliam, A. Giridharan, Glen, J. Gomez-Mosquera,
+Gonzalo,
+S.
+de la
+Puente Gonz´alez,
+J. Gorzinski,
+
+16
+I. Gould, D. Greenberg, D. Grinko, W. Guan, D. Guijo,
+Guillermo-Mijares-Vilarino, J. A. Gunnels, H. Gupta,
+N. Gupta,
+J. M. G¨unther,
+M. Haglund,
+I. Haide,
+I. Hamamura, O. C. Hamido, F. Harkins, K. Hartman,
+A. Hasan, V. Havlicek, J. Hellmers, �L. Herok, R. Hill,
+S. Hillmich, C. Hong, H. Horii, C. Howington, S. Hu,
+W. Hu, C.-H. Huang, J. Huang, R. Huisman, H. Imai,
+T. Imamichi, K. Ishizaki, Ishwor, R. Iten, T. Itoko,
+A. Ivrii, A. Javadi, A. Javadi-Abhari, W. Javed, Q. Jian-
+hua, M. Jivrajani, K. Johns, S. Johnstun, Jonathan-
+Shoemaker, JosDenmark, JoshDumo, J. Judge, T. Kach-
+mann, A. Kale, N. Kanazawa, J. Kane, Kang-Bae,
+A. Kapila, A. Karazeev, P. Kassebaum, T. Kehrer,
+J. Kelso, S. Kelso, H. van Kemenade, V. Khanderao,
+S. King, Y. Kobayashi, Kovi11Day, A. Kovyrshin, R. Kr-
+ishnakumar, P. Krishnamurthy, V. Krishnan, K. Kr-
+sulich, P. Kumkar, G. Kus, R. LaRose, E. Lacal, R. Lam-
+bert, H. Landa, J. Lapeyre, D. Lasecki, J. Latone,
+S. Lawrence, C. Lee, G. Li, T. J. Liang, J. Lish-
+man, D. Liu, P. Liu, Lolcroc, A. K. M, L. Mad-
+den, Y. Maeng, S. Maheshkar, K. Majmudar, A. Maly-
+shev, M. E. Mandouh, J. Manela, Manjula, J. Mare-
+cek, M. Marques, K. Marwaha, D. Maslov, P. Mas-
+zota, D. Mathews, A. Matsuo, F. Mazhandu, D. Mc-
+Clure, M. McElaney, J. McElroy, C. McGarry, D. McKay,
+D. McPherson, S. Meesala, D. Meirom, C. Mendell,
+T. Metcalfe, M. Mevissen, A. Meyer, A. Mezzacapo,
+R. Midha, D. Millar, D. Miller, H. Miller, Z. Minev,
+A. Mitchell,
+N. Moll,
+A. Montanez,
+G. Monteiro,
+M. D. Mooring, R. Morales, N. Moran, D. Morcuende,
+S. Mostafa, M. Motta, R. Moyard, P. Murali, D. Murata,
+J. M¨uggenburg, T. NEMOZ, D. Nadlinger, K. Nakanishi,
+G. Nannicini, P. Nation, E. Navarro, Y. Naveh, S. W.
+Neagle, P. Neuweiler, A. Ngoueya, T. Nguyen, J. Nican-
+der, Nick-Singstock, P. Niroula, H. Norlen, NuoWenLei,
+L. J. O’Riordan, O. Ogunbayo, P. Ollitrault, T. Onodera,
+R. Otaolea, S. Oud, D. Padilha, H. Paik, S. Pal, Y. Pang,
+A. Panigrahi, V. R. Pascuzzi, S. Perriello, E. Peterson,
+A. Phan, K. Pilch, F. Piro, M. Pistoia, C. Piveteau,
+J. Plewa, P. Pocreau, C. Possel, A. Pozas-Kerstjens,
+R. Pracht, M. Prokop, V. Prutyanov, S. Puri, D. Puz-
+zuoli, Pythonix, J. P´erez, Quant02, Quintiii, R. I. Rah-
+man, A. Raja, R. Rajeev, I. Rajput, N. Ramagiri, A. Rao,
+R. Raymond, O. Reardon-Smith, R. M.-C. Redondo,
+M. Reuter, J. Rice, M. Riedemann, Rietesh, D. Risinger,
+P. Rivero, M. L. Rocca, D. M. Rodr´ıguez, RohithKarur,
+B. Rosand, M. Rossmannek, M. Ryu, T. SAPV, N. R. C.
+Sa, A. Saha, A. Ash-Saki, A. Salman, S. Sanand,
+M. Sandberg, H. Sandesara, R. Sapra, H. Sargsyan,
+A. Sarkar, N. Sathaye, N. Savola, B. Schmitt, C. Schn-
+abel, Z. Schoenfeld, T. L. Scholten, E. Schoute, M. Schul-
+terbrandt, J. Schwarm, P. Schweigert, J. Seaward, Sergi,
+I. F. Sertage, K. Setia, F. Shah, N. Shammah, W. Shanks,
+R. Sharma, P. Shaw, Y. Shi, J. Shoemaker, A. Silva,
+A. Simonetto, D. Singh, D. Singh, P. Singh, P. Singka-
+nipa, Y. Siraichi, Siri, J. Sistos, J. Sistos, I. Sitdikov,
+S. Sivarajah, Slavikmew, M. B. Sletfjerding, J. A. Smolin,
+M. Soeken, I. O. Sokolov, I. Sokolov, V. P. Soloviev,
+SooluThomas, Starfish, D. Steenken, M. Stypulkoski,
+A. Suau, S. Sun, K. J. Sung, M. Suwama, O. S�lowik,
+R. Taeja, H. Takahashi, T. Takawale, I. Tavernelli,
+C. Taylor, P. Taylour, S. Thomas, K. Tian, M. Tillet,
+M. Tod, M. Tomasik, C. Tornow, E. de la Torre, J. L. S.
+Toural, K. Trabing, M. Treinish, D. Trenev, TrishaPe,
+F. Truger, TsafrirA, G. Tsilimigkounakis, D. Tulsi,
+D. Tuna, W. Turner, Y. Vaknin, C. R. Valcarce, F. Var-
+chon, A. Vartak, A. C. Vazquez, P. Vijaywargiya, V. Vil-
+lar, B. Vishnu, D. Vogt-Lee, C. Vuillot, WQ, J. Weaver,
+J. Weidenfeller, R. Wieczorek, J. A. Wildstrom, J. Wil-
+son, E. Winston, WinterSoldier, J. J. Woehr, S. Woerner,
+R. Woo, C. J. Wood, R. Wood, S. Wood, J. Wootton,
+M. Wright, L. Xing, J. YU, Yaiza, B. Yang, U. Yang,
+J. Yao,
+D. Yeralin,
+R. Yonekura,
+D. Yonge-Mallo,
+R. Yoshida, R. Young, J. Yu, L. Yu, Yuma-Nakamura,
+C. Zachow, L. Zdanski, H. Zhang, E. Zheltonozhskii,
+I. Zidaru, B. Zimmermann, B. Zindorf, C. Zoufal, aed-
+dins ibm, alexzhang13, b63, bartek bartlomiej, bcamor-
+rison, brandhsn, nick bronn, chetmurthy, choerst ibm,
+comet, dalin27, deeplokhande, dekel.meirom, derwind,
+dime10, ehchen, ewinston, fanizzamarco, fs1132429, ga-
+dial, galeinston, georgezhou20, georgios ts, gruu, hhorii,
+hhyap, hykavitha, itoko, jeppevinkel, jessica angel7, jez-
+erjojo14, jliu45, johannesgreiner, jscott2, kUmezawa,
+klinvill, krutik2966, ma5x, michelle4654, msuwama, nico
+lgrs, nrhawkins, ntgiwsvp, ordmoj, sagar pahwa, pritam-
+sinha2304, rithikaadiga, ryancocuzzo, saktar unr, saswati
+qiskit, sebastian mair, septembrr, sethmerkel, sg495,
+shaashwat, smturro2, sternparky, strickroman, tiger-
+jack, tsura crisaldo, upsideon, vadebayo49, welien, will-
+hbang, wmurphy collabstar, yang.luh, yuri@FreeBSD,
+and M. ˇCepulkovskis, “Qiskit: An open-source frame-
+work for quantum computing,” (2021).
+[6] X.-Z. Luo, J.-G. Liu, P. Zhang, and L. Wang, Quantum
+4, 341 (2020).
+[7] “Cirq: A python framework for creating, editing, and in-
+voking noisy intermediate scale quantum (nisq) circuits,”
+.
+[8] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost,
+N. Wiebe, and S. Lloyd, Nature 549, 195 (2017).
+[9] M. Schuld, I. Sinayskiy, and F. Petruccione, Contempo-
+rary Physics 56, 172 (2015).
+[10] M. Schuld and N. Killoran, Physical review letters 122,
+040504 (2019).
+[11] H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush,
+S. Boixo, H. Neven, and J. R. McClean, Nature commu-
+nications 12, 1 (2021).
+[12] X. Yuan, S. Endo, Q. Zhao, Y. Li, and S. C. Benjamin,
+Quantum 3, 191 (2019).
+[13] M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin,
+S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan,
+L. Cincio, et al., Nature Reviews Physics 3, 625 (2021).
+[14] L. Bittel and M. Kliesch, Physical Review Letters 127,
+120502 (2021).
+[15] J. Preskill, Quantum 2, 79 (2018).
+[16] K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug,
+S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen,
+J. S. Kottmann, T. Menke, et al., Reviews of Modern
+Physics 94, 015004 (2022).
+[17] A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury,
+G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga,
+A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison,
+A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai,
+and S. Chintala, in Advances in Neural Information Pro-
+cessing Systems 32 (Curran Associates, Inc., 2019) pp.
+8024–8035.
+[18] J. Aycock, ACM Computing Surveys (CSUR) 35, 97
+(2003).
+[19] “Paddle Quantum,” (2020).
+
+17
+[20] M. A. Nielsen and I. L. Chuang, Quantum Computa-
+tion and Quantum Information: 10th Anniversary Edi-
+tion (Cambridge University Press, 2011).
+[21] J. Gray and S. Kourtis, Quantum 5, 410 (2021).
+[22] V.
+Gogate
+and
+R.
+Dechter,
+arXiv
+preprint
+arXiv:1207.4109 (2012).
+[23] G. Daniel, J. Gray, et al., Journal of Open Source Soft-
+ware 3, 753 (2018).
+[24] S. Schlag, High-Quality Hypergraph Partitioning, Ph.D.
+thesis, Karlsruhe Institute of Technology,
+Germany
+(2020).
+[25] Y. Akhremtsev, T. Heuer, P. Sanders,
+and S. Schlag,
+in 19th Workshop on Algorithm Engineering and Exper-
+iments, (ALENEX 2017) (2017) pp. 28–42.
+[26] C. Huang, F. Zhang, M. Newman, X. Ni, D. Ding, J. Cai,
+X. Gao, T. Wang, F. Wu, G. Zhang, et al., Nature Com-
+putational Science 1, 578 (2021).
+[27] E. Pednault, J. A. Gunnels, G. Nannicini, L. Horesh,
+T. Magerlein, E. Solomonik, E. W. Draeger, E. T. Hol-
+land, and R. Wisnieff, arXiv preprint arXiv:1710.05867
+(2017).
+[28] A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang,
+Z. DeVito, Z. Lin, A. Desmaison, L. Antiga,
+and
+A. Lerer, (2017).
+[29] J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson,
+C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. Vander-
+Plas, S. Wanderman-Milne, et al., Astrophysics Source
+Code Library , ascl (2021).
+[30] M. Schuld, V. Bergholm, C. Gogolin, J. Izaac,
+and
+N. Killoran, Phys. Rev. A 99, 032331 (2019).
+[31] G.-L. R. Anselmetti, D. Wierichs, C. Gogolin, and R. M.
+Parrish, New Journal of Physics 23, 113010 (2021).
+[32] V. Bergholm, J. Izaac, M. Schuld, C. Gogolin, M. S.
+Alam, S. Ahmed, J. M. Arrazola, C. Blank, A. Del-
+gado,
+S.
+Jahangiri,
+K.
+McKiernan,
+J.
+J.
+Meyer,
+Z.
+Niu,
+A.
+Sz´ava,
+and
+N.
+Killoran,
+(2018),
+10.48550/ARXIV.1811.04968.
+[33] R. Nandkishore and D. A. Huse, Annu. Rev. Condens.
+Matter Phys. 6, 15 (2015).
+[34] I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu,
+D. Warde-Farley, S. Ozair, A. Courville,
+and Y. Ben-
+gio, Communications of the ACM 63, 139 (2020).
+[35] J. Tian, X. Sun, Y. Du, S. Zhao, Q. Liu, K. Zhang,
+W. Yi, W. Huang, C. Wang, X. Wu, et al., arXiv preprint
+arXiv:2206.03066 (2022).
+[36] H.-L. Huang, Y. Du, M. Gong, Y. Zhao, Y. Wu, C. Wang,
+S. Li, F. Liang, J. Lin, Y. Xu, et al., Physical Review
+Applied 16, 024051 (2021).
+[37] Y. Du, T. Huang, S. You, M.-H. Hsieh, and D. Tao, npj
+Quantum Information 8, 1 (2022).
+[38] K. Linghu, Y. Qian, R. Wang, M.-J. Hu, Z. Li, X. Li,
+H. Xu, J. Zhang, T. Ma, P. Zhao, et al., arXiv preprint
+arXiv:2201.00934 (2022).
+[39] D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Rev.
+Mod. Phys. 91, 021001 (2019).
+[40] M. Gong, H.-L. Huang, S. Wang, C. Guo, S. Li, Y. Wu,
+Q. Zhu, Y. Zhao, S. Guo, H. Qian, et al., arXiv preprint
+arXiv:2201.05957 (2022).
+[41] H.-L. Huang, Y. Du, M. Gong, Y. Zhao, Y. Wu, C. Wang,
+S. Li, F. Liang, J. Lin, Y. Xu, R. Yang, T. Liu, M.-
+H. Hsieh, H. Deng, H. Rong, C.-Z. Peng, C.-Y. Lu, Y.-
+A. Chen, D. Tao, X. Zhu,
+and J.-W. Pan, Phys. Rev.
+Applied 16, 024051 (2021).
+
diff --git a/o9E5T4oBgHgl3EQfIw4s/content/tmp_files/load_file.txt b/o9E5T4oBgHgl3EQfIw4s/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8411e1a1570b28b689683dd74463f7d83b1af11d
--- /dev/null
+++ b/o9E5T4oBgHgl3EQfIw4s/content/tmp_files/load_file.txt
@@ -0,0 +1,1687 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf,len=1686
+page_content='TeD-Q: a tensor network enhanced distributed hybrid quantum machine learning  framework  Yaocheng Chen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ∗ Xingyao Wu ∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' † Chung-Yun Kuo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 3 Yuxuan Du,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ‡ and Dacheng Tao3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' §  1Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' National Taiwan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Taipei,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Taiwan  2Leung Center for Cosmology and Particle Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' National Taiwan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Taipei,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Taiwan  3JD Explore Academy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Beijing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' China  (Dated: January 16,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 2023)  TeD-Q is an open-source software framework for quantum machine learning,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' variational quan-  tum algorithm (VQA),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' and simulation of quantum computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It seamlessly integrates classical  machine learning libraries with quantum simulators, giving users the ability to leverage the power  of classical machine learning while training quantum machine learning models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q supports  auto-differentiation that provides backpropagation, parameters shift, and finite difference methods  to obtain gradients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' With tensor contraction, simulation of quantum circuits with large number of  qubits is possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q also provides a graphical mode in which the quantum circuit and the  training progress can be visualized in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  INTRODUCTION  Quantum computing is one of the most promising di-  rections that may save us from Moore’s law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Recent re-  sults show that quantum computing is indeed advanta-  geous over classical computing in certain problems [1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  With the progress in quantum hardware, quantum soft-  ware and research in algorithms are also catching up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Quantum software plays a crucial role in bridging quan-  tum hardware and real-world applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  There has  been a decent amount of work in quantum software plat-  forms in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Some of these already allow users  to access real quantum hardware [4–6], while others fo-  cus more on building a complete software environment  for better quantum algorithm development [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  TeD-Q is a Python-based quantum programming  framework that has differentiable functionality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It is op-  timized particularly for quantum machine learning prob-  lems [8–11] and variational quantum algorithms [12–14],  which constitute the majority of contemporary Noisy  Intermediate-Scale Quantum (NISQ) algorithms [15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  TeD-Q provides a universal framework for program-  ming on different backends, including quantum hardware,  quantum simulator, and distributed GPU accelerators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  In terms of top-level applications, users could enjoy the  convenience of using TeD-Q without worrying about how  to deal with different backends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' One could simply treat  a quantum neural network (QNN) training as in classical  machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  With TeD-Q, the quantum circuit is treated as a  Python function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It is free to choose either PyTorch or  JAX as the interface with the execution backends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Due  to this systematic integration, one could also leverage the  rich features provided by the well-developed AI-oriented  ∗ These two authors contributed equally  † wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='yao@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='com  ‡ duyuxuan123@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='com  § dacheng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='tao@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='com  libraries [17] to help the implementation of quantum algo-  rithms better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Specific benefits include batch execution,  Just In Time compilation (JIT) [18], parallel GPU opti-  mization, and auto-differentiation for backpropagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  TeD-Q has both full amplitude quantum simulation  and a tensor network enhanced multi-amplitude simula-  tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q will estimate the complexity of both modes,  and users could choose on their own which mode to exe-  cute the code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  TeD-Q is also equipped with a built-in tensor network  module and contraction path optimizer JDtensorPath,  which could provide additional improvements on the per-  formance in the tensor network simulation mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This  is achieved by optimizing the tensor network contraction  order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Besides, TeD-Q provides a graphical circuit composer  that makes it user-friendly to beginners with intuitive  visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Table I shows the comparison among TeD-Q and three  major general-purpose quantum machine learning plat-  forms – PennyLane [4], Qiskit [5] and Paddle Quan-  tum [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  PennyLane is a cross-platform Python package for pro-  gramming quantum and hybrid quantum-classical algo-  rithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It builds upon the idea of auto differentiable pro-  gramming and integrates mainstream classical machine  learning libraries with quantum algorithms to provide an  easy-to-use interface[4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Qiskit is an open source quan-  tum software development framework of IBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It inte-  grates PyTorch and can be executed with IBMQ on real  quantum hardware[5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Paddle Quantum is developed by  Baidu, it is based on the PaddlePaddle deep learning  platform and can access real quantum computers Quan-  tum Leaf[19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The main distinct features of TeD-Q are hypergraph-  based tensor network contraction (TNC) and paralleling  via index slicing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Simulation of quantum circuits nor-  mally can be carried out by matrix multiplication and  tensor network contraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Current quantum software  platforms generally support only matrix multiplication  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='05451v1  [quant-ph]  13 Jan 2023  2  Table I: A summary of features of existing quantum  simulation frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  TeD-Q  Pennylane Qiskit  Paddle  Quantum  Backpropagation  v  v v  Hypergraph-based TNC  v Slicing paralleling  v PyTorch interface  v  v  v Noise model  future release  v  v  v  Hardware compatibility  via Qiskit  v  v  v  Circuit composer  v v mode [4, 5, 19], which is enough while the number of  qubits is below roughly 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  However, when the num-  ber of qubits exceeds 38, the time cost and storage cost  surge exponentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The TNC mode of TeD-Q could eas-  ily handle quantum circuit simulation with qubit number  larger than 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hypergraph-based TNC method can pro-  vide several orders of magnitude improvement in both  computation and memory complexity while paralleling  via index slicing delivers advantages in GPU device com-  munication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Since the order of tensor network contrac-  tion will affect the time cost a lot, TeD-Q also provides  a dedicated tensor network contraction optimizer, called  JDTensorPath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' These new features are designed to im-  prove the efficiency of large-scale quantum circuit simu-  lation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Compared to Qiskit, Pennylane and Paddle Quantum,  TeD-Q also featured a reusable mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In most of  the quantum algorithms including NISQ algorithms, the  parameterized quantum circuit will be evaluated multiple  times without changing the circuit structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In TeD-Q,  the quantum state and quantum gate objects inside a  quantum circuit will be reused in every evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This  feature can save a considerable amount of time for class  instantiation in small quantum circuits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This advantage  could be easily seen in the performance comparison of  multiple qubits rotation example in Section VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  ARCHITECTURE OF TED-Q  TeD-Q is designed for fast and efficient implementation  of quantum algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  For this purpose, the compo-  nents of application design, computation backends, and  the interface in between are packed into relatively inde-  pendent modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q is composed of four main mod-  ules, QInterpreter, Backends, Interface, and Optimizer,  as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Any quantum algorithm will eventually be passed  through and processed as classical codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This is where  the QInterpreter plays its role, transforming quantum  algorithms into executable codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Quantum state and  quantum gate classes are the basic building blocks of  QInterpreter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A series of quantum gates applied to the  quantum state will make up a quantum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The quantum circuit object in TeD-Q is agnostic with  respect to simulation and hardware backends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  It is  an abstraction of user-defined quantum function, that  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 1: The design of TeD-Q architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The part in  yellow is quantum while the rest is classical processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  bridges the high-level quantum algorithms and low-level  backend-specific instructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  QInterpreter of TeD-Q  provides tools for obtaining and manipulating represen-  tations of quantum operators and measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' These  tools and representations are useful for generating a  quantum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The user needs to provide a quantum  function, the number of qubits, and the parameters or the  shape of the parameters (in this case, random parame-  ters will be generated and used) to construct a quantum  circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  A quantum function is defined as a normal Python  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It accepts classical input parameters and uses  their elements for quantum gate parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The user  needs to put quantum operations inside the quantum  function in the order that matches how they are applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  A keyword argument ”qubit”, which is a list of integers,  need to be specified to denote which qubit each quantum  operation applies on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' After all the quantum operations,  a single or a list of measurements must be placed as part  of the return statement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Code Listing 1 shows a simple  example of defining a quantum function and constructing  a quantum circuit from it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1  import  tedq  2  3 # Define  quantum  circuit  4 def  circuitDef (params):  5  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='RX(params [0],  qubits =[0])  6  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='RY(params [1],  qubits =[1])  7  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='CNOT(qubits =[0, 1])  8  return [tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='expval(tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='PauliZ(qubits =[0]))  9  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='expval(tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='PauliZ(qubits =[1]))]  10  11  number_of_qubits = 2  12  parameter_shapes = [(2 ,)]  13  14 # Quantum  circuit  construction  15  circuit = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Circuit(circuitDef , number_of_qubits ,  parameter_shapes = parameter_shapes )  Code Listing 1: How to construct a quantum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Line 4-9 define a quantum circuit function while line 15  constructs a TeD-Q quantum circuit object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The quantum circuit is not yet executable since the  computation mode and backend have not been chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  After specifying these, it can be compiled into an exe-  QInterpreter  Quantum function  Tools  Circuit  Gates  Observables  Visualization  QNN  Measurements  Template  circuit to  execute  Backends  Hardware  Optimizer  Simulator  Training  Tensor network  State vector  1/O  JDTensorPath  Interface  Input/output data3  cutable compiled circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The compiled circuit can be  used like a standard Python function to compute the re-  sult.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The order of input parameters must be the same as  the order of the corresponding quantum gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A quan-  tum circuit can be run on different backends by manu-  ally compiling it with different specifications, as shown  in Code Listing 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  This is why it is called a reusable  quantum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 # compile  quantum  circuit  with "jax" backend  2  compileCir1 = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (backend="jax")  3  4 # compile  quantum  circuit  with "pytorch" backend  5  compileCir2 = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (backend="pytorch")  Code Listing 2: Compile quantum circuit with different  backends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  SIMULATION MODES  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  State vector propagation mode  In quantum theory, the wave function is used as a  mathematical description of the quantum state of a sys-  tem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A state vector is denoted by a complex ket vector  |ψ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In this mode, quantum gates act on the state vector  as a sequence of matrix operators, so that the resulting  state after each operation is:  |ψ⟩ = U|ψ0⟩,  (1)  where U is the matrix operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The state vector prop-  agation mode is the default simulation backend of TeD-  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A user-defined initial quantum state can be used by  putting tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='InitStateVector() as the first line of the  quantum circuit definition function as shown in Code  Listing 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Notice that the length of the initial state vec-  tor must match 2n, where n is the number of qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' If no  initial state is specified, TeD-Q will set it to the ground  state |0⟩⊗n by default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' With TeD-Q, this mode allows a  normal laptop to deal with a non-trival quantum circuit  of up to 20 qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 # Prepare  quantum  state  vector  2  init_state = np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='array ([1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='/ np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='sqrt (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=') , 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='/np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='sqrt (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=') ])  3  4 # Define  the  quantum  circuit  with a specific  initial  quantum  state  5 def  circuitDef(parameters):  6  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' InitStateVector (init_state)  7  # other  circuit  definition  Code Listing 3: Define quantum circuit with user-defined  initial quantum state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Tensor network contraction mode  In the state vector propagation mode, the number  of amplitudes grows exponentially with the number of  qubits, 2n complex numbers are needed to describe the  quantum state for an n-qubit system [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Therefor, it is  extremely difficult for classical state vector-based simu-  lator to handle NISQ devices with more than 50 qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  TeD-Q integrates the tensor network contraction method  and mainstream deep learning frameworks – PyTorch and  JAX, providing an efficient built-in tensor network-based  quantum simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This mode can easily simulate cer-  tain quantum circuits of 50 ∼ 100 qubits on a single CPU  or GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The workflow of the tensor contraction mode in TeD-  Q consists of the following steps: (a) manipulating the  quantum circuit according to its output type and con-  verting it into a tensor network by the built-in Tensor-  Network module;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' (b) applying structural simplification  on the tensor network;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' (c) searching for best contraction  sequences for the simplified tensor network;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' (d) slicing  the contractions down to memory limit;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' (e) carrying out  the actual contraction with the backend library accord-  ing to sliced contraction sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The computational  complexity of steps (a) and (b) are very low, which can be  done by a single CPU thread.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Step (b) is optional, how-  ever, it will generally reduce the size of the tensor network  significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Except for the default trivial pathfinder,  two cutting-edge hyper-graph partition-based packages  – CoTenGra[21] & JDtensorPath can also be chosen for  step (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' JDtensorPath was originally a built-in module  in TeD-Q and was separated into an independent soft-  ware for better code structure management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It perfectly  matches TeD-Q’s design paradigm and will be introduced  in the Section III B 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Step (d) can also be carried out  with CoTenGra or JDtensorPath libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This is also  an optional step and will cost some extra overhead of  the total contraction floating point operations (FLOPs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  In JDtensorPath, step (c) and (d) are done parallelly in  CPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The path found in step (c) or (d) can be re-used in  step (e) to obtain the result of the same quantum circuit  but with different input parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Step (e) is the most  time-consuming part, which will be executed repeatedly  in the machine learning training loop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Step (e) can be  run on a single CPU, single GPU, or a cluster of GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Tensor network and simplification  A quantum circuit can be simulated in various ways,  of which tensor network method is increasingly popular  recently years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q can represent a quantum circuit  with the corresponding graphical tensor network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Both  the quantum state and any quantum gate can be rep-  resented as tensors while the tensor network preserves  the topological structure of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The resulting graph  G = (V, E) thus contains vertexes associated with the  tensors, while the edges are labeled by their indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The  rank of a tensor is given by the number of edges connect-  ing to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Since a single qubit lives in a 2D Hilbert space,  meaning each index takes value from {0, 1}, a rank-k ten-  sor will require O(2k) storage space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  To calculate the  probability of finding certain final state |φout⟩ from the  output of the quantum circuit U |φin⟩, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ⟨φin| U |φout⟩,  4  the tensor network needs to be contracted, meaning  shared indices between vertices will be summed up;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' while  open edges remains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 2 gives an example of a trivial  two qubits quantum circuit and its graphical tensor net-  work representation in TeD-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Each vertex in the tensor  network is associated with a tensor representing either  the quantum state or one quantum gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Aa and Bb are  tensors corresponding to state |0⟩s of the two qubits while  Cca and Ddb are representing single qubit Pauli X and  rotational Ry quantum gates respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' the two qubits  CNOT gate corresponds to Eefcd and the measurement  in the z direction is presented by Fgf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Since the expecta-  tion value is derived by ⟨I⊗Z⟩ = ⟨00|U †(θ)I⊗ZU(θ)|00⟩,  to calculate it with tensor network, we must append the  tensor network corresponding to the complex conjugate  of the original quantum circuit, which is ⟨00| U †(θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The  Ry(θ) gate could then be represented by Ddb which in  tensor form will be:  Ddb =  �  cos(θ/2) − sin(θ/2)  sin(θ/2)  cos(θ/2)  �  ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (2)  while the tensor form of the CNOT gate is:  E00cd =  �  1 0  0 1  �  , E11cd =  �  0 1  1 0  �  ,  E01cd = E10cd =  �  0 0  0 0  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (3)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 2: A quantum circuit and its graphical tensor  network representation in TeD-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' (a) A two qubits  quantum circuit with expectation value measurement  on second qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' (b) The corresponding graphical  tensor network representation, each vertex is associated  with a tensor given by quantum state or operator (gate,  state or observable).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Thus, the expectation value can be calculated by the  summation:  T =  �  a,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=',k  AaBbCcaDdbEefcdFgfE∗  hiegC∗  jhD∗  kiA∗  jB∗  k  = sin2(θ/2) − cos2(θ/2),  which can be verified with the traditional vector mode  calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It is shown that the actual order of carry-  ing these summation (for instance, whether to sum a or k  first) does matter a lot and finding a good contraction or-  der composes most part of the tensor network algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  TeD-Q supports an efficient local processing of the ten-  sor network prior to the searching of the contraction or-  der by a set of simplifications based on its structure and  sparsity of the tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The simplifications include ten-  sor shape squeezing, diagonal and anti-diagonal reduc-  tion, and rank simplification, which are designed to de-  crease the complexity and the rank of the tensor [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  After the local pre-procession, the tensor network will be  transferred from a line graph into a hyper-graph (a gen-  eralization of the graph that allows an edge connecting  any number of vertices).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  An illustration of the tensor network and its hyper-  graph representation is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 3 (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Notice that  the red hyper-edge (corresponding to index c) is con-  nected with three vertices (tensors).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The original tensor  network is defined as:  Tde :=  �  a,c,b,f  AacBabfCbceDcdEef,  (4)  where the upper-case and lower-case letters denote ten-  sors and its indices respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 3: An illustration of tensor network and its  hypergraph representation, binary contraction tree, and  index slicing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' (a) An example of a tensor network and  its hypergraph representation, edge c is a hyper-edge  connecting three vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Dashed lines represent open  edges while solid lines correspond to closed edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' (b) A  binary contraction tree, each node represents a pairwise  contraction of two tensors as well as a bi-partitioning of  its hyper-graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The upward edges indicate the indices  of the intermediate tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' (c) Slicing the green edge  (index a), generating simpler tensor networks with the  same structure labeled by all possible values of a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Each  individual contraction is to be carried out independently  and the summed of them gives the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (a)  <0ol  X  <ol  Z  (b)  e  h  E  Et  BH  DtBt(a)  a  B  AacBabfCbceDcdEef  C  a,c,b,f  E  (b)  [de}  C  [ace}  [acd)  C  (abe)  d  D  E  B5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  hyper-graph-based tensor contraction path optimizer  The time and memory complexity of tensor network  contraction depend on its tensor ranks and contraction  order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Despite finding optimal contraction sequences is  theoretically a non-deterministic polynomial-time (NP)-  hard task for general cases, efficient heuristic algo-  rithms [22] exist in practice for obtaining ’good enough’  sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Several established algorithms are supported  by TeD-Q from third party libraries, including brute-  force search, branching strategy, greedy and random-  greedy path, dynamic programming approach, line-graph  tree decomposition via QuickBB or FlowCutter, commu-  nity detection, Boltzmann-greedy agglomerative contrac-  tion trees, and hypergraph partitioning method [21, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The default basic pathfinder of TeD-Q supports the first  four methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  For better performance, we adopt the  hyper-graph partitioning method which is original pro-  posed in CoTenGra and develop our own hypergraph  based pathfinder library – JDtensorPath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The key idea of this algorithm is to recursively divide  the hypergraph of a given tensor network, and explicitly  build an incomplete binary contraction tree in a ’top-  down’ fashion as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 3b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The root node of the  tree corresponds to the initial whole graph of the tensor  network and the effective tensor of the final result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bi-  partitioning the hypergraph of the parent node will create  two child nodes that represent the effective intermediate  tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The contraction tree can be generated in this re-  cursively divisive manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The contraction sequences are  obtained by ascending the tree from the bottom up, and  combining two child nodes to a parent node corresponds  to a pair contraction of two intermediate tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The FLOPs for an individual contraction (node bi-  partitioning) is given by:  FLOPs = p ∗ (2 ∗ q − 1),  (5)  where p is the product of the dimensions of the outer in-  dices (indices that are not contracted) and q is that of the  contracted indices (which equals to 1 if no index is con-  tracted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' For each node bi-partitioning, p is fixed;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' there-  fore, the cost of the corresponding pairwise contraction  can be minimized by minimizing the sum of the weighted  edges (indices) cut by the partition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This method is like a  greedy approach from top to down since it only considers  the cost of every single contraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Furthermore, JDten-  sorPath not only requires partitioning of the current node  to be optimal, but also takes the partitioning of its child  nodes into consideration, so that the overall tree size and  total contraction FLOPs could be minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Specifi-  cally, it is required that the outer indices of the parent  node must be distributed as evenly as possible on two  child nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This requirement can reduce p in the parti-  tioning of the child nodes and thus affects the FLOPs of  their contractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The memory usage of a pairwise con-  traction is given by the sum of the sizes of all the related  tensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Since the parent node tensor of each contraction  is fixed, evenly distributing its indices on children node  tensors can also reduce the memory usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This is due  to the fact that, supposing p is fixed and defining m, n  to be the product of the dimensions of remaining indices  of children node tensors respectively during contraction,  the memory cost of the contraction m ∗ q + n ∗ q will be  minimized when m = n given m ∗ n = p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Advanced multilevel hypergraph partitioning frame-  work KaHyPar[24, 25] is employed to construct the con-  traction tree, modern parallel and distributed Python  package–Ray is used to generating multiple trials in par-  allel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' JDtensorPath can provide high-quality contraction  sequences to TeD-Q and enables tensor network contrac-  tion mode to achieve orders of magnitude speedup for  various quantum circuits simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Slicing  Slicing is an optional step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It is designed to solve the  memory limit problem and provides an efficient way for  parallel computing[26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Even with an excellent contrac-  tion path, contraction of a large tensor network is still  limited by its intrinsic memory complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In addition,  the elaborated data dependency between the tensors be-  comes a bottleneck for contraction with multiple com-  putational units since it needs a lot of inter-processor  communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Slicing the indices can split the original  tensor network into multiple tensor networks with iden-  tical structures (same hypergraph), each with a memory  cost small enough to fit into a single processing unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The  simulator can execute these sub-tasks in parallel without  dependencies or sequentially depending on the computa-  tional resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The value of the original tensor network  is given by summing up the partial results obtained from  the contractions of each sub-tasks, in which the assign-  ment of the selected sliced indices is fixed[27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Take Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 3  as an example, after slicing, the original tensor network  can be further represented as:  Tde :=  �  i=a  (  �  c,b,f  A(i)  c B(i)  bf CbceDcdEef).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (6)  Finding the optimal subset of indices to slice is also an  NP-hard task with complexity O(mn), where m and n are  the number of all and sliced indices, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The  strategy here is to use a heuristically greedy algorithm  described as the following:  (a) find out all intermediate tensors that are larger than  the target size;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (b) pick up one index shared by the largest tensors or  appears most frequently among step (a) tensors random;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (c) repeat the above steps until the contraction width is  low enough.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Finding slicing indices is strongly entangled with  searching for the best contraction path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Slicing is based  on an existing contraction path, but the optimal path  for the original tensor network is not guaranteed to be  suitable for slicing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Therefore, JDtensorPath proposes a  two-phase indices-slicing-incorporated contraction path  6  finding heuristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The first phase generates contraction  tree trials followed by 128 pseudo-slicing trials, which  only calculate the FLOPs without actually slicing indices  on contraction trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In the second phase, apply “real”  slicing trials (default is 1024 times) on the contraction  tree with the lowest FLOPs after pseudo-slicing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Then,  the simulator can obtain a “good enough” slicing indices  and contraction path for sub-tasks in a reasonable search-  ing time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The implementation of the slicing heuristic is  based on set operations, and the simulator will store only  the best-sliced contraction tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' By doing so, it becomes  a very efficient and memory-saving algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Besides,  this slicing subroutine can also be carried out in parallel  in the CPU computation using the Ray framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Users API  TeD-Q enables users to customize their control of the  tensor network contraction process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Code Listing 4 shows  an example of compiling a quantum circuit with tensor  network contraction mode using JDtensorPath.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 def  circuitDef(parameters):  2  # Circuit  definition  3 # parse  and  construct  the  circuit  4  circuit = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='circuit(circuitDef , n_qubits , parameters  )  5 # compile  the  quantum  with  tensor  network  contraction  mode by using  JDtensorPath  6 from  jdtensorpath  import  JDOptTN  as  jdopttn  7  slicing_opts = {’target_size ’:2**28 ,  8  ’repeats ’:512 ,  9  ’target_num_slices ’:None ,  10  ’contract_parallel ’:True}  11  12  hyper_opts = {’max_time ’:120 ,  13  ’max_repeats ’:128 ,  14  ’search_parallel ’:8,  15  ’slicing_opts ’: slicing_opts }  16  17  compileCir = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (  18  backend = "pytorch",  19  use_jdopttn = jdopttn ,  20  hyper_opt = hyper_opts ,  21  tn_simplify = False)  Code Listing 4: How to use tensor network contraction  mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  To enable the tensor contraction mode, user needs to  specify the options for slicing and hypergraph-based op-  timizer, shown as “slicing opts” and “hyper opts”, and  pass these options and a contraction path optimizer,  shown as “jdopttn”, into the circuit compiler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The com-  piled circuit would be constructed in tensor contraction  mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The detailed description of each option and ar-  gument can be found in the github repository and the  documentation of TeD-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  VARIATIONAL QUANTUM CIRCUIT  Optimization is an important common factor of most  NISQ algorithms, including quantum machine learning  and quantum chemistry simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  It relies on a hy-  brid quantum-classical optimization process on the pa-  rameterized quantum circuit, or the so-called variational  quantum circuit (VQC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' For instance, quantum neural  network (QNN) can be regarded as a VQC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In quantum  machine learning tasks, a VQC could work as a com-  ponent together with some pre- and post-processing like  feature extraction and prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Typically, the cost  function of a task can be taken as the expectation value  of a VQC:  f(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' θ) = ⟨ ˆO⟩ = ⟨0|U †(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' θ) ˆOU(x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' θ)|0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (7)  The optimization process relies on the gradient of the cir-  cuit output with respect to the parameters of the quan-  tum gates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The parameter shift and finite differential  methods are the common methods to obtain gradients  of a quantum circuit for both quantum hardware and  simulation, which are the built-in methods of TeD-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  However, the simulation with such methods usually takes  a very long time due to the computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Meanwhile, the demand for fast simulation of circuits  with large number of qubits has become urgent due to  recent development of large-scale quantum devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' To  this end, TeD-Q provides an efficient method to com-  pute the gradient of a circuit in the simulation via the  conventional backpropagation technique and the newly-  developed tensor-network engine of TeD-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Backpropagation method  The backpropagation method in TeD-Q is based on the  well-developed automatic differentiation libraries, such  as PyTorch[28] and JAX[29], which have been widely  used in classical machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  These libraries are  integrated into TeD-Q as simulation backends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  When  the backend is specified, TeD-Q will convert the matrix  data of the quantum circuit to the corresponding format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  While evaluating the quantum circuit, known as the ”for-  ward” computation, the backend will store all of the in-  termediate results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The backend will use the chain rule  to obtain the gradient of the gate parameters from the  circuit output, known as backpropagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This function  will store the gradient of each intermediate result so that  the gradient of all of the parameters can be evaluated at  one time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Although the backpropagation method cannot  be applied to real quantum devices, this is the fastest  method to obtain the gradient in quantum simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Thus, this is the default method for the simulation back-  ends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 def  circuitDef ( parameters):  2  # Circuit  definition  3 # parse  and  compile  the  circuit  4 cir = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='circuit(circuitDef , n_qubits , parameters )  5  myCompileCir = cir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (  6  backend="pytorch")  Code Listing 5: How to use backpropagation method to  get the gradient of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  7  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Parameter shift and finite differential method  In real quantum devices, the gradients of the variables  can only be obtained by the parameter shift method or  finite differential method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The parameter shift method  can provide the analytical derivatives, while the finite-  differential method provides only numerical derivatives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  In TeD-Q, we implement the parameter shift method  based on the theoretical paper [30, 31] and recent devel-  opments by [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This method can be applied to quantum  gates with the form eiµH, where H is a Hermitian opera-  tor with two or four eigenvalues, and µ is the parameter  of the gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' For a single gate parameter, the analytical  derivative can be calculated by evaluating the expecta-  tion value of the circuit twice with the parameter value  being µ + s and µ − s[30], as shown in Equation 8, where  s is the shift and k is the shift constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q’s back-  end will shift the parameters automatically with proper  spacing for each gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' For the simulation backend, like  PyTorch or JAX, the user can use the parameter shift  method to obtain the gradient by specifying it in the dif-  ferential option while compiling the circuit, as shown in  Code Listing 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' For the hardware backend, the param-  eter shift is the default and only method to obtain the  gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  ∂f  ∂µ =  �  �  �  k[f(µ + s) − f(µ − s)]  parameter shift  f(µ+∆µ)−f(µ)  ∆µ  finite differential  (8)  1 def  circuitDef(parameters):  2  # Circuit  definition  3 # parse  and  compile  the  circuit  4 cir = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='circuit(circuitDef , n_qubits , parameters )  5  compileCir = cir.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (  6  backend="pytorch",  7  diff_method = " param_shift ")  Code Listing 6: How to use parameter shift method to  get the gradient of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Quantum to classical computing interface  The design paradigm of TeD-Q provides seamless inte-  gration of quantum and classical processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In this hy-  brid algorithm, a quantum circuit that is parameterized  by tunable variables is seen as a normal Python function  with a specific interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It can be inserted into a classical  optimization function or wrapped in a layer of a machine  learning framework module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  TeD-Q supports two interfaces – JAX array and Py-  Torch tensor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' For the JAX simulation backend, the JAX  array is the default one, but the PyTorch tensor inter-  face can also be used via the interface keyword argument  (interface=”pytorch”) while compiling the quantum cir-  cuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' As for the PyTorch simulation backend and hard-  ware backend, TeD-Q only supports the PyTorch back-  end at the time of writing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The interfaces provide a  seamless connection to the classical part in ”forward”  calculation and in ”backward” gradient extraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' For  simulation backends with their own interface and de-  fault backpropagation gradient method, the integration  is straightforward, relying on built-in data structure and  automatic differentiation algorithm of JAX or PyTorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  For other cases (JAX backend with PyTorch tensor in-  terface, hardware backend, parameter shift method), the  classical backpropagation algorithm cannot process the  quantum information inside the quantum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  For  this situation, the quantum circuit is treated as a black  box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q implements custom autograd functions and  will compute and provide the gradient (one output) or  Jacobian (multiple inputs and multiple outputs) of the  quantum circuit with respect to its classical inputs and  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Code Listing 7 shows an example of connecting  the JAX backend quantum circuit to the classical calcu-  lation by the PyTorch tensor interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  More detailed  examples can refer to Section V A 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The integration is  imperceptible to the user, via JAX or PyTorch, with the  flexibility to run the hybrid quantum-classical algorithms  code on CPUs, GPUs, and TPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 # Quantum  circuit  construction  2  # Neglect  here  3  4 # Compile  quantum  circuit  with  JAX  quantum  simulation  backend  and  PyTorch  interface  5  compileCirJAX = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (  6  backend="jax",  7  interface="pytorch")  8  9 # Connect  quantum  systems  to  classical  cost  function  by  PyTorch  interface  10 def  cost(weight , params):  11  return  weight * compileCirJAX (params)  12  13 # PyTorch  tensor is used as input  14  weight = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='tensor (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5)  15  params = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='tensor ([0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='12])  16 cost(weight , params)  Code  Listing  7:  Quantum  to  classical  computing  interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  A quantum circuit is compiled into an  executable quantum object by using JAX simulation  backend and PyTorch tensor interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The executable  quantum circuit is then integrated with classical cost  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  USE CASE  The detailed introduction and manual of the user in-  terface can be found in the online documentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It in-  cludes step-by-step examples demonstrating the feature  of Ted-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In the following section, We briefly go through  the main features and its use cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Basic quantum circuits  Quantum circuit evaluation is the basic function of  TeD-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It provides a universal set of quantum gates so  8  all kinds of quantum circuits can be constructed and sim-  ulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' With the tensor network engine described in Sec-  tion III B, TeD-Q can process the simulation faster than  the conventional quantum simulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Besides, TeD-Q is  equipped with an easy-to-use graphical circuit composer  and circuit drawer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' These tools are well integrated with  TeD-Q’s simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Users can use it for quick prototyping  of the quantum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Moreover, the hardware backend  in Ted-Q provides an interface to the real quantum de-  vices like Qiskit[5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Users Can switch the simulation to a  real experiment with a simple command.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The following  sections demonstrate these features via TeD-Q API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Fast simulation  Consider a simple two-qubit quantum circuit with a  Hadamard gate on qubit 0, a CNOT gate on qubits 0  and 1, and a rotation gate Rot on qubit 1 apply to the ini-  tial zero state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' And we want to obtain its quantum state  with some input rotation angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q can implement  the simulation as code block 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Qubits are counted from  0 and multiqubit registers labeled with the first (zeroth)  qubit on the left.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Measurement of a quantum state is only  available by the simulation backend, while both simula-  tion and hardware backend enables expectation values  and probability measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Keyword argument “re-  quires grad” can disable the gradient feature and improve  the simulation speed since the backend doesn’t need to  store the intermediate state for backpropagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1  import  tedq  2  import  torch  3  n_qubits =2  4  5 # Circuit  definition  6 def  circuitDef(phi , theta , omega):  7  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Hadamard(qubits =[0])  8  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='CNOT(qubits =[0, 1])  9  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Rot(phi , theta , omega , qubits =[1])  10  # Return  quantum  state  11  return  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='state ()  12  13 phi = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='tensor ([0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='4])  14  theta = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='tensor ([0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5])  15  omega = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='tensor ([0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='6])  16  circuit = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Circuit(circuitDef , n_qubits , phi , theta  , omega)  17 # Parse  and  compile  the  circuit  18  compileCir = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (backend="pytorch",  requires_grad =False)  19  20 # Obtain  the  quantum  state  21  quantum_state = compileCir ()  Code Listing 8:  An example of a simple two-qubits  quantum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Hadamard and CNOT gates are  used to generate a entangled state, Rot gate is used for  adding some rotation angle and the final quantum state  is measured at the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Intuitive prototyping  Circuit composer in TeD-Q is a WYSIWYG (what you  see is what you get) editor for a quantum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The  graphical composer can be initialized with a single line  command, as shown in Code Listing 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  It consists of  a panel for the template quantum gates and the several  qubits indicated by lines, as shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Users can  construct the circuit by dragging the icon of the quantum  gate to a specific qubit line or remove one quantum gate  by dragging it away from the qubit line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Users can also  adjust the sequence of the operations by pulling the icons  to the desired location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 # Enable  circuit  composer  2  composer = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' circuit_composer (4, figsize =(11 ,5))  Code Listing 9: Usage of circuit composer  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 4: Circuit composer  The composing result can be converted and fed into  TeD-Q’s tensor network engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The user can obtain the  simulation result using the same method mentioned in  the previous section, as shown in the Code Listing 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Users can also get the circuit definition from the com-  posing result for further development with TeD-Q API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 # Convert  to  circuit  class  2  circuit = composer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='toCircuit ()  3  compiledCircuit = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit ()  4  5 # Evaluating  the  circuit  6 prob = compiledCircuit ()  7  8 # Print  the  circuit  definition  9  print(circuit)  Code Listing 10: Converting the composing result to a  TeD-Q circuit and obtaining the circuit definition  Besides the circuit composer, the circuit initialized by  the script can also be visualized with the circuit drawer,  as shown in the Code Listing 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  It follows the same  drawing style as the circuit composer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Moreover, the  function will automatically fit the circuit to the correct  size of the plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 # Init a circuit  2  circuit = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='circuit(circuitDef ())  3 # Draw a circuit  4 tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' draw_circuit (circuit)  Code Listing 11: Usage of circuit drawer  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Hardware compatibility  Aside from simulation, the circuit can also be adopted  to real quantum devices with the hardware backend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' At  the time of writing, TeD-Q only supports IBM-Q quan-  tum devices, and more quantum hardware devices will be  Del  X  Z  S  H  RX  Y  RZ  CNOT  x9  available soon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The built-in parameter shift method is re-  sponsible for obtaining gradients of the quantum circuit,  and the PyTorch tensor interface is provided for com-  munication with other functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Code Listing 12 shows  an example of compiling a quantum circuit into two exe-  cutable quantum objects with both simulation and hard-  ware backends and tries to minimize their difference by  tuning input parameters with a built-in gradient-descent  optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 # Quantum  circuit  construction  2  # Neglect  here  3  4 # Compile  quantum  circuit  with  hardware  backend ,  default  PyTorch  interface  5 from  qiskit  import  IBMQ  6 IBMQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' enable_account (’your  IBMQ  token ’)  7  compileCirHardware = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (backend="  IBMQ_hardware ")  8  9 # Compile  quantum  circuit  with  JAX  quantum  simulation  backend  and  PyTorch  interface  10  compileCirJAX = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (backend="jax",  interface="pytorch")  11  12 # Connect  two  quantum  systems  to  classical  cost  function  by  PyTorch  interface  13 def  cost(params):  14  results = ( compileCirHardware (params) -  compileCirJAX (params))**2  15  return  results  16  17 # Tuning  variables  with built -in  optimizer  18  Optimizer = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' GradientDescentOptimizer (  19  objective_fn =cost ,  20  trainable_params =[0, 1],  21  interface="pytorch")  22  params = (torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='tensor ([0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='12] ,  requires_grad =True),  23  torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='tensor ([0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='75] ,  requires_grad =True))  24  new_variables = Optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='step (* params)  Code Listing 12: Hardware compatibility example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  A  quantum circuit is compiled into two executable quantum  objects with JAX simulation backend and hardware  backend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  And these two executable quantum circuit  are connected to classical cost function with PyTorch  interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Variational quantum algorithm  A variation quantum algorithm consists of a variational  quantum circuit and a classical optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The method  to obtain the gradient of a gate parameter in a quantum  circuit is described in Section IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Recursively updating  the gate parameters allows the circuit to be optimized  according to a certain cost function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It’s widely used in  current NISQ devices and quantum simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' With  TeD-Q’s tensor engine, simulation can be processed at a  very high speed compared to other simulation packages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Besides, with the hardware backend, the variational al-  gorithm can also be adapted to a real quantum device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The following example shows a simple circuit based on  the variational quantum algorithm to demonstrate how  to construct a VQA circuit by TeD-Q API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1  import  tedq  2  import  torch  3  n_qubits =3  4  5 # Circuit  definition  6 def  circuitDef (theta):  7  # Circuit  8  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='RX(theta [0], qubits =[0])  9  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='RY(theta [1], qubits =[1])  10  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='RZ(theta [2], qubits =[2])  11  12  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='CNOT(qubits =[0, 1])  13  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='CNOT(qubits =[1, 2])  14  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='CNOT(qubits =[2, 0])  15  16  # Measurement  17  for idx in range(n_qubits):  18  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' measurement .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='expval(tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='PauliZ(qubits =[ idx  ]))  19  20 # Parse  and  compile  the  circuit  21  circuit = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Circuit(circuitDef , n_qubits , torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='rand  (n_qubits))  22  my_compilecircuit = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (backend="  pytorch" )  23  24 # Init  the  parameters  by the  torch  library  25  params = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='rand(n_qubits , requires_grad =True)  26  27 # Forward  computation  of the  expectation  value  28  exp_val = my_compilecircuit (params)  29  30 # Define  the  loss  function  31  optimizer = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Adam ([ params], lr =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5)  32 loss = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='nn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='MSELoss(reduction=’mean ’)  33 l = loss(exp_val , torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Tensor ([0, 1, 1]))  34  35 # Backward  computation  for the  gradient  of the  parameters  36 l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='backward ()  37  38 # Output  the  result  39  print("Expected  value  from  circuit: ", exp_val)  40  print("Gradient  of  parameters ", params.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='grad)  Code Listing 13:  Example of variational quantum  algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Quantum machine learning  Machine learning deals with the problem of generaliza-  tion from finite data in high-dimensional Hilbert spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  It is a very appealing application for quantum compu-  tation since both of them involve statistics theories at  a fundamental level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Users can transform classical fea-  ture information into the quantum state through encod-  ing schemes (basis encoding, amplitude encoding, angle  encoding, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ):  |ψ(x)⟩ =  �  �  �  �  �  �  �  �  �  |ix⟩  basis encoding  �n  i xi|i⟩  amplitude encoding  ⊗n  i R(xi)|0n⟩  angle encoding  (9)  VQA can be designed as a linear model to classify data  explicitly in Hilbert space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' With a nice performance of  TeD-Q’s tensor engine, a more complex VQA circuit can  be constructed and simulated, which allows testing of a  large-scale quantum and hybrid quantum-classical ma-  chine learning algorithm with the simulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  10  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Templates  TeD-Q equips several pre-defined quantum circuit tem-  plates, or ansatz, commonly used in the quantum ma-  chine learning field to enable the fast development of  the circuit for quantum machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The following  briefly introduces three templates in TeD-Q – Random-  generated layer, Fully-connected layer, and Hardware-  efficient layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The randomly-generated layer can provide a circuit  with a single- and two-qubits gate while their locations  and parameters are random (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It’s suitable for sim-  ulating a non-linear transformation, as shown in TeD-Q’s  Quanvolution Neural Network example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 5: Randomly-generated circuit  The fully-connected layer is a parameterized circuit  to provide maximum entanglement among each qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The number of layers is called depth, which the user  can customize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Each qubit is connected to the other  qubits in each layer by a CNOT gate followed by a two-  parameterized rotation gate (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This template is  usually used to simulate a classical fully-connected layer  in quantum machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 6: Fully-connected circuit  The hardware-efficient layer is a practical implemen-  tation of a fully-connected circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In the real quantum  device, a two-qubit operation is only efficient between the  qubit nearby the qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Therefore, the CNOT gates in  this template are only placed between the qubits nearby  a selected qubit (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Quantum layer wrapping  Users can easily exploit quantum machine learning by  replacing some layers of a well-developed classical ma-  chine learning model with a wrapped quantum layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 7: Hardware efficient circuit  Code Listing 14 illustrates how to build the pipeline in  TeD-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1 # Global  variable  2  n_qubits = 8  # Number of  qubits  3  q_depth = 12  # Number  of  variational  layers  4  n_classes = 10  # Number of image  classes  5  6 # Angle  encoding  7 def  features_encoding (nqubits , w):  8  for idx in range(nqubits):  9  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Hadamard(qubits =[ idx ])  10  for idx , element  in  enumerate(w):  11  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='RX(element , qubits =[ idx ])  12  13 # Define a variational  quantum  circuit  14 def  circuitDef (q_input_features , q_weights_flat ):  15  # Reshape  weights  16  q_weights = q_weights_flat .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='reshape (( q_depth +1)*2,  n_qubits)  17  18  # Encode  classical  features  into  quantum  state  19  features_encoding (n_qubits , q_input_features )  20  21  # Built -in  template  circuit  22  tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='templates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' HardwareEfficient (n_qubits , q_depth ,  q_weights)  23  24  # Expectation  values  measurement  25  exp_vals = [tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='expval(tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='PauliZ(qubits =[  position ])) for  position  in range(n_qubits)]  26  return  tuple(exp_vals)  27  28 # Quantum  circuit  construction  29  circuit = tedq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Circuit(circuitDef , n_qubits , torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  zeros(n_qubits), torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='zeros (( q_depth +1)*2,  n_qubits))  30  compiledCircuit = circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' compilecircuit (backend="  pytorch")  31  32 # Quantum  layer  with  PyTorch  NN  interface  33  class  DressedQuantumNet (nn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Module):  34  def  __init__(self):  35  super ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='__init__ ()  36  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='pre_net = nn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Linear (2048 ,  n_qubits)  37  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='q_params = nn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Parameter(q_delta * torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  randn (( q_depth +1) * n_qubits *2))  38  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='post_net = nn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='Linear(n_qubits , n_classes)  39  def  q_func( q_input_features ):  40  return  compiledCircuit (q_input_features ,  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='q_params)  41  from  functorch  import  vmap  42  # for  batch  executation  43  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' batched_q_func = vmap(q_func)  44  45  # Tensors  moves  through  quantum  circuit  46  def  forward(self , input_features ):  47  pre_out = self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='pre_net( input_features )  48  q_in = torch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='tanh(pre_out) * np.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='pi / 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  49  q_out = self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' batched_q_func (q_in).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='float ()  50  return  self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='post_net(q_out)  51  52 # Replacing  classical  machine  learning  model  ResNet -50  fully -connected  layer  with  quantum  layer  53  model_hybrid = torchvision .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='resnet50 ()  x  Rx  Rz  Rx  RyRy  Ry  Rz  Ry  Rz  Ry  Ry  Rz  X  Ry  Rz  Ry  Ry  Rz  X  +  Ry  Rz  Ry  Ry  Rz  X  X  Ry  Rz  Z  XRy  Ry  Rz  Ry  Rz  Ry  Ry  Rz  X  Ry  Rz  Ry  Ry  Rz  X  Ry  Rz  Ry  Ry  Rz  X  Ry  Rz11  54  model_hybrid .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='fc = DressedQuantumNet ()  Code Listing 14: Code snippet for creating a hybrid-  quantum-classical machine learning model for image  recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The quantum circuit is wrapped into a  quantum layer and used to replace the fully-connected  layer of the classical deep learning model ResNet-50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The  main structure of this example follows the PennyLane  tutorial on quantum transfer learning[32]  The above example shows a way of constructing a hy-  brid quantum-classical machine learning model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q  can straightforwardly integrate quantum algorithms with  various well-established machine learning practices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The  quantum circuit model behaves as if it was a pure classi-  cal one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' All the following processes, like cost function or  optimization, can be seamlessly adopted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In the next ,  a pure quantum machine learning example is introduced  and used as a benchmark to compare the performance of  TeD-Q and other software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  PERFORMANCE  We benchmark TeD-Q’s performance with other quan-  tum software through two examples – multiple qubits ro-  tation (MQR) and many body localization (MBL) [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  MQR is a very simple algorithm which uses hardware-  efficient network to flip the quantum state from all ze-  ros state |0⟩⊗n to all ones state |1⟩⊗n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It is suitable for  evaluating TeD-Q’s performance on small and simple cir-  cuit which can be run on personal computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' MBL is  a relatively complex problem of great significance both  theoretically and practically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It is used to demonstrate  the great advantage of TeD-Q tensor network contraction  mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The source code of the comparison can be found  on TeD-Q’s Github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Multiple qubits rotation  In this simulation, the initial quantum state is set to be  all zeros state |0⟩⊗n followed by a variational hardware-  efficient network and expectation value measurement on  Pauli-Z basis for each qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The learning is done by min-  imizing sum of the measurements through tuning param-  eters via gradient descent method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' And the performance  of platforms are evaluated by the time cost for finishing  500 iterations of training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Since there is a great demand  for user to develop and learn quantum algorithm through  simple circuit on their personal computer, the evaluation  is done with single AMD RyzenT M 5 3500U mobile pro-  cessor CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 8 shows the advantage of TeD-Q in this  application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 8: Performance comparison among TeD-Q,  PennyLane, Paddle Quantum and Qiskit for small  simple circuit on single laptop CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q result uses  the PyTorch backend with backpropagation gradient  method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  VQE of Hydrogen Molecule  Variational quantum eigensolver (VQE) method is one  of the popular applications of quantum computing in the  NISQ era [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  It is a concrete example of variational  quantum algorithm (VQA) used for solving quantum  chemistry problems, specifically, the eigenstate problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  In a VQE algorithm, a parameterized quantum circuit  would prepare a quantum state, dubbed as the ansatz  state, which is supposed to be the ground state of the  Hamiltonian of the molecule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' By repeatedly measuring  the ansatz state with different measurement settings, the  expectation value of the Hamiltonian could be evaluated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  An optimization process could be applied to the parame-  ters of the quantum circuit so that the expectation value  could be minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Here we use the VQE of Hydrogen molecule to illus-  trate the performance of TeD-Q versus other platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  In this experiment, there are totally four qubits and the  quantum circuit contains 12 freely changing parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (The problem can in principle be simplified to use just  one qubit, but we did not do this since we only want to  compare the speed on the same ground.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=')  We run the experiment on a Macbook Air with Intel  CoreT M i5-1030NG7 CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' As we could see from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 9,  TeD-Q converges to an error of 10−6 Hartree about 3  times faster than Pennylane and around 15 times faster  than Qiskit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' With a limited time of execution, for in-  stance, within 5 seconds as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 10a, TeD-Q  can correctly plot the energy curve of the ground state  with different H-O distances, while Pennylane can almost  do it and Qiskit being far away from that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' When the time  limit is set to 30 seconds Pennylane can converge to the  correct energy curve but Qiskit still cannot, as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 10b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' From this comparison, we can see TeD-Q  indeed has advantages in simulating traditional VQE al-  gorithm over the compared platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  102  time (s)  101  TeD-Q State Vector Propagation Mode  PennyLane  Paddle Quantum  100  Qiskit  2  4  6  8  10  Number of qubits12  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 9: Error between the VQE result and the FCI  reference energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (a) Execution time limited to 5 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (b) Execution time limited to 30 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 10: Energy curve of the Hydrogen atom from VQE  with limited execution time and FCI methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Quantum GAN  Classical generative adversarial network (GAN) has  found its position in artificial intelligence via rapid grow-  ing applications recent years [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The idea is to utilize a  generative network to create new data that resembles the  (a) QGAN patch  (b) QGAN non-patch  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 11: Performance comparison between TeD-Q and  PennyLane for quantum GAN training on single laptop  CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q result uses the PyTorch backend with  backpropagation gradient method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  original data, while a discriminative network tries to eval-  uate the distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The two networks contest with each  other to play a zero-sum game, which leads to improved  quality of the newly generated data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Quantum GAN borrowed this idea and wishes to boost  the performance by quantum computing [35, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' While  it is possible to use QNN in both the generative and  discriminative networks, here, we adopt both the patch  and non-patch quantum GAN methods where only the  generative part is made quantum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  In this example, the generator tries to mimic the hand-  written zeros from a small set of grayscale samples im-  ages with size 8 × 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Please see [36] for details of the  QGAN example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Similar to the multiple qubits rotation  example, we run the experiment with an AMD RyzenT M  5 3500U mobile processor CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' As we can see from the  result Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 11, in either patch or non-patch scenario, TeD-  Q outperforms Pennylane in the training of the quantum  GAN model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  15  TeD-Q  Pennylane  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  Qiskit  Energy(Hartree)  FCI reference energy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5  Distance(ao)0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='75  TeD-Q  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='50  Pennylane  Qiskit  nergy(Hartree]  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='25  FCI reference energy  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='25  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='50  6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='75  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5  10  15  20  25  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='5  Distance(ao)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='6  TeD-Q State Vector Propagation Mode  PennyLane  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  S  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='8  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  0  200  400  600  800  1000  1200  1400  time (s)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='4  TeD-Q State Vector Propagation Mode  PennyLane  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='8  S  oss  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='0  0  200  400  600  800  1000  1200  1400  time (s)100  TeD-Q  Pennylane  10~1  Qiskit  10~2  W  Jau  E-OT  10-4  105  10~6  0  20  40  60  80  100  120  140  Time(s)13  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Quantum Architecture Search  Quantum architecture search (QAS) was recently pro-  posed to generate better variational ansatz circuits for  given VQA tasks [37, 38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  By constructing an ansatz  pool, QAS iteratively samples a new ansatz at every step  of the optimization in the VQA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It can be shown that  by doing this, the resulting ansatz improves the perfor-  mance of the VQA in terms of both circuit output and  learnability in learning tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  In the training of the QAS task, the ansatz circuit is  replaced by new sample from the pool at every step of  the optimization, which requires the backend to compile  the new ansatz circuit at every step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Thus, the differ-  ence of the performance mainly depends on the speed of  implementing each circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' We run the experiment on a  Macbook Air with Intel CoreT M i5-1030NG7 CPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The  result in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 12 shows the time the training takes with  increasing iteration numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q is more than 2 time  faster than Pennylane when performing QAS tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 12: QAS performance comparison between TeD-Q  and Pennylane  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Many body localization  Many body localization (MBL) is a phase of an iso-  lated many-body quantum system that prevents it from  thermalization;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' that is, a system in this phase can pre-  serve the initial information as time evolves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It provides  a possibility to hold the quantum effect for a long time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The experimental and theoretical research in this field  has been dramatically progressing in recent years due to  the rapid development of quantum technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In this  section, we demonstrate that TeD-Q can process a sim-  ulation of a 1-D MBL along with a quantum neural net-  work with more than 50 qubits at a reasonable speed,  which is not achievable by conventional quantum simu-  lators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  For an isolated many-body quantum system, it evolves  under its intrinsic Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The interaction between  the particles exchanges information and energy so that  the close system reaches thermal equilibrium as the whole  system is the thermal bath of its subsystem[39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The in-  formation of its initial state is eventually washed out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  However, in the presence of sufficient disorder poten-  tial, the system can reach the many-body localization  phase and prevent it from falling into thermal states even  though the particles in the system still interact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Ergodic state  Localized state  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 13: Many body localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The shade of the  circles represents probability to be |1⟩ state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The  system is initially prepared in the Neel state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' After the  evolution under its intrinsic Hamiltonian and a  controllable disorder potential, the system can fall into  either ergodic state, as shown in the bottom left, or  localized state as shown in the bottom right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The system would fall into thermalization with a small  disorder potential, known as the ergodic state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' On the  other hand, with sufficient disorder power, the system  would be in the MBL phase and stay in its initial state,  known as the localized state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' However, multiple measure-  ments are required to distinguish a localized state from  an ergodic state for a many-body system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Following the  circuit architecture shown in [40], we develop and train  a quantum neural network for classifying the states of a  1-D many-body system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' With this QNN circuit, we can  identify whether the circuit is either an ergodic state or  a localized state with a single measurement on the first  qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Simulation setup  In our simulation, the qubits are placed in a chain and  prepared in the Neel state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It is followed by a simulated  Hamiltonian Hd includes the interactions between the  nearest qubits and a controllable random disorder di for  each qubit, which is  Hd = ℏ  �  i,j  diσi  z + gi,j(σi  xσj  x + σi  yσj  y)/2,  (10)  and the system is evolving under this Hamiltonian for a  period of time td.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' For the state classification, the cir-  cuit is then connected to a classifier built in a digital-  analog quantum neural network, proposed by [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  It  is consist of Nq + 1 single-qubit operation R(θi, φi) =  350  TeD-Q  Pennylane  300  250  200  150  100  50  0  0  100  300  400  500  Iteratian [#)U=e  Hdtd14  Z(θi)X(φi)Z(−θi), which is the digital part, and an uni-  tary operation H0, which is the analog part, on each  qubit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  H0 = gi,j(σi  xσj  x + σi  yσj  y)/2,  (11)  Finally, the only measurement was placed on one of the  qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The parameters of QNN would be trained so that  the measurement of it can classify the state of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The circuit diagram is shown in Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  …  State preparation  Quantum neural network  BCE loss  Gradient  Truth  Classical optimizer  Localized state  Ergodic state  Recursively update the parameters  …  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 14: The quantum circuit and the classical  optimizer used in MBL simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The diagram can be  separated into three stages – state preparation,  quantum neural network (QNN), and classical  optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The state preparation stage generates the  state in either ergodic or localized state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The QNN  stage is trained to distinguish ergodic states from  localized states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The optimizer stage evaluates the  result and optimizes the QNN based on the loss  function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The simulation parameters, like gi,j and td, follow the  setting used in [40], which are the properties of a 64-qubit  quantum computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' The parameters in the classifier are  then trained with the binary cross entropy loss so that  the expected value of the the selected qubit can be 1  when the system is in an ergodic state and 0 when the  system is in a localized state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Speed comparison  The performance of TeD-Q is evaluated by the time  cost for finishing 50 epochs of 1D-MBL training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  The  circuit depth is about 89, and each epoch consists of 40  training iterations of the circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' For the comparison, we  also set up the same simulation using Qiskit and Penny-  lane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' CPU simulations use Intel(R) Xeon(R) Processor  E5-2680 v4 @ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='4GHz CPU while GPU simulations use  Nvidia Tesla P40 24 GB GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Figure 15 compares these three quantum simulation  methods on CPU and GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q can provide similar  behavior as PennyLane while using state vector propaga-  tion mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This method becomes computationally infea-  sible while the simulation involves more than 20 qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  However, TeD-Q, using tensor network contraction mode,  can process the same simulation with up to 50 qubits  within a comparable time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  (a) Single CPU mode  (b) Single GPU mode  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 15: Performance comparison among TeD-Q,  PennyLane and Qiskit for the MBL task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Discussion  Generally, the state vector propagation mode of TeD-  Q and PennyLane have similar performance both in CPU  and GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This is with-in our expectation since both of  them calculate the full amplitude and use backpropaga-  tion method for obtaining gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q has a slight  advantage (20 ∼ 30%) over Pennylane on CPU for qubits  less than 11, this can be explained by the reusable mech-  anism that saves the time for state and gate class instan-  tiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Tensor network contraction mode shows its power on  large qubit systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It can reduce the computation and  memory complexity substantially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' But currently its per-  formance is constrained by inefficient use of GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Most  pair contractions in the contraction path involve small  tensors, they contribute very small portions of the over-  all computation and memory complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' But the trans-  mission of these small tensors to GPU will cost sizable  overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This overhead problem can be improved by  pre-computing contractions with small sizes on CPU and  only performing the large ones on GPU[26], which will  be included in the future release of TeD-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  104  time (s)  103  TeD-Q State Vector Propagation Mode  TeD-Q Tensor Network Contraction Mode  PennyLane  102  Qiskit  5  10  15  20  25  30  3540 45 50  Number of qubits104  time (s)  103  TeD-Q State Vector Propagation Mode  TeD-Q Tensor Network Contraction Mode  PennyLane  Qiskit  5  10  15  20  25  30  35 40 45 50  Number of qubitsR(0,Φ-Hoto  U=e0U=e  HdtdR(0o, Φ0R(ON, ΦNR(01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 01R(02, Φ215  VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  SUMMARY  In this work, we introduced TeD-Q, an open-source  software framework for quantum machine learning, varia-  tional quantum algorithm, and quantum computing sim-  ulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' With tensor contraction, simulation of quantum  circuit with large number of qubits is possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q  seamlessly integrates classical machine learning libraries  with quantum simulators, allowing users to leverage the  power of classical machine learning while training quan-  tum machine learning models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q is also empowered  with the capability of training quantum machine learn-  ing models in a distributed manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' This is an important  feature considering that most NISQ quantum algorithms  require results from multiple instances of the same quan-  tum circuit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In TeD-Q, the quantum circuit is seen as a  Python function, which makes it easy to use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' TeD-Q is  device independent so that users can run the circuits on  different backends, including software simulators (JAX  and PyTorch) and quantum hardwares.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  To better facilitate the implementation of quantum  machine learning, TeD-Q supports automatic differen-  tiation, for instance, backpropagation, parameters shift,  and finite difference methods, to obtain gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' It also  has a flexible interface that bridges quantum circuits  to powerful machine learning libraries (like PyTorch).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  In addition, TeD-Q supports visualization functionality,  where users can visualize quantum circuits and training  progress in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  There are still challenges in future works of TeD-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  One crucial aspect is how to leverage distributed com-  putation’s ability to solve real quantum machine learn-  ing problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Even though TeD-Q supports distributed  computation, algorithms, and applications that make the  most use of it are still lacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Another aspect that TeD-  Q can improve is to work completely compatible with  different kinds of quantum hardwares on the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' We  have demonstrated how TeD-Q can access the hardware  resources on the IBM cloud in Section V A 3 and in later  releases support for other platforms, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pennylane and  Amazon, will be introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' In principle, TeD-Q is ready  to connect with any device;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' however, due to the lack of  quantum hardware resources, this has not been tested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  It would be exciting to see TeD-Q working with differ-  ent hardware backends and implementing real distributed  quantum algorithms, especially QML algorithms, in the  future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  ACKNOWLEDGMENTS  We appreciate the helpful discussion with Juhua Liu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Author contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' conceived the project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' de-  signed the architecture of the software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' did the coding and carried out the  numerical simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-  Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' analyzed the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  All authors  contributed to discussions of the results and the develop-  ment of the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' wrote the manuscript with input from all co-authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' supervised the whole  project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [1] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Arute, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Arya, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Babbush, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bacon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bardin,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Barends, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Biswas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Boixo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Brandao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Buell, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Nature 574, 505 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [2] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Madsen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Laudenbach, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Askarani, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rortais,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vincent, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bulmer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Miatto, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Neuhaus,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Helt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Collins, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Nature 606, 75 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [3] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chen,  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chung, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Deng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Du, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fan, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=',  Physical review letters 127, 180501 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [4] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bergholm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Izaac, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schuld, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gogolin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Alam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ahmed, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Arrazola, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Blank, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Delgado,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Jahangiri, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', arXiv preprint arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='04968  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' tA v, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ANIS, Abby-Mitchell, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Abraham,  AduOffei, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Agarwal, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Agliardi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Aharoni, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ajith,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Akhalwaya, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Aleksandrowicz, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Alexander,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Amy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Anagolum, Anthony-Gandon, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Araujo,  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Arbel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Asfaw, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Athalye, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Avkhadiev, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Azaus-  tre, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' BHOLE, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bajpe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Banerjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Banerjee,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bansal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Barkoutsos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Barnawal, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bar-  ron, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Barron, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bello, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ben-Haim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bennett,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bevenius, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bhatnagar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bhatnagar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bhobe,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bianchini, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bishop, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Blank, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bolos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bopar-  dikar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bosch, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Brandhofer, Brandon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bravyi,  Bryce-Fuller,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bucher,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Burgholzer,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Burov,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cabrera, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Calpin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Capelluto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Carballo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Car-  rascal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Carriker, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Carvalho, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chakrabarti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chen,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cheval-  lier, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chinda, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cholarajan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chow, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Churchill,  CisterMoke, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Claus, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Clauss, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Clothier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cock-  ing, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cocuzzo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Connor, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Correa, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Crockett,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cross, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cross, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cross, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cruz-Benito,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Culver, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C´orcoles-Gonzales, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' D, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Dague,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Dandachi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Dangwal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Daniel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Daniels,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Dartiailh, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Davila, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Debouni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Dekusar,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Deshmukh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Deshpande, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ding, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Doi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Dow, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Downing, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Drechsler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Drudis, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Du-  mitrescu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Dumon, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Duran, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' EL-Safty, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' East-  man, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Eberle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ebrahimi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Eendebak, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Egger,  ElePT, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Elsayed, Emilio, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Espiricueta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Everitt,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Facoetti, Farida, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fern´andez, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ferracin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fer-  rari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ferrera, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fouilland, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Frisch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fuhrer,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fuller, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' GEORGE, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gacon, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gago, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gam-  bella, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gambetta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gammanpila, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Garcia,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Garg, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Garion, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Garrison, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Garrison, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gates,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gavrielov,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gentinetta,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Georgiev,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gil,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gilliam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Giridharan, Glen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gomez-Mosquera,  Gonzalo,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  de la  Puente Gonz´alez,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gorzinski,  16  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gould, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Greenberg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Grinko, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Guan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Guijo,  Guillermo-Mijares-Vilarino, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gunnels, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gupta,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gupta,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' G¨unther,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Haglund,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Haide,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hamamura, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hamido, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Harkins, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hartman,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hasan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Havlicek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hellmers, �L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Herok, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hill,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hillmich, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Horii, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Howington, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hu,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huisman, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Imai,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Imamichi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ishizaki, Ishwor, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Iten, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Itoko,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ivrii, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Javadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Javadi-Abhari, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Javed, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Jian-  hua, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Jivrajani, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Johns, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Johnstun, Jonathan-  Shoemaker, JosDenmark, JoshDumo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Judge, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kach-  mann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kale, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kanazawa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kane, Kang-Bae,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kapila, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Karazeev, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kassebaum, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kehrer,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kelso, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kelso, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' van Kemenade, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Khanderao,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' King, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kobayashi, Kovi11Day, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kovyrshin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kr-  ishnakumar, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Krishnamurthy, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Krishnan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kr-  sulich, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kumkar, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kus, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' LaRose, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lacal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lam-  bert, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Landa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lapeyre, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lasecki, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Latone,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lawrence, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lee, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Liang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lish-  man, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Liu, Lolcroc, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mad-  den, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Maeng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Maheshkar, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Majmudar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Maly-  shev, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mandouh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Manela, Manjula, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mare-  cek, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Marques, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Marwaha, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Maslov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mas-  zota, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mathews, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Matsuo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mazhandu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mc-  Clure, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' McElaney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' McElroy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' McGarry, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' McKay,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' McPherson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Meesala, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Meirom, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mendell,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Metcalfe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mevissen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Meyer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mezzacapo,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Midha, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Millar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Miller, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Miller, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Minev,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mitchell,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Moll,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Montanez,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Monteiro,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mooring, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Morales, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Moran, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Morcuende,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mostafa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Motta, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Moyard, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Murali, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Murata,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M¨uggenburg, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' NEMOZ, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Nadlinger, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Nakanishi,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Nannicini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Nation, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Navarro, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Naveh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Neagle, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Neuweiler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ngoueya, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Nguyen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Nican-  der, Nick-Singstock, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Niroula, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Norlen, NuoWenLei,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' O’Riordan, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ogunbayo, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ollitrault, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Onodera,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Otaolea, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Oud, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Padilha, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Paik, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pal, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pang,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Panigrahi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pascuzzi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Perriello, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Peterson,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Phan, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pilch, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Piro, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pistoia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Piveteau,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Plewa, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pocreau, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Possel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pozas-Kerstjens,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pracht, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Prokop, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Prutyanov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Puri, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Puz-  zuoli, Pythonix, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' P´erez, Quant02, Quintiii, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rah-  man, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Raja, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rajeev, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rajput, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ramagiri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rao,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Raymond, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Reardon-Smith, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Redondo,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Reuter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rice, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Riedemann, Rietesh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Risinger,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rivero, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rocca, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rodr´ıguez, RohithKarur,  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rosand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rossmannek, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ryu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' SAPV, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Sa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Saha, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ash-Saki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Salman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sanand,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sandberg, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sandesara, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sapra, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sargsyan,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sarkar, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sathaye, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Savola, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schmitt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schn-  abel, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schoenfeld, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Scholten, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schoute, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schul-  terbrandt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schwarm, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schweigert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Seaward, Sergi,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sertage, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Setia, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Shah, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Shammah, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Shanks,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sharma, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Shaw, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Shi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Shoemaker, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Silva,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Simonetto, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Singh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Singh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Singh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Singka-  nipa, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Siraichi, Siri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sistos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sistos, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sitdikov,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sivarajah, Slavikmew, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sletfjerding, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Smolin,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Soeken, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sokolov, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sokolov, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Soloviev,  SooluThomas, Starfish, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Steenken, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Stypulkoski,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Suau, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sun, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sung, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Suwama, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S�lowik,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Taeja, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Takahashi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Takawale, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tavernelli,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Taylor, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Taylour, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Thomas, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tian, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tillet,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tod, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tomasik, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tornow, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' de la Torre, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Toural, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Trabing, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Treinish, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Trenev, TrishaPe,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Truger, TsafrirA, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tsilimigkounakis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tulsi,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tuna, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Turner, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vaknin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Valcarce, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Var-  chon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vartak, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vazquez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vijaywargiya, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vil-  lar, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vishnu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vogt-Lee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vuillot, WQ, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Weaver,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Weidenfeller, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wieczorek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wildstrom, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wil-  son, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Winston, WinterSoldier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Woehr, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Woerner,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Woo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wood, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wood, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wood, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wootton,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wright, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Xing, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' YU, Yaiza, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yang, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yang,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yao,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yeralin,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yonekura,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yonge-Mallo,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yoshida, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Young, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yu, Yuma-Nakamura,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zachow, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zdanski, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zheltonozhskii,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zidaru, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zimmermann, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zindorf, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zoufal, aed-  dins ibm, alexzhang13, b63, bartek bartlomiej, bcamor-  rison, brandhsn, nick bronn, chetmurthy, choerst ibm,  comet, dalin27, deeplokhande, dekel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='meirom,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' derwind,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  dime10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ehchen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ewinston,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' fanizzamarco,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' fs1132429,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ga-  dial,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' galeinston,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' georgezhou20,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' georgios ts,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' gruu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' hhorii,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  hhyap,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' hykavitha,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' itoko,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' jeppevinkel,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' jessica angel7,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' jez-  erjojo14,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' jliu45,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' johannesgreiner,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' jscott2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' kUmezawa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  klinvill,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' krutik2966,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ma5x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' michelle4654,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' msuwama,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' nico  lgrs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' nrhawkins,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ntgiwsvp,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ordmoj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' sagar pahwa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' pritam-  sinha2304,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' rithikaadiga,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ryancocuzzo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' saktar unr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' saswati  qiskit,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' sebastian mair,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' septembrr,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' sethmerkel,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' sg495,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  shaashwat,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' smturro2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' sternparky,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' strickroman,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' tiger-  jack,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' tsura crisaldo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' upsideon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' vadebayo49,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' welien,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' will-  hbang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' wmurphy collabstar,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' yang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='luh, yuri@FreeBSD,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' ˇCepulkovskis, “Qiskit: An open-source frame-  work for quantum computing,” (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [6] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Luo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Liu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhang, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wang, Quantum  4, 341 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [7] “Cirq: A python framework for creating, editing, and in-  voking noisy intermediate scale quantum (nisq) circuits,”  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Biamonte, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wittek, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pancotti, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rebentrost,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wiebe, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lloyd, Nature 549, 195 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schuld, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sinayskiy, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Petruccione, Contempo-  rary Physics 56, 172 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schuld and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Killoran, Physical review letters 122,  040504 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Broughton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mohseni, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Babbush,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Boixo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Neven, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' McClean, Nature commu-  nications 12, 1 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [12] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yuan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Endo, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Li, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Benjamin,  Quantum 3, 191 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cerezo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Arrasmith, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Babbush, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Benjamin,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Endo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fujii, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' McClean, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mitarai, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yuan,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cincio, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Nature Reviews Physics 3, 625 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [14] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bittel and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kliesch, Physical Review Letters 127,  120502 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Preskill, Quantum 2, 79 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [16] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bharti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cervera-Lierta, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kyaw, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Haug,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Alperin-Lea, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Anand, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Degroote, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Heimonen,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kottmann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Menke, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Reviews of Modern  Physics 94, 015004 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Paszke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gross, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Massa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lerer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bradbury,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chanan, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Killeen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lin, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gimelshein, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Antiga,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Desmaison, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kopf, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' DeVito, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Raison,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tejani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chilamkurthy, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Steiner, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Fang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bai,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chintala, in Advances in Neural Information Pro-  cessing Systems 32 (Curran Associates, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', 2019) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  8024–8035.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Aycock, ACM Computing Surveys (CSUR) 35, 97  (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [19] “Paddle Quantum,” (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  17  [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Nielsen and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chuang, Quantum Computa-  tion and Quantum Information: 10th Anniversary Edi-  tion (Cambridge University Press, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gray and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Kourtis, Quantum 5, 410 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [22] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Gogate  and  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Dechter,  arXiv  preprint  arXiv:1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='4109 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [23] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Daniel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gray, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Journal of Open Source Soft-  ware 3, 753 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [24] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schlag, High-Quality Hypergraph Partitioning, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  thesis, Karlsruhe Institute of Technology,  Germany  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [25] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Akhremtsev, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Heuer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sanders,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schlag,  in 19th Workshop on Algorithm Engineering and Exper-  iments, (ALENEX 2017) (2017) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 28–42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [26] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Newman, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ni, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ding, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Cai,  X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Nature Com-  putational Science 1, 578 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [27] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pednault, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gunnels, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Nannicini, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Horesh,  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Magerlein, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Solomonik, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Draeger, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hol-  land, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wisnieff, arXiv preprint arXiv:1710.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='05867  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [28] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Paszke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gross, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chintala, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chanan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yang,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' DeVito, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Desmaison, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Antiga,  and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lerer, (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bradbury, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Frostig, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hawkins, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Johnson,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Leary, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Maclaurin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Necula, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Paszke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Vander-  Plas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wanderman-Milne, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Astrophysics Source  Code Library , ascl (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schuld, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bergholm, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gogolin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Izaac,  and  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Killoran, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A 99, 032331 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [31] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Anselmetti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wierichs, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gogolin, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Parrish, New Journal of Physics 23, 113010 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [32] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bergholm, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Izaac, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Schuld, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gogolin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Alam, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ahmed, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Arrazola, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Blank, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Del-  gado,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Jahangiri,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  McKiernan,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Meyer,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Niu,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Sz´ava,  and  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Killoran,  (2018),  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='04968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [33] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Nandkishore and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huse, Annu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Matter Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 6, 15 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [34] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Goodfellow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pouget-Abadie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Mirza, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Xu,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Warde-Farley, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ozair, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Courville,  and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ben-  gio, Communications of the ACM 63, 139 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tian, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Sun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Du, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhang,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wu, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', arXiv preprint  arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='03066 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [36] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Du, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wang,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Li, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Liang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Xu, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', Physical Review  Applied 16, 024051 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [37] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Du, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' You, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hsieh, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tao, npj  Quantum Information 8, 1 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [38] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Linghu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Qian, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Li,  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Ma, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhao, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', arXiv preprint  arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='00934 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [39] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Abanin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Altman, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Bloch, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Serbyn, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' 91, 021001 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Guo, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wu,  Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Guo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Qian, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=', arXiv preprint  arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='05957 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  [41] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Du, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Gong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Wang,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Li, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Liang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Xu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Yang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-  H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Hsieh, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Deng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rong, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Peng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Lu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Tao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Zhu,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Pan, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
+page_content='  Applied 16, 024051 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/o9E5T4oBgHgl3EQfIw4s/content/2301.05451v1.pdf'}
diff --git a/o9FMT4oBgHgl3EQf7jFB/vector_store/index.pkl b/o9FMT4oBgHgl3EQf7jFB/vector_store/index.pkl
new file mode 100644
index 0000000000000000000000000000000000000000..34e637bd990b17c7aa21f26326f42f8cef017752
--- /dev/null
+++ b/o9FMT4oBgHgl3EQf7jFB/vector_store/index.pkl
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bff313710c810197dafa6fa976780576e3118f041b9ed8a7997ad03eaa931c7d
+size 67526
diff --git a/qdE1T4oBgHgl3EQfigS7/content/tmp_files/2301.03253v1.pdf.txt b/qdE1T4oBgHgl3EQfigS7/content/tmp_files/2301.03253v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..feafac759285882da4ef696670a3139e2bccfbc1
--- /dev/null
+++ b/qdE1T4oBgHgl3EQfigS7/content/tmp_files/2301.03253v1.pdf.txt
@@ -0,0 +1,3948 @@
+arXiv:2301.03253v1  [math.AP]  9 Jan 2023
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATOR IN
+HEISENBERG GROUP: EXISTENCE & REGULARITY OF SOLUTIONS
+PRIYANK OZA, JAGMOHAN TYAGI
+Abstract. We establish the comparison principle, existence and regularity of solutions to the following problem
+concerning the mixed operator:
+�
+αM+
+λ,Λ
+�
+D2
+HN ,Su
+�
+− β
+�
+− ∆
+HN
+�su = f
+in Ω,
+u = g
+in
+HN \ Ω,
+where M+
+λ,Λ is the extremal Pucci’s operator and (−∆
+HN )s denotes the fractional sub-Laplacian on Heisenberg group.
+Contents
+1.
+Introduction
+1
+2.
+Preliminaries
+3
+3.
+Proofs of main results
+7
+4.
+Funding and/or Conflicts of interests/Competing interests
+21
+References
+22
+1. Introduction
+In this article, we study viscosity solutions to a class of mixed operators defined by super-positioning Pucci-
+Heisenberg maximal operator with the fractional sub-Laplacian. We establish the comparison principle, existence
+and regularity of solutions to the following problem:
+�
+αM+
+λ,Λ
+�
+D2
+HN,Su
+�
+− β
+�
+− ∆
+HN
+�su = f
+in Ω,
+u = g
+in
+HN \ Ω,
+(1.1)
+where Ω is a bounded domain (open, connected set) in Heisenberg group
+HN ≃ R2N+1, f ∈ C(Ω), g ∈ C(HN \ Ω)
+are bounded and α ≥ 0 & β > 0 are constants. Here,
+Lu := αM+
+λ,Λ
+�
+D2
+HN ,Su
+�
+− β
+�
+− ∆
+HN
+�su
+(1.2)
+is a mixed operator on
+HN, where M+
+λ,Λ is the Pucci’s extremal (maximal) operator which is the fully nonlinear
+operator and (−∆
+HN )s is the fractional sub-Laplacian.
+Recently, mixed operators have been studied in the Euclidean framework by several researchers. These operators
+occur naturally, for instance, in the study of plasma physics [9], population dynamics [18] and many others. One
+may see [2, 5, 6, 7] for the works on mixed operators in the Euclidean setting. In the above works, the local term is
+second order linear elliptic operator and nonlocal term is the fractional Laplacian. There are several articles, where
+authors have established the existence of solution of the Dirichlet problem using the classical Perron’s method [20].
+For instance, one may see [12, 25] and the reference therein for the Euclidean setting.
+In recent years, there has been a significant amount of works on the existence and qualitative properties of solutions
+to PDEs in non-Euclidean settings, for e.g., Heisenberg group, and more generally on sub-Riemannian, Carnot-
+Carath´eodory spaces. T. Bieske [8] studied infinite harmonic functions in the Heisenberg group using the notion
+of viscosity solutions. C. Y. Wang [31] established the uniqueness of viscosity solution of ∆∞ (infinity Laplacian)
+2010 Mathematics Subject Classification. Primary 35A01, 35J60, 35R03, 35D40, 47G20; Secondary 45K05.
+Key words and phrases. Nonlocal and local operators, Partial differential equations on the Heisenberg group, Pucci’s extremal operator,
+Integro-PDE, viscosity solutions, Perron’s method.
+Submitted January 10, 2023. Published—–.
+1
+
+2
+P. OZA, J. TYAGI
+equation on Carnot groups.
+B. Wang [30] investigated the removable singularities for viscosity subsolutions to
+degenerate elliptic Pucci operators in the Heisenberg group.
+It is easy to see that when α = 0, the operator in (1.2) is the fractional sub-Laplacian. Very recently, G. Palatucci
+and M. Piccinini [28] considered a large class of nonlinear integro-differential operators in the Heisenberg group
+setting
+HN. They proved the general Harnack inequalities for the solutions to Dirichlet problem concerning nonlinear
+integro-differential operators. It is worth noticing that these problems have connections in quantum mechanics [32],
+ferromagnetic trajectories [27], image segmentation models [13], non-Markovian coupling for Brownian motions [1]
+and many others. We recall that in the above contexts, the non-Euclidean geometry occurs naturally.
+F. Ferrari and E. Vecchi [19] established the H¨older regularity of uniformly continuous and bounded viscosity
+solutions of degenerate fully nonlinear equations in
+H1. We also refer to [16] for the existence results and Liouville,
+Harnack type qualitative properties of fundamental solutions. Y. Y. Li and B. Wang [30] established a form of
+comparison principle for sub-elliptic equations in the Heisenberg setting. One may also see Manfredini [23] et al. for
+the H¨older continuity and boundedness estimates for nonlinear fractional equations in
+HN, where authors considered
+equations driven by integro-differential operators whose model is the fractional p-Laplacian on Heisenberg group
+given by
+Lu(ξ) := P.V.
+�
+HN
+��u(ξ) − u(η)
+��p−2(u(ξ) − u(η))
+d0(η−1 o ξ)Q+sp
+dη, ξ ∈
+HN.
+Here the symbol P.V. in the expression stands for “in the principal value sense” and d0 denotes a homogeneous norm
+on
+HN(see Definition 2.8). Q = 2N + 2 is the homogeneous dimension of
+HN.
+To the best of our knowledge, the mixed operators of type (1.2) have not been yet considered in the Heisenberg
+group setting. Motivated by the above works on the mixed operators and recent works on non-Euclidean setting, we
+consider a class of mixed operators (1.2) on
+HN.
+The main results of this paper are the following theorems:
+Theorem 1.1. (Stability). Let un ∈ LSC(Ω) be bounded in
+HN and satisfy
+αM+
+λ,Λ
+�
+D2
+HN,Sun
+�
+− β
+�
+− ∆HN
+�sun ≤ fn in Ω
+in the viscosity sense. Let the following be hold:
+(i) un converges to u in the Γ-sense in Ω,
+(ii) un converges to u a.e. in
+HN,
+(iii) fn −→ f locally uniformly in Ω.
+Then
+αM+
+λ,Λ
+�
+D2
+HN,Su
+�
+− β
+�
+− ∆HN
+�su ≤ f in Ω.
+Next, we state the comparison principle for viscosity solutions of PDE concerning operators given by (1.2). The
+proof is immediate by making use of Lemma 3.5 and Lemma 3.7 (see, next).
+Theorem 1.2. (Comparison Principle). Let Ω be a bounded domain in
+HN. Let f ∈ C(Ω) and u, v be bounded
+USC and LSC functions in Ω, respectively, which satisfy
+αM+
+λ,Λ
+�
+D2
+HN,Su
+�
+− β
+�
+− ∆HN
+�su ≥ f
+and
+αM+
+λ,Λ
+�
+D2
+HN,Sv
+�
+− β
+�
+− ∆HN
+�sv ≤ f
+in the viscosity sense in Ω. Also, if u ≤ v in
+HN \ Ω. Then u ≤ v in
+HN.
+Further, adapting the standard techniques of using comparison principle for sub and super-solutions and then
+following Perron’s method, we have the following existence result.
+Theorem 1.3. Let Ω ⊂
+HN be satisfy the exterior Heisenberg ball condition. Let g ∈ C(HN \ Ω) and bounded in
+HN. Then there exists a viscosity solution u ∈ C(Ω) of
+�
+αM+
+λ,Λ
+�
+D2
+HN,Su
+�
+− β
+�
+− ∆HN
+�su = 0
+in Ω
+u = g
+in
+HN \ Ω.
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+3
+As mentioned earlier, several authors have established the existence of solutions to Dirichlet problems using the
+Perron’s method. For the Heisenberg group setting, we refer to [26], where the authors prove the existence of a
+viscosity solution for a class of linear second order equations in Heisenberg group. Making use of the comparison
+principle (Theorem 1.2), the proof of Theorem 1.3 follows using the standard arguments.
+We mention that F. Ferrari and E. Vecchi [19] studied the H¨older behaviour of fully nonlinear local equations. In
+particular, we have the following result due to [19]:
+Corollary 1.4. (Theorem 1.3 [19]) Let u ∈ C(H1) be a bounded and uniformly continuous viscosity solution of
+M+
+λ,Λ
+�
+D2
+HN,Su(ξ)
+�
+− c(ξ)u(ξ) = f(ξ) in
+H1.
+Let L1, L2, γ1, and γ2 be positive constants s. t. γi ∈ (0, 1], i = 1, 2 and for any ξ, η ∈
+H1,
+��c(ξ) − c(η)
+�� ≤ L1
+��ξ o η−1��γ1
+H1,
+��f(ξ) − f(η)
+�� ≤ L2
+��ξ o η−1��γ2
+H1.
+Let c(ξ) be positive for all ξ ∈
+H1 and
+inf
+ξ∈B
+H1
+R (P )
+c(ξ) := c0 > 0.
+Then there exists γ := γ(c0, p, L1, L2, Λ) ∈ (0, 1], γ ≤ min{γ1, γ2} such that
+��u(ξ) − u(η)
+�� ≤ L
+��ξ o η−1��γ
+H1, for ξ ∈
+H1,
+for some L = L(c0, P, L1, L2, Λ) > 0.
+For more such results on regularity in the Euclidean setting, when there is no local term and integro-differential
+operators are of fractional Laplacian type, we refer to [11, 12]. We also mention a very recent work by Biagi et al.
+[6], where authors established the interior Sobolev regularity as well as boundary regularity of Lipschitz type for
+mixed local and nonlocal operators in the Euclidean framework. More precisely, authors proved the following interior
+regularity result:
+Corollary 1.5. (Theorem 1.4 [6]) Let Ω ⊂ RN be a bounded C1 domain. Let f ∈ Hk(Ω)
+�
+W 2,k(Ω)
+�
+for some integer
+k ≥ 0. Let u ∈ H1(RN) be a weak solution of
+−∆u + (−∆)su = f in Ω.
+Then u ∈ Hk+2
+loc (Ω).
+Motivated by the above results, we establish the following interior H¨older regularity result.
+Theorem 1.6. (Interior regularity) Let u be a bounded function in
+HN and viscosity solution to
+αM+
+λ,Λ
+�
+D2
+HN,Su
+�
+− β
+�
+− ∆HN
+�su = 0 in B
+HN
+1
+.
+Then there exist constants C and γ = γ(λ, Λ, N) ∈ (0, 1) such that
+��u(ξ) − u(0)
+�� ≤ C|ξ|γ
+HN ∥u∥∞, HN, ∀ξ ∈ B
+HN
+1
+2
+,
+where B
+HN
+r
+denotes the ball of radius r with center at the origin.
+The organization of this paper is as follows. In Section 2, we list the basic definitions and introduce the framework
+in which we work. Section 3 is dedicated to the proofs of our main results.
+2. Preliminaries
+We first recall the briefs about the Heisenberg group
+HN. The points in
+HN are denoted by
+ξ := (z, t) = (x1, . . . , xN, y1, . . . , yN, t)
+and the group
+HN is defined as the triplet
+�
+RN+1, o, {Φλ}
+�
+, where the group law o is defined as follows:
+ξ o ξ′ =
+�
+x + x′, y + y′, t + t′ + 2⟨y, x′⟩ − 2⟨x, y′⟩
+�
+=
+�
+x1 + x′
+1, . . . , xN + x′
+N, y1 + y′
+1, . . . , yN + y′
+N, t + t′ + 2
+N
+�
+i=1
+�
+yix′
+i − xiy′
+i
+��
+,
+
+4
+P. OZA, J. TYAGI
+where ⟨., .⟩ denotes the standard inner product in RN. (R2N+1, o) is a Lie group with identity element the origin 0
+and inverse ξ−1 = −ξ. The dilation group {Φλ}λ>0 is given by
+Φ(λ) : R2N+1 −→ R2N+1
+such that
+ξ �→ Φλ(ξ) :=
+�
+λx, λy, λ2t
+�
+.
+HN is also known as Heisenberg-Weyl group in R2N+1. The Jacobian basis of the Heisenberg Lie algebra of
+HN is
+given by
+Xi = ∂xi + 2yi∂t, Yi = ∂yi − 2xi∂t, 1 ≤ i ≤ N, T = ∂t.
+Given a domain Ω ⊂
+HN, for u ∈ C1(Ω, R), the subgradient or the Heisenberg gradient ∇
+HN u is defined as follows:
+∇
+HN u(ξ) :=
+�
+X1u(ξ), . . . , XNu(ξ), Y1u(ξ), . . . , YNu(ξ)
+�
+.
+Also,
+D2
+HN,Su :=
+
+
+X1X1u
+· · ·
+XNX1u
+Y1X1u
+· · ·
+YNX1u
+...
+...
+...
+...
+...
+...
+X1XNu
+. . .
+XNXNu
+Y1XNu
+. . .
+YNXNu
+X1Y1u
+. . .
+XNY1u
+Y1Y1u
+. . .
+YNY1u
+...
+...
+...
+...
+...
+...
+X1YNu
+. . .
+XNYNu
+Y1YNu
+. . .
+YNYNu
+
+
+Sym
+,
+where
+ASym = 1
+2
+�
+A + AT �
+, for any matrix A,
+i.e., symmetric part of the matrix A. Now, since
+[Xi, Yi] = XiYi − YiXi
+= (∂xi + 2yi∂t)(∂yi − 2xi∂t) − (∂yi − 2xi∂t)(∂xi + 2yi∂t)
+= −4∂t,
+so it follows that
+rank
+�
+Lie{X1, X2, . . . , X2N, T }(0, 0)
+�
+= 2N + 1,
+which is the Euclidean dimension of
+HN. We denote by Q, the homogeneous dimension of
+HN, which is Q = 2N +2.
+The norm on
+HN is defined by
+|ξ|
+HN :=
+�� N
+�
+i=1
+�
+x2
+i + y2
+i
+�2
+�
++ t2
+� 1
+4
+.
+The corresponding distance on
+HN is defined as follows:
+d
+HN (ξ, ˆξ) := |ˆξ−1o ξ|
+HN ,
+where ˆξ−1 is the inverse of ˆξ w. r. to o, i.e., ˆξ−1 = −ˆξ.
+The sub-Laplacian or the Heisenberg Laplacian (also known as Laplacian-Kohn operator), ∆
+HN is the self-adjoint
+operator defined as
+∆
+HNu :=
+N
+�
+i=1
+X2
+i + Y 2
+i
+=
+N
+�
+i=1
+∂2
+∂x2
+i
++ ∂2
+∂y2
+i
++ 4yi
+∂2
+∂xi∂t − 4xi
+∂2
+∂yi∂t + 4
+�
+x2
+i + y2
+i
+� ∂2
+∂t2 .
+It is useful to observe that
+∆
+HN = div
+�
+σT σ∇u
+�
+,
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+5
+where
+σ =
+�IN
+0
+2y
+0
+IN
+−2x
+�
+and σT is its transpose. Note that
+A = σT σ =
+
+
+IN
+0
+2y
+0
+IN
+−2x
+2y
+−2x
+4
+�
+|x|2 + |y|2�
+
+
+is a positive semi-definite matrix with det(A) = 0, ∀ξ ∈
+HN.
+Let us recall the definition of viscosity sub/super-solution of (1.1) by evaluating the operators in C2 test function
+φ (ψ) touching u locally from above (below) and then the final test function v (w) is defined by taking v = φ
+(v = ψ) in a small ball and v = u outside. One may see [3, 11], where the notion of viscosity solution for second
+order elliptic integro-differential equations and fully nonlinear integro-differential equations is given in the Euclidean
+setting, respectively. For the analogous definitions in the Heisenberg group setting, we refer to [16]. We give the
+definition of viscosity solution for the operator under consideration in the Heisenberg group setting which is consistent
+with that given in the above mentioned articles.
+Definition 2.1. A function u :
+HN −→ R, upper semicontinuous (USC) in Ω ⊂
+HN is called a viscosity subsolution
+of (1.1) if for any ξ ∈ Ω and C2 function ϕ : U −→ R, for some neighborhood U of ξ in Ω such that ϕ(ξ) = u(ξ) and
+ϕ(η) > u(η) for η ∈ U \ {ξ}, we have
+αM+
+λ,Λ
+�
+D2
+HN,Sv(ξ)
+�
+− β(−∆
+HN )sv(ξ) ≥ f(ξ),
+where
+v :=
+�
+ϕ
+in U,
+u
+in
+HN \ U.
+Moreover, we say u satisfies αM+
+λ,Λ(D2
+HN ,Su) − β(−∆
+HN )su ≥ f in Ω in the viscosity sense.
+Definition 2.2. A function u :
+HN −→ R, lower semicontinuous (LSC) in Ω ⊂
+HN is called a viscosity supersolution
+of (1.1) if for any ξ ∈ Ω and C2 function ψ : U −→ R, for some neighborhood U of ξ in Ω such that ψ(ξ) = u(ξ) and
+ψ(η) < u(η) for η ∈ U \ {ξ}, we have
+αM+
+λ,Λ
+�
+D2
+HN ,Sw(ξ)
+�
+− β(−∆
+HN )sw(ξ) ≤ f(ξ),
+where
+w :=
+�
+ψ
+in U,
+u
+in
+HN \ U.
+Moreover, we say u satisfies αM+
+λ,Λ(D2
+HN ,Su) − β(−∆
+HN )su ≤ f in Ω in the viscosity sense.
+Definition 2.3. A continuous function u is said to be a viscosity solution of (1.1) if it is a subsolution as well as a
+supersolution of (1.1).
+Now, we recall the exterior Heisenberg ball condition. For the analogous condition in the Euclidean setting, one
+may see, for instance [25].
+Definition 2.4. [16] Ω is said to satisfy the exterior Heisenberg ball condition if there exists R > 0 such that for
+any ξ ∈ ∂Ω and 0 < r ≤ R, there exists ηr
+ξ ∈ Ωc satisfying B
+HN
+r
+(ηr
+ξ) ∩ Ω = {ξ}.
+Next, we recall the definition of sup (inf)-convolution. The construction of convolutions was done by Jensen et
+al. [21] and further developed on Carnot groups by C. Y. Wang [31].
+Definition 2.5. For an USC function u, the sup-convolution approximation uε is given by
+uε(ξ) = sup
+η∈ HN
+�
+u(η) − |ξ o η−1|4
+HN
+ε
+�
+.
+
+6
+P. OZA, J. TYAGI
+Definition 2.6. For an LSC function u, the inf-convolution approximation uε is given by
+uε(ξ) =
+inf
+η∈ HN
+�
+u(η) + |ξ o η−1|4
+HN
+ε
+�
+.
+It is easy to see that uε ≥ u and uε ≤ u.
+Definition 2.7. A sequence of LSC functions, uk is said to Γ-converge to u in a set Ω if the following hold:
+(i) For every sequence ξn −→ ξ in Ω, we have
+lim inf
+n−→∞ un(ξn) ≥ u(ξ).
+(ii) For every ξ ∈ Ω, there exists a sequence {ξn} converging to ξ in Ω (known as Γ-realising sequence) such that
+lim sup
+n−→∞ un(ξn) = u(ξ).
+This is known as Γ-limit in literature, see [11, 17]. Note that uniform convergence =⇒ Γ-convergence. Also, an
+important property of Γ-limits is that if un converges to u, which has a strict local minimum at ξ, then un would
+have local minimum at ξn for a sequence ξn −→ ξ.
+Definition 2.8. [28] A homogeneous norm on
+HN is a continuous function (w. r. to Euclidean topology)
+d0 :
+HN −→ [0, ∞) s.t.
+(i) d0(Φλ(ξ)) = λd0(ξ), ∀λ > 0 and ξ ∈
+HN
+(ii) d0(ξ) = 0 iff ξ = 0.
+Moreover, we say that the homogeneous norm is symmetric if
+d0(ξ−1) = d0(ξ), ∀ξ ∈
+HN.
+Throughout the paper, we consider the standard homogeneous norm on
+HN. For fixed ξ0 ∈
+HN and R > 0,
+B
+HN
+R (ξ0) :=
+�
+ξ ∈
+HN ; |ξ−1
+0
+o ξ|
+HN < R
+�
+denotes the Kor´anyi ball of radius R around ξ0 in
+HN.
+One can see that the Jacobian determinant of the dilation Φλ is λQ, where Q = 2N +2, which is the homogeneous
+dimension of the Heisenberg group. Let us consider 2N × (2N + 1) matrix whose rows are the coefficients of the
+vector fields Xi, i.e.,
+σ =
+�IN
+0
+2y
+0
+IN
+−2x
+�
+for x = (ξ1, . . . , ξN)T and y = (ξN+1, . . . , ξ2N)T . Then the Heisenberg gradient of a function Φ : R2N+1 −→ R is
+given by
+∇
+HN Φ = (X1Φ, . . . , X2NΦ) = σ(ξ)∇Φ,
+where ∇ denotes the usual gradient. Also, the Heisenberg Hessian of Φ is given by
+D2
+HN,SΦ = (XiXjΦ)Sym
+= σ(ξ)D2ΦσT (ξ),
+where Sym denotes the symmetrized matrix. We recall that the fractional sub-Laplacian operator is defined as
+(−∆
+HN )su(ξ) = −1
+2c(N, s)
+�
+HN
+u(ξ o η) + u(ξ o η−1) − 2u(ξ)
+|η|Q+2s
+HN
+dη, u ∈ Hs(HN), ξ ∈
+HN; Q = 2N + 2,
+see 5.1 [28]. Here, c(N, s) is a positive constant depending on N & s. For given two parameters 0 < λ ≤ Λ, Pucci-
+Heisenberg operators are defined by the composition of Pucci’s extremal operators M±
+λ,Λ (see 2.2 [10]) with the
+Heisenberg Hessian as follows:
+M+
+λ,Λ
+�
+D2
+HN,Su
+�
+:= Λ
+�
+ei≥0
+ei + λ
+�
+ei<0
+ei
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+7
+&
+M−
+λ,Λ
+�
+D2
+HN,Su
+�
+:= Λ
+�
+ei≤0
+ei + λ
+�
+ei>0
+ei,
+where {ei}2N
+i=1 are the eigenvalues of the symmetrized horizontal Hessian matrix D2
+HN,Su. Let S2N be denote the
+set of all real symmetric 2N × 2N matrices. Consider a subset S2N
+λ,Λ of S2N whose eigenvalues are in [λ, Λ]. These
+operators are also defined as
+M+
+λ,Λ
+�
+D2
+HN,Su
+�
+:=
+max
+M∈SN
+λ,Λ
+tr
+�
+MD2
+HN,Su
+�
+(2.1)
+&
+M−
+λ,Λ
+�
+D2
+HN,Su
+�
+:=
+min
+M∈SN
+λ,Λ
+tr
+�
+MD2
+HN,Su
+�
+.
+Furthermore, consider a set K consisting of 2N × 2N matrices γ such that γγT ∈ S2N
+λ,Λ. Using this, we can re-write
+(2.1) as
+M+
+λ,Λ
+�
+D2
+HN,Su
+�
+= max
+γ∈K ⟨γγT , D2
+HN,Su⟩.
+Now, for any fixed γ ∈ K, we have the following linear operator, say, Lγ given by
+Lγ
+�
+D2
+HN,Su
+�
+:= ⟨γγT , D2
+HN,Su⟩.
+(2.2)
+It is easy to observe that when λ = Λ = 1, the above mentioned operators reduce to the Heisenberg Laplacian ∆
+HN,S.
+3. Proofs of main results
+Proof of Theorem 1.1. Consider a C2 function ψ that touches u from below at ξ in a neighbourhood U in Ω. By
+definition of Γ-convergence, there exists a sequence ξn −→ ξ such that
+�
+un − ψ
+�
+(ξn) = inf
+U
+�
+un − ψ
+�
+= δn.
+Therefore, δn −→ 0 as n −→ ∞ and ψ + δn touches un at ξn. Now, since
+αM+
+λ,Λ
+�
+D2
+HN,Sun
+�
+− β
+�
+− ∆HN
+�sun ≤ fn in Ω,
+so for
+ξn =
+�
+ψ + δn
+in U,
+un
+in
+HN \ U,
+we have by the definition of viscosity solution,
+αM+
+λ,Λ
+�
+D2
+HN,Sun(ξn)
+�
+− β
+�
+− ∆HN
+�sun(ξn) ≤ fn(ξn) in Ω.
+Further, take τ ∈ U such that
+d
+�
+τ, ∂U
+�
+= inf
+�τ∈∂U
+���τ
+−1 o τ
+��
+HN > ρ > 0.
+
+8
+P. OZA, J. TYAGI
+Then
+���
+αM+
+λ,Λ
+�
+D2
+HN,Swn(τ)
+�
+− β
+�
+− ∆HN
+�swn(τ)
+�
+−
+�
+αM+
+λ,Λ
+�
+D2
+HN ,Sw(τ)
+�
+− β
+�
+− ∆HN
+�sw(τ)
+���
+≤
+���
+αM+
+λ,Λ
+�
+D2
+HN,Swn(τ)
+�
+− αM+
+λ,Λ
+�
+D2
+HN,Sw(τ)
+��
+− β
+�
+(−∆HN )swn(τ) − (−∆HN)sw(τ)
+���
+≤ α max
+��� max
+M∈SN
+λ,Λ
+tr
+�
+MD2
+HN,S(wn(τ) − w(τ))
+���,
+�� max
+M∈SN
+λ,Λ
+tr
+�
+MD2
+HN,S(w(τ) − wn(τ))
+���
+�
++ β
+��(−∆HN)swn(τ) − (−∆HN)sw(τ)
+�� (by (2.2))
+≤ α max
+γ∈K
+��Lγ
+�
+D2(wn − w)(τ)
+��� + β
+���
+− ∆HN
+�s(wn − w)(τ)
+��
+= α max
+γ∈K
+��Lγ
+�
+D2δn(τ)
+��� + β
+���
+− ∆HN
+�s(wn − w)(τ)
+��
+≤ β
+2 c(N, s)
+�
+HN
+��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)
+��
+|η|Q+2s
+HN
+dη
+= β
+2 c(N, s)
+�
+B
+HN
+ρ
+��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)
+��
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+HN\B
+HN
+ρ
+��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)
+��
+|η|Q+2s
+HN
+dη
+= β
+2 c(N, s)
+�
+B
+HN
+ρ
+��δn(τ o η) + δn(τ o η−1) − 2δn(τ)
+��
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+HN\B
+HN
+ρ
+��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)
+��
+|η|Q+2s
+HN
+dη
+= β
+2 c(N, s)
+�
+HN\B
+HN
+ρ
+��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)
+��
+|η|Q+2s
+HN
+dη.
+Now, using the fact that sequence wn is bounded and that (wn − w)(τ o η) + (wn − w)(τ o η−1) − (wn − w)(τ) −→ 0
+a.e. along with the fact that
+1
+|η|Q+2s ∈ L1(HN \ Bρ), we have by the dominated convergence theorem that
+���
+αM+
+λ,λ
+�
+D2
+HN,S(wn)(τ)
+�
+− β(−∆
+HN )swn(τ)
+�
+−
+�
+αM+
+λ,λ
+�
+D2
+HN,S(w)(τ)
+�
+− β(−∆
+HN )sw(τ)
+��� −→ 0 as n −→ ∞ uniformly in τ.
+(3.1)
+Equivalently,
+αM+
+λ,Λ
+�
+D2
+HN,S(wn)(τ)
+�
+− β(−∆
+HN )swn(τ) −→ αM+
+λ,Λ
+�
+D2
+HN,S(w)(τ)
+�
+− β(−∆
+HN )sw(τ) locally uniformly in U.
+Also,
+���
+αM+
+λ,Λ
+�
+D2
+HN,S(wn)(ξn)
+�
+− β(−∆
+HN )swn(ξn)
+�
+−
+�
+αM+
+λ,Λ
+�
+D2
+HN,S(w)(ξ)
+�
+− β(−∆
+HN )sw(ξ)
+���
+(3.2)
+≤
+���
+αM+
+λ,Λ
+�
+D2
+HN,Swn(ξn)
+�
+− β(−∆
+HN)swn(ξn)
+�
+−
+�
+αM+
+λ,Λ
+�
+D2
+HN,Sw(ξn)
+�
+− β(−∆
+HN )sw(ξn)
+���
++
+���
+αM+
+λ,Λ
+�
+D2
+HN,Sψ(ξn)
+�
+− β(−∆
+HN )sw(ξn)
+�
+−
+�
+αM+
+λ,Λ
+�
+D2
+HN,Sψ(ξ)
+�
+− β(−∆
+HN )sw(ξ)
+���
+≤
+���
+αM+
+λ,Λ
+�
+D2
+HN,Swn(ξn)
+�
+− β(−∆
+HN)swn(ξn)
+�
+−
+�
+αM+
+λ,Λ
+�
+D2
+HN,Sw(ξn)
+�
+− β(−∆
+HN )sw(ξn)
+���
++
+��αM+
+λ,Λ
+�
+D2
+HN,Sψ(ξn)
+�
+− αM+
+λ,Λ
+�
+D2
+HN,Sψ(ξ)
+��� +
+��β(−∆
+HN )sw(ξn) − β(−∆
+HN )sw(ξ)
+��.
+Further, the first term in the R.H.S. of (3.2) vanishes as n −→ ∞ by (3.1). The third term goes to zero as n −→ ∞
+by the continuity of Iw in U. Also, the first term vanishes by an application of Theorem VI.2.1 [4]. Thus, we have
+that
+αM+
+λ,Λ
+�
+D2
+HN,Swn(ξn)
+�
+− β(−∆
+HN )swn(ξn) −→ αM+
+λ,Λ
+�
+D2
+HN ,S(w)(ξ)
+�
+− β(−∆
+HN )sw(ξ) as n −→ ∞.
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+9
+Further, we get
+αM+
+λ,Λ
+�
+D2
+HN,Swn(ξn)
+�
+− β(−∆
+HN )swn(ξ)
+≤ αM+
+λ,Λ
+�
+D2
+HN,Swn(ξn)
+�
+− β(−∆
+HN )swn(ξ)
++
+��αM+
+λ,Λ
+�
+D2
+HN,Swn(ξn)
+�
+− β(−∆
+HN )swn(ξn) −
+�
+αM+
+λ,Λ
+�
+D2
+HN,Sw(ξ)
+�
+− β(−∆
+HN )sw(ξ)
+���
+≤ fn(ξn) +
+��αM+
+λ,Λ
+�
+D2
+HN,Swn(ξn)
+�
+− β(−∆
+HN )swn(ξn) −
+�
+αM+
+λ,Λ
+�
+D2
+HN,Sw(ξ)
+�
+− β(−∆
+HN )sw(ξ)
+���
+≤ f(ξ) + |fn(ξn) − f(ξ)|
++
+��αM+
+λ,Λ
+�
+D2
+HN,Swn(ξn)
+�
+− β(−∆
+HN )swn(ξn) −
+�
+αM+
+λ,Λ
+�
+D2
+HN,Sw(ξ)
+�
+− β(−∆
+HN )sw(ξ)
+���.
+Finally, using (3.2) together with the fact that fn(ξn) −→ f(ξ), since fn −→ f locally uniformly and ξn −→ ξ proves
+the claim.
+□
+Remark 3.1. One can see that an analogous result can be obtained for subsolutions using the Γ-convergence of USC
+functions.
+More precisely, we have the following immediate corollary:
+Corollary 3.2. Let un ∈ C(Ω) be bounded in
+HN and satisfy
+αM+
+λ,Λ
+�
+D2
+HN,Sun
+�
+− β
+�
+− ∆HN
+�sun = fn in Ω
+in the viscosity sense. Let the following be hold:
+(i) un converges to u in the Γ-sense in Ω,
+(ii) un converges to u a.e. in HN,
+(iii) fn −→ f locally uniformly in Ω.
+Then
+αM+
+λ,Λ
+�
+D2
+HN,Su
+�
+− β
+�
+− ∆HN
+�su = f in Ω.
+Lemma 3.3. Let f ∈ C(Ω) and u ∈ USC(Ω) be a viscosity subsolution of (1.1). Then
+αM+
+λ,Λ
+�
+D2
+HN,Suε�
+−
+�
+− ∆HN
+�suε ≥ f − dε in Ω1 ⋐ Ω,
+where dε −→ 0 in Ω1 as ε −→ 0 and depends on the modulus of continuity of f.
+Proof of Lemma 3.3. Let x0 ∈ Ω1 and ϕ be a C2 smooth function touching uε from above in some neighbourhood
+B
+HN
+r
+(ξ0) ⊂ Ω1 of ξ0. Let us define
+Ψ :=
+�
+ϕ
+in B
+HN
+r
+(ξ0)
+uε
+in
+HN \ B
+HN
+r
+(ξ0).
+Next, consider a function
+Φ(ξ) = Ψ
+�
+ξ o ξ∗
+0
+−1 o ξ0
+�
++ 1
+ε|ξ0 o ξ∗
+0
+−1|4
+HN,
+(3.3)
+where ξ∗ = (x1∗, x2∗, . . . , x2N∗, t∗) ∈ Ω such that
+uε(ξ0) = u(ξ∗
+0) − |ξ0 o ξ∗
+0
+−1|4
+HN
+ε
+(see p. 9 [22]).
+Now, by definition, we have
+uε�
+ξ0 o ξ∗
+0
+−1 o ξ
+�
+≥ u(ξ) − |
+�
+ξ0 o ξ∗
+0
+−1 o ξ
+�
+o ξ−1|
+HN.
+Since
+�
+ξ0 o ξ∗
+0
+−1 o ξ
+�
+o ξ−1 = ξ0 o ξ∗
+0
+−1,
+so it implies
+uε�
+ξ0 o ξ∗
+0
+−1 o ξ
+�
+≥ u(ξ) − |ξ0 o ξ∗
+0
+−1|4
+HN .
+In other words,
+u(ξ) ≤ uε�
+ξ0 o ξ∗
+0
+−1 o ξ
+�
++ |ξ0 o ξ∗
+0
+−1|4
+HN
+ε
+.
+
+10
+P. OZA, J. TYAGI
+Let ξ be close enough to ξ∗
+0, then by definition,
+u(ξ) ≤ Ψ
+�
+ξ0 o ξ∗
+0
+−1 o ξ
+�
++ |ξ0 o ξ∗
+0
+−1|4
+HN
+ε
+= Φ(ξ)
+and u(ξ∗
+0) = Φ(ξ∗
+0). It implies that Φ(ξ) touches u from above at ξ∗
+0 in B
+HN
+r
+(ξ∗
+0). Next, we consider a function
+v :=
+�
+Φ
+in B
+HN
+r
+(ξ∗
+0)
+u
+in
+HN \ B
+HN
+r
+(ξ∗
+0).
+It yields by the definition of viscosity subsolution,
+αM+
+λ,Λ
+�
+D2
+HN,Sv(ξ∗
+0)
+�
+− β(−∆
+HN )sv(ξ∗
+0) ≥ f(ξ∗
+0).
+In other words,
+αM+
+λ,Λ
+�
+D2
+HN ,sv(ξ∗
+0)
+�
++ β
+2 c(N, s)
+�
+HN
+v(ξ o η) + v(ξ o η−1) − 2v(ξ)
+|η−1 o ξ|Q+2s
+HN
+dη ≥ f(ξ∗
+0).
+(3.4)
+It is easy to see that (3.3) yields
+v(ξ∗
+0) = Φ(ξ∗
+0) = Ψ(ξ0) + 1
+ε|ξ0 o ξ∗
+0
+−1|4
+HN,
+(3.5)
+Φ(ξ∗
+0 o η) = Ψ(ξ0 o η) + 1
+ε|ξ0 o ξ∗
+0
+−1|4
+HN
+&
+Φ(ξ∗
+0 o η−1) = Ψ(ξ0 o η−1) + 1
+ε|ξ0 o ξ∗
+0
+−1|4
+HN.
+It gives
+Φ(ξ∗
+0 o η) − Φ(ξ∗
+0) = Ψ(ξ0 o η) − Ψ(ξ0)
+(3.6)
+&
+Φ(ξ∗
+0 o η−1) − Φ(ξ∗
+0) = Ψ(ξ0 o η−1) − Ψ(ξ0).
+Now, we claim that
+∇
+HNΦ(ξ∗
+0) = ∇
+HN Ψ(ξ0).
+(3.7)
+Since
+XiΦ(ξ) = ∂xiΦ(ξ) + 2yi∂tΦ(ξ)
+= ∂xiΦ
+�
+x1, . . . , xN, y1, . . . , yN, t
+�
++ 2yi∂tΦ
+�
+x1, . . . , xN, y1, . . . , yN, t
+�
+= ∂xiΨ
+�
+ξ o ξ∗
+0
+−1 o ξ0
+�
++ 2yi∂tΨ
+�
+ξ o ξ∗
+0
+−1 o ξ0
+�
+for 1 ≤ i ≤ N,
+so it gives
+XiΦ(ξ∗
+0) = ∂xiΨ(ξ0) + 2yi∂tΨ(ξ0) for 1 ≤ i ≤ N.
+Similarly, one may see that
+YiΦ(ξ∗
+0) = ∂yiΨ(ξ0) − 2xi∂tΨ(ξ0), 1 ≤ i ≤ N.
+Therefore, (3.7) holds. Also,
+D2
+HN ,SΦ(ξ∗
+0) = D2
+HN,SΨ(ξ0)
+and therefore
+M+
+λ,Λ
+�
+D2
+HN,SΦ(ξ∗
+0)
+�
+= M+
+λ,Λ
+�
+D2
+HN,SΨ(ξ0)
+�
+= M+
+λ,Λ
+�
+D2
+HN,Sϕ(ξ0)
+�
+.
+(3.8)
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+11
+Using (3.6) & (3.8) in (3.4) yields
+f(ξ∗
+0) ≤ αM+
+λ,Λ
+�
+D2
+HN,Sv(ξ∗
+0)
+�
++ β
+2 c(N, s)
+�
+HN
+v(ξ∗
+0 o η) + v(ξ∗
+0 o η−1) − 2v(ξ∗
+0)
+|η|Q+2s
+HN
+dη
+(3.9)
+= αM+
+λ,Λ
+�
+D2
+HN,Sϕ(ξ0)
+�
++ β
+2 c(N, s)
+�
+{η∈ HN; ξ∗
+0 o η, ξ∗
+0 o η−1∈B
+HN
+r
+(ξ∗
+0 )}
+Φ(ξ∗
+0 o η) + Φ(ξ∗
+0 o η−1) − 2Φ(ξ∗
+0)
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+HN\{η∈ HN ; ξ∗
+0 o η, ξ∗
+0 o η−1∈B
+HN
+r
+(ξ∗
+0 )}
+u(ξ∗
+0 o η) + u(ξ∗
+0 o η−1) − 2u(ξ∗
+0)
+|η|Q+2s
+HN
+dη
+= αM+
+λ,Λ
+�
+D2
+HN,Sϕ(ξ0)
+�
++ β
+2 c(N, s)
+�
+{η∈ HN; ξ∗
+0 o η, ξ∗
+0 o η−1∈B
+HN
+r
+(ξ∗
+0 )}
+Φ(ξ∗
+0 o η) + Φ(ξ∗
+0 o η−1) − 2Φ(ξ∗
+0)
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+HN\{η∈ HN ; ξ∗
+0 o η, ξ∗
+0 o η−1∈B
+HN
+r
+(ξ∗
+0 )}
+u(ξ∗
+0 o η) + u(ξ∗
+0 o η−1) − 2Φ(ξ∗
+0)
+|η|Q+2s
+HN
+dη.
+By the definition of uε,
+u(η) ≤ uε(ξ) +
+��ξ o η−1��4
+HN
+ε
+for all ξ, η ∈
+HN.
+It further implies
+u(ξ∗
+0 o η) ≤ u(ξ0 o η) +
+��(ξ0 o η) o (ξ∗
+0 o η)−1��4
+HN
+ε
+(3.10)
+and
+u(ξ∗
+0 o η−1) ≤ u(ξ0 o η−1) +
+��(ξ0 o η−1) o (ξ∗
+0 o η−1)
+−1��4
+HN
+ε
+.
+(3.11)
+Let
+ξ∗
+0 = (x∗
+0, y∗
+0, t∗
+0) =
+�
+x1∗
+0 , . . . , xN∗
+0 , y1∗
+0 , . . . , yN∗
+0 , t∗
+0
+�
+,
+ξ0 = (x0, y0, z0, t) =
+�
+x1
+0, . . . , xN
+0 , y1
+0, . . . , yN
+0 , t0
+�
+,
+η = (x, y, z, t) =
+�
+x1, . . . , xN, y1, . . . , yN, t
+�
+.
+It implies that
+ξ0 o η =
+�
+x1
+0 + x1, . . . , xN
+0 + xN, y1
+0 + y1, . . . , yN
+0 + yN, t0 + t + 2⟨y0, x⟩ − 2⟨x0, y⟩
+�
+,
+ξ∗
+0 o η =
+�
+x1∗
+0 + x1, . . . , xN∗
+0
++ xN, y1∗
+0 + y1, . . . , yN∗
+0
++ yN, t∗
+0 + t + 2⟨y∗
+0, x⟩ − 2⟨x∗
+0, y⟩
+�
+.
+It immediately gives
+(ξ∗
+0 o η)−1 =
+�
+− x1∗
+0 − x1, . . . , −xN∗
+0
+− xN, −y1∗
+0 − y1, . . . , −yN∗
+0
+− yN, −t∗
+0 − t − 2⟨y∗
+0, x⟩ + 2⟨x∗
+0, y⟩
+�
+.
+
+12
+P. OZA, J. TYAGI
+It yields
+(ξ0 o η) o (ξ∗
+0 o η)−1 =
+�
+x1
+0 − x1∗
+0 , . . . , xN
+0 − xN∗
+0 , y1
+0 − y1∗
+0 , . . . , yN
+0 − yN∗
+0 , t0 − t∗
+0
+(3.12)
++ 2⟨y, x∗
+0⟩ − 2⟨x, y∗
+0⟩ − 2⟨y, x0⟩ + 2⟨x, y0⟩ + 2⟨y0 + y, −x∗
+0 − x⟩ − 2⟨x0 + x, −y∗
+0 − y⟩
+�
+=
+�
+x1
+0 − x1∗
+0 , . . . , xN
+0 − xN∗
+0 , y1
+0 − y1∗
+0 , . . . , yN
+0 − yN∗
+0 , t0 − t∗
+0
++ 2⟨y, x∗
+0⟩ − 2⟨x, y∗
+0⟩ − 2⟨y, x0⟩ + 2⟨x, y0⟩ + 2⟨y0, −x∗
+0 − x⟩
++ 2⟨y, −x∗
+0 − x⟩ − 2⟨x0, −y∗
+0 − y⟩ − 2⟨x, −y∗
+0 − y⟩
+�
+=
+�
+x1
+0 − x1∗
+0 , . . . , xN
+0 − xN∗
+0 +, y1
+0 − y1∗
+0 , . . . , yN
+0 − yN∗
+0
+, t0 − t∗
+0
++ 2⟨y, x∗
+0⟩ − 2⟨x, y∗
+0⟩ − 2⟨y, x0⟩ + 2⟨x, y0⟩ + 2⟨y0, −x∗
+0⟩ + 2⟨y0, −x⟩ + 2⟨y, −x∗
+0⟩ + 2⟨y, −x⟩
+− 2⟨x0, −y∗
+0⟩ − 2⟨x0, −y⟩ − 2⟨x, −y∗
+0⟩ − 2⟨x, −y⟩
+�
+=
+�
+x1
+0 − x1∗
+0 , . . . , xN
+0 − xN∗
+0 +, y1
+0 − y1∗
+0 , . . . , yN
+0 − yN∗
+0
+, t0 − t∗
+0
++ 2⟨y, x∗
+0⟩ − 2⟨x, y∗
+0⟩ − 2⟨y, x0⟩ + 2⟨x, y0⟩ + 2⟨x0, y∗
+0⟩ + 2⟨x0, y⟩ + 2⟨x, y∗
+0⟩ + 2⟨x, y⟩
+− 2⟨y0, x∗
+0⟩ − 2⟨y0, x⟩ − 2⟨y, x∗
+0⟩ − 2⟨y, x⟩
+�
+=
+�
+x0 − x∗
+0, y0 − y∗
+0, t0 − t∗
+0 + 2⟨x0, y∗
+0⟩ − ⟨y0, x∗
+0⟩
+�
+=
+�
+x0 − x∗
+0, y0 − y∗
+0, t0 − t∗
+0 + 2⟨y0, −x∗
+0⟩ − 2⟨x0, −y∗
+0⟩
+�
+= ξ0 o ξ∗
+0
+−1.
+Similarly, one may see that
+(ξ0 o η−1) o (ξ∗
+0 o η−1)
+−1 = ξ0 o ξ∗
+0
+−1.
+(3.13)
+Using (3.12) & (3.13) in (3.10) & (3.11), respectively infers
+u(ξ∗
+0 o η) + u(ξ∗
+0 o η−1) − 2Φ(ξ∗
+0) ≤ uε(ξ0 o η) + uε(ξ0 o η−1) + 2
+��ξ0 o ξ∗
+0
+−1��4
+HN
+ε
+− 2Φ(ξ∗
+0)
+(3.14)
+= uε(ξ0 o η) + uε(ξ0 o η−1) + 2
+��ξ0 o ξ∗
+0
+−1��4
+HN
+ε
+− 2
+�
+Ψ(ξ0) + 1
+ε
+��ξ0 o ξ∗
+0
+−1��4
+HN
+�
+(by (3.5))
+= uε(ξ0 o η) + uε(ξ0 o η−1) − 2Ψ(ξ0).
+We also have
+��ξ o ξ∗
+0
+−1��4
+HN ≤ ε osc
+Ω u,
+(3.15)
+see [22, 31] for the details. It immediately grants that |ξ o ξ∗
+0
+−1|
+HN can be made as small as possible by the suitable
+choice of ε. Using (3.14) in (3.9), we get
+f(ξ∗
+0) ≤ αM+
+λ,Λ
+�
+D2
+HN,Sϕ(ξ0)
+�
++ β
+2 c(N, s)
+�
+{η∈ HN; ξ∗
+0 o η, ξ∗
+0 o η−1∈B
+HN
+r
+(ξ∗
+0 )}
+Φ(ξ∗
+0 o η) + Φ(ξ∗
+0 o η−1) − 2Φ(ξ∗
+0)
+|η|Q+2s
+HN
+dη
+(3.16)
++ β
+2 c(N, s)
+�
+HN\{η∈ HN ; ξ∗
+0 o η, ξ∗
+0 o η−1∈B
+HN
+r
+(ξ∗
+0 )}
+u(ξ∗
+0 o η) + u(ξ∗
+0 o η−1) − 2Φ(ξ∗
+0)
+|η|Q+2s
+HN
+dη
+≤ αM+
+λ,Λ
+�
+D2
+HN,Sϕ(ξ0)
+�
++ c(N, s)
+�
+{η∈ HN ; ξ∗
+0 o η, ξ∗
+0 o η−1∈B
+HN
+r
+(ξ∗
+0 )}
+ϕ(ξ0 o η) + ϕ(ξ0 o η−1) − 2ϕ(ξ0)
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+HN\{η∈ HN ; ξ∗
+0 o η, ξ∗
+0 o η−1∈B
+HN
+r
+(ξ∗
+0 )}
+uε(ξ0 o η) + uε(ξ0 o η−1) − 2Ψ(ξ0)
+|η|Q+2s
+HN
+dη
+= αM+
+λ,Λ
+�
+D2
+HN,Sϕ(ξ0)
+�
+− β
+�
+− ∆
+HN
+�sΨ(ξ0).
+Now, adding and subtracting f(ξ0) in the L.H.S. of (3.16) gives
+αM+
+λ,Λ
+�
+D2
+HN,Sϕ(ξ0)
+�
+− β
+�
+− ∆
+HN
+�sΨ(ξ0) ≥ f(ξ0) −
+�
+f(ξ0) − f(ξ∗
+0)
+�
+≥ f(ξ0) − |f(ξ0) − f(ξ∗
+0)|.
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+13
+Next, using (3.15) together with the continuity of f, we define
+dε =
+sup
+B
+HN
+δ√ε(ξ0)
+|f(ξ0) − f(ξ∗
+0)|,
+for some δ = δ(osc
+Ω u). Clearly, dε −→ 0 as ε −→ 0. Hence the claim.
+□
+Remark 3.4. Using the similar arguments, one may see that an analogous result also holds for supersolutions.
+Lemma 3.5. Let f & g be two continuous functions.
+Let u & v be bounded USC and LSC functions in HN,
+respectively. Let
+αM+
+λ,Λ
+�
+D2
+HN,Su
+�
+− β(−∆HN )su ≥ f
+&
+αM+
+λ,Λ
+�
+D2
+HN,Sv
+�
+− β(−∆HN )sv ≤ g
+be hold in the viscosity sense in Ω. Then
+αM+
+λ,Λ
+�
+D2
+HN,S(u − v)
+�
+− β(−∆HN )s(u − v) ≥ f − g in Ω in the viscosity sense.
+Proof of Lemma 3.5. By Lemma 3.3, we have
+αM+
+λ,Λ
+�
+D2
+HN,Suε�
+− β(−∆
+HN )suε ≥ f − dε
+(3.17)
+&
+αM+
+λ,Λ
+�
+D2
+HN,Svε
+�
+− β(−∆
+HN )svε ≤ g + dε.
+(3.18)
+Our aim is to show that
+αM+
+λ,Λ
+�
+D2
+HN,S(uε − vε)
+�
+− β(−∆
+HN )s(uε − vε) ≥ f − g − 2dε,
+so that further using the stability result (Theorem 1.1) yields the claim.
+Let P ∈ C2
+b (HN) be a paraboloid in B
+HN
+r
+⊂ Ω1 such that
+P(ξ0) = uε(ξ0) − vε(ξ0)
+and
+P(τ) ≥ uε(τ) − vε(τ) for all τ ∈ B
+HN
+r
+(ξ0).
+We assume that B
+HN
+2r (ξ0) ⊂ Ω. Consider
+Φ(x) =
+�
+P
+in B
+HN
+r
+(ξ0)
+uε − vε
+in
+HN \ B
+HN
+r
+(ξ0).
+Take δ > 0 and let us define
+w(ξ) = vε(ξ) − uε(ξ) + Φ(ξ) + δ
+���ξ0
+−1o ξ
+��
+HN ∧ r
+�4 − δr4
+1,
+for 0 < r1 < δ ∧ r
+2. We observe that w ≥ 0 on ∂B
+HN
+r1 (ξ0) and w(ξ0) = −δr2 < 0. By Theorem 5.1 [10], we have
+that for any ξ ∈ B
+HN
+r1 (ξ0), there exists a convex paraboloid P ξ of opening K (some constant independent of ξ) which
+touches w from above at ξ ∈ B
+HN
+r1 (ξ0). Further, by Lemma 3.5 [10] and w(ξ0) < 0, we have that
+0 <
+�
+B
+HN
+r
+(ξ0)∩{w=Γw}
+det D2Γw,
+(3.19)
+where Γw is the convex envelope of w in A given by
+Γw(ξ) = sup
+v
+�
+v(ξ) ; v ≤ w in A, v convex in A
+�
+,
+for ξ ∈ A. Moreover, uε and vε are punctually second order differentiable in A (see 2.2 (ii) [22]). It gives that
+M+
+λ,Λ(D2
+HN ,Suε) − (−∆
+HN )suε and M+
+λ,Λ(D2
+HN ,Svε) − (−∆
+HN)svε are defined in the classical sense for ξ ∈ A.
+By the convexity of Γw and that Γw ≤ w, we have that the Hessian matrix D2w(ξ) is semi-positive definite for
+ξ ∈ A ∩ {w = Γw}. It yields that
+M+
+λ,Λ
+�
+D2
+HN ,Sw(ξ)
+�
+≥ 0
+(3.20)
+
+14
+P. OZA, J. TYAGI
+&
+(3.21)
+1
+2c(N, s)
+�
+{η∈ HN; ξ o η∈B
+HN
+r
+(ξ0)}
+w(ξ o η) + w(ξ o η−1) − 2w(ξ)
+|η|Q+2s
+HN
+dη
+= 1
+2c(N, s)
+�
+{η∈ HN ; ξ o η∈B
+HN
+r
+(ξ0)}
+w(ξ o η) − w(ξ) −
+1{|η|
+HN ≤1}η.(∇
+HN w(ξ), ∂tw(ξ))
+|η|Q+2s
+HN
+dη
+≥ 0,
+for ξ ∈ A ∩ {w = Γw} using Proposition 2.4 [28] and
+w(ξ o η) − w(ξ) −
+1{|η|
+HN ≤1}η.(∇
+HN w(ξ), ∂tw(ξ)) ≥ Γw(ξ o η) − Γw(ξ) −
+1{|η|
+HN ≤1}η.(∇
+HN Γw(ξ), ∂tΓw(ξ))
+≥ 0
+along with ∇w(ξ) = ∇Γw(ξ) for ξ ∈ {w = Γw}. It is clear from (3.19) and
+��B
+HN
+r
+(ξ0) \ A
+�� = 0 that
+��{w = Γw} ∩ A
+�� > 0,
+i.e., there is a point ξδ ∈ {w = Γw} ∩ A such that (3.17) and (3.18) hold classically. Let IN be denote the identity
+matrix of order N. We have
+(3.22)
+f(ξδ) − dε ≤ αM+
+λ,Λ
+�
+D2
+HN,Suε(ξδ)
+�
+− β(−∆
+HN )suε(ξδ)
+≤ αM+
+λ,Λ
+�
+D2
+HN,Svε(ξδ) − D2
+HN,Sw(ξδ) + D2
+HN ,SΦ(ξδ) + D2
+HN,S
+�
+δ
+��ξ0
+−1o ξ
+��4
+HN (ξδ)
+��
+− β(−∆
+HN)suε(ξδ)
+= αM+
+λ,Λ
+�
+D2
+HN,Svε(ξδ) + D2
+HN,SΦ(ξδ) + δD2
+HN,S
+���ξ0
+−1o ξ
+��4
+HN(ξδ)
+��
+− D2
+HN,Sw(ξδ)
+�
+− β(−∆
+HN)suε(ξδ)
+≤ αM+
+λ,Λ
+�
+D2
+HN,Svε(ξδ) + D2
+HN,SΦ(ξδ) + δD2
+HN,S
+���ξ0
+−1o ξ
+��4
+HN(ξδ)
+��
++ αM+
+λ,Λ
+�
+− D2
+HN,Sw(ξδ)
+�
+− β(−∆
+HN )suε(ξδ)
+= αM+
+λ,Λ
+�
+D2
+HN,Svε(ξδ) + D2
+HN,SΦ(ξδ) + δD2
+HN,S
+���ξ0
+−1o ξ
+��4
+HN(ξδ)
+��
+− αM−
+λ,Λ
+�
+D2
+HN,Sw(ξδ)
+�
+− β(−∆
+HN )suε(ξδ)
+≤ αM+
+λ,Λ
+�
+D2
+HN,Svε(ξδ) + D2
+HN,SΦ(ξδ) + δD2
+HN,S
+���ξ0
+−1o ξ
+��4
+HN(ξδ)
+��
+− β(−∆
+HN )suε(ξδ) (by (3.20)),
+where in the second last step, we used the relation
+M+
+λ,Λ(−M) = −M−
+λ,Λ(M).
+Now, since
+��ξ0
+−1o ξ
+��4
+HN is a radial function so using Lemma 3.2 [16] together with sub-additivity property of Pucci’s
+maximal operator and (3.22) yields
+f(ξδ) − dε ≤ αM+
+λ,Λ
+�
+D2
+HN,Svε(ξδ)
+�
++ αM+
+λ,Λ
+�
+D2
+HN,SΦ(ξδ)
+�
++ αδM+
+λ,Λ
+�
+D2
+HN,S
+���ξ0
+−1o ξδ
+��4
+HN
+��
+− β(−∆
+HN )suε(ξδ)
+= αM+
+λ,Λ
+�
+D2
+HN,Svε(ξδ)
+�
++ αM+
+λ,Λ
+�
+D2
+HN,SΦ(ξδ)
+�
++ αΛδ
+�
+(2N − 2)
+�
+4
+N
+�
+i=1
+(xi
+δ − xi
+0)2 + (yi
+δ − yi
+0)2
+�
++ 2
+�
+12
+N
+�
+i=1
+(xi
+δ − xi
+0)2 + (yi
+δ − yi
+0)2
+��
+− β(−∆
+HN )suε(ξδ),
+where (x1
+δ, . . . , xN
+δ , y1
+δ, . . . , yN
+δ ) and (x1
+0, . . . , xN
+0 , y1
+0, . . . , yN
+0 ) are the first 2N coordinates of ξδ and ξ0, respectively.
+Next, since w(ξ o η) − w(ξ) > 0 for ξ o η ∈ Bc
+r(ξ) and r1 small enough so we have by (3.21),
+−(−∆
+HN)suε(ξδ) = −(−∆
+HN)svε(ξδ) + (−∆
+HN )sw(ξδ) − (−∆
+HN )sΦ(ξδ) − δ(−∆
+HN )s(|ξ−1
+0
+o ξ|4)(ξδ)
+(3.23)
+≤ −(−∆
+HN)svε(ξδ) −
+�
+{η∈ HN ; ξδ o η∈ HN \B
+HN
+r
+(ξδ)}
+1{|η|
+HN ≤1}η.(∇
+HN w(ξδ), ∂tw(ξδ))
+|η|Q+2s
+HN
+dη
+− (−∆
+HN)sΦ(ξδ) − δ(−∆
+HN)s(|ξ−1
+0
+o ξ|4
+HN)(ξδ)
+= −(−∆
+HN)svε(ξδ) −
+�
+{η∈ HN ; r≤|η|
+HN ≤1}
+η.(∇
+HN w(ξδ), ∂tw(ξδ))
+|η|Q+2s
+HN
+dη
+− (−∆
+HN)sΦ(ξδ) − δ(−∆
+HN)s�
+|ξ−1
+0
+o ξ|4
+HN
+�
+(ξδ).
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+15
+Further, using (3.23) together with (3.21) yields
+f(ξδ) − dε ≤ αM+
+λ,Λ
+�
+D2
+HN,Svε(ξδ)
+�
+− β(−∆
+HN )svε(ξδ) + αM+
+λ,Λ
+�
+D2
+HN ,SΦ(ξδ)
+�
+− β(−∆
+HN )sΦ(ξδ)
++ αΛδ
+�
+(2N − 2)
+�
+4
+N
+�
+i=1
+(xi
+δ − xi
+0)2 + (yi
+δ − yi
+0)2
+�
++ 2
+�
+12
+N
+�
+i=1
+(xi
+δ − xi
+0)2 + (yi
+δ − yi
+0)2
+��
+− β
+2 c(N, s)
+�
+{η∈ HN; r≤|η|
+HN ≤1}
+η.(∇
+HN w(ξδ), ∂tw(ξδ))
+|η|Q+2s
+HN
+dη − βδ(−∆
+HN )s(|ξ−1
+0
+o ξ|4
+HN )(ξδ)
+≤ g(ξδ) + dε + αΛδ
+�
+(2N − 2)
+�
+4
+N
+�
+i=1
+(xi
+δ − xi
+0)2 + (yi
+δ − yi
+0)2
+�
++ 2
+�
+12
+N
+�
+i=1
+(xi
+δ − xi
+0)2 + (yi
+δ − yi
+0)2
+��
+− β
+2 c(N, s)
+�
+{η∈ HN; r≤|η|
+HN ≤1}
+η.(∇
+HN w(ξδ), ∂tw(ξδ))
+|η|Q+2s
+HN
+dη − δ(−∆
+HN)s(|ξ−1
+0
+o ξ|4
+HN )(ξδ)
++ αM+
+λ,Λ
+�
+D2
+HN,SΦ(ξδ)
+�
+− β(−∆
+HN )sΦ(ξδ) (using (3.18)).
+It is easy to observe that ξδ −→ ξ0 and ∇Γw(ξδ) −→ ∇Γw(ξ0) = 0 as r1 −→ 0. Now, letting δ −→ 0 gives
+f(ξ0) − dε ≤ g(ξ0) + dε + αM+
+λ,Λ
+�
+D2
+HN,SΦ(ξ0)
+�
+− β(−∆
+HN )sΦ(ξ0).
+In other words,
+αM+
+λ,Λ
+�
+D2
+HN,SΦ(ξ0)
+�
+− β(−∆
+HN)sΦ(ξ0) ≥ f(ξ0) − g(ξ0) − 2dε.
+The above equation clearly implies that
+αM+
+λ,Λ
+�
+D2
+HN,S(uε − vε)
+�
+− β(−∆
+HN )sΦ(uε − vε) ≥ f − g − 2dε in Ω1
+in the viscosity sense. Finally, letting ε −→ 0 along with using Theorem 1.1 yields the claim.
+□
+In order to derive comparison principle, we next state and prove the following lemma. We mention that a similar
+lemma has been proven in the Euclidean setting (see Lemma 5.5 [24]).
+Lemma 3.6. There exists a C2(Ω) ∩ Cb(HN) function ϕh such that
+αM+
+λ,Λ
+�
+D2
+HN,Sϕh
+�
+− β
+�
+− ∆
+HN
+�sϕh ≤ −1, in Ω.
+Proof of Lemma 3.6. Let diam(Ω) = R. We may assume without of loss of generality that Ω ⊂ BR
+HN (ξR), where
+ξR := (2R, 0, . . . , 0). Let us define
+ϕh(ξ) =
+�
+2 − e−Cξ1
+for ξ1 ≥ 0
+1
+2 + 1
+4
+�
+1
+1−Cξ1
+�
++ 1
+4
+�
+sin 3Cξ1 + cos
+√
+6 Cξ1
+�
+for ξ1 < 0,
+where ξ1 is the first coordinate of ξ = (ξ1, . . . , ξN, ξN+1, . . . , ξ2N, t) ∈ Ω and C > 0 is some constant. It is easy to
+calculate for ξ1 > 0,
+∂xiϕh =
+�
+Ce−Cξ1
+if i = 1,
+0
+if 2 ≤ i ≤ 2N,
+and ∂tϕh = 0. Also, for ξ1 > 0,
+∂2
+xixjϕh =
+�
+−C2e−Cξ1
+if i = j = 1
+0
+otherwise,
+and ∂2
+txi = 0 = ∂2
+tt for i = 1, 2, . . . , 2N. Using this, we first compute ∇
+HN ϕh(ξ) and D2
+HN,Sϕh(ξ) as follows:
+∇
+HNϕh(ξ) = σ(ξ)∇ϕh(ξ) =
+�IN
+0N
+2y
+0N
+IN
+−2x
+�
+2N×(2N+1)
+
+
+Ce−Cξ1
+0
+...
+0
+
+
+(2N+1)×1
+=
+
+
+Ce−Cξ1
+0
+...
+0
+
+
+2N×1
+.
+
+16
+P. OZA, J. TYAGI
+Also,
+D2
+HNϕh(ξ) = σ(ξ)D2ϕhσT (ξ) =
+�IN
+0N
+2y
+0N
+IN
+−2x
+�
+2N×(2N+1)
+
+
+−C2e−Cξ1
+0
+. . .
+0
+0
+0
+. . .
+0
+...
+...
+...
+...
+0
+0
+. . .
+0
+
+
+(2N+1)×(2N+1)
+
+
+IN
+0N
+0N
+IN
+2y
+−2x
+
+
+(2N+1)×2N
+=
+
+
+−C2e−Cξ1
+0
+. . .
+0
+0
+0
+. . .
+0
+...
+...
+...
+...
+0
+0
+. . .
+0
+
+
+2N×2N
+.
+Now, let δ = min{1, R}. Then for any ξ ∈ Ω, we get
+αM+
+λ,Λ
+�
+D2
+HN,Sϕh(ξ)
+�
+− β(−∆
+HN)sϕh(ξ)
+= −λαC2e−Cξ1 + β
+2 c(N, s)
+�
+HN
+ϕh(ξ o η) − ϕh(ξ) −
+1{|η|
+HN ≤1}η.(∇
+HN ϕh(ξ), ∂tϕh(ξ))
+|η|Q+2s
+HN
+dη
+= −λαC2e−Cξ1 + β
+2 c(N, s)
+�
+B
+HN
+δ
+ϕh(ξ o η) − ϕh(ξ) −
+1{|η|
+HN ≤1}η.(∇
+HN ϕh(ξ), ∂tϕh(ξ))
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+CB
+HN
+δ
+∩{η;η1≤0}
+ϕh(ξ o η) − ϕh(ξ) −
+1{|η|
+HN ≤1}η.(∇
+HN ϕh(ξ), ∂tϕh(ξ))
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+B
+HN
+1
+∩ CB
+HN
+δ
+∩ {η;η1>0}
+ϕh(ξ o η) − ϕh(ξ) −
+1{|η|
+HN ≤1}η.(∇
+HN ϕh(ξ), ∂tϕh(ξ))
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+CB
+HN
+1
+∩ {η;η1>0}
+ϕh(ξ o η) − ϕh(ξ) −
+1{|η|
+HN ≤1}η.(∇
+HN ϕh(ξ), ∂tϕh(ξ))
+|η|Q+2s
+HN
+dη.
+where CB
+HN
+r
+denotes the complement of B
+HN
+r
+in
+HN, i.e.,
+HN \ B
+HN
+r
+. We can re-write the above equation as
+αM+
+λ,Λ
+�
+D2
+HN,Sϕh(ξ)
+�
+− β
+�
+− ∆
+HN
+�sϕh(ξ)
+= −λαC2e−Cξ1 + β
+2 c(N, s)
+�
+B
+HN
+δ
+ϕh(ξ o η) − ϕh(ξ) − η.(∇
+HN ϕh(ξ), ∂tϕh(ξ))
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+CB
+HN
+δ
+∩{η;η1≤0}
+ϕh(ξ o η) − ϕh(ξ)
+|η|Q+2s
+HN
+dη + β
+2 c(N, s)
+�
+B
+HN
+1
+∩ CB
+HN
+δ
+∩ {η;η1>0}
+ϕh(ξ o η) − ϕh(ξ)
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+B
+HN
+1
+∩CB
+HN
+1
+−η.(∇
+HN ϕh(ξ), ∂tϕh(ξ))
+|η|Q+2s
+HN
+dη + β
+2 c(N, s)
+�
+CB
+HN
+1
+∩ {η;η1>0}
+ϕh(ξ o η) − ϕh(ξ)
+|η|Q+2s
+HN
+dη.
+It further gives
+αM+
+λ,Λ(D2
+HN,Sϕh(ξ)) − β(−∆
+HN )sϕh(ξ) = −λαC2e−Cξ1
+(3.24)
++ β
+2 c(N, s)
+�
+B
+HN
+δ
+�
+2 − e−C(ξ1+η1)�
+−
+�
+2 − e−Cξ1�
+− η1Ce−Cξ1
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+CB
+HN
+δ
+∩{η;η1≤0}
+�
+2 − e−C(ξ1+η1)�
+−
+�
+2 − e−Cξ1�
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+B
+HN
+1
+∩ CB
+HN
+δ
+∩ {η;η1>0}
+�
+2 − e−C(ξ1+η1)�
+−
+�
+2 − e−Cξ1�
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+B
+HN
+1
+∩CB
+HN
+δ
+−η1Ce−Cξ1
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+CB
+HN
+1
+∩ {η;η1>0}
+�
+2 − e−C(ξ1+η1)�
+−
+�
+2 − e−Cξ1�
+|η|Q+2s
+HN
+dη.
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+17
+Similarly,
+αM+
+λ,Λ(D2
+HN,Sϕh(ξ)) − β(−∆
+HN )sϕh(ξ)
+(3.25)
+= −λαC2e−Cξ1 + β
+2 c(N, s)
+�
+B
+HN
+δ
+�
+− e−C(ξ1+η1) + e−Cξ1�
+− η1Ce−Cξ1
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+CB
+HN
+δ
+∩{η;η1≤0}
+�
+− e−C(ξ1+η1) + e−Cξ1�
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+B
+HN
+1
+∩ CB
+HN
+δ
+∩ {η;η1>0}
+�
+− e−C(ξ1+η1) + e−Cξ1�
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+B
+HN
+1
+∩CB
+HN
+δ
+−η1Ce−Cξ1
+|η|Q+2s
+HN
+dη + β
+�
+CB
+HN
+1
+∩ {η;η1>0}
+�
+− e−C(ξ1+η1) + e−Cξ1�
+|η|Q+2s
+HN
+dη.
+Now, since e−Cξ1 is a convex function so we have
+0 ≤ e−C(ξ1+η1) − e−Cξ1 + η.(∇
+HN ϕh(ξ), ∂tϕh(ξ))
+(3.26)
+= e−C(ξ1+η1) − e−Cξ1 + Cη1e−Cξ1.
+Also, if η1 ≤ 0 then
+e−C(ξ1+η1) − e−Cξ1 ≥ 0.
+(3.27)
+Using (3.26) and (3.27) in the first and second integrals in the R.H.S. of (3.25), respectively, it confers that these
+integrals are non-positive. We further have that
+|e−C(ξ1+η1) − e−Cξ1| = e−Cξ1|e−Cη1 − 1| ≤ Ce−Cξ1|η|
+HN .
+It infers
+�����β
+�
+B
+HN
+1
+∩ CB
+HN
+δ
+∩ {η;η1>0}
+�
+−e−C(ξ1+η1) + e−Cξ1�
+|η|Q+2s
+HN
+dη
+����� ≤ β
+�
+B
+HN
+1
+∩ CB
+HN
+δ
+Ce−Cξ1|η|
+HN
+|η|Q+2s
+HN
+dη
+(3.28)
+≤ β
+�
+B
+HN
+1
+∩ CB
+HN
+δ
+Ce−Cξ1|η|2
+HN
+δ|η|Q+2s
+HN
+dη
+≤ βe−Cξ1 C
+δ
+�
+B
+HN
+1
+∩ CB
+HN
+δ
+|η|2
+HN
+|η|Q+2s
+HN
+dη
+≤ βe−Cξ1 C
+δ
+�
+B
+HN
+1
+|η|2
+HN
+|η|Q+2s
+HN
+dη.
+It is easy to see that for η1 > 0, we have
+��e−C(ξ1+η1) − e−Cξ1�� ≤ e−Cξ1 so
+�����β
+�
+CB
+HN
+1
+∩ {η;η1>0}
+�
+− e−C(ξ1+η1) + e−Cξ1�
+|η|Q+2s
+HN
+dη
+����� ≤ βe−Cξ1
+�
+CB
+HN
+1
+1
+|η|Q+2s
+HN
+dη.
+(3.29)
+Also, it is easy to observe that
+�����β
+�
+B
+HN
+1
+∩CB
+HN
+δ
+−η1Ce−Cξ1
+|η|Q+2s
+HN
+dη
+����� ≤ β
+�
+B
+HN
+1
+∩CB
+HN
+δ
+|η|
+HNCe−Cξ1
+|η|Q+2s
+HN
+dη
+(3.30)
+≤ βe−Cξ1 C
+δ
+�
+B
+HN
+1
+|η|2
+HN
+|η|Q+2s
+HN
+dη.
+Using (3.28), (3.29) & (3.30) in (3.25) yields that for sufficiently large enough C > 0 we can make the L.H.S. of
+(3.25) less than −1, i.e.,
+αM+
+λ,Λ
+�
+D2
+HN,Sϕh
+�
+− β
+�
+− ∆
+HN
+�sϕh =≤ −1.
+□
+Further, using the above lemma, we prove the comparison principle.
+Lemma 3.5 together with a standard
+approximation argument produces the following lemma.
+
+18
+P. OZA, J. TYAGI
+Lemma 3.7. Let u be bounded in
+HN and USC in Ω such that
+αM+
+λ,Λ
+�
+D2
+HN,Su
+�
+− β(−∆HN )su ≥ 0 in Ω in the viscosity sense.
+Then
+sup
+Ω
+u ≤ sup
+HN \Ω
+u.
+Proof of Lemma 3.7. By Lemma 3.6, we have a function ϕh ∈ C2(Ω) ∩ Cb(HN) such that
+αM+
+λ,Λ
+�
+D2
+HN ,Sϕh
+�
+− β
+�
+− ∆
+HN
+�sϕh ≤ −1.
+Now, let us define a function
+ϕM(x) = M + εϕh(x) for ε > 0.
+Then
+αM+
+λ,Λ
+�
+D2
+HN,SϕM
+�
+− β
+�
+− ∆
+HN
+�sϕM = αεM+
+λ,Λ
+�
+D2
+HN,Sϕh
+�
+− βε
+�
+− ∆
+HN
+�sϕh
+(3.31)
+≤ −ε in Ω.
+Further, let M0 be the smallest value of M such that ϕM ≥ u. We aim to prove M0 ≤ sup
+HN\Ω
+u by the method of
+contradiction. Let us assume that
+M0 > sup
+HN\Ω
+u,
+then we have that there exists a point ξ0 ∈ Ω such that u(ξ0) = ϕM0(ξ0). It immediately implies that ϕM0 touches
+u at ξ0 from above and by the definition, it gives
+αM+
+λ,Λ
+�
+D2
+HN,SϕM0
+�
+(ξ0) − β
+�
+− ∆
+HN
+�sϕM0(ξ0) ≥ 0.
+This contradicts (3.31). Thus, we have
+M0 ≤ sup
+HN\Ω
+u,
+which further entails that
+u(ξ) ≤ ϕM0(ξ0)
+≤ M0 + ε sup
+HN ϕh
+≤ sup
+HN u + ε sup
+HN ϕh, ξ ∈
+HN.
+Finally, letting ε −→ 0 offers the claim.
+□
+Proof of Theorem 1.6. We follow the similar arguments as in the Euclidean setting, see for instance, [11, 12, 29].
+Without loss of generality, we may assume that ∥u∥∞, HN = 1. We first show the existence of a universal constant
+0 < δ < 1 such that
+osc
+B
+HN
+2−k
+u ≤ 2(1 − δ)k.
+We use the principle of mathematical induction to show the claim. Now, since ∥u∥∞, HN = 1 so the claim holds
+trivially for k ≤ 0. Let the above inequality holds true up to some k, we need to show that it also holds for k + 1.
+For this, consider a function
+v(ξ) := u(2−kξ)
+(1 − δ)k − ak ,
+where ak is a constant chosen such that − 1
+2 ≤ v ≤ 1
+2 in B
+HN
+1
+. Also, by the induction hypothesis, we have
+osc
+B
+HN
+2−j
+u ≤ 2(1 − δ)j for all j ≤ k,
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+19
+i.e.,
+osc
+B
+HN
+2j
+u ≤ 2(1 − δ)−j for all j ≥ 0.
+We aim to show that
+osc
+B
+HN
+1
+2
+v ≤ osc
+B
+HN
+1
+v.
+One may show this either by showing that supremum of v in B
+HN
+1
+2
+is smaller than that in B
+HN
+1
+or the infimum is
+larger. It is trivial that either v ≥ 0 or v ≤ 0 for atleast half of the points (in measure) in B
+HN
+1
+. Without loss of
+generality, we may assume that
+|N| ≥ 1
+2
+��B
+HN
+1
+��,
+where N := {v ≤ 0} ∩ B
+HN
+1
+. We show now that the induction hypothesis implies that
+v(ξ) ≤
+�
+2|ξ|
+HN
+�α − 1
+2 for all ξ ∈ B
+HN
+1
+.
+Let ξ ∈ B
+HN
+2j+1 \ B
+HN
+2j
+for some j > 0. That is
+2j+1 > |ξ|
+HN > 2j.
+In other words,
+2−k+j+1 > |2−kξ|
+HN > 2−k+j.
+v(x) = (1 − δ)−ku(2−kx) − ak.
+For ξ ∈ B
+HN
+1
+,
+−1
+2 ≤ (1 − δ)−ku(2−kξ) − ak ≤ 1
+2.
+Now, for ξ /∈ B
+HN
+1
+, we have for any index j ≥ 0,
+v(ξ) ≤
+�
+2|ξ|
+HN
+�γ − 1
+2,
+(3.32)
+where γ is a number such that (1 − δ) = 2−γ. Also, for any ξ ∈ B
+HN
+1
+,
+αM+
+λ,Λ
+�
+D2
+HNv
+�
+− β(−∆HN )sv = (1 − δ)k �
+αM+
+λ,Λ
+�
+D2
+HNu
+�
+− β
+�
+− ∆HN
+�su
+�
+= 0.
+Now, we show that the following three points
+• v(ξ) ≤
+�
+2|ξ|
+HN
+�γ − 1
+2 for ξ /∈ B
+HN
+1
+• |N| =
+��{v ≤ 0} ∩ B
+HN
+1
+�� ≥ 1
+2
+��B
+HN
+1
+��
+• αM+
+λ,Λ(D2
+HNv) − β(−∆HN )sv = 0 in B
+HN
+1
+imply that v ≤
+� 1
+2 − δ
+�
+in B
+HN
+1
+2
+. Let us assume the contrary. Let v(ξ) >
+� 1
+2 − δ
+�
+for some ξ ∈ B
+HN
+1
+2
+. Consider a
+smooth radial function whose support is contained in B
+HN
+3
+4
+and ρ ≡ 1 in B
+HN
+1
+2
+. It immediately gives that v + δρ
+attains a local maximum at some point ξ0 ∈ B
+HN
+3
+4
+such that
+�
+v + δρ
+�
+(ξ0) > 1
+2, i.e., max
+B
+HN
+1
+(v + δρ) = (v + δρ)(ξ0) > 1
+2.
+Let us evaluate L(v + δρ), which further entails getting a contradiction.
+L
+�
+v + δρ
+�
+(ξ0) = αM+
+λ,Λ
+�
+D2
+HN(v + δρ)
+�
+(ξ0) − β
+�
+− ∆HN
+�s(v + δρ)(ξ0)
+≥ αM+
+λ,Λ
+�
+D2
+HNv
+�
+(ξ0) + δαM−
+λ,Λ
+�
+D2
+HNρ
+�
+(ξ0) − β
+�
+− ∆HN
+�sv(ξ0) − δβ
+�
+− ∆HN
+�sρ(ξ0)
+= αM+
+λ,Λ
+�
+D2
+HNv
+�
+(ξ0) − β
+�
+− ∆HN
+�sv(ξ0) + δαM+
+λ,Λ
+�
+D2
+HNρ
+�
+(ξ0) − δβ
+�
+− ∆HN
+�sρ(ξ0)
+= δαM+
+λ,Λ
+�
+D2
+HNρ
+�
+(ξ0) − δβ
+�
+− ∆HN
+�sρ(ξ0)
+≥ δ min
+ξ∈B
+HN
+3
+4
+�
+αM+
+λ,Λ
+�
+D2
+HN ρ
+�
+(ξ) − β(−∆HN )sρ(ξ)
+�
+.
+
+20
+P. OZA, J. TYAGI
+On the other hand,
+(3.33)
+L(v + δρ)(ξ0) = αM+
+λ,Λ(D2
+HN (v + δρ))(ξ0) − β(−∆HN )s(v + δρ)(ξ0)
+≤ αM+
+λ,Λ(D2
+HN (v + δρ))(ξ0) + β
+2 c(N, s)
+�
+HN
+(v + δρ)(ξ0 o η) + (v + δρ)(ξ0 o η−1) − 2(v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη
+= αM+
+λ,Λ(D2
+HN (v + δρ))(ξ0)
++ β
+2 c(N, s)
+�
+HN
+(v + δρ)(ξ0 o η) − (v + δρ)(ξ0) −
+1{|η|
+HN ≤1}η.
+�
+∇
+HN (v + δρ)(ξ0), ∂t(v + δρ)(ξ0)
+�
+|η|Q+2s
+HN
+dη
+= αM+
+λ,Λ(D2
+HN (v + δρ))(ξ0)
++ β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η∈B
+HN
+1
+�
+(v + δρ)(ξ0 o η) − (v + δρ)(ξ0) −
+1{|η|
+HN ≤1}η.
+�
+∇
+HN (v + δρ)(ξ0), ∂t(v + δρ)(ξ0)
+�
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η /∈B
+HN
+1
+�
+(v + δρ)(ξ0 o η) − (v + δρ)(ξ0) −
+1{|η|
+HN ≤1}η.
+�
+∇
+HN (v + δρ)(ξ0), ∂t(v + δρ)(ξ0)
+�
+|η|Q+2s
+HN
+dη
+= αM+
+λ,Λ(D2
+HN (v + δρ))(ξ0)
++ β
+2 c(N, s)
+�
+�
+η∈ HN ;ξ0 o η∈B
+HN
+1
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+�
+η∈ HN ;ξ0 o η /∈B
+HN
+1
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη
+≤ β
+2 c(N, s)
+�
+�
+η∈ HN ;ξ0 o η∈B
+HN
+1
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+�
+η∈ HN ;ξ0 o η /∈B
+HN
+1
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη.
+Note that in the last two steps, we used the fact that v + δρ has a local maximum at ξ0 which also gives the
+non-positivity of integrand in the last integral. Moreover, we have
+β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η∈B
+HN
+1
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη
+= β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η∈N
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ)
+|η|Q+2s
+HN
+dη
++ β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η∈B
+HN
+1
+\N
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη
+≤ β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η∈N
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη
+≤ β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η∈N
+� δρ(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη
+< β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η∈N
+�
+�
+δρ(ξ0 o η) − 1
+2
+�
+|η|Q+2s
+HN
+dη
+≤ β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η∈N
+�
+�
+δM − 1
+2
+�
+|η|Q+2s
+HN
+dη,
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+21
+for M = max
+B
+HN
+3
+4
+ρ. Taking δ <
+1
+2M along with using |N| ≥
+��B
+HN
+1
+��
+2
+, we get
+β
+2 c(N, s)
+�
+�
+η∈ HN;ξ0 o η∈N
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη ≤ −C for some C > 0.
+(3.34)
+Next, using (3.32), we get a bound on the integrand of first integral in the last line of (3.33) . In particular, we have
+(3.35)
+1
+2c(N, s)
+�
+�
+η∈ HN ;ξ0 o η /∈B
+HN
+1
+� (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη = β
+2 c(N, s)
+�
+�
+η∈ HN ;ξ0 o η /∈B
+HN
+1
+� v(ξ0 o η) − (v + δρ)(ξ0)
+|η|Q+2s
+HN
+dη
+≤ β
+2 c(N, s)
+�
+�
+η∈ HN ;ξ0 o η /∈B
+HN
+1
+�
+|ξ0 o η|γ
+HN − 1
+2 − 1
+2
+|η|Q+2s
+HN
+dη
+= β
+2 c(N, s)
+�
+�
+η∈ HN ;ξ0 o η /∈B
+HN
+1
+�
+|ξ0 o η|γ
+HN − 1
+|η|Q+2s
+HN
+dη.
+Further, taking small enough γ, we can make the above integral in the R.H.S. much less than 1. Therefore, by using
+together (3.34) and (3.35) for small enough δ and γ, we can make the L.H.S. of (3.33) arbitrarily small. Hence, we
+can make it smaller than δ min
+ξ∈B
+HN
+3
+4
+�
+αM−
+λ,Λ(D2
+HNρ)(ξ) − β(−∆HN )sρ(ξ)
+�
+, which yield a contradiction. Thus, we have
+v ≤ 1
+2 − δ in B
+HN
+1
+2
+.
+It gives
+osc
+B
+HN
+1
+2
+v ≤ (1 − δ) osc
+B
+HN
+1
+v.
+More precisely, we have
+1
+(1 − δ)k osc
+B
+HN
+1
+2
+u(2−kξ) =
+1
+(1 − δ)k
+osc
+B
+HN
+2−k−1
+u(ξ) ≤ (1 − δ)
+(1 − δ)k osc
+B
+HN
+1
+u(2−kξ) = (1 − δ)
+(1 − δ)k osc
+B
+HN
+2−k
+u(ξ),
+which immediately offers
+osc
+B
+HN
+2−k−1
+u(ξ) ≤ (1 − δ) osc
+B
+HN
+2−k
+u(ξ)
+≤ 2(1 − δ)k+1
+= 2.2−γ(k+1).
+Let for some k > 0, ξ ∈ B
+HN
+2−k \ B
+HN
+2−(k+1). Then we get
+|u(ξ) − u(0)| ≤ 2.2−γk = 2.2γ2−γ(k+1) ≤ C|ξ|γ
+HN ,
+for C = 2.2γ. Hence the claim.
+□
+4. Funding and/or Conflicts of interests/Competing interests
+The research of Priyank Oza was financially supported by Council of Scientific & Industrial Research (CSIR)
+under the grant no. 09/1031(0005)/2019–EMR–I. The second author thanks DST/SERB for the financial support
+under the grant CRG/2020/000041.
+There are no conflict of interests of any type. This manuscript does not use any kind of data.
+
+22
+P. OZA, J. TYAGI
+References
+[1] S. Banerjee, M. Gordina, P. Mariano, Coupling in the Heisenberg group and its applications to gradient estimates, Ann. Probab.
+46(6), 3275–3312 (2018).
+[2] G. Barles, E. Chasseigne, C. Imbert, On the Dirichlet problem for second-order elliptic integro-differential equations, Indiana Univ.
+Math. J. 57, no. 1, 213–246 (2008).
+[3] G. Barles, C. Imbert, Second-order elliptic integro-differential equations: viscosity solutions’ theory revisited, Ann. Inst. H. Poincar´e
+Anal. Non Lin´eaire 25, 567–585 (2008).
+[4] R. Bhatia, Matrix Analysis, Graduate texts in Mathematics, Vol. 169, Springer New York (1997).
+[5] S. Biagi, S. Dipierro, E. Valdinoci, E. Vecchi, A Faber-Krahn inequality for mixed local and nonlocal operators, Preprint,
+arXiv:2104.00830 (2022).
+[6] S. Biagi, S. Dipierro, E. Valdinoci, E. Vecchi, Mixed local and nonlocal elliptic operators: regularity and maximum principles, Comm.
+Partial Differential Equations 47(3), 585–629 (2022).
+[7] S. Biagi, S. Dipierro, E. Valdinoci, E. Vecchi, Semilinear elliptic equations involving mixed local and nonlocal operators, Proceedings
+of the Royal Society of Edinburgh: Section A Mathematics, 151 (5), 1611–1641 (2021).
+[8] T. Bieske, On ∞–harmonic functions on the Heisenberg group, Comm. Partial Differential Equations 27(3–4), 727–761 (2002).
+[9] D. Blazevski, D. del-Castillo-Negrete, Local and nonlocal anisotropic transport in reversed shear magnetic fields shearless Cantori
+and nondiffusive transport, Phys. Rev. E, 87 (2013).
+[10] L. Caffarelli, X. Cabr´e, Fully Nonlinear Elliptic Equations, Amer. Math. Soc. Colloq. Publ. 43, American Mathematical Society,
+Providence (1995).
+[11] L. Caffarelli, L. Silvestre, Regularity theory for fully nonlinear integro-differential equations, Comm. Pure Appl. Math. 62, 597–638
+(2009).
+[12] H. Chang-Lara, G. D´avila, Regularity for solutions of nonlocal, nonsymmetric equations, Annales de I’I.H.P. Analyse Non lin´eaire,
+No. 6, Tome 29, 833–859 (2012).
+[13] G. Citti, M. Manfredini, A. Sarti, Finite difference approximation of the Mumford and Shah functional in a contact manifold of the
+Heisenberg space, Commun. Pure Appl. Anal. 9(4), 905–927 (2010).
+[14] M. G. Crandall, H. Ishii, P.-L. Lions, User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer.
+Math. Soc., 27(1), 1–68 (1992).
+[15] M. G. Crandall, P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277, 1–42 (1983).
+[16] A. Cutr´ı, N. Tchou, Barrier functions for Pucci–Heisenberg operators and applications, Int. J. Dyn. Syst. Differ. Equ. 1 (2), 117–131
+(2007).
+[17] G. Dal Maso, An introduction to Γ-convergence, Progr. in Nonlinear Differential Equations Appl. 8, Birkhauser, Basel, (1993).
+[18] S. Dipierro, E. Lippi, E. Valdinoci, (Non)local logistic equations with Neumann conditions, arXiv:2101.02315 (2021).
+[19] F. Ferrari, E. Vecchi, H¨older behavior of viscosity solutions of some fully nonlinear equations in the Heisenberg group, Topol. Methods
+Nonlinear Anal. 55, no. 1, 227–242 (2020).
+[20] H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs, Comm. Pure Appl. Math.,
+42(1), 15–45 (1989).
+[21] R. Jensen, P.–L. Lions, P. Souganidis, A uniqueness result for viscosity solutions of second order fully nonlinear partial differential
+equations. Proc. Amer. Math. Soc. 102, no. 4, 975–978 (1988).
+[22] Y. Y. Li, B. Wang, Comparison principles for some fully nonlinear sub-elliptic equations on the Heisenberg group, Anal. Theory
+Appl. 35, no. 3, 312–334 (2019).
+[23] M. Manfredini, G. Palatucci, M. Piccinini, S. Polidoro, H¨older continuity and boundedness estimates for nonlinear fractional equations
+in the Heisenberg group, J. Geom. Anal. (2022).
+[24] C. Mou, Existence of Cα solutions to integro-PDEs, Calculus of Variations and Partial Differential Equations 58, no. 4, Paper No.
+143, 28 pp (2019).
+[25] C. Mou, Perron’s method for nonlocal fully nonlinear equations, Anal. PDE 10(5), 1227–1254 (2017).
+[26] P. Ochoa, J. A. Ruiz, Existence and uniqueness results for linear second-order equations in the Heisenberg group, Ann. Acad. Sci.
+Fenn. Math. 42, no. 2, 1065–1083 (2017).
+[27] G. P. Ovando, M. Sublis, Magnetic trajectories on 2-step nilmanifolds, arXiv:2201.02258, Preprint (2022).
+[28] G. Palatucci, M. Piccinini, Nonlocal Harnack inequalities in the Heisenberg group, Calculus of Variations and Partial Differential
+Equations 61 (2022).
+[29] L. Silvestre, H¨older estimates for solutions of integro-differential equations like the fractional Laplace, Indiana Univ. Math. J., Vol.
+55, No. 3, 1155–1174 (2006)
+[30] B. Wang, Removable singularities for degenerate elliptic Pucci operator on the Heisenberg group, Nonlinear Analysis 160, 177–190
+(2017).
+[31] C. Y. Wang, The Aronsson equation for absolute minimizers of L∞-functionals associated with vector fields satisfying H¨ormander’s
+condition, Trans. Amer. Math. Soc. 359, no. 1, 91–113 (2007).
+[32] H. Weyl, The theory of groups and quantum mechanics, Dover Publications, New York (1950).
+Priyank Oza
+Indian Institute of Technology Gandhinagar
+Palaj, Gandhinagar Gujarat, India-382355.
+Email address: priyank.k@iitgn.ac.in, priyank.oza3@gmail.com
+
+MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP
+23
+JagmohanTyagi
+Indian Institute of Technology Gandhinagar
+Palaj, Gandhinagar Gujarat, India-382355.
+Email address: jtyagi@iitgn.ac.in, jtyagi1@gmail.com
+
diff --git a/qdE1T4oBgHgl3EQfigS7/content/tmp_files/load_file.txt b/qdE1T4oBgHgl3EQfigS7/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cc90ba0d2f38f3a24732195271f7519840131f9b
--- /dev/null
+++ b/qdE1T4oBgHgl3EQfigS7/content/tmp_files/load_file.txt
@@ -0,0 +1,1105 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf,len=1104
+page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='03253v1  [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='AP]  9 Jan 2023  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATOR IN  HEISENBERG GROUP: EXISTENCE & REGULARITY OF SOLUTIONS  PRIYANK OZA, JAGMOHAN TYAGI  Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We establish the comparison principle, existence and regularity of solutions to the following problem  concerning the mixed operator:  �  αM+  λ,Λ  �  D2  HN ,Su  �  − β  �  − ∆  HN  �su = f  in Ω,  u = g  in  HN \\ Ω,  where M+  λ,Λ is the extremal Pucci’s operator and (−∆  HN )s denotes the fractional sub-Laplacian on Heisenberg group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Contents  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Introduction  1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Preliminaries  3  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Proofs of main results  7  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Funding and/or Conflicts of interests/Competing interests  21  References  22  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Introduction  In this article, we study viscosity solutions to a class of mixed operators defined by super-positioning Pucci-  Heisenberg maximal operator with the fractional sub-Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We establish the comparison principle, existence  and regularity of solutions to the following problem:  �  αM+  λ,Λ  �  D2  HN,Su  �  − β  �  − ∆  HN  �su = f  in Ω,  u = g  in  HN \\ Ω,  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1)  where Ω is a bounded domain (open, connected set) in Heisenberg group  HN ≃ R2N+1, f ∈ C(Ω), g ∈ C(HN \\ Ω)  are bounded and α ≥ 0 & β > 0 are constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Here,  Lu := αM+  λ,Λ  �  D2  HN ,Su  �  − β  �  − ∆  HN  �su  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2)  is a mixed operator on  HN, where M+  λ,Λ is the Pucci’s extremal (maximal) operator which is the fully nonlinear  operator and (−∆  HN )s is the fractional sub-Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Recently, mixed operators have been studied in the Euclidean framework by several researchers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' These operators  occur naturally, for instance, in the study of plasma physics [9], population dynamics [18] and many others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' One  may see [2, 5, 6, 7] for the works on mixed operators in the Euclidean setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' In the above works, the local term is  second order linear elliptic operator and nonlocal term is the fractional Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' There are several articles, where  authors have established the existence of solution of the Dirichlet problem using the classical Perron’s method [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  For instance, one may see [12, 25] and the reference therein for the Euclidean setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  In recent years, there has been a significant amount of works on the existence and qualitative properties of solutions  to PDEs in non-Euclidean settings, for e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=', Heisenberg group, and more generally on sub-Riemannian, Carnot-  Carath´eodory spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Bieske [8] studied infinite harmonic functions in the Heisenberg group using the notion  of viscosity solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Wang [31] established the uniqueness of viscosity solution of ∆∞ (infinity Laplacian)  2010 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Primary 35A01, 35J60, 35R03, 35D40, 47G20;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Secondary 45K05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Nonlocal and local operators, Partial differential equations on the Heisenberg group, Pucci’s extremal operator,  Integro-PDE, viscosity solutions, Perron’s method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Submitted January 10, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Published—–.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  1  2  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  equation on Carnot groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Wang [30] investigated the removable singularities for viscosity subsolutions to  degenerate elliptic Pucci operators in the Heisenberg group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It is easy to see that when α = 0, the operator in (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2) is the fractional sub-Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Very recently, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Palatucci  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Piccinini [28] considered a large class of nonlinear integro-differential operators in the Heisenberg group  setting  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' They proved the general Harnack inequalities for the solutions to Dirichlet problem concerning nonlinear  integro-differential operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It is worth noticing that these problems have connections in quantum mechanics [32],  ferromagnetic trajectories [27], image segmentation models [13], non-Markovian coupling for Brownian motions [1]  and many others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We recall that in the above contexts, the non-Euclidean geometry occurs naturally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Ferrari and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Vecchi [19] established the H¨older regularity of uniformly continuous and bounded viscosity  solutions of degenerate fully nonlinear equations in  H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We also refer to [16] for the existence results and Liouville,  Harnack type qualitative properties of fundamental solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Li and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Wang [30] established a form of  comparison principle for sub-elliptic equations in the Heisenberg setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' One may also see Manfredini [23] et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' for  the H¨older continuity and boundedness estimates for nonlinear fractional equations in  HN, where authors considered  equations driven by integro-differential operators whose model is the fractional p-Laplacian on Heisenberg group  given by  Lu(ξ) := P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  �  HN  ��u(ξ) − u(η)  ��p−2(u(ξ) − u(η))  d0(η−1 o ξ)Q+sp  dη, ξ ∈  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Here the symbol P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' in the expression stands for “in the principal value sense” and d0 denotes a homogeneous norm  on  HN(see Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Q = 2N + 2 is the homogeneous dimension of  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  To the best of our knowledge, the mixed operators of type (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2) have not been yet considered in the Heisenberg  group setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Motivated by the above works on the mixed operators and recent works on non-Euclidean setting, we  consider a class of mixed operators (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2) on  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  The main results of this paper are the following theorems:  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (Stability).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let un ∈ LSC(Ω) be bounded in  HN and satisfy  αM+  λ,Λ  �  D2  HN,Sun  �  − β  �  − ∆HN  �sun ≤ fn in Ω  in the viscosity sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let the following be hold:  (i) un converges to u in the Γ-sense in Ω,  (ii) un converges to u a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' in  HN,  (iii) fn −→ f locally uniformly in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Then  αM+  λ,Λ  �  D2  HN,Su  �  − β  �  − ∆HN  �su ≤ f in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Next, we state the comparison principle for viscosity solutions of PDE concerning operators given by (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' The  proof is immediate by making use of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5 and Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='7 (see, next).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (Comparison Principle).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let Ω be a bounded domain in  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let f ∈ C(Ω) and u, v be bounded  USC and LSC functions in Ω, respectively, which satisfy  αM+  λ,Λ  �  D2  HN,Su  �  − β  �  − ∆HN  �su ≥ f  and  αM+  λ,Λ  �  D2  HN,Sv  �  − β  �  − ∆HN  �sv ≤ f  in the viscosity sense in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Also, if u ≤ v in  HN \\ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Then u ≤ v in  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Further, adapting the standard techniques of using comparison principle for sub and super-solutions and then  following Perron’s method, we have the following existence result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let Ω ⊂  HN be satisfy the exterior Heisenberg ball condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let g ∈ C(HN \\ Ω) and bounded in  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Then there exists a viscosity solution u ∈ C(Ω) of  �  αM+  λ,Λ  �  D2  HN,Su  �  − β  �  − ∆HN  �su = 0  in Ω  u = g  in  HN \\ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  3  As mentioned earlier, several authors have established the existence of solutions to Dirichlet problems using the  Perron’s method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' For the Heisenberg group setting, we refer to [26], where the authors prove the existence of a  viscosity solution for a class of linear second order equations in Heisenberg group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Making use of the comparison  principle (Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2), the proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='3 follows using the standard arguments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  We mention that F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Ferrari and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Vecchi [19] studied the H¨older behaviour of fully nonlinear local equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' In  particular, we have the following result due to [19]:  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='3 [19]) Let u ∈ C(H1) be a bounded and uniformly continuous viscosity solution of  M+  λ,Λ  �  D2  HN,Su(ξ)  �  − c(ξ)u(ξ) = f(ξ) in  H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Let L1, L2, γ1, and γ2 be positive constants s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' γi ∈ (0, 1], i = 1, 2 and for any ξ, η ∈  H1,  ��c(ξ) − c(η)  �� ≤ L1  ��ξ o η−1��γ1  H1,  ��f(ξ) − f(η)  �� ≤ L2  ��ξ o η−1��γ2  H1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Let c(ξ) be positive for all ξ ∈  H1 and  inf  ξ∈B  H1  R (P )  c(ξ) := c0 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Then there exists γ := γ(c0, p, L1, L2, Λ) ∈ (0, 1], γ ≤ min{γ1, γ2} such that  ��u(ξ) − u(η)  �� ≤ L  ��ξ o η−1��γ  H1, for ξ ∈  H1,  for some L = L(c0, P, L1, L2, Λ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  For more such results on regularity in the Euclidean setting, when there is no local term and integro-differential  operators are of fractional Laplacian type, we refer to [11, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We also mention a very recent work by Biagi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [6], where authors established the interior Sobolev regularity as well as boundary regularity of Lipschitz type for  mixed local and nonlocal operators in the Euclidean framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' More precisely, authors proved the following interior  regularity result:  Corollary 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='4 [6]) Let Ω ⊂ RN be a bounded C1 domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let f ∈ Hk(Ω)  �  W 2,k(Ω)  �  for some integer  k ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let u ∈ H1(RN) be a weak solution of  −∆u + (−∆)su = f in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Then u ∈ Hk+2  loc (Ω).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Motivated by the above results, we establish the following interior H¨older regularity result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (Interior regularity) Let u be a bounded function in  HN and viscosity solution to  αM+  λ,Λ  �  D2  HN,Su  �  − β  �  − ∆HN  �su = 0 in B  HN  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Then there exist constants C and γ = γ(λ, Λ, N) ∈ (0, 1) such that  ��u(ξ) − u(0)  �� ≤ C|ξ|γ  HN ∥u∥∞, HN, ∀ξ ∈ B  HN  1  2  ,  where B  HN  r  denotes the ball of radius r with center at the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  The organization of this paper is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' In Section 2, we list the basic definitions and introduce the framework  in which we work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Section 3 is dedicated to the proofs of our main results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Preliminaries  We first recall the briefs about the Heisenberg group  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' The points in  HN are denoted by  ξ := (z, t) = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN, y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN, t)  and the group  HN is defined as the triplet  �  RN+1, o, {Φλ}  �  , where the group law o is defined as follows:  ξ o ξ′ =  �  x + x′, y + y′, t + t′ + 2⟨y, x′⟩ − 2⟨x, y′⟩  �  =  �  x1 + x′  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN + x′  N, y1 + y′  1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN + y′  N, t + t′ + 2  N  �  i=1  �  yix′  i − xiy′  i  ��  ,  4  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  where ⟨.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='⟩ denotes the standard inner product in RN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (R2N+1, o) is a Lie group with identity element the origin 0  and inverse ξ−1 = −ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' The dilation group {Φλ}λ>0 is given by  Φ(λ) : R2N+1 −→ R2N+1  such that  ξ �→ Φλ(ξ) :=  �  λx, λy, λ2t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  HN is also known as Heisenberg-Weyl group in R2N+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' The Jacobian basis of the Heisenberg Lie algebra of  HN is  given by  Xi = ∂xi + 2yi∂t, Yi = ∂yi − 2xi∂t, 1 ≤ i ≤ N, T = ∂t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Given a domain Ω ⊂  HN, for u ∈ C1(Ω, R), the subgradient or the Heisenberg gradient ∇  HN u is defined as follows:  ∇  HN u(ξ) :=  �  X1u(ξ), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , XNu(ξ), Y1u(ξ), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , YNu(ξ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Also,  D2  HN,Su :=  \uf8ee  \uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8ef\uf8f0  X1X1u  · ·  XNX1u  Y1X1u  · ·  YNX1u  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  X1XNu  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  XNXNu  Y1XNu  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  YNXNu  X1Y1u  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  XNY1u  Y1Y1u  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  YNY1u  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  X1YNu  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  XNYNu  Y1YNu  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  YNYNu  \uf8f9  \uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fa\uf8fb  Sym  ,  where  ASym = 1  2  �  A + AT �  , for any matrix A,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=', symmetric part of the matrix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Now, since  [Xi, Yi] = XiYi − YiXi  = (∂xi + 2yi∂t)(∂yi − 2xi∂t) − (∂yi − 2xi∂t)(∂xi + 2yi∂t)  = −4∂t,  so it follows that  rank  �  Lie{X1, X2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , X2N, T }(0, 0)  �  = 2N + 1,  which is the Euclidean dimension of  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We denote by Q, the homogeneous dimension of  HN, which is Q = 2N +2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  The norm on  HN is defined by  |ξ|  HN :=  �� N  �  i=1  �  x2  i + y2  i  �2  �  + t2  � 1  4  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  The corresponding distance on  HN is defined as follows:  d  HN (ξ, ˆξ) := |ˆξ−1o ξ|  HN ,  where ˆξ−1 is the inverse of ˆξ w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' to o, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=', ˆξ−1 = −ˆξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  The sub-Laplacian or the Heisenberg Laplacian (also known as Laplacian-Kohn operator), ∆  HN is the self-adjoint  operator defined as  ∆  HNu :=  N  �  i=1  X2  i + Y 2  i  =  N  �  i=1  ∂2  ∂x2  i  + ∂2  ∂y2  i  + 4yi  ∂2  ∂xi∂t − 4xi  ∂2  ∂yi∂t + 4  �  x2  i + y2  i  � ∂2  ∂t2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It is useful to observe that  ∆  HN = div  �  σT σ∇u  �  ,  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  5  where  σ =  �IN  0  2y  0  IN  −2x  �  and σT is its transpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Note that  A = σT σ =  \uf8ee  \uf8f0  IN  0  2y  0  IN  −2x  2y  −2x  4  �  |x|2 + |y|2�  \uf8f9  \uf8fb  is a positive semi-definite matrix with det(A) = 0, ∀ξ ∈  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Let us recall the definition of viscosity sub/super-solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1) by evaluating the operators in C2 test function  φ (ψ) touching u locally from above (below) and then the final test function v (w) is defined by taking v = φ  (v = ψ) in a small ball and v = u outside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' One may see [3, 11], where the notion of viscosity solution for second  order elliptic integro-differential equations and fully nonlinear integro-differential equations is given in the Euclidean  setting, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' For the analogous definitions in the Heisenberg group setting, we refer to [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We give the  definition of viscosity solution for the operator under consideration in the Heisenberg group setting which is consistent  with that given in the above mentioned articles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' A function u :  HN −→ R, upper semicontinuous (USC) in Ω ⊂  HN is called a viscosity subsolution  of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1) if for any ξ ∈ Ω and C2 function ϕ : U −→ R, for some neighborhood U of ξ in Ω such that ϕ(ξ) = u(ξ) and  ϕ(η) > u(η) for η ∈ U \\ {ξ}, we have  αM+  λ,Λ  �  D2  HN,Sv(ξ)  �  − β(−∆  HN )sv(ξ) ≥ f(ξ),  where  v :=  �  ϕ  in U,  u  in  HN \\ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Moreover, we say u satisfies αM+  λ,Λ(D2  HN ,Su) − β(−∆  HN )su ≥ f in Ω in the viscosity sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' A function u :  HN −→ R, lower semicontinuous (LSC) in Ω ⊂  HN is called a viscosity supersolution  of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1) if for any ξ ∈ Ω and C2 function ψ : U −→ R, for some neighborhood U of ξ in Ω such that ψ(ξ) = u(ξ) and  ψ(η) < u(η) for η ∈ U \\ {ξ}, we have  αM+  λ,Λ  �  D2  HN ,Sw(ξ)  �  − β(−∆  HN )sw(ξ) ≤ f(ξ),  where  w :=  �  ψ  in U,  u  in  HN \\ U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Moreover, we say u satisfies αM+  λ,Λ(D2  HN ,Su) − β(−∆  HN )su ≤ f in Ω in the viscosity sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' A continuous function u is said to be a viscosity solution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1) if it is a subsolution as well as a  supersolution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, we recall the exterior Heisenberg ball condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' For the analogous condition in the Euclidean setting, one  may see, for instance [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' [16] Ω is said to satisfy the exterior Heisenberg ball condition if there exists R > 0 such that for  any ξ ∈ ∂Ω and 0 < r ≤ R, there exists ηr  ξ ∈ Ωc satisfying B  HN  r  (ηr  ξ) ∩ Ω = {ξ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Next, we recall the definition of sup (inf)-convolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' The construction of convolutions was done by Jensen et  al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' [21] and further developed on Carnot groups by C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Wang [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' For an USC function u, the sup-convolution approximation uε is given by  uε(ξ) = sup  η∈ HN  �  u(η) − |ξ o η−1|4  HN  ε  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  6  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' For an LSC function u, the inf-convolution approximation uε is given by  uε(ξ) =  inf  η∈ HN  �  u(η) + |ξ o η−1|4  HN  ε  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It is easy to see that uε ≥ u and uε ≤ u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' A sequence of LSC functions, uk is said to Γ-converge to u in a set Ω if the following hold:  (i) For every sequence ξn −→ ξ in Ω, we have  lim inf  n−→∞ un(ξn) ≥ u(ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (ii) For every ξ ∈ Ω, there exists a sequence {ξn} converging to ξ in Ω (known as Γ-realising sequence) such that  lim sup  n−→∞ un(ξn) = u(ξ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  This is known as Γ-limit in literature, see [11, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Note that uniform convergence =⇒ Γ-convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Also, an  important property of Γ-limits is that if un converges to u, which has a strict local minimum at ξ, then un would  have local minimum at ξn for a sequence ξn −→ ξ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' [28] A homogeneous norm on  HN is a continuous function (w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' to Euclidean topology)  d0 :  HN −→ [0, ∞) s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (i) d0(Φλ(ξ)) = λd0(ξ), ∀λ > 0 and ξ ∈  HN  (ii) d0(ξ) = 0 iff ξ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Moreover, we say that the homogeneous norm is symmetric if  d0(ξ−1) = d0(ξ), ∀ξ ∈  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Throughout the paper, we consider the standard homogeneous norm on  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' For fixed ξ0 ∈  HN and R > 0,  B  HN  R (ξ0) :=  �  ξ ∈  HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' |ξ−1  0  o ξ|  HN < R  �  denotes the Kor´anyi ball of radius R around ξ0 in  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  One can see that the Jacobian determinant of the dilation Φλ is λQ, where Q = 2N +2, which is the homogeneous  dimension of the Heisenberg group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let us consider 2N × (2N + 1) matrix whose rows are the coefficients of the  vector fields Xi, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=',  σ =  �IN  0  2y  0  IN  −2x  �  for x = (ξ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , ξN)T and y = (ξN+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , ξ2N)T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Then the Heisenberg gradient of a function Φ : R2N+1 −→ R is  given by  ∇  HN Φ = (X1Φ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , X2NΦ) = σ(ξ)∇Φ,  where ∇ denotes the usual gradient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Also, the Heisenberg Hessian of Φ is given by  D2  HN,SΦ = (XiXjΦ)Sym  = σ(ξ)D2ΦσT (ξ),  where Sym denotes the symmetrized matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We recall that the fractional sub-Laplacian operator is defined as  (−∆  HN )su(ξ) = −1  2c(N, s)  �  HN  u(ξ o η) + u(ξ o η−1) − 2u(ξ)  |η|Q+2s  HN  dη, u ∈ Hs(HN), ξ ∈  HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Q = 2N + 2,  see 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1 [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Here, c(N, s) is a positive constant depending on N & s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' For given two parameters 0 < λ ≤ Λ, Pucci-  Heisenberg operators are defined by the composition of Pucci’s extremal operators M±  λ,Λ (see 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2 [10]) with the  Heisenberg Hessian as follows:  M+  λ,Λ  �  D2  HN,Su  �  := Λ  �  ei≥0  ei + λ  �  ei<0  ei  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  7  &  M−  λ,Λ  �  D2  HN,Su  �  := Λ  �  ei≤0  ei + λ  �  ei>0  ei,  where {ei}2N  i=1 are the eigenvalues of the symmetrized horizontal Hessian matrix D2  HN,Su.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let S2N be denote the  set of all real symmetric 2N × 2N matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Consider a subset S2N  λ,Λ of S2N whose eigenvalues are in [λ, Λ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' These  operators are also defined as  M+  λ,Λ  �  D2  HN,Su  �  :=  max  M∈SN  λ,Λ  tr  �  MD2  HN,Su  �  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1)  &  M−  λ,Λ  �  D2  HN,Su  �  :=  min  M∈SN  λ,Λ  tr  �  MD2  HN,Su  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Furthermore, consider a set K consisting of 2N × 2N matrices γ such that γγT ∈ S2N  λ,Λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Using this, we can re-write  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1) as  M+  λ,Λ  �  D2  HN,Su  �  = max  γ∈K ⟨γγT , D2  HN,Su⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, for any fixed γ ∈ K, we have the following linear operator, say, Lγ given by  Lγ  �  D2  HN,Su  �  := ⟨γγT , D2  HN,Su⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2)  It is easy to observe that when λ = Λ = 1, the above mentioned operators reduce to the Heisenberg Laplacian ∆  HN,S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Proofs of main results  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Consider a C2 function ψ that touches u from below at ξ in a neighbourhood U in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' By  definition of Γ-convergence, there exists a sequence ξn −→ ξ such that  �  un − ψ  �  (ξn) = inf  U  �  un − ψ  �  = δn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Therefore, δn −→ 0 as n −→ ∞ and ψ + δn touches un at ξn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Now, since  αM+  λ,Λ  �  D2  HN,Sun  �  − β  �  − ∆HN  �sun ≤ fn in Ω,  so for  ξn =  �  ψ + δn  in U,  un  in  HN \\ U,  we have by the definition of viscosity solution,  αM+  λ,Λ  �  D2  HN,Sun(ξn)  �  − β  �  − ∆HN  �sun(ξn) ≤ fn(ξn) in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Further, take τ ∈ U such that  d  �  τ, ∂U  �  = inf  �τ∈∂U  ���τ  −1 o τ  ��  HN > ρ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  8  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  Then  ���  αM+  λ,Λ  �  D2  HN,Swn(τ)  �  − β  �  − ∆HN  �swn(τ)  �  −  �  αM+  λ,Λ  �  D2  HN ,Sw(τ)  �  − β  �  − ∆HN  �sw(τ)  ���  ≤  ���  αM+  λ,Λ  �  D2  HN,Swn(τ)  �  − αM+  λ,Λ  �  D2  HN,Sw(τ)  ��  − β  �  (−∆HN )swn(τ) − (−∆HN)sw(τ)  ���  ≤ α max  ��� max  M∈SN  λ,Λ  tr  �  MD2  HN,S(wn(τ) − w(τ))  ���,  �� max  M∈SN  λ,Λ  tr  �  MD2  HN,S(w(τ) − wn(τ))  ���  �  + β  ��(−∆HN)swn(τ) − (−∆HN)sw(τ)  �� (by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2))  ≤ α max  γ∈K  ��Lγ  �  D2(wn − w)(τ)  ��� + β  ���  − ∆HN  �s(wn − w)(τ)  ��  = α max  γ∈K  ��Lγ  �  D2δn(τ)  ��� + β  ���  − ∆HN  �s(wn − w)(τ)  ��  ≤ β  2 c(N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' s)  �  HN  ��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)  ��  |η|Q+2s  HN  dη  = β  2 c(N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' s)  �  B  HN  ρ  ��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)  ��  |η|Q+2s  HN  dη  + β  2 c(N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' s)  �  HN\\B  HN  ρ  ��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)  ��  |η|Q+2s  HN  dη  = β  2 c(N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' s)  �  B  HN  ρ  ��δn(τ o η) + δn(τ o η−1) − 2δn(τ)  ��  |η|Q+2s  HN  dη  + β  2 c(N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' s)  �  HN\\B  HN  ρ  ��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)  ��  |η|Q+2s  HN  dη  = β  2 c(N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' s)  �  HN\\B  HN  ρ  ��(wn − w)(τ o η) + (wn − w)(τ o η−1) − 2(wn − w)(τ)  ��  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, using the fact that sequence wn is bounded and that (wn − w)(τ o η) + (wn − w)(τ o η−1) − (wn − w)(τ) −→ 0  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' along with the fact that  1  |η|Q+2s ∈ L1(HN \\ Bρ), we have by the dominated convergence theorem that  ���  αM+  λ,λ  �  D2  HN,S(wn)(τ)  �  − β(−∆  HN )swn(τ)  �  −  �  αM+  λ,λ  �  D2  HN,S(w)(τ)  �  − β(−∆  HN )sw(τ)  ��� −→ 0 as n −→ ∞ uniformly in τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1)  Equivalently,  αM+  λ,Λ  �  D2  HN,S(wn)(τ)  �  − β(−∆  HN )swn(τ) −→ αM+  λ,Λ  �  D2  HN,S(w)(τ)  �  − β(−∆  HN )sw(τ) locally uniformly in U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Also,  ���  αM+  λ,Λ  �  D2  HN,S(wn)(ξn)  �  − β(−∆  HN )swn(ξn)  �  −  �  αM+  λ,Λ  �  D2  HN,S(w)(ξ)  �  − β(−∆  HN )sw(ξ)  ���  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2)  ≤  ���  αM+  λ,Λ  �  D2  HN,Swn(ξn)  �  − β(−∆  HN)swn(ξn)  �  −  �  αM+  λ,Λ  �  D2  HN,Sw(ξn)  �  − β(−∆  HN )sw(ξn)  ���  +  ���  αM+  λ,Λ  �  D2  HN,Sψ(ξn)  �  − β(−∆  HN )sw(ξn)  �  −  �  αM+  λ,Λ  �  D2  HN,Sψ(ξ)  �  − β(−∆  HN )sw(ξ)  ���  ≤  ���  αM+  λ,Λ  �  D2  HN,Swn(ξn)  �  − β(−∆  HN)swn(ξn)  �  −  �  αM+  λ,Λ  �  D2  HN,Sw(ξn)  �  − β(−∆  HN )sw(ξn)  ���  +  ��αM+  λ,Λ  �  D2  HN,Sψ(ξn)  �  − αM+  λ,Λ  �  D2  HN,Sψ(ξ)  ��� +  ��β(−∆  HN )sw(ξn) − β(−∆  HN )sw(ξ)  ��.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Further, the first term in the R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2) vanishes as n −→ ∞ by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' The third term goes to zero as n −→ ∞  by the continuity of Iw in U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Also, the first term vanishes by an application of Theorem VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1 [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Thus, we have  that  αM+  λ,Λ  �  D2  HN,Swn(ξn)  �  − β(−∆  HN )swn(ξn) −→ αM+  λ,Λ  �  D2  HN ,S(w)(ξ)  �  − β(−∆  HN )sw(ξ) as n −→ ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  9  Further,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' we get  αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Swn(ξn)  �  − β(−∆  HN )swn(ξ)  ≤ αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Swn(ξn)  �  − β(−∆  HN )swn(ξ)  +  ��αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Swn(ξn)  �  − β(−∆  HN )swn(ξn) −  �  αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Sw(ξ)  �  − β(−∆  HN )sw(ξ)  ���  ≤ fn(ξn) +  ��αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Swn(ξn)  �  − β(−∆  HN )swn(ξn) −  �  αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Sw(ξ)  �  − β(−∆  HN )sw(ξ)  ���  ≤ f(ξ) + |fn(ξn) − f(ξ)|  +  ��αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Swn(ξn)  �  − β(−∆  HN )swn(ξn) −  �  αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Sw(ξ)  �  − β(−∆  HN )sw(ξ)  ���.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Finally, using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2) together with the fact that fn(ξn) −→ f(ξ), since fn −→ f locally uniformly and ξn −→ ξ proves  the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  □  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' One can see that an analogous result can be obtained for subsolutions using the Γ-convergence of USC  functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  More precisely, we have the following immediate corollary:  Corollary 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let un ∈ C(Ω) be bounded in  HN and satisfy  αM+  λ,Λ  �  D2  HN,Sun  �  − β  �  − ∆HN  �sun = fn in Ω  in the viscosity sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let the following be hold:  (i) un converges to u in the Γ-sense in Ω,  (ii) un converges to u a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' in HN,  (iii) fn −→ f locally uniformly in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Then  αM+  λ,Λ  �  D2  HN,Su  �  − β  �  − ∆HN  �su = f in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let f ∈ C(Ω) and u ∈ USC(Ω) be a viscosity subsolution of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Then  αM+  λ,Λ  �  D2  HN,Suε�  −  �  − ∆HN  �suε ≥ f − dε in Ω1 ⋐ Ω,  where dε −→ 0 in Ω1 as ε −→ 0 and depends on the modulus of continuity of f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let x0 ∈ Ω1 and ϕ be a C2 smooth function touching uε from above in some neighbourhood  B  HN  r  (ξ0) ⊂ Ω1 of ξ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let us define  Ψ :=  �  ϕ  in B  HN  r  (ξ0)  uε  in  HN \\ B  HN  r  (ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Next, consider a function  Φ(ξ) = Ψ  �  ξ o ξ∗  0  −1 o ξ0  �  + 1  ε|ξ0 o ξ∗  0  −1|4  HN,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='3)  where ξ∗ = (x1∗, x2∗, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , x2N∗, t∗) ∈ Ω such that  uε(ξ0) = u(ξ∗  0) − |ξ0 o ξ∗  0  −1|4  HN  ε  (see p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 9 [22]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, by definition, we have  uε�  ξ0 o ξ∗  0  −1 o ξ  �  ≥ u(ξ) − |  �  ξ0 o ξ∗  0  −1 o ξ  �  o ξ−1|  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Since  �  ξ0 o ξ∗  0  −1 o ξ  �  o ξ−1 = ξ0 o ξ∗  0  −1,  so it implies  uε�  ξ0 o ξ∗  0  −1 o ξ  �  ≥ u(ξ) − |ξ0 o ξ∗  0  −1|4  HN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  In other words,  u(ξ) ≤ uε�  ξ0 o ξ∗  0  −1 o ξ  �  + |ξ0 o ξ∗  0  −1|4  HN  ε  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  10  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  Let ξ be close enough to ξ∗  0, then by definition,  u(ξ) ≤ Ψ  �  ξ0 o ξ∗  0  −1 o ξ  �  + |ξ0 o ξ∗  0  −1|4  HN  ε  = Φ(ξ)  and u(ξ∗  0) = Φ(ξ∗  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It implies that Φ(ξ) touches u from above at ξ∗  0 in B  HN  r  (ξ∗  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Next, we consider a function  v :=  �  Φ  in B  HN  r  (ξ∗  0)  u  in  HN \\ B  HN  r  (ξ∗  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It yields by the definition of viscosity subsolution,  αM+  λ,Λ  �  D2  HN,Sv(ξ∗  0)  �  − β(−∆  HN )sv(ξ∗  0) ≥ f(ξ∗  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  In other words,  αM+  λ,Λ  �  D2  HN ,sv(ξ∗  0)  �  + β  2 c(N, s)  �  HN  v(ξ o η) + v(ξ o η−1) − 2v(ξ)  |η−1 o ξ|Q+2s  HN  dη ≥ f(ξ∗  0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='4)  It is easy to see that (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='3) yields  v(ξ∗  0) = Φ(ξ∗  0) = Ψ(ξ0) + 1  ε|ξ0 o ξ∗  0  −1|4  HN,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5)  Φ(ξ∗  0 o η) = Ψ(ξ0 o η) + 1  ε|ξ0 o ξ∗  0  −1|4  HN  &  Φ(ξ∗  0 o η−1) = Ψ(ξ0 o η−1) + 1  ε|ξ0 o ξ∗  0  −1|4  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It gives  Φ(ξ∗  0 o η) − Φ(ξ∗  0) = Ψ(ξ0 o η) − Ψ(ξ0)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='6)  &  Φ(ξ∗  0 o η−1) − Φ(ξ∗  0) = Ψ(ξ0 o η−1) − Ψ(ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, we claim that  ∇  HNΦ(ξ∗  0) = ∇  HN Ψ(ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='7)  Since  XiΦ(ξ) = ∂xiΦ(ξ) + 2yi∂tΦ(ξ)  = ∂xiΦ  �  x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN, y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN, t  �  + 2yi∂tΦ  �  x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN, y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN, t  �  = ∂xiΨ  �  ξ o ξ∗  0  −1 o ξ0  �  + 2yi∂tΨ  �  ξ o ξ∗  0  −1 o ξ0  �  for 1 ≤ i ≤ N,  so it gives  XiΦ(ξ∗  0) = ∂xiΨ(ξ0) + 2yi∂tΨ(ξ0) for 1 ≤ i ≤ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Similarly, one may see that  YiΦ(ξ∗  0) = ∂yiΨ(ξ0) − 2xi∂tΨ(ξ0), 1 ≤ i ≤ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Therefore, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='7) holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Also,  D2  HN ,SΦ(ξ∗  0) = D2  HN,SΨ(ξ0)  and therefore  M+  λ,Λ  �  D2  HN,SΦ(ξ∗  0)  �  = M+  λ,Λ  �  D2  HN,SΨ(ξ0)  �  = M+  λ,Λ  �  D2  HN,Sϕ(ξ0)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='8)  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  11  Using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='6) & (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='8) in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='4) yields  f(ξ∗  0) ≤ αM+  λ,Λ  �  D2  HN,Sv(ξ∗  0)  �  + β  2 c(N, s)  �  HN  v(ξ∗  0 o η) + v(ξ∗  0 o η−1) − 2v(ξ∗  0)  |η|Q+2s  HN  dη  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='9)  = αM+  λ,Λ  �  D2  HN,Sϕ(ξ0)  �  + β  2 c(N, s)  �  {η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ∗  0 o η, ξ∗  0 o η−1∈B  HN  r  (ξ∗  0 )}  Φ(ξ∗  0 o η) + Φ(ξ∗  0 o η−1) − 2Φ(ξ∗  0)  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  HN\\{η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ∗  0 o η, ξ∗  0 o η−1∈B  HN  r  (ξ∗  0 )}  u(ξ∗  0 o η) + u(ξ∗  0 o η−1) − 2u(ξ∗  0)  |η|Q+2s  HN  dη  = αM+  λ,Λ  �  D2  HN,Sϕ(ξ0)  �  + β  2 c(N, s)  �  {η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ∗  0 o η, ξ∗  0 o η−1∈B  HN  r  (ξ∗  0 )}  Φ(ξ∗  0 o η) + Φ(ξ∗  0 o η−1) − 2Φ(ξ∗  0)  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  HN\\{η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ∗  0 o η, ξ∗  0 o η−1∈B  HN  r  (ξ∗  0 )}  u(ξ∗  0 o η) + u(ξ∗  0 o η−1) − 2Φ(ξ∗  0)  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  By the definition of uε,  u(η) ≤ uε(ξ) +  ��ξ o η−1��4  HN  ε  for all ξ, η ∈  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It further implies  u(ξ∗  0 o η) ≤ u(ξ0 o η) +  ��(ξ0 o η) o (ξ∗  0 o η)−1��4  HN  ε  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='10)  and  u(ξ∗  0 o η−1) ≤ u(ξ0 o η−1) +  ��(ξ0 o η−1) o (ξ∗  0 o η−1)  −1��4  HN  ε  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='11)  Let  ξ∗  0 = (x∗  0, y∗  0, t∗  0) =  �  x1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN∗  0 , y1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN∗  0 , t∗  0  �  ,  ξ0 = (x0, y0, z0, t) =  �  x1  0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN  0 , y1  0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN  0 , t0  �  ,  η = (x, y, z, t) =  �  x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN, y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN, t  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It implies that  ξ0 o η =  �  x1  0 + x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN  0 + xN, y1  0 + y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN  0 + yN, t0 + t + 2⟨y0, x⟩ − 2⟨x0, y⟩  �  ,  ξ∗  0 o η =  �  x1∗  0 + x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN∗  0  + xN, y1∗  0 + y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN∗  0  + yN, t∗  0 + t + 2⟨y∗  0, x⟩ − 2⟨x∗  0, y⟩  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It immediately gives  (ξ∗  0 o η)−1 =  �  − x1∗  0 − x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , −xN∗  0  − xN, −y1∗  0 − y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , −yN∗  0  − yN, −t∗  0 − t − 2⟨y∗  0, x⟩ + 2⟨x∗  0, y⟩  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  12  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  It yields  (ξ0 o η) o (ξ∗  0 o η)−1 =  �  x1  0 − x1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN  0 − xN∗  0 , y1  0 − y1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN  0 − yN∗  0 , t0 − t∗  0  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='12)  + 2⟨y, x∗  0⟩ − 2⟨x, y∗  0⟩ − 2⟨y, x0⟩ + 2⟨x, y0⟩ + 2⟨y0 + y, −x∗  0 − x⟩ − 2⟨x0 + x, −y∗  0 − y⟩  �  =  �  x1  0 − x1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN  0 − xN∗  0 , y1  0 − y1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN  0 − yN∗  0 , t0 − t∗  0  + 2⟨y, x∗  0⟩ − 2⟨x, y∗  0⟩ − 2⟨y, x0⟩ + 2⟨x, y0⟩ + 2⟨y0, −x∗  0 − x⟩  + 2⟨y, −x∗  0 − x⟩ − 2⟨x0, −y∗  0 − y⟩ − 2⟨x, −y∗  0 − y⟩  �  =  �  x1  0 − x1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN  0 − xN∗  0 +, y1  0 − y1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN  0 − yN∗  0  , t0 − t∗  0  + 2⟨y, x∗  0⟩ − 2⟨x, y∗  0⟩ − 2⟨y, x0⟩ + 2⟨x, y0⟩ + 2⟨y0, −x∗  0⟩ + 2⟨y0, −x⟩ + 2⟨y, −x∗  0⟩ + 2⟨y, −x⟩  − 2⟨x0, −y∗  0⟩ − 2⟨x0, −y⟩ − 2⟨x, −y∗  0⟩ − 2⟨x, −y⟩  �  =  �  x1  0 − x1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN  0 − xN∗  0 +, y1  0 − y1∗  0 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN  0 − yN∗  0  , t0 − t∗  0  + 2⟨y, x∗  0⟩ − 2⟨x, y∗  0⟩ − 2⟨y, x0⟩ + 2⟨x, y0⟩ + 2⟨x0, y∗  0⟩ + 2⟨x0, y⟩ + 2⟨x, y∗  0⟩ + 2⟨x, y⟩  − 2⟨y0, x∗  0⟩ − 2⟨y0, x⟩ − 2⟨y, x∗  0⟩ − 2⟨y, x⟩  �  =  �  x0 − x∗  0, y0 − y∗  0, t0 − t∗  0 + 2⟨x0, y∗  0⟩ − ⟨y0, x∗  0⟩  �  =  �  x0 − x∗  0, y0 − y∗  0, t0 − t∗  0 + 2⟨y0, −x∗  0⟩ − 2⟨x0, −y∗  0⟩  �  = ξ0 o ξ∗  0  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Similarly, one may see that  (ξ0 o η−1) o (ξ∗  0 o η−1)  −1 = ξ0 o ξ∗  0  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='13)  Using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='12) & (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='13) in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='10) & (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='11), respectively infers  u(ξ∗  0 o η) + u(ξ∗  0 o η−1) − 2Φ(ξ∗  0) ≤ uε(ξ0 o η) + uε(ξ0 o η−1) + 2  ��ξ0 o ξ∗  0  −1��4  HN  ε  − 2Φ(ξ∗  0)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='14)  = uε(ξ0 o η) + uε(ξ0 o η−1) + 2  ��ξ0 o ξ∗  0  −1��4  HN  ε  − 2  �  Ψ(ξ0) + 1  ε  ��ξ0 o ξ∗  0  −1��4  HN  �  (by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5))  = uε(ξ0 o η) + uε(ξ0 o η−1) − 2Ψ(ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  We also have  ��ξ o ξ∗  0  −1��4  HN ≤ ε osc  Ω u,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='15)  see [22, 31] for the details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It immediately grants that |ξ o ξ∗  0  −1|  HN can be made as small as possible by the suitable  choice of ε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='14) in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='9), we get  f(ξ∗  0) ≤ αM+  λ,Λ  �  D2  HN,Sϕ(ξ0)  �  + β  2 c(N, s)  �  {η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ∗  0 o η, ξ∗  0 o η−1∈B  HN  r  (ξ∗  0 )}  Φ(ξ∗  0 o η) + Φ(ξ∗  0 o η−1) − 2Φ(ξ∗  0)  |η|Q+2s  HN  dη  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='16)  + β  2 c(N, s)  �  HN\\{η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ∗  0 o η, ξ∗  0 o η−1∈B  HN  r  (ξ∗  0 )}  u(ξ∗  0 o η) + u(ξ∗  0 o η−1) − 2Φ(ξ∗  0)  |η|Q+2s  HN  dη  ≤ αM+  λ,Λ  �  D2  HN,Sϕ(ξ0)  �  + c(N, s)  �  {η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ∗  0 o η, ξ∗  0 o η−1∈B  HN  r  (ξ∗  0 )}  ϕ(ξ0 o η) + ϕ(ξ0 o η−1) − 2ϕ(ξ0)  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  HN\\{η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ∗  0 o η, ξ∗  0 o η−1∈B  HN  r  (ξ∗  0 )}  uε(ξ0 o η) + uε(ξ0 o η−1) − 2Ψ(ξ0)  |η|Q+2s  HN  dη  = αM+  λ,Λ  �  D2  HN,Sϕ(ξ0)  �  − β  �  − ∆  HN  �sΨ(ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, adding and subtracting f(ξ0) in the L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='16) gives  αM+  λ,Λ  �  D2  HN,Sϕ(ξ0)  �  − β  �  − ∆  HN  �sΨ(ξ0) ≥ f(ξ0) −  �  f(ξ0) − f(ξ∗  0)  �  ≥ f(ξ0) − |f(ξ0) − f(ξ∗  0)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  13  Next, using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='15) together with the continuity of f, we define  dε =  sup  B  HN  δ√ε(ξ0)  |f(ξ0) − f(ξ∗  0)|,  for some δ = δ(osc  Ω u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Clearly, dε −→ 0 as ε −→ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Hence the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  □  Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Using the similar arguments, one may see that an analogous result also holds for supersolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let f & g be two continuous functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Let u & v be bounded USC and LSC functions in HN,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let  αM+  λ,Λ  �  D2  HN,Su  �  − β(−∆HN )su ≥ f  &  αM+  λ,Λ  �  D2  HN,Sv  �  − β(−∆HN )sv ≤ g  be hold in the viscosity sense in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Then  αM+  λ,Λ  �  D2  HN,S(u − v)  �  − β(−∆HN )s(u − v) ≥ f − g in Ω in the viscosity sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='3, we have  αM+  λ,Λ  �  D2  HN,Suε�  − β(−∆  HN )suε ≥ f − dε  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='17)  &  αM+  λ,Λ  �  D2  HN,Svε  �  − β(−∆  HN )svε ≤ g + dε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='18)  Our aim is to show that  αM+  λ,Λ  �  D2  HN,S(uε − vε)  �  − β(−∆  HN )s(uε − vε) ≥ f − g − 2dε,  so that further using the stability result (Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1) yields the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Let P ∈ C2  b (HN) be a paraboloid in B  HN  r  ⊂ Ω1 such that  P(ξ0) = uε(ξ0) − vε(ξ0)  and  P(τ) ≥ uε(τ) − vε(τ) for all τ ∈ B  HN  r  (ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  We assume that B  HN  2r (ξ0) ⊂ Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Consider  Φ(x) =  �  P  in B  HN  r  (ξ0)  uε − vε  in  HN \\ B  HN  r  (ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Take δ > 0 and let us define  w(ξ) = vε(ξ) − uε(ξ) + Φ(ξ) + δ  ���ξ0  −1o ξ  ��  HN ∧ r  �4 − δr4  1,  for 0 < r1 < δ ∧ r  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We observe that w ≥ 0 on ∂B  HN  r1 (ξ0) and w(ξ0) = −δr2 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' By Theorem 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1 [10], we have  that for any ξ ∈ B  HN  r1 (ξ0), there exists a convex paraboloid P ξ of opening K (some constant independent of ξ) which  touches w from above at ξ ∈ B  HN  r1 (ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Further, by Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5 [10] and w(ξ0) < 0, we have that  0 <  �  B  HN  r  (ξ0)∩{w=Γw}  det D2Γw,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='19)  where Γw is the convex envelope of w in A given by  Γw(ξ) = sup  v  �  v(ξ) ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' v ≤ w in A, v convex in A  �  ,  for ξ ∈ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Moreover, uε and vε are punctually second order differentiable in A (see 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2 (ii) [22]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It gives that  M+  λ,Λ(D2  HN ,Suε) − (−∆  HN )suε and M+  λ,Λ(D2  HN ,Svε) − (−∆  HN)svε are defined in the classical sense for ξ ∈ A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  By the convexity of Γw and that Γw ≤ w, we have that the Hessian matrix D2w(ξ) is semi-positive definite for  ξ ∈ A ∩ {w = Γw}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It yields that  M+  λ,Λ  �  D2  HN ,Sw(ξ)  �  ≥ 0  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='20)  14  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  &  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='21)  1  2c(N, s)  �  {η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ o η∈B  HN  r  (ξ0)}  w(ξ o η) + w(ξ o η−1) − 2w(ξ)  |η|Q+2s  HN  dη  = 1  2c(N, s)  �  {η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξ o η∈B  HN  r  (ξ0)}  w(ξ o η) − w(ξ) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN w(ξ), ∂tw(ξ))  |η|Q+2s  HN  dη  ≥ 0,  for ξ ∈ A ∩ {w = Γw} using Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='4 [28] and  w(ξ o η) − w(ξ) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN w(ξ), ∂tw(ξ)) ≥ Γw(ξ o η) − Γw(ξ) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN Γw(ξ), ∂tΓw(ξ))  ≥ 0  along with ∇w(ξ) = ∇Γw(ξ) for ξ ∈ {w = Γw}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It is clear from (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='19) and  ��B  HN  r  (ξ0) \\ A  �� = 0 that  ��{w = Γw} ∩ A  �� > 0,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=', there is a point ξδ ∈ {w = Γw} ∩ A such that (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='17) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='18) hold classically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let IN be denote the identity  matrix of order N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We have  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='22)  f(ξδ) − dε ≤ αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Suε(ξδ)  �  − β(−∆  HN )suε(ξδ)  ≤ αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Svε(ξδ) − D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Sw(ξδ) + D2  HN ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='SΦ(ξδ) + D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S  �  δ  ��ξ0  −1o ξ  ��4  HN (ξδ)  ��  − β(−∆  HN)suε(ξδ)  = αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Svε(ξδ) + D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='SΦ(ξδ) + δD2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S  ���ξ0  −1o ξ  ��4  HN(ξδ)  ��  − D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Sw(ξδ)  �  − β(−∆  HN)suε(ξδ)  ≤ αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Svε(ξδ) + D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='SΦ(ξδ) + δD2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S  ���ξ0  −1o ξ  ��4  HN(ξδ)  ��  + αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  − D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Sw(ξδ)  �  − β(−∆  HN )suε(ξδ)  = αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Svε(ξδ) + D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='SΦ(ξδ) + δD2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S  ���ξ0  −1o ξ  ��4  HN(ξδ)  ��  − αM−  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Sw(ξδ)  �  − β(−∆  HN )suε(ξδ)  ≤ αM+  λ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Λ  �  D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='Svε(ξδ) + D2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='SΦ(ξδ) + δD2  HN,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S  ���ξ0  −1o ξ  ��4  HN(ξδ)  ��  − β(−∆  HN )suε(ξδ) (by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='20)),  where in the second last step, we used the relation  M+  λ,Λ(−M) = −M−  λ,Λ(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, since  ��ξ0  −1o ξ  ��4  HN is a radial function so using Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2 [16] together with sub-additivity property of Pucci’s  maximal operator and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='22) yields  f(ξδ) − dε ≤ αM+  λ,Λ  �  D2  HN,Svε(ξδ)  �  + αM+  λ,Λ  �  D2  HN,SΦ(ξδ)  �  + αδM+  λ,Λ  �  D2  HN,S  ���ξ0  −1o ξδ  ��4  HN  ��  − β(−∆  HN )suε(ξδ)  = αM+  λ,Λ  �  D2  HN,Svε(ξδ)  �  + αM+  λ,Λ  �  D2  HN,SΦ(ξδ)  �  + αΛδ  �  (2N − 2)  �  4  N  �  i=1  (xi  δ − xi  0)2 + (yi  δ − yi  0)2  �  + 2  �  12  N  �  i=1  (xi  δ − xi  0)2 + (yi  δ − yi  0)2  ��  − β(−∆  HN )suε(ξδ),  where (x1  δ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN  δ , y1  δ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN  δ ) and (x1  0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , xN  0 , y1  0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , yN  0 ) are the first 2N coordinates of ξδ and ξ0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Next, since w(ξ o η) − w(ξ) > 0 for ξ o η ∈ Bc  r(ξ) and r1 small enough so we have by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='21),  −(−∆  HN)suε(ξδ) = −(−∆  HN)svε(ξδ) + (−∆  HN )sw(ξδ) − (−∆  HN )sΦ(ξδ) − δ(−∆  HN )s(|ξ−1  0  o ξ|4)(ξδ)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='23)  ≤ −(−∆  HN)svε(ξδ) −  �  {η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' ξδ o η∈ HN \\B  HN  r  (ξδ)}  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN w(ξδ), ∂tw(ξδ))  |η|Q+2s  HN  dη  − (−∆  HN)sΦ(ξδ) − δ(−∆  HN)s(|ξ−1  0  o ξ|4  HN)(ξδ)  = −(−∆  HN)svε(ξδ) −  �  {η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' r≤|η|  HN ≤1}  η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN w(ξδ), ∂tw(ξδ))  |η|Q+2s  HN  dη  − (−∆  HN)sΦ(ξδ) − δ(−∆  HN)s�  |ξ−1  0  o ξ|4  HN  �  (ξδ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  15  Further, using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='23) together with (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='21) yields  f(ξδ) − dε ≤ αM+  λ,Λ  �  D2  HN,Svε(ξδ)  �  − β(−∆  HN )svε(ξδ) + αM+  λ,Λ  �  D2  HN ,SΦ(ξδ)  �  − β(−∆  HN )sΦ(ξδ)  + αΛδ  �  (2N − 2)  �  4  N  �  i=1  (xi  δ − xi  0)2 + (yi  δ − yi  0)2  �  + 2  �  12  N  �  i=1  (xi  δ − xi  0)2 + (yi  δ − yi  0)2  ��  − β  2 c(N, s)  �  {η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' r≤|η|  HN ≤1}  η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN w(ξδ), ∂tw(ξδ))  |η|Q+2s  HN  dη − βδ(−∆  HN )s(|ξ−1  0  o ξ|4  HN )(ξδ)  ≤ g(ξδ) + dε + αΛδ  �  (2N − 2)  �  4  N  �  i=1  (xi  δ − xi  0)2 + (yi  δ − yi  0)2  �  + 2  �  12  N  �  i=1  (xi  δ − xi  0)2 + (yi  δ − yi  0)2  ��  − β  2 c(N, s)  �  {η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' r≤|η|  HN ≤1}  η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN w(ξδ), ∂tw(ξδ))  |η|Q+2s  HN  dη − δ(−∆  HN)s(|ξ−1  0  o ξ|4  HN )(ξδ)  + αM+  λ,Λ  �  D2  HN,SΦ(ξδ)  �  − β(−∆  HN )sΦ(ξδ) (using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='18)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It is easy to observe that ξδ −→ ξ0 and ∇Γw(ξδ) −→ ∇Γw(ξ0) = 0 as r1 −→ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Now, letting δ −→ 0 gives  f(ξ0) − dε ≤ g(ξ0) + dε + αM+  λ,Λ  �  D2  HN,SΦ(ξ0)  �  − β(−∆  HN )sΦ(ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  In other words,  αM+  λ,Λ  �  D2  HN,SΦ(ξ0)  �  − β(−∆  HN)sΦ(ξ0) ≥ f(ξ0) − g(ξ0) − 2dε.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  The above equation clearly implies that  αM+  λ,Λ  �  D2  HN,S(uε − vε)  �  − β(−∆  HN )sΦ(uε − vε) ≥ f − g − 2dε in Ω1  in the viscosity sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Finally, letting ε −→ 0 along with using Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='1 yields the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  □  In order to derive comparison principle, we next state and prove the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We mention that a similar  lemma has been proven in the Euclidean setting (see Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5 [24]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' There exists a C2(Ω) ∩ Cb(HN) function ϕh such that  αM+  λ,Λ  �  D2  HN,Sϕh  �  − β  �  − ∆  HN  �sϕh ≤ −1, in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let diam(Ω) = R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We may assume without of loss of generality that Ω ⊂ BR  HN (ξR), where  ξR := (2R, 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let us define  ϕh(ξ) =  �  2 − e−Cξ1  for ξ1 ≥ 0  1  2 + 1  4  �  1  1−Cξ1  �  + 1  4  �  sin 3Cξ1 + cos  √  6 Cξ1  �  for ξ1 < 0,  where ξ1 is the first coordinate of ξ = (ξ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , ξN, ξN+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , ξ2N, t) ∈ Ω and C > 0 is some constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It is easy to  calculate for ξ1 > 0,  ∂xiϕh =  �  Ce−Cξ1  if i = 1,  0  if 2 ≤ i ≤ 2N,  and ∂tϕh = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Also, for ξ1 > 0,  ∂2  xixjϕh =  �  −C2e−Cξ1  if i = j = 1  0  otherwise,  and ∂2  txi = 0 = ∂2  tt for i = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' , 2N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Using this, we first compute ∇  HN ϕh(ξ) and D2  HN,Sϕh(ξ) as follows:  ∇  HNϕh(ξ) = σ(ξ)∇ϕh(ξ) =  �IN  0N  2y  0N  IN  −2x  �  2N×(2N+1)  \uf8ee  \uf8ef\uf8ef\uf8ef\uf8f0  Ce−Cξ1  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  \uf8f9  \uf8fa\uf8fa\uf8fa\uf8fb  (2N+1)×1  =  \uf8ee  \uf8ef\uf8ef\uf8ef\uf8f0  Ce−Cξ1  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  \uf8f9  \uf8fa\uf8fa\uf8fa\uf8fb  2N×1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  16  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  Also,  D2  HNϕh(ξ) = σ(ξ)D2ϕhσT (ξ) =  �IN  0N  2y  0N  IN  −2x  �  2N×(2N+1)  \uf8ee  \uf8ef\uf8ef\uf8ef\uf8f0  −C2e−Cξ1  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  0  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  \uf8f9  \uf8fa\uf8fa\uf8fa\uf8fb  (2N+1)×(2N+1)  \uf8ee  \uf8f0  IN  0N  0N  IN  2y  −2x  \uf8f9  \uf8fb  (2N+1)×2N  =  \uf8ee  \uf8ef\uf8ef\uf8ef\uf8f0  −C2e−Cξ1  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  0  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  0  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  0  \uf8f9  \uf8fa\uf8fa\uf8fa\uf8fb  2N×2N  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, let δ = min{1, R}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Then for any ξ ∈ Ω, we get  αM+  λ,Λ  �  D2  HN,Sϕh(ξ)  �  − β(−∆  HN)sϕh(ξ)  = −λαC2e−Cξ1 + β  2 c(N, s)  �  HN  ϕh(ξ o η) − ϕh(ξ) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN ϕh(ξ), ∂tϕh(ξ))  |η|Q+2s  HN  dη  = −λαC2e−Cξ1 + β  2 c(N, s)  �  B  HN  δ  ϕh(ξ o η) − ϕh(ξ) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN ϕh(ξ), ∂tϕh(ξ))  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  CB  HN  δ  ∩{η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1≤0}  ϕh(ξ o η) − ϕh(ξ) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN ϕh(ξ), ∂tϕh(ξ))  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  B  HN  1  ∩ CB  HN  δ  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  ϕh(ξ o η) − ϕh(ξ) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN ϕh(ξ), ∂tϕh(ξ))  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  CB  HN  1  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  ϕh(ξ o η) − ϕh(ξ) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN ϕh(ξ), ∂tϕh(ξ))  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  where CB  HN  r  denotes the complement of B  HN  r  in  HN, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=',  HN \\ B  HN  r  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We can re-write the above equation as  αM+  λ,Λ  �  D2  HN,Sϕh(ξ)  �  − β  �  − ∆  HN  �sϕh(ξ)  = −λαC2e−Cξ1 + β  2 c(N, s)  �  B  HN  δ  ϕh(ξ o η) − ϕh(ξ) − η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN ϕh(ξ), ∂tϕh(ξ))  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  CB  HN  δ  ∩{η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1≤0}  ϕh(ξ o η) − ϕh(ξ)  |η|Q+2s  HN  dη + β  2 c(N, s)  �  B  HN  1  ∩ CB  HN  δ  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  ϕh(ξ o η) − ϕh(ξ)  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  B  HN  1  ∩CB  HN  1  −η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN ϕh(ξ), ∂tϕh(ξ))  |η|Q+2s  HN  dη + β  2 c(N, s)  �  CB  HN  1  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  ϕh(ξ o η) − ϕh(ξ)  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It further gives  αM+  λ,Λ(D2  HN,Sϕh(ξ)) − β(−∆  HN )sϕh(ξ) = −λαC2e−Cξ1  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='24)  + β  2 c(N, s)  �  B  HN  δ  �  2 − e−C(ξ1+η1)�  −  �  2 − e−Cξ1�  − η1Ce−Cξ1  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  CB  HN  δ  ∩{η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1≤0}  �  2 − e−C(ξ1+η1)�  −  �  2 − e−Cξ1�  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  B  HN  1  ∩ CB  HN  δ  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  �  2 − e−C(ξ1+η1)�  −  �  2 − e−Cξ1�  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  B  HN  1  ∩CB  HN  δ  −η1Ce−Cξ1  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  CB  HN  1  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  �  2 − e−C(ξ1+η1)�  −  �  2 − e−Cξ1�  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  17  Similarly,  αM+  λ,Λ(D2  HN,Sϕh(ξ)) − β(−∆  HN )sϕh(ξ)  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='25)  = −λαC2e−Cξ1 + β  2 c(N, s)  �  B  HN  δ  �  − e−C(ξ1+η1) + e−Cξ1�  − η1Ce−Cξ1  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  CB  HN  δ  ∩{η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1≤0}  �  − e−C(ξ1+η1) + e−Cξ1�  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  B  HN  1  ∩ CB  HN  δ  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  �  − e−C(ξ1+η1) + e−Cξ1�  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  B  HN  1  ∩CB  HN  δ  −η1Ce−Cξ1  |η|Q+2s  HN  dη + β  �  CB  HN  1  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  �  − e−C(ξ1+η1) + e−Cξ1�  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, since e−Cξ1 is a convex function so we have  0 ≤ e−C(ξ1+η1) − e−Cξ1 + η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (∇  HN ϕh(ξ), ∂tϕh(ξ))  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='26)  = e−C(ξ1+η1) − e−Cξ1 + Cη1e−Cξ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Also, if η1 ≤ 0 then  e−C(ξ1+η1) − e−Cξ1 ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='27)  Using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='26) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='27) in the first and second integrals in the R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='25), respectively, it confers that these  integrals are non-positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We further have that  |e−C(ξ1+η1) − e−Cξ1| = e−Cξ1|e−Cη1 − 1| ≤ Ce−Cξ1|η|  HN .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It infers  �����β  �  B  HN  1  ∩ CB  HN  δ  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  �  −e−C(ξ1+η1) + e−Cξ1�  |η|Q+2s  HN  dη  ����� ≤ β  �  B  HN  1  ∩ CB  HN  δ  Ce−Cξ1|η|  HN  |η|Q+2s  HN  dη  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='28)  ≤ β  �  B  HN  1  ∩ CB  HN  δ  Ce−Cξ1|η|2  HN  δ|η|Q+2s  HN  dη  ≤ βe−Cξ1 C  δ  �  B  HN  1  ∩ CB  HN  δ  |η|2  HN  |η|Q+2s  HN  dη  ≤ βe−Cξ1 C  δ  �  B  HN  1  |η|2  HN  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It is easy to see that for η1 > 0, we have  ��e−C(ξ1+η1) − e−Cξ1�� ≤ e−Cξ1 so  �����β  �  CB  HN  1  ∩ {η;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='η1>0}  �  − e−C(ξ1+η1) + e−Cξ1�  |η|Q+2s  HN  dη  ����� ≤ βe−Cξ1  �  CB  HN  1  1  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='29)  Also, it is easy to observe that  �����β  �  B  HN  1  ∩CB  HN  δ  −η1Ce−Cξ1  |η|Q+2s  HN  dη  ����� ≤ β  �  B  HN  1  ∩CB  HN  δ  |η|  HNCe−Cξ1  |η|Q+2s  HN  dη  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='30)  ≤ βe−Cξ1 C  δ  �  B  HN  1  |η|2  HN  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='28), (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='29) & (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='30) in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='25) yields that for sufficiently large enough C > 0 we can make the L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' of  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='25) less than −1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=',  αM+  λ,Λ  �  D2  HN,Sϕh  �  − β  �  − ∆  HN  �sϕh =≤ −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  □  Further, using the above lemma, we prove the comparison principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='5 together with a standard  approximation argument produces the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  18  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let u be bounded in  HN and USC in Ω such that  αM+  λ,Λ  �  D2  HN,Su  �  − β(−∆HN )su ≥ 0 in Ω in the viscosity sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Then  sup  Ω  u ≤ sup  HN \\Ω  u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='6, we have a function ϕh ∈ C2(Ω) ∩ Cb(HN) such that  αM+  λ,Λ  �  D2  HN ,Sϕh  �  − β  �  − ∆  HN  �sϕh ≤ −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, let us define a function  ϕM(x) = M + εϕh(x) for ε > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Then  αM+  λ,Λ  �  D2  HN,SϕM  �  − β  �  − ∆  HN  �sϕM = αεM+  λ,Λ  �  D2  HN,Sϕh  �  − βε  �  − ∆  HN  �sϕh  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='31)  ≤ −ε in Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Further, let M0 be the smallest value of M such that ϕM ≥ u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We aim to prove M0 ≤ sup  HN\\Ω  u by the method of  contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let us assume that  M0 > sup  HN\\Ω  u,  then we have that there exists a point ξ0 ∈ Ω such that u(ξ0) = ϕM0(ξ0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It immediately implies that ϕM0 touches  u at ξ0 from above and by the definition, it gives  αM+  λ,Λ  �  D2  HN,SϕM0  �  (ξ0) − β  �  − ∆  HN  �sϕM0(ξ0) ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  This contradicts (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Thus, we have  M0 ≤ sup  HN\\Ω  u,  which further entails that  u(ξ) ≤ ϕM0(ξ0)  ≤ M0 + ε sup  HN ϕh  ≤ sup  HN u + ε sup  HN ϕh, ξ ∈  HN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Finally, letting ε −→ 0 offers the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  □  Proof of Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We follow the similar arguments as in the Euclidean setting, see for instance, [11, 12, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Without loss of generality, we may assume that ∥u∥∞, HN = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We first show the existence of a universal constant  0 < δ < 1 such that  osc  B  HN  2−k  u ≤ 2(1 − δ)k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  We use the principle of mathematical induction to show the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Now, since ∥u∥∞, HN = 1 so the claim holds  trivially for k ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let the above inequality holds true up to some k, we need to show that it also holds for k + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  For this, consider a function  v(ξ) := u(2−kξ)  (1 − δ)k − ak ,  where ak is a constant chosen such that − 1  2 ≤ v ≤ 1  2 in B  HN  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Also, by the induction hypothesis, we have  osc  B  HN  2−j  u ≤ 2(1 − δ)j for all j ≤ k,  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  19  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=',  osc  B  HN  2j  u ≤ 2(1 − δ)−j for all j ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  We aim to show that  osc  B  HN  1  2  v ≤ osc  B  HN  1  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  One may show this either by showing that supremum of v in B  HN  1  2  is smaller than that in B  HN  1  or the infimum is  larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It is trivial that either v ≥ 0 or v ≤ 0 for atleast half of the points (in measure) in B  HN  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Without loss of  generality, we may assume that  |N| ≥ 1  2  ��B  HN  1  ��,  where N := {v ≤ 0} ∩ B  HN  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' We show now that the induction hypothesis implies that  v(ξ) ≤  �  2|ξ|  HN  �α − 1  2 for all ξ ∈ B  HN  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Let ξ ∈ B  HN  2j+1 \\ B  HN  2j  for some j > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' That is  2j+1 > |ξ|  HN > 2j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  In other words,  2−k+j+1 > |2−kξ|  HN > 2−k+j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  v(x) = (1 − δ)−ku(2−kx) − ak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  For ξ ∈ B  HN  1  ,  −1  2 ≤ (1 − δ)−ku(2−kξ) − ak ≤ 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, for ξ /∈ B  HN  1  , we have for any index j ≥ 0,  v(ξ) ≤  �  2|ξ|  HN  �γ − 1  2,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='32)  where γ is a number such that (1 − δ) = 2−γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Also, for any ξ ∈ B  HN  1  ,  αM+  λ,Λ  �  D2  HNv  �  − β(−∆HN )sv = (1 − δ)k �  αM+  λ,Λ  �  D2  HNu  �  − β  �  − ∆HN  �su  �  = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Now, we show that the following three points  v(ξ) ≤  �  2|ξ|  HN  �γ − 1  2 for ξ /∈ B  HN  1  |N| =  ��{v ≤ 0} ∩ B  HN  1  �� ≥ 1  2  ��B  HN  1  ��  αM+  λ,Λ(D2  HNv) − β(−∆HN )sv = 0 in B  HN  1  imply that v ≤  � 1  2 − δ  �  in B  HN  1  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let us assume the contrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Let v(ξ) >  � 1  2 − δ  �  for some ξ ∈ B  HN  1  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Consider a  smooth radial function whose support is contained in B  HN  3  4  and ρ ≡ 1 in B  HN  1  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' It immediately gives that v + δρ  attains a local maximum at some point ξ0 ∈ B  HN  3  4  such that  �  v + δρ  �  (ξ0) > 1  2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=', max  B  HN  1  (v + δρ) = (v + δρ)(ξ0) > 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Let us evaluate L(v + δρ), which further entails getting a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  L  �  v + δρ  �  (ξ0) = αM+  λ,Λ  �  D2  HN(v + δρ)  �  (ξ0) − β  �  − ∆HN  �s(v + δρ)(ξ0)  ≥ αM+  λ,Λ  �  D2  HNv  �  (ξ0) + δαM−  λ,Λ  �  D2  HNρ  �  (ξ0) − β  �  − ∆HN  �sv(ξ0) − δβ  �  − ∆HN  �sρ(ξ0)  = αM+  λ,Λ  �  D2  HNv  �  (ξ0) − β  �  − ∆HN  �sv(ξ0) + δαM+  λ,Λ  �  D2  HNρ  �  (ξ0) − δβ  �  − ∆HN  �sρ(ξ0)  = δαM+  λ,Λ  �  D2  HNρ  �  (ξ0) − δβ  �  − ∆HN  �sρ(ξ0)  ≥ δ min  ξ∈B  HN  3  4  �  αM+  λ,Λ  �  D2  HN ρ  �  (ξ) − β(−∆HN )sρ(ξ)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  20  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  On the other hand,  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='33)  L(v + δρ)(ξ0) = αM+  λ,Λ(D2  HN (v + δρ))(ξ0) − β(−∆HN )s(v + δρ)(ξ0)  ≤ αM+  λ,Λ(D2  HN (v + δρ))(ξ0) + β  2 c(N, s)  �  HN  (v + δρ)(ξ0 o η) + (v + δρ)(ξ0 o η−1) − 2(v + δρ)(ξ0)  |η|Q+2s  HN  dη  = αM+  λ,Λ(D2  HN (v + δρ))(ξ0)  + β  2 c(N, s)  �  HN  (v + δρ)(ξ0 o η) − (v + δρ)(ξ0) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  �  ∇  HN (v + δρ)(ξ0), ∂t(v + δρ)(ξ0)  �  |η|Q+2s  HN  dη  = αM+  λ,Λ(D2  HN (v + δρ))(ξ0)  + β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈B  HN  1  �  (v + δρ)(ξ0 o η) − (v + δρ)(ξ0) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  �  ∇  HN (v + δρ)(ξ0), ∂t(v + δρ)(ξ0)  �  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η /∈B  HN  1  �  (v + δρ)(ξ0 o η) − (v + δρ)(ξ0) −  1{|η|  HN ≤1}η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  �  ∇  HN (v + δρ)(ξ0), ∂t(v + δρ)(ξ0)  �  |η|Q+2s  HN  dη  = αM+  λ,Λ(D2  HN (v + δρ))(ξ0)  + β  2 c(N, s)  �  �  η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈B  HN  1  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  �  η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η /∈B  HN  1  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη  ≤ β  2 c(N, s)  �  �  η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈B  HN  1  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  �  η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η /∈B  HN  1  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Note that in the last two steps, we used the fact that v + δρ has a local maximum at ξ0 which also gives the  non-positivity of integrand in the last integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Moreover, we have  β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈B  HN  1  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη  = β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈N  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ)  |η|Q+2s  HN  dη  + β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈B  HN  1  \\N  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη  ≤ β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈N  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη  ≤ β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈N  � δρ(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη  < β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈N  �  �  δρ(ξ0 o η) − 1  2  �  |η|Q+2s  HN  dη  ≤ β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈N  �  �  δM − 1  2  �  |η|Q+2s  HN  dη,  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  21  for M = max  B  HN  3  4  ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Taking δ <  1  2M along with using |N| ≥  ��B  HN  1  ��  2  , we get  β  2 c(N, s)  �  �  η∈ HN;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η∈N  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη ≤ −C for some C > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='34)  Next, using (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='32), we get a bound on the integrand of first integral in the last line of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='33) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' In particular, we have  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='35)  1  2c(N, s)  �  �  η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η /∈B  HN  1  � (v + δρ)(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη = β  2 c(N, s)  �  �  η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η /∈B  HN  1  � v(ξ0 o η) − (v + δρ)(ξ0)  |η|Q+2s  HN  dη  ≤ β  2 c(N, s)  �  �  η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η /∈B  HN  1  �  |ξ0 o η|γ  HN − 1  2 − 1  2  |η|Q+2s  HN  dη  = β  2 c(N, s)  �  �  η∈ HN ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ξ0 o η /∈B  HN  1  �  |ξ0 o η|γ  HN − 1  |η|Q+2s  HN  dη.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Further, taking small enough γ, we can make the above integral in the R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' much less than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Therefore, by using  together (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='34) and (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='35) for small enough δ and γ, we can make the L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' of (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='33) arbitrarily small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Hence, we  can make it smaller than δ min  ξ∈B  HN  3  4  �  αM−  λ,Λ(D2  HNρ)(ξ) − β(−∆HN )sρ(ξ)  �  , which yield a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Thus, we have  v ≤ 1  2 − δ in B  HN  1  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  It gives  osc  B  HN  1  2  v ≤ (1 − δ) osc  B  HN  1  v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  More precisely, we have  1  (1 − δ)k osc  B  HN  1  2  u(2−kξ) =  1  (1 − δ)k  osc  B  HN  2−k−1  u(ξ) ≤ (1 − δ)  (1 − δ)k osc  B  HN  1  u(2−kξ) = (1 − δ)  (1 − δ)k osc  B  HN  2−k  u(ξ),  which immediately offers  osc  B  HN  2−k−1  u(ξ) ≤ (1 − δ) osc  B  HN  2−k  u(ξ)  ≤ 2(1 − δ)k+1  = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2−γ(k+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Let for some k > 0, ξ ∈ B  HN  2−k \\ B  HN  2−(k+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Then we get  |u(ξ) − u(0)| ≤ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2−γk = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2γ2−γ(k+1) ≤ C|ξ|γ  HN ,  for C = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='2γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Hence the claim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  □  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Funding and/or Conflicts of interests/Competing interests  The research of Priyank Oza was financially supported by Council of Scientific & Industrial Research (CSIR)  under the grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 09/1031(0005)/2019–EMR–I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' The second author thanks DST/SERB for the financial support  under the grant CRG/2020/000041.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  There are no conflict of interests of any type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' This manuscript does not use any kind of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  22  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' OZA, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' TYAGI  References  [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Banerjee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Gordina, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Mariano, Coupling in the Heisenberg group and its applications to gradient estimates, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Probab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  46(6), 3275–3312 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [2] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Barles, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Chasseigne, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Imbert, On the Dirichlet problem for second-order elliptic integro-differential equations, Indiana Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 57, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 1, 213–246 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Barles, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Imbert, Second-order elliptic integro-differential equations: viscosity solutions’ theory revisited, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Inst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Poincar´e  Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Non Lin´eaire 25, 567–585 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [4] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Bhatia, Matrix Analysis, Graduate texts in Mathematics, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 169, Springer New York (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [5] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Biagi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Dipierro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Valdinoci, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Vecchi, A Faber-Krahn inequality for mixed local and nonlocal operators, Preprint,  arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='00830 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Biagi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Dipierro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Valdinoci, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Vecchi, Mixed local and nonlocal elliptic operators: regularity and maximum principles, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Partial Differential Equations 47(3), 585–629 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [7] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Biagi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Dipierro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Valdinoci, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Vecchi, Semilinear elliptic equations involving mixed local and nonlocal operators, Proceedings  of the Royal Society of Edinburgh: Section A Mathematics, 151 (5), 1611–1641 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [8] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Bieske, On ∞–harmonic functions on the Heisenberg group, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Partial Differential Equations 27(3–4), 727–761 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [9] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Blazevski, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' del-Castillo-Negrete, Local and nonlocal anisotropic transport in reversed shear magnetic fields shearless Cantori  and nondiffusive transport, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' E, 87 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [10] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Caffarelli, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Cabr´e, Fully Nonlinear Elliptic Equations, Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Colloq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Publ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 43, American Mathematical Society,  Providence (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [11] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Caffarelli, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Silvestre, Regularity theory for fully nonlinear integro-differential equations, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 62, 597–638  (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [12] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Chang-Lara, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' D´avila, Regularity for solutions of nonlocal, nonsymmetric equations, Annales de I’I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Analyse Non lin´eaire,  No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 6, Tome 29, 833–859 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [13] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Citti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Manfredini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Sarti, Finite difference approximation of the Mumford and Shah functional in a contact manifold of the  Heisenberg space, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 9(4), 905–927 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Crandall, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Ishii, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Lions, User’s guide to viscosity solutions of second order partial differential equations, Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=', 27(1), 1–68 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [15] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Crandall, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 277, 1–42 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Cutr´ı, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Tchou, Barrier functions for Pucci–Heisenberg operators and applications, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Dyn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Equ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 1 (2), 117–131  (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [17] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Dal Maso, An introduction to Γ-convergence, Progr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' in Nonlinear Differential Equations Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 8, Birkhauser, Basel, (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Dipierro, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Lippi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Valdinoci, (Non)local logistic equations with Neumann conditions, arXiv:2101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='02315 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [19] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Ferrari, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Vecchi, H¨older behavior of viscosity solutions of some fully nonlinear equations in the Heisenberg group, Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Methods  Nonlinear Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 55, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 1, 227–242 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [20] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=',  42(1), 15–45 (1989).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [21] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Jensen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='–L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Lions, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Souganidis, A uniqueness result for viscosity solutions of second order fully nonlinear partial differential  equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 102, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 4, 975–978 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [22] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Wang, Comparison principles for some fully nonlinear sub-elliptic equations on the Heisenberg group, Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Theory  Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 35, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 3, 312–334 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Manfredini, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Palatucci, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Piccinini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Polidoro, H¨older continuity and boundedness estimates for nonlinear fractional equations  in the Heisenberg group, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [24] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Mou, Existence of Cα solutions to integro-PDEs, Calculus of Variations and Partial Differential Equations 58, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 4, Paper No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  143, 28 pp (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [25] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Mou, Perron’s method for nonlocal fully nonlinear equations, Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' PDE 10(5), 1227–1254 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [26] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Ochoa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Ruiz, Existence and uniqueness results for linear second-order equations in the Heisenberg group, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Fenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 42, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 2, 1065–1083 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [27] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Ovando, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Sublis, Magnetic trajectories on 2-step nilmanifolds, arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='02258, Preprint (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [28] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Palatucci, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Piccinini, Nonlocal Harnack inequalities in the Heisenberg group, Calculus of Variations and Partial Differential  Equations 61 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [29] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Silvestre, H¨older estimates for solutions of integro-differential equations like the fractional Laplace, Indiana Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=', Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  55, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 3, 1155–1174 (2006)  [30] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Wang, Removable singularities for degenerate elliptic Pucci operator on the Heisenberg group, Nonlinear Analysis 160, 177–190  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Wang, The Aronsson equation for absolute minimizers of L∞-functionals associated with vector fields satisfying H¨ormander’s  condition, Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 359, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' 1, 91–113 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  [32] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content=' Weyl, The theory of groups and quantum mechanics, Dover Publications, New York (1950).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Priyank Oza  Indian Institute of Technology Gandhinagar  Palaj, Gandhinagar Gujarat, India-382355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Email address: priyank.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='k@iitgn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='in, priyank.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='oza3@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='com  MIXED FULLY NONLINEAR LOCAL AND NONLOCAL ELLIPTIC OPERATORS IN HEISENBERG GROUP  23  JagmohanTyagi  Indian Institute of Technology Gandhinagar  Palaj, Gandhinagar Gujarat, India-382355.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='  Email address: jtyagi@iitgn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='in, jtyagi1@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
+page_content='com' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qdE1T4oBgHgl3EQfigS7/content/2301.03253v1.pdf'}
diff --git a/rNE3T4oBgHgl3EQfMQnG/content/tmp_files/2301.04372v1.pdf.txt b/rNE3T4oBgHgl3EQfMQnG/content/tmp_files/2301.04372v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ea32262c6fd8c72add4f388f8faedd68a869c58c
--- /dev/null
+++ b/rNE3T4oBgHgl3EQfMQnG/content/tmp_files/2301.04372v1.pdf.txt
@@ -0,0 +1,2081 @@
+Geometric Operator Quantum Speed Limit, Wegner
+Hamiltonian Flow and Operator Growth
+Niklas Hörnedal1, Nicoletta Carabba1, Kazutaka Takahashi1,2, and Adolfo del Campo1,3
+1Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G. D. Luxembourg
+2Department of Physics Engineering, Faculty of Engineering, Mie University, Mie 514–8507, Japan
+3Donostia International Physics Center, E-20018 San Sebastián, Spain
+Quantum speed limits (QSLs) provide lower bounds on the minimum time
+required for a process to unfold by using a distance between quantum states
+and identifying the speed of evolution or an upper bound to it. We introduce a
+generalization of QSL to characterize the evolution of a general operator when
+conjugated by a unitary. The resulting operator QSL (OQSL) admits a geomet-
+ric interpretation, is shown to be tight, and holds for operator flows induced
+by arbitrary unitaries, i.e., with time- or parameter-dependent generators. The
+derived OQSL is applied to the Wegner flow equations in Hamiltonian renor-
+malization group theory and the operator growth quantified by the Krylov
+complexity.
+In what time scale does a physical process unfold? Time-energy uncertainty relations have
+long been used to estimate characteristic time scales in physical processes, including life-
+times in quantum decay, tunneling times, and the duration of a quantum jump, among
+others [1–4]. In the quantum domain, Mandelstam and Tamm put the time-energy uncer-
+tainty relation on firm ground in their 1945 work [5]. They provided its rigorous derivation
+by combining the Heisenberg equation of motion and the Robertson uncertainty relation.
+They went a step further by identifying the minimum time for the quantum state of a
+system to evolve into a distinct state, using the energy dispersion of the initial state as an
+upper bound to the speed of evolution. In doing so, they introduced an early example of
+a quantum speed limit (QSL).
+Over the last decades, such an approach has been refined and generalized to a great extent
+[6, 7]. Margolus and Levitin found an alternative bound to the speed of evolution in terms
+of the mean energy of the system [8], and ensuing works showed that an infinite family
+of bounds exist in terms of other moments of the generator of evolution [9, 10]. QSLs
+have also been derived for time-dependent Hamiltonians [11–13], open systems described
+by master equations [14–17], and with a stochastic evolution under continuous quantum
+measurements [18]. They have been further extended to the classical domain, with appli-
+cations ranging from Hamiltonian dynamics to stochastic thermodynamics [19–25]. QSLs
+generally involve a notion of distance between quantum states and an upper bound to the
+speed of quantum evolution. While the Bures angle, defined in terms of the Uhlmann
+fidelity [26], is often the default choice for the distance between quantum states, other
+1
+arXiv:2301.04372v1  [quant-ph]  11 Jan 2023
+
+alternatives can provide tighter QSLs [17, 27–29]. This freedom is particularly important
+in the context of many-body systems given the orthogonality catastrophe and the growth
+of the Hilbert space with the system size [30–34].
+The emphasis on quantum state distinguishability was a key stepping stone in developing
+QSLs. Today, QSLs find manifold applications in quantum metrology and parameter esti-
+mation [35–38], quantum control [39–42], and quantum thermodynamics [43, 44], among
+other fields. However, certain phenomena are naturally described in terms of operator
+flows, i.e., the continuous evolution of an operator according to given equations of motion.
+A typical example is the description of quantum evolution in the Heisenberg picture, but
+the relevance of operator flows is not restricted to quantum dynamics in rotating frames.
+Operator flows naturally arise in the Wegner flow equations for Hamiltonian renormaliza-
+tion [45–49], the study of operator growth and quantum complexity [50–54], and correlation
+functions [55], to name some examples.
+Motivated by these applications, we have introduced the notion of QSL for operator flows
+in Ref. [56], which we shall term Operator QSL (OQSL) hereafter. Another approach
+pursuing QSLs for observables was proposed in [57]. At variance with conventional QSLs,
+OQSLs involve a notion of distance between operators (instead of quantum states) and
+an upper bound on the corresponding speed of evolution. OQSLs have proved useful in
+characterizing the time evolution of autocorrelation functions, setting bounds on dynamical
+susceptibilities arising in linear response theory, and the precision in parameter estimation
+with thermal quantum systems [56]. However, in their current form, OQSLs are restricted
+to flows associated with a constant generator, i.e., one that is independent of time or the
+relevant parameter characterizing the evolution. In addition, OQSLs lack in their present
+formulation an intuitive geometric description, common in other bounds arising in quantum
+information geometry, such as the Mandelstam-Tamm QSL.
+In this work, we introduce an OQSL valid under unitary dynamics generated by a time-
+(or parameter-) dependent generator, that can be a generic operator or an observable, e.g.,
+a Hamiltonian. The resulting bound admits a geometric interpretation and is shown to
+be tight. We illustrate its usefulness in the study of Wegner flow equations in the theory
+of Hamiltonian continuous renormalization group [46–48]. We characterize the OQSL for
+the Hamiltonian flow in detail and illustrate the possibility of saturating it when the flow
+of Hamiltonian parameters is described by the Toda equations. We further apply the new
+OQSL to the problem of operator growth in unitary quantum dynamics in Krylov space,
+i.e., as characterized by the Krylov complexity [54, 58–62]. We close with a discussion and
+an outlook pointing out directions for further work.
+1
+Motivation
+In quantum physics, a broad class of time-correlation functions is defined through a positive
+semi-definite inner product. Consider any operator A evolving unitarily according to ˙At =
+iLAt, where L = [H, ·] is the Liouvillian superoperator.
+One class of time-correlation
+functions that have been considered in the literature takes the form C(t) = (A|At), defined
+with the help of a Hermitian bilinear form in the space of operators,
+(A|B) = Tr
+�
+A†ρ1Bρ2
+�
+.
+(1)
+2
+
+The operators ρ1 and ρ2 are in general positive semi-definite, commute with the Hamilto-
+nian, and need not have unit trace. A familiar example of this type of correlation function
+is obtained by setting ρ1 = ρ2 = 1. Eq. (1) reduces then to the Hilbert-Schmidt inner
+product. Another familiar instance corresponds to the choice of the identity ρ1 = 1 and
+the canonical Gibbs state ρ2 = e−βH/Z at inverse temperature β, with partition function
+Z = Tr e−βH. Note that in general, the bilinear form in (1) is not positive definite, which
+means that it does not always define an inner product; instead, it will define a positive
+semi-definite inner product.1
+As a result, there might exist cases in which A ̸= 0 and
+(A|A) = 0 are simultaneously fulfilled. Another example of a correlation function defined
+through a positive semi-definite inner product, i.e. C(t) = (A|At), is given by the so-called
+Kubo inner product [55, 63–65]
+(A|B) = 1
+β
+� β
+0
+dλ⟨eλHA†e−λHB⟩β − ⟨A†⟩β⟨B⟩β.
+(2)
+Here, ⟨·⟩β denote the thermal expectation value and β is once again the inverse tempera-
+ture.
+The function ∥A∥ =
+�
+(A|A) is a seminorm and we note that the condition ∥At∥ = ∥A∥ is
+satisfied in the above examples for all t.2 We might then ask, given a unitary flow induced
+by a possibly time-dependent Hamiltonian H, what is the minimal time τ for an initial
+observable A to reach some specific value of C(t) provided that ∥At∥ = ∥A∥ is satisfied
+during the whole evolution? What follows is a derivation of a speed limit that lower bounds
+this minimum time.
+2
+An Operator Quantum Speed Limit
+The complex Hilbert space H used to model the system will be assumed throughout this
+paper to be finite-dimensional. We define B to be the space of linear operators acting on
+this space. Moreover, let End(B) be the space consisting of all vector space endomorphism
+of B. This linear space is commonly referred to as the Liouville space in the literature
+[66, 67] and its elements are referred to as superoperators.
+Positive semi-definiteness of (·|·) makes it possible for C(t) to be constant for certain paths
+At even though the operator is changing in time. We will see that there is a way of “carving
+away” the degrees of freedom in H that do not contribute to changes in C(t). In doing so,
+we obtain an effective Hilbert subspace HP, where the restriction of (·|·) onto this subspace
+defines a proper inner-product. We will see that the condition ∥At∥ = ∥A∥ implies that At
+will be situated on a sphere centered at the origin in HP with radius ∥A∥ . This observation
+will then enable us to derive a geometric OQSL.
+2.1
+Construction of the effective Hilbert space
+We let ⟨·, ·⟩h denote the Hilbert-Schmidt inner product on B. It can be shown that any
+positive semi-definite inner product (·|·) can be expressed as (·|·) = ⟨·, P·⟩h, where P is
+1We use the convention that an inner product must satisfy positive-definiteness, be linear in the second
+argument and conjugate symmetric
+2A seminorm fulfills all the properties of regular norm except that non-zero vectors can have norm 0.
+3
+
+a positive semi-definite superoperator with respect to the Hilbert-Schmidt inner product.
+This superoperator will be unique, provided that (·|·) has been specified—see Appendix A.
+As we prove in Appendix B, a useful relation between (·|·) and P is that
+∥A∥ = 0 ⇐⇒ PA = 0.
+(3)
+Since P is self-adjoint, it follows from the spectral theorem that the linear space B can
+be expressed as a direct sum of the eigenspaces of P [68]. Consequently, the image of P
+will be spanned by the eigenvectors corresponding to non-zero eigenvalues, and we thus
+have that B = im(P) ⊕ ker(P), where im(P) and ker(P) are the image and kernel of P
+respectively. Relation (3) then implies that the restriction of (·|·) to im(P) will be positive
+definite and will thus define an inner product on the Hilbert space defined by HP = im(P).
+We will express this inner product with the usual bracket notation ⟨·, ·⟩.
+For any operator A ∈ B, we will let ˆA ∈ HP denote the orthogonal projection of A onto
+HP.3 More explicitly, given the spectral decomposition P = �
+k pkΠk, where pk are the
+non-zero eigenvalues of P and Πk are the corresponding eigenprojections, we have that
+ˆA = �
+k ΠkA. We show in Appendix C that
+(A|B) = ⟨ ˆA| ˆB⟩
+∀A, B ∈ B.
+(4)
+An important consequence of (4) is that C(t) = ⟨ ˆA| ˆAt⟩.
+This means that if we are
+interested in how C(t) changes over time, then we only need to consider the projected
+dynamics ˆA(t) of A(t).
+2.2
+Deriving the speed limit
+If d is the complex dimension of the Hilbert space HP, then we can view it as a real vector
+space isomorphic to R2d. We endow this space with the Riemannian metric given by the
+real part of the inner product ⟨·, ·⟩. The condition that (A|A) = (At|At) holds for all
+t ∈ [0, τ] then means that ˆAt will be situated on the (2d − 1)-dimensional sphere S∥A∥
+with radius ∥A∥ centered at the origin. The shortest path connecting two points on the
+sphere lies on a great circle with a distance given by the angle between the points times
+the radius. In other words, if ˆA and ˆB are two operators on the sphere with radius ∥A∥,
+then the geodesic distance is given by
+dist( ˆA, ˆB) = ∥A∥ arccos
+�
+Re(A|B)
+∥A∥2
+�
+.
+(5)
+The length of any curve ˆAt on the sphere must be greater or equal to the geodesic distance.
+As a consequence, we obtain an operator quantum speed limit τqsl by noting that
+τ = length([ ˆAt])
+1
+τ length([ ˆAt])
+≥ dist( ˆA0, ˆAτ)
+1
+τ length([ ˆAt])
+,
+(6)
+where length([ ˆAt]) =
+� τ
+0 ∥LtAt∥dt is the length of the evolution. More explicitly, the speed
+limit can be written in terms of C(t) as
+τ ≥ τqsl,
+τqsl =
+�
+C(0) arccos
+�
+Re C(τ)
+C(0)
+�
+Vτ
+,
+(7)
+3By orthogonal, we mean orthogonality measured by the Hilbert-Schmidt inner product.
+4
+
+where Vτ = 1
+τ
+� τ
+0 ∥LtAt∥dt is the time averaged speed of the evolution. For non-constant
+speeds, Vτ needs in practice be replaced by an upper bound on the speed of the evolution
+in order to make τqsl independent on the time τ one is trying to estimate.
+We stress that the speed limit τ is only guaranteed to hold whenever ∥At∥ is preserved
+for the evolving operator. This is always satisfied in the case when P = 1 so that (·|·)
+becomes the Hilbert-Schmidt inner product. For more general choices of P however, norm
+preservation will not be guaranteed to hold for all initial operators. In fact, the norm is
+preserved for all initial operators if and only if [L, P] = 0. Assuming [L, P] = 0, let Pnm
+and ωα = En − Em be the eigenvalues of P and L with respect to a common eigenbasis.
+Moreover, let Aij be the components of A with respect to this basis. Define vα = Pnm|Anm|2
+C(0)
+,
+where C(0) = �
+n,m Pnm|Anm|2. We can then express (7) more explicitly, as
+τqsl = arccos
+�Re �
+α vαeiωατ�
+��
+γ vγω2γ
+,
+(8)
+where the indices α and γ runs from 1 to dim(H)2.
+Example 1. In the case when C(t) = Tr
+�
+A†Ate−βH/Z
+�
+we have that PA = Ae−βH/Z
+and a common eigenbasis between L and P is given by the operators |En⟩⟨Em| where the
+eigenvalues of P are given by Pnm = e−βEm/Z.
+Example 2. For the Kubo inner-product we can view P as the composition P = A ◦ B ◦ C
+of the three superoperators defined by A(A) = Ae−βH
+Z
+, B(A) = 1
+β
+� β
+0 dλe−λHAeλH and
+CA = A − Tr(A)1. The superoperators A and B commute with a common eigenbasis being
+given by the eigenvectors |En⟩⟨Em|. A speed limit for a time-evolving operator At using
+the Kubo inner-product can then be obtained by using ˜At = C(At) and ˜P = A ◦ B instead
+of At and P and then use that ˜Pnm = e−βEm
+βZ
+� β
+0 eλ(Em−En)dλ and ˜Anm = Anm − �
+k Akk.
+Let us note that the OQSL (7) is saturated by any traceless observable involving solely
+the coupling of the ground state and an excited state of a time-independent Hamiltonian,
+in the same spirit as the superposition of these eigenstates saturates the standard QSLs
+for states [69]. To show this, let us consider a time-independent Hamiltonian H and let us
+denote by |0⟩ and |E⟩ its ground state and the eigenstate with energy E: H |0⟩ = 0 and
+H |E⟩ = E |E⟩. Then, it is straightforward to see that the operator A =
+1
+√
+2(|0⟩⟨E|+|E⟩⟨0|)
+exactly saturates the OQSL (7) with respect to the Hilbert-Schmidt inner product (A|B) =
+Tr
+�
+A†B
+�
+. Indeed, the autocorrelation function reduces to C(t) = cos(Et), in natural units,
+while the velocity is constant and takes the value V = ∥[H, A]∥ = E. Therefore, being
+C(0) = 1 due to the normalization, the OQSL (7) reduces to an identity at any time.
+This intuition, that when the operator dynamics is confined to two time-independent Hamil-
+tonian eigenspaces the evolution occurs along a geodesic trajectory, can be made more
+rigorous and general, as we shall describe below identifying the general conditions for the
+saturation of the OQSL (7).
+2.3
+Refined speed Limit
+Suppose we can find a decomposition of ˆAt such that ˆAt = S + Vt, where S and Vt stays
+orthogonal with respect to the metric Re⟨·, ·⟩ throughout the evolution. We then have that
+5
+
+the minimal time it takes V to reach the operator Vτ is smaller or equal to the time it takes
+ˆA to reach ˆAτ. We can thus obtain another speed limit by substituting C(t) with (V |Vt)
+in (7). Using that S and Vt are orthogonal, one can write Re(V |Vt) = Re C(t)−∥S∥2. Our
+refined speed limit thus takes the form
+τ ≥ τref,
+τref =
+�
+C(0) − ∥S∥2 arccos
+�
+Re C(τ)−∥S∥2
+C(0)−∥S∥2
+�
+Vτ
+.
+(9)
+This OQSL is a generalization of (7) since we can always trivially consider the case when
+S = 0. Also, since 1 stays invariant throughout the flow generated by the Hamiltonian,
+we can always consider the choice S = (1|A)1. In the particular case when (·|·) is the
+Hilbert-Schmidt inner product, this choice of S reduces (9) to the speed limit, denoted by
+TΘ, in [28].
+What is worth noting is that the speed limit (9) becomes tighter the larger the norm
+of S is.
+We can understand this from a geometrical perspective.
+The speed limit is
+saturated whenever the traced-out curve of Vt follows a great circle on the sphere S∥V ∥.
+This means that the evolution will be contained in a two-dimensional subspace. If we
+then let X and Y be a pair of orthonormal vectors spanning this subspace, we must have
+that Vt/∥V ∥ = cos θ(t)X + sin θ(t)Y , where θ(t) is some real-valued function of t.4 Given
+that S is non-zero, the corresponding curve of ˆA must then be situated on an effective
+Bloch sphere spanned by the operators X, Y and S.5
+More explicitly, we have that
+ˆA = ∥V ∥ cos θ(t)X + ∥V ∥ sin θ(t)Y + S will trace out a curve following a circle centered
+at S (see figure 1). Since this circle is not centered at the origin, it will not be a great
+circle on the sphere S∥A∥. A consequence of this is that the length of this curve must be
+strictly larger than the geodesic distance on S∥A∥. This length is precisely the numerator
+in (9) and we can thus conclude that (9) gives a strictly tighter inequality than (7). The
+difference between these inequalities becomes greater the larger ∥S∥ is, which can be seen
+in figure 2.
+Consider the case when ker(L) ∩ HP is invariant throughout the evolution, for example,
+when the Hamiltonian commutes with itself for any two points in time. We then have
+that the norm of S is maximal when S is equal to the orthogonal projection of ˆA onto the
+subspace ker(L) ∩ HP—see Appendix E.6 Calling this component P0, we thus have that
+the tightest possible refinement, in this case, is given by
+τ ≥ τoref ≥ τref ≥ τqsl,
+τoref =
+�
+C(0) − ∥P0∥2 arccos
+�
+Re C(τ)−∥P0∥2
+C(0)−∥P0∥2
+�
+Vτ
+.
+(10)
+We will refer to this as the optimal refinement of the OQSL.
+4In fact, if we choose X and Y so that X = V , then θ is the angle between V and Vt and is given by
+θ(t) = arccos
+�
+Re C(τ)−∥S∥2
+C(0)−∥S∥2
+�
+.
+5We emphasize that the operators S, X and Y are orthogonal with respect to Re⟨·, ·⟩ and not necessarily
+the Hilbert-Schmidt inner product.
+6The orthogonal projection here is with respect to the inner product ⟨·, ·⟩.
+6
+
+Figure 1: As the evolving operator saturates the refined speed limit, it will move along a circle
+that is displaced from the origin by S. As a consequence, the length of the traced-out curve will be
+strictly larger than the geodesic distance in S∥A∥. The numerator in (9) is exactly the length of this
+traced-out curve, and we can thus conclude that the refined speed limit is strictly tighter than the
+original one, given that S ̸= 0.
+3
+More on the Conditions for Saturation
+As discussed in section 2, the part of the evolution that induces a change in the time-
+correlation function will be situated on the sphere S∥A∥ in the effective Hilbert space
+HP. The OQSL (7) will then be saturated whenever the traced-out curve follows a great
+circle. In the case when we could find a decomposition ˆAt = S + Vt, where S and Vt
+remain orthogonal, we could consider the refined speed limit (9), which is saturated if and
+only if Vt follows a great circle on the sphere S∥V ∥. We discussed that for saturation of
+(9), there exists a pair of orthonormal vectors X and Y such that ˆA = ∥V ∥ cos θ(t)X +
+∥V ∥ sin θ(t)Y + S. If we choose X = ˆA/∥A∥, then the function θ(t) is the angle between
+V and Vt with respect to the real-valued inner product Re⟨·, ·⟩ and is more explicitly given
+by θ(t) = arccos
+�
+Re C(τ)−∥S∥2
+C(0)−∥S∥2
+�
+.
+This section will discuss the conditions for saturation for two particular cases.
+In the
+first case, we consider the consequences of the operator ˆA having support in only two of
+the eigenspaces of the Hamiltonian. In the second case, we assume ˆA to be Hermitian,
+allowing us to draw connections between the saturation of the OQSLs and the dimension
+of an underlying Krylov space.
+3.1
+Evolution with support in only two eigenspaces of the Hamiltonian
+Consider the case when the Hamiltonian commutes with itself at any two points in time.
+We will consider the case when ˆA has non-zero support in only two of the eigenspaces of the
+Hamiltonian.7 Let E and E′ denote the energies of these two eigenspaces through time and
+let ω = E−E′ be the energy gap. If PE and PE′ are the corresponding eigenspace projectors,
+then ˆA = PE ˆAPE + PE ˆAPE′ + PE′ ˆAPE + PE′ ˆAPE′ and it is straight forward to check that
+7An operator A is said to have non-zero support in a subspace X ⊆ H if ∃ |ψ⟩ ∈ X s.t. A |ψ⟩ ̸= 0.
+7
+
+SilAll N span[S, X, Y]
+V
+S
+A
+Y
+XFigure 2: As ∥S∥ grows larger, the center of the circle that ˆAt follows will be closer to the poles of
+the sphere. Consequently, ˆAt moves in a more curved path, as highlighted by the yellow segments
+where the right figure shows a top view of the sphere, and have to travel further in order to reach
+the same angle θ. The result of this is that the refined speed limit becomes increasingly tight the
+larger ∥S∥ is.
+LPE ˆAPE′ = ωPE ˆAPE′, LPE ˆAPE′ = −ωPE′ ˆAPE and LPE ˆAPE = LPE′ ˆAPE′ = 0. In other
+words, ˆA is spanned by the eigenspaces of the Liouvillian with eigenvalues 0, ω, and −ω.
+Let P0, Pω, and P−ω be the corresponding projections of ˆA onto these three eigenspaces.
+More explicitly, we have in this specific case that P0 = PE ˆAPE + PE′ ˆAPE′, Pω = PE ˆAPE′
+and P−ω = PE′ ˆAPE and we can write ˆA = P0 + Pω + P−ω. The evolution of ˆA is given
+by
+ˆAt = P0 + ei� t
+0 ω(t′)dt′Pω + e−i� t
+0 ω(t′)dt′P−ω
+= P0 + cos
+�� t
+0
+ω(t′)dt′
+��Pω + P−ω
+� + sin
+�� t
+0
+ω(t′)dt′
+��iPω − iP−ω
+�
+= P0 + cos θ(t)Xω + sin θ(t)Yω.
+(11)
+Here, we have introduced the non normalized operators Xω = Pω + P−ω and Yω = iPω −
+iP−ω and the angle θ(t) =
+� t
+0 ω(t′)dt′ between ˆA − P0 and ˆAt − P0. The requirement that
+∥At∥ is constant in the interval [0, τ] implies that P0, X and Y are orthogonal and that
+X and Y have the same norm—see Appendix F.8 We can thus conclude that ˆAt − P0
+moves along a great arc and thus saturates the optimal refined speed limit (10). One of
+the consequences of this is that any qubit system with a commutative Hamiltonian must
+satisfy the speed limit (10).
+The above result can be extended to non-commuting Hamiltonians that keep the eigenspaces
+corresponding to E and E′ invariant. One might wonder whether the Hamiltonian must
+keep these eigenspaces invariant for the evolving operator ˆAt to achieve saturation. The
+answer is no. To see this, we can consider the commuting Hamiltonian Ht above and add
+to it any non-trivial Hamiltonian ˜Ht that commutes with ˆAt for all times t ∈ [0, τ]. The
+Hamiltonian Ht + ˜Ht then generates the same path for ˆAt as the Hamiltonian Ht. The
+difference is that Ht + ˜Ht will not keep the eigenspaces of E and E′ invariant.
+8Note that we never need to assume that ˆA is Hermitian in order to conclude this.
+8
+
+03.2
+Relation to Krylov dimension for Hermitian operators
+When ˆA is Hermitian, it can be illuminating to describe the saturation conditions in terms
+of the dimension of the Krylov space of the evolving operator ˆAt. The Krylov space is
+defined to be the smallest subspace containing the evolution. In the Hermitian case, this
+is a real vector space. We can then conclude that saturation of (7) happens if and only if
+the dimension of the Krylov space is equal to two. Similarly, given that S ̸= 0, we have
+that a necessary condition for saturation of (7) is that the dimension of the Krylov space
+is equal to three.
+In the case when the Liouvillian is time-independent, the Krylov dimension is given by
+the number of eigenspaces of L that ˆA has support in—see Appendix D. If one of these
+eigenspaces is the kernel of L, then we can say that the bound will be saturated if and only
+if the Krylov dimension is smaller or equal to three.
+4
+Hamiltonian Flow Equations in Continuous Renormalization Group
+Operator flows are ubiquitous in physics and are not restricted to time evolution. In this
+section, we show that the continuous renormalization group provides an arena in which
+Hamiltonian flows naturally occur and where OQSLs are of relevance.
+As a preamble, we note that the continuous renormalization group is also extensively used
+in the study of the complexity of quantum states. For instance, the continuous version of
+the Entanglement Renormalization tensor networks, cMERA [70, 71], implements a real
+space renormalization in which the flow of a quantum state is described as a function of
+a continuous parameter characterizing the length scale. A cMERA Hamiltonian generates
+translations of the cMERA parameter. The use of conventional QSL has been explored
+in this context to investigate the complexity of states in quantum field theory [72], using
+the path integral description of tensor networks [73, 74]. These works result from an effort
+to characterize the growth of quantum complexity in quantum field theories, a context in
+which conventional QSLs had been applied [75, 76]. Indeed, all these results concern flows
+of quantum states and can thus be tackled with conventional QSL.
+In this section, we consider a different framework for the continuous renormalization group
+as a paradigmatic example and test bed for our result, the OQSL (7). Specifically, we focus
+on the Hamiltonian flow formulated by Wegner [45] and Glazek and Wilson [46, 47], as
+a method for Hamiltonian block-diagonalization [48, 49]. Consider the Hamiltonian flow
+H(l) = U(l)H(0)U(l)† with respect to some parameter l, where U(l) is a unitary operator
+satisfying U(0) = 1, and H(0) is the Hamiltonian of which the block diagonal form is
+desired. The flowing Hamiltonian satisfies the differential equation
+dH(l)
+dl
+= [η(l), H(l)],
+(12)
+where η(l) =
+dU(l)
+dl U(l)† is the l-dependent generator of the unitary flow.
+For specific
+choices of η(l), the initial Hamiltonian H(0) eventually flows to its (block)-diagonal form,
+thus achieving the desired diagonalization. At each point of the flow, let us define the
+target Hamiltonian HT (l) as the diagonal part of H(l),
+HT (l) =
+�
+n
+ϵn(l) |n⟩ ⟨n| ,
+(13)
+9
+
+where we have defined ϵn(l) ≡ Hnn(l). One instance of a generator that achieves this is
+η = [HT , H], as originally proposed in [45, 48]. We shall refer to this specific choice as
+the Wegner flow, for simplicity, even when any Hamiltonian flow described by (12) and
+converging to HT (l) is generally referred to as a Wegner flow in the literature. Clearly,
+the choice η = [HT , H] is not the only possibility and we shall consider a different choice
+in an example below. Let us stress that the l-dependent diagonal entries ϵn(l) in Eq. (13)
+do not correspond to the Hamiltonian eigenvalues unless we have reached the end of the
+flow l = lf. In that case, the flowing Hamiltonian has been transformed into its diagonal
+form to coincide with the target part, H(lf) = HT (lf). The final lf is typically reached as
+l → ∞, as shown explicitly in the practical example below.
+By applying our general result (7) to the evolution (12), with t → l, At → H(l) and
+H(t) → −iη(l), we obtain the following OQSL on the Hamiltonian flow
+l ≥ lqsl,
+lqsl =
+∥H∥ arccos (H(0)|H(l))
+∥H∥2
+Vl
+,
+(14)
+where the speed, averaged over the interval [0, l], is given by
+Vl = 1
+l
+� l
+0
+∥[η(t), H(t)]∥dt.
+(15)
+For the rest of this section, we will only consider the case when (·|·) is the Hilbert-Schmidt
+inner product. In this case we have that ∥[η, H]∥ = Tr
+�[η, H]2�.
+4.1
+Dephasing-like Wegner flow
+Before applying the OQSL (14) in an explicit example, we show that the Wegner flow,
+although unitary, features formal similarities with a dephasing evolution, under which the
+off-diagonal entries of the density matrix ρ(t) decay and the fixed point is set by its diagonal
+part only. The crucial difference is that in the Wegner flow, the diagonal part evolves as
+well, and it does so in such a way that the total evolution is unitary and the final diagonal
+form coincides with the diagonalized initial Hamiltonian. Here we aim to characterize the
+decay of the off-diagonal elements Hnm(l) with n ̸= m and reveal its formal analogy with
+dephasing. To this end, let us adopt the approach of vectorization [77] and represent an
+operator A = �
+n,m Anm |n⟩ ⟨m| as a normalized vector
+|A⟩ =
+1
+∥A∥
+�
+n,m
+Anm |n, m⟩ ,
+(16)
+where |n, m⟩ = |n⟩ ⊗ |m⟩ and the normalization factor has been introduced to enhance
+the comparison with the evolution of a quantum state ρ. Now, since we are interested in
+the decay of the off-diagonal elements, let us introduce the (super)projector Q over the
+non-diagonal part of the Hamiltonian,
+Q = 1B − PHT ,
+(17)
+where 1B is the identity on the operator space B and PHT is the (super)projector over the
+target Hamiltonian
+PHT = |HT ⟩⟨HT | =
+1
+∥HT ∥2
+�
+n,m
+ϵnϵm |n, n⟩ ⟨m, m| .
+(18)
+10
+
+From this expression, it follows that PHT |HT ⟩ = |HT ⟩ and Q |HT ⟩ = 0. To characterize
+the dephasing-like decay realized by the Wegner flow, let us consider the overlap between
+the flowing Hamiltonian and its non-diagonal part
+AQ(l) ≡ ⟨H(l)| Q |H(l)⟩ ,
+(19)
+which quantifies how far H(l) is from being diagonal and vanishes as l → lf, that is as
+H(l) → HT (l). By substituting Eqs. (17) and (18) we obtain
+AQ(l) = 1 − ∥HT ∥2
+∥H∥2 ,
+(20)
+where we stress that ∥HT ∥2 = �
+n ϵ2
+n(l) depends on l. The quantity AQ identically van-
+ishes at the end of the flow, when the Hamiltonian is diagonalized and H(l) = HT (l).
+Remarkably, if we choose the Wegner generator to be η = [HT , H] [48], then AQ decays
+monotonically. Indeed, its decay rate reads as
+d
+dlAQ(l) = −
+1
+∥H∥2
+d
+dl
+�
+n
+ϵ2
+n =
+1
+∥H∥2
+d
+dl
+�
+n̸=m
+|Hnm|2,
+(21)
+where the last inequality follows from the conservation of the total norm,
+d
+dl∥H∥ = 0. If
+η = [HT , H] [48], it is straightforward to compute that
+dHnm
+dl
+=
+�
+k
+(ϵn + ϵm − 2ϵk)HnkHkm
+(22)
+and therefore
+d
+dlAQ(l) = −
+2
+∥H∥2
+�
+n,m
+(ϵn − ϵm)2|Hnm|2 < 0.
+(23)
+As a result, the overlap (19), quantifying how far we are from the target, is monotonically
+decreasing during the flow. This feature suggests an analogy with the well-known model of
+dephasing, where the purity is found to decrease monotonically [78], in a similar manner
+as in Eq. (23). To show this, let us consider the case of pure dephasing
+dρ
+dt = −[X, [X, ρ]],
+(24)
+where X is a time-independent Hermitian operator satisfying X |n⟩ = xn |n⟩. Then it can
+be shown [78] that the purity Tr ρ2 decreases monotonically with time as
+d Tr ρ2
+dt
+= −2
+�
+nm
+(xn − xm)2|ρmn|2.
+(25)
+Now, Eq. (23) can be also expressed as a “purity”-decay of the off-diagonal Hamiltonian
+Hoff-diag(l) = H(l) − HT (l) and it reads as
+d Tr H2
+off-diag
+dl
+= d
+dl
+�
+i̸=j
+|Hij|2 = −2
+�
+i,j
+(ϵi − ϵj)2|(Hoff-diag)ij|2,
+(26)
+which formally corresponds to Eq. (25) with ρ → Hoff-diag and X → HT . We conclude that
+the Wegner flow (12) generated by η = [HT , H],
+dH
+dl = [[HT , H], H],
+(27)
+which is unitary, suppresses the off-diagonal part of the Hamiltonian as if it was undergoing
+a dephasing evolution under the action of the diagonal part.
+11
+
+4.2
+Wegner and Toda flows
+As already advanced, there are several choices of the generator η for diagonalizing a given
+N × N matrix H(0). As a possible form, consider
+ηnm(l) = Hnm(l)sgn (m − n),
+(28)
+for m ̸= n and ηnn = 0. Equation (12) then reduces to
+dHnm(l)
+dl
+=
+�
+k
+Hnk(l)Hkm(l) [sgn (k − n) − sgn (m − k)] .
+(29)
+Further, assume that the matrix H(l) takes a symmetric tridiagonal form.
+Then, the
+equations for diagonal and off-diagonal components are written respectively as
+dHnn(l)
+dl
+= 2(H2
+n,n+1(l) − H2
+n−1,n(l))
+(n = 1, 2, . . . , N),
+(30)
+dHn,n+1(l)
+dl
+= Hn,n+1(l)(Hn+1,n+1(l) − Hnn(l))
+(n = 1, 2, . . . , N − 1),
+(31)
+with H01 = HN,N+1 = 0.
+This set of equations takes a closed form and is known as
+the Toda equations in classical nonlinear integrable systems [79–81]. We thus refer to the
+Hamiltonian flow generated by (28) as the Toda flow.
+We note that Eq. (23) is not satisfied in the present choice of η.
+However, it is still
+guaranteed that the matrix is diagonalized at large l due to the relation
+d
+dl
+k
+�
+n=1
+Hnn(l) = 2H2
+k,k+1(l) ≥ 0,
+(32)
+where k = 1, 2, . . . , N [82, 83].
+The relation for k = 1 denotes that H11(l) is a non-
+decreasing function. Since Tr H2(l) is independent of l, each component of H(l) is not di-
+vergent, if each component of the original matrix H0 takes a finite value. We conclude that
+liml→∞ H11(l) converges to a finite value and liml→∞ H12(l) = 0. Then, we examine the re-
+lation for k = 2 to conclude that liml→∞ H22(l) takes a finite value and liml→∞ H23(l) = 0.
+We can repeat the same consideration for the other values of k to conclude that H(l) is
+diagonalized at l → ∞ keeping the eigenvalues of the matrix unchanged.
+A possible realization of the tridiagonal matrix is the one-dimensional XY model with
+isotropic interaction [84],
+H(l) = 1
+2
+N−1
+�
+n=1
+vn(l) (XnXn+1 + YnYn+1) + 1
+2
+N
+�
+n=1
+hn(l)Zn.
+(33)
+In the z-basis, the second term represents the diagonal part and the first term represents
+the off-diagonal part. The corresponding generator of the time evolution is
+η(l) = i
+2
+N−1
+�
+n=1
+vn(l) (XnYn+1 − YnXn+1) ,
+(34)
+and the set of coupling functions {v1(l), v2(l), . . . , vN(l), h1(l), h2(l), . . . , hN−1(l)} satisfies
+the Toda equations
+dhn(l)
+dl
+= 2(v2
+n(l) − v2
+n−1(l)),
+(35)
+dvn(l)
+dl
+= vn(l)(hn+1(l) − hn(l)).
+(36)
+12
+
+Figure 3:
+OQSLs for the Wegner and Toda flows.
+The upper panels represent θ(l)
+=
+arccos
+�
+Tr(H(0)H(l))/∥H(0)∥2�
+(bold lines) and its bound
+� l
+0 ds ||[η(s), H(s)]||/||H|| (thin lines)
+for Wegner and Toda flows with N = 3 (left panel) and N = 10 (right). We set the initial matrix as
+a symmetric tridiagonal form and each component is taken from a uniform random number between
+−1 and 1. In the lower panels, we plot the sum of off-diagonal components �
+m̸=n H2
+mn(l).
+This Hamiltonian commutes with the total magnetization M = �N
+n=1 Zn and the matrix
+form of the single flip sector with M = ±(N − 2) takes a tridiagonal form.
+We plot examples of the Wegner and Toda flows in Fig. 3. We take a traceless symmetric
+tridiagonal matrix as an initial given Hamiltonian H(0) in which each nonzero component
+is taken from a uniform random number between −1 and 1. The numerical results in Fig. 3
+implies that the Toda flow gives a tight bound for a small l and becomes worse for a large
+l due to the nonmonotonic decay of the off-diagonal components.
+In Fig. 4, we show how the result is dependent on the dimension of the matrix N. For the
+Wegner flow, when N is not considerably large, the angle θ(l) between H(0) and H(l) grows
+faster by the l-evolution as N becomes large. In the Wegner flow, even though we start
+the time evolution from a tridiagonal form, the matrix breaks the band structure during
+the flow, which makes θ a large value. It does not necessarily give the property that the
+overlap (H(0)|H(l)) decays rapidly as a function of N, as we can see in some many-body
+systems exhibiting the orthogonality catastrophe. On the other hand, the Toda flow does
+not show any growing behavior as a function of N. This is due to the property that the
+tridiagonal form is kept throughout the time evolution. As for lqsl, a saturating behavior
+is seen for the Wegner flow and is not seen for the Toda flow.
+The independence of the Toda flow on the matrix dimension implies that we can find a
+tight OQSL for specific initial Hamiltonians. As we have discussed in section 3.1, saturation
+is possible when the flowing operator has support in only two of the eigenspaces of the
+generator. In what follows, we will consider the condition that the eigenvectors of the
+generator η(l) are l-independent.
+13
+
+0
+0
+2
+Todabound
+2
+Toda bound
+Wegner bound
+元/2
+元/2
+Wegnerbound
+Toda
+Wegner
+Toda
+Wegner
+N=3
+N=10
+0
+0
+0
+10
+20
+ZmnHmn?
+Zm≠nHmn?
+N=3
+4
+N=10
+Toda
+2
+Toda
+Wegner
+Wegner
+0
+0
+0
+10
+0
+20Figure 4: Plot of the θ(l) = arccos
+�
+Tr(H(0)H(l))/∥H(0)∥2�
+(top panels) and lqsl (bottom panels)
+for several values of N. We set the initial matrix as a symmetric tridiagonal form and each
+component is taken from a uniform random number between −1 and 1. The left panels represent
+the Wegner flow, while the right panels correspond to the Toda flow.
+Hereafter, we write Hnn(l) = hn(l) and Hn,n+1(l) = vn(l).
+The eigenvalue equation
+η(l)|ϕ⟩ = iλ(l)|ϕ⟩, with a real eigenvalue λ(l) and the corresponding eigenvector |ϕ⟩ is
+written as
+�
+�
+�
+�
+�
+�
+�
+�
+�
+ϕ2
+0
+−ϕ1
+ϕ3
+0
+0
+−ϕ2
+ϕ4
+...
+...
+0
+−ϕN−2
+ϕN
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+�
+v1(l)
+v2(l)
+v3(l)
+...
+vN−1(l)
+�
+�
+�
+�
+�
+�
+�
+�
+�
+= iλ(l)
+�
+�
+�
+�
+�
+�
+�
+�
+�
+ϕ1
+ϕ2
+ϕ3
+...
+ϕN−1
+�
+�
+�
+�
+�
+�
+�
+�
+�
+,
+(37)
+and −vN−1(l)ϕN−1 = iλ(l)ϕN, where (ϕ1, ϕ2, . . . , ϕN) denotes the l-independent eigenvec-
+tor |ϕ⟩. When the diagonal components of the matrix on the left-hand side are nonzero,
+the matrix is invertible and vn(l) for any index n is proportional to the same l-dependent
+function λ(l). The possibility that some of the components of |ϕ⟩ are identically zero is
+excluded since that condition only results in |ϕ⟩ = 0.
+As an exceptional case, we can find the eigenvector with λ(l) = 0 when N is odd. In that
+case, the eigenvector is written as
+|ϕ⟩ ∝
+�
+1, 0, v1(l)
+v2(l), 0, v3(l)v1(l)
+v4(l)v2(l), 0, . . . , 0, vN−2(l)vN−4(l) · · · v1(l)
+vN−1(l)vN−3(l) · · · v2(l)
+�T
+.
+(38)
+The l-independence of |ϕ⟩ gives the conditions v2k(l) ∝ v2k−1(l) with k = 1, 2, · · · , (N −
+1)/2.
+We note that the eigenvector with λ(l) = 0 is unique if it exists. Therefore, when we impose
+the condition that two of the eigenvectors of η(l) are l-independent, the dependence of η(l)
+14
+
+0
+N=3
+N=3
+N=10
+N=10
+Wegner
+N=20
+Toda
+N=20
+N=40
+N=40
+0
+N=100
+0
+N=100
+0
+10
+0
+20
+40
+IQSL
+40
+N=3
+N=3
+N=10
+IQSL
+N=10
+N=20
+N=20
+Toda
+10
+N=40
+N=40
+N=100
+N=100
+20
+Wegner
+0
+0
+10
+0
+20
+40on l is described by a single function f(l). Each of the nonzero components is written
+as
+vn(l) = f(l)vn.
+(39)
+We insert the condition (39) into Eqs. (30) and (31) to find
+h′
+n(l) = 2f2(l)(v2
+n − v2
+n−1),
+(40)
+f′(l) = f(l)(hn+1(l) − hn(l)),
+(41)
+where the prime symbol denotes the derivative with respect to l. The second equation (41)
+shows that hn(l) is a linear function in n. Since the constant shift hn(l) → hn(l) + h0 does
+not change Eqs. (30) and (31), we set �N
+n=1 hn(l) = 0 and obtain
+hn(l) = f′(l)
+f(l)
+�
+n − N + 1
+2
+�
+.
+(42)
+We use this form for the first equation (40). Then, v2
+n(l) is a quadratic function of n and
+f(l) obeys the differential equation
+�f′(l)
+f(l)
+�′
+= −2d1f2(l),
+(43)
+where d1 represents a constant. The corresponding form of vn is
+v2
+n = 1
+2d1n(N − n) + d0,
+(44)
+where d0 represents a constant.
+To determine d0, we look at the following condition, which follows from the conservation
+of the norm
+N
+�
+n=1
+h2
+n(l) + 2
+N−1
+�
+n=1
+v2
+n(l) = const.
+(45)
+Without losing the generality, we can put the form f(l) = cos θ(l). Using Eqs. (43) and
+(45), we find as the possible solution
+d0 = 0,
+(46)
+� θ′(l)
+cos θ(l)
+�2
+= 2d1.
+(47)
+The l dependence of each component is specified as hn(l) = hn sin θ(l) and vn(l) =
+vn cos θ(l). By representing d1 with respect to h1, we finally obtain
+hn(l) = − 2h1
+N − 1
+�
+n − N + 1
+2
+�
+sin θ(l),
+(48)
+v2
+n(l) = n(N − n)
+(N − 1)2 h2
+1 cos2 θ(l),
+(49)
+and
+θ′(l)
+cos θ(l) =
+2h1
+N − 1.
+(50)
+15
+
+Figure 5: Left: The parameters of the initial matrix H, {hn}n=1,2,··· ,N and {vn}n=1,2,··· ,N−1, result-
+ing in the tight bound in the Toda flow with N = 20. Right: θ(l) = arccos
+�
+Tr(H(0)H(l))/∥H(0)∥2�
+.
+We set l0 = (N − 1)/4h1 and sin θ(0) = 0.
+The differential equation for θ(l) is easily solved as
+sin θ(l) =
+sinh
+�
+4h1
+N−1l
+�
++ sin θ(0) cosh
+�
+4h1
+N−1l
+�
+cosh
+�
+4h1
+N−1l
+�
++ sin θ(0) sinh
+�
+4h1
+N−1l
+�.
+(51)
+In Fig. 5, we plot {hn}n=1,2,··· ,N, {vn}n=1,2,··· ,N−1, and θ(l) for N = 20.
+All components of the matrix H(l) are parameterized by a single l-dependent function θ(l),
+which implies that the time evolution can be denoted by a motion along an arc in the
+Bloch space. In fact, we find that θ(l) denotes the operator angle and the dynamics gives
+the tight bound:
+arccos
+����
+Tr(H(l)H(0))
+Tr(H(0)2)
+���� =
+� l
+0
+dt
+�
+Tr([η(t), H(t)]2)
+Tr(H(0)2)
+= θ(l) − θ(0).
+(52)
+5
+Operator Growth and Krylov Complexity
+In the previous section, we have considered the flow of an observable, the Hamiltonian,
+with respect to a parameter different than time. Here we illustrate another application of
+the OQSL, pointing out that operator flows need not necessarily concern an observable.
+In particular, given a Liouvillian operator L = [H, ·], we show that the geometrical OQSL
+(7) can also be applied to the unitary flow of a superoperator, generated under the action
+of S = [L, ·], which can be accordingly viewed as a “super Liouvillian”. This kind of flow
+arises naturally in characterizing the complexity of a given quantum evolution. Specifi-
+cally, in the context of operator growth, the notion of Krylov complexity [54, 58–62] has
+recently gained attention as a measure of operator complexity for the Heisenberg evolution
+of an observable under the action of a time-independent Hamiltonian. The evolution of
+simple, local observables into increasingly complex and nonlocal ones can be described as
+the operator spreading in the so-called Krylov space. As mentioned in section 3.2, the
+latter provides the minimal subspace in which the Heisenberg dynamics unfolds and is
+uniquely determined by the Hamiltonian of the system and the initial operator O0. Krylov
+complexity can then be understood as the mean position of the evolving operator Ot in
+the so-called Krylov basis. It can be expressed as an expectation value (Ot|KOt) of a cor-
+responding (super)operator K, known as the complexity operator. At this point, one can
+16
+
+Vn/h1
+0/(元/2)
+0
+hn/h1
+10
+20
+0
+0
+I/lo
+10
+nagain change representation and let the superoperators, such as K, evolve while keeping the
+observable |O) fixed. We shall call this representation the super-Heisenberg picture from
+the evident analogy with the standard Heisenberg representation of the quantum evolution
+in the Hilbert space. In this picture, the complexity operator evolves accordingly to the
+equation
+˙K = i[L, K]
+(53)
+and the corresponding unitary flow is constrained by the speed limit (7), upon identifying
+A and H with K and L, respectively. We note that our result (7) holds for finite dimensions
+and that the dimension of the Krylov space is always finite whenever the Hilbert space
+that the observables are defined over is finite [61].
+5.1
+Quantum dynamics in Krylov space
+Let us start by briefly recalling how the Krylov space and the corresponding notion of
+complexity are constructed. For a more detailed discussion, we refer to [54, 58–62]. The
+evolution in the Heisenberg picture of an operator Ot = eiHtO0e−iHt can be formally
+written in terms of the nested commutators with the Hamiltonian H, that is, the powers
+of the Liouvillian L = [H, ·], as Ot = �∞
+n=0
+(it)n
+n! LnO. The space explored during this
+evolution is given by the span of the infinite set {LnO}∞
+n=0 and is precisely the Krylov
+space. From this infinite set, one can extract an orthonormal, finite basis {On}D−1
+n=0 by
+applying the so-called Lanczos algorithm. The first element of the basis coincides with the
+initial operator O0, which we will assume to be normalized to one. Then, at each iterative
+step, the next orthogonal vector is constructed as |An+1) = L|On) − bn|On−1), where
+bn = ∥An∥ is the n-th Lanczos coefficient, and the corresponding element of the Krylov
+basis |On+1) is obtained upon normalization as On = An/bn. Throughout this section, we
+will use the Hilbert-Schmidt inner product (A|B) = Tr A†B between operators. By making
+use of the Krylov space, the unitary evolution of the operator Ot is effectively mapped to
+a hopping problem on the one-dimensional, semi-infinite chain represented by the Krylov
+basis {On}D−1
+n=0 , where the Lanczos coefficients bn play the role of hopping parameters and
+the Liouvillian, which takes the tridiagonal form
+L =
+D−1
+�
+n=0
+bn+1|On+1)(On| + bn|On−1)(On|,
+(54)
+with |O−1) = |OD) = 0, acts as an Hamiltonian for the so-called operator wavefunction
+|Ot). The Krylov complexity operator K is then defined as the position operator
+K =
+D−1
+�
+n=0
+n|On)(On|,
+(55)
+on this lattice. The most studied object in this context is the expectation value of the
+above (super)-operator with respect to Ot and is simply known as the Krylov complexity:
+K = (Ot|KOt). Its rate of growth is constrained by the speed limit
+|∂tK(t)| ≤ 2b1∆K,
+(56)
+introduced in [62] and known as the dispersion bound, given that (∆K)2 = (Ot|K2Ot) −
+(Ot|KOt)2 is the variance of K with respect to Ot. The dispersion bound is saturated
+17
+
+at any time if and only if the structure of Krylov space features the so-called complexity
+algebra (57), which we shall introduce below.
+It was pointed out in [59] that the Liouvillian in Krylov space, given by Eq. (54), can
+be written as the sum L = L+ + L− of raising and lowering operators that act on the
+Krylov basis as L+|On) = bn+1|On+1) and L−|On) = bn|On−1), respectively. It appears
+then natural to introduce a super-operator B = L+ − L−, conjugated to the Liouvillian,
+and consider their commutator ˜K = [L, B] [59]. The dispersion bound (56) is identically
+saturated if and only if these three operators close an algebra, which can only take the
+form [62]
+[L, B] = ˜K,
+[ ˜K, L] = αB,
+[ ˜K, B] = αL
+(57)
+and implies also that ˜K = αK + γ1, where α, γ ∈ R [59]. The Krylov complexity growth
+rate is then maximal [62]. It can be shown that γ is always a positive number and α is a
+real number satisfying the condition α = − 2γ
+D−1 for finite Krylov dimension D and α ≥ 0
+if D = ∞ [62]. Moreover, the algebraic closure (57), or equivalently the saturation of the
+bound (56), implies that the Lanczos coefficients evolve according to [59, 62]
+bn =
+�1
+4αn(n − 1) + 1
+2γn.
+(58)
+For α > 0, this dependence captures the asymptotic linear growth bn = √αn conjectured
+by Parker et al. to hold in generic non-integrable systems, leading to the maximal growth
+of Krylov complexity [54]. A paradigmatic example of this class of systems is the celebrated
+Sachdev-Ye-Kitaev (SYK) model [85].
+5.2
+Saturation of the OQSL by the complexity algebras
+In the “super” Heisenberg picture, the observable operator is kept fixed while the complexity
+operator K evolves unitarily according to
+Kt = e−iLtK0eiLt =
+∞
+�
+n=0
+(−i)n
+n!
+Sn(K0) tn,
+(59)
+where S = [L, ·] will be referred to as super Liouvillian. In the case of closed complexity
+algebras, thanks to the commutation relations (57), all the powers Sn(K0) reduce to terms
+proportional to either K0 or B. In particular, if α ̸= 0 one can show that [62]
+S2n(K0)
+=
+(−1)nαn−1(αK0 + γ1),
+(60)
+S2n+1(K0)
+=
+(−1)n+1αnB,
+(61)
+where the first equation clearly holds only for n > 0, being S0(K0) = K0. Conversely,
+when α = 0 only S(K0) = −B and S2(K0) = −γ1 survive, being Sn(K0) = 0 for n > 2.
+Thus,
+Kt =
+�
+(1 − α)K0 − γ1 + cosh(√αt)
+�K0 + γ
+α1
+� + i sinh(√αt) 1
+αB
+α ̸= 0,
+K0 + iBt + γ
+2t21
+α = 0.
+(62)
+Equation (59), together with Eqs. (60)-(61), implies that whenever the dispersion bound
+(56) is saturated, the full time-evolution of the Krylov complexity operator Kt must be
+18
+
+contained in a 3-dimensional space, spanned by the identity 1, the initial complexity K0
+and B = [K0, L]:
+Kt ∈ Span{1, K0, B}.
+(63)
+This space defines the “super” Krylov space of Krylov complexity itself and turns out to
+be dramatically simplified by the assumption of closed complexity algebra. From the dis-
+cussion in section 3.2, we can conclude that Kt having a 3-dimensional Krylov space is a
+sufficient condition for it to saturate the refined OQSL (10). We recall that here At and L
+are replaced by Kt and S, respectively. Then Eq. (63) implies that K has support in only
+three eigenspaces of S, one of them corresponding to the eigenvalue 0: Kt = P0+Pω +P−ω.
+Therefore, we conclude that the super operator Kt − P0 saturates the OQSL (10); that is,
+it evolves along a geodesic trajectory. In other words, the maximal growth rate of Krylov
+complexity, leading to the saturation of the dispersion bound (56), is equivalent to the
+geodesic evolution of the Krylov complexity operator, provided that we subtract its sta-
+tionary component P0. Indeed, we remark that P0 is necessarily different from zero since
+Tr K ̸= 0, and must be removed to obtain a tight OQSL. From the explicit computation
+performed below, we shall conclude that the identity is indeed the only stationary compo-
+nent of the Krylov complexity, i.e., P0 = Tr K
+1
+∥1∥2 . By doing so, we shall also explicitly
+assess the improvement achieved by replacing the OQSL (7) with its refined counterpart
+(10).
+5.3
+Computation of the OQSL for the complexity algebras
+The geometrical OQSL (7) for the Krylov complexity reads as
+t ≥ ∥K0∥
+arccos
+� (K0|Kt)
+∥K0∥2
+�
+∥[L, K0]∥
+,
+(64)
+where, given a time-independent Liouvillian L, the velocity of the flow ∥[L, K0]∥ is constant.
+The initial complexity K0 coincides with the usual Krylov complexity operator (55) in the
+standard Heisenberg picture. In order to assess its deviation from saturation, we explicitly
+evaluate the OQSL (64) in the case of the SU(2) complexity algebra, that is, when the
+complexity growth saturates the dispersion bound (56) in finite dimension [62]. Let us
+define VK ≡ ∥K0∥−1∥[L, K0]∥ as the (normalized) velocity of the complexity flow.
+By
+explicit computation in the Krylov basis, one can verify that VK, being [L, K0] = −B by
+construction, always reduces to
+V2
+K = ∥B∥2
+∥K0∥2 =
+2
+∥K0∥2
+D−1
+�
+n=1
+b2
+n,
+(65)
+where the norm of the complexity is fixed by the Krylov dimension as
+∥K0∥2 =
+D−1
+�
+n=0
+n2 = D(D − 1)(2D − 1)
+6
+.
+(66)
+The velocity (65) of the complexity flow is maximized whenever the Lanczos coefficients
+growth is maximal, i.e., linear in n, which is the case for maximally chaotic systems accord-
+ing to the universal growth hypothesis [54]. Indeed, by focusing on the initial scrambling
+period and neglecting the role of the following plateau and descent in the bn’s [61], we
+19
+
+conclude that a sub-polynomial behavior bn ∝ nδ with 0 < δ < 1 always leads to a smaller
+velocity VK than the linear growth bn ∝ n. We stress that this observation also holds for
+infinite-dimensional Krylov spaces. As shown below, the velocity (65) remains finite in
+this limit, and once we fix the proportionality constant, the velocity is maximized by the
+linear growth of the bn’s. In other words, according to the universal growth hypothesis
+[54], complexity flows at the highest speed in maximally chaotic systems.
+Let us now focus on the instances of Krylov dynamics that saturate another notion of the
+speed limit for operator growth, namely the above-mentioned dispersion bound (56). As
+reviewed above, in such cases, the dynamics of Krylov complexity is determined by an
+underlying 3-dimensional algebra [62] and the Lanczos coefficients obey Eq. (58). As a
+result, the velocity (65) of the complexity flow can be expressed as
+V2
+K = α(D − 2) + 3γ
+2D − 1
+.
+(67)
+Before restricting the analysis to the finite-dimensional case α < 0, where the geometrical
+QSL (7) can be applied, let us stress that this notion of velocity is well defined also in
+the limit D → ∞, where α ≥ 0. In particular, if α > 0, when the Krylov complexity
+diverges exponentially with time as K(t) ∼ e
+√αt [59, 62], we obtain that VK →
+�
+α/2:
+the speed of the complexity operator flow is proportional to the characteristic time scale
+of the exponential divergence of the Krylov complexity. Instead, if α = 0, which leads to
+a quadratic divergence of K [59, 62], the above-defined speed of the flow vanishes. This
+singular behavior can be understood as the QSL (64), derived under the assumption of
+finite dimension D, may not have a well-defined counterpart for D → ∞. In particular,
+as we shall see below, the numerator in Eq. (64) also vanishes for α = 0, resulting in
+an indeterminate form 0/0. Finally, for the Krylov dynamics to saturate the dispersion
+bound (56) over a finite-dimensional space, the underlying complexity algebra must be that
+of SU(2), corresponding to the case α < 0 [62]. In such case, given the condition bD = 0,
+the parameters α and γ of Eq. (58) are subject to the further constraint 2γ = |α|(D−1) [62],
+which also ensures the expression (67) to be positive. Indeed, the velocity of the complexity
+flow generated by the SU(2) algebra reduces to V2
+K = |α|(D + 1)/[2(2D − 1)]. For this
+class of models, we compute the QSL (64) exactly, thus establishing a direct comparison
+between the geometrical OQSL introduced in the present work and the dispersion bound
+that constraints the growth of Krylov complexity [62].
+In addition to the velocity of the flow, the other quantity that characterizes the speed limit
+is the notion of distance spanned during the evolution, which appears at the numerator of
+Eqs. (7) and (64) and is given in terms of the autocorrelation function, i.e., the operator
+overlap.
+In the case of closed complexity algebras, the autocorrelation function of the
+complexity
+(K0|Kt) =
+∞
+�
+n=0
+(−i)n
+n!
+(K0|Sn(K0)) tn
+(68)
+can be explicitly evaluated by making use of Eqs. (60)-(61). We note that, since (K0|B) = 0,
+only the even powers of the super Liouvillian S contribute to the sum in Eq. (68). Moreover,
+the only finite-dimensional case where we can straightforwardly apply the OQSL (64) is
+that of the SU(2) complexity algebra, i.e., when α < 0.
+For this class of models, by
+substituting Eqs. (60)-(61) into the expression (68) and recognizing the Taylor expansion
+20
+
+a
+0
+5
+10
+15
+20
+25
+30
+-1.0
+-0.5
+0.0
+0.5
+1.0
+t
+SU(2)
+Geodesic
+b
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+0.0
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+t
+QSL
+t
+Figure 6: We illustrate the deviation from the saturation of the OQSL (64) for the SU(2) complexity
+algebra, with Krylov dimension D = 1000 and α = −1. a We compare the evolution (69) of the
+complexity autocorrelation function (K0|Kt) (red curve) with the geodesic trajectory (K0|Kt)|geodesic
+(71) (blue dashed curve). b We show the left and right-hand side of the inequality (70) (blue dashed
+and red curves, respectively). The OQSL is tight only near t = 0, and the deviation increases with
+time.
+of the cosine, we obtain
+(K0|Kt) = (∥K∥2 + γ
+α Tr K) cos
+�
+|α|t − γ
+α Tr K,
+(69)
+where Tr K = D(D − 1)/2 and ∥K∥2 is given by Eq. (66). Therefore, in the case of the
+SU(2) complexity algebra, the autocorrelation function (K0|Kt) oscillates at the frequency
+�
+|α|, which, we note, is half the frequency of oscillation of the Krylov complexity K itself
+[62]. By substituting Eq. (69) into Eq. (64) and using that 2γ = |α|(D − 1), we rewrite
+the OQSL as
+t ≥ 1
+VK
+arccos
+��
+1 − 3(D − 1)
+2(2D − 1)
+�
+cos
+�
+|α|t + 3(D − 1)
+2(2D − 1)
+�
+,
+(70)
+where V2
+K = |α|(D + 1)/[2(2D − 1)]. As argued above, we expect this bound not to be
+tight due to the presence of a stationary component in the complexity flow given by the
+non-vanishing of its trace. We illustrate the deviation from the geodesic trajectory
+(K0|Kt)|geodesic = ∥K∥2 cos VKt
+(71)
+and the divergence of the two sides of Eq. (70) in Fig. 6. In what follows, we shall explicitly
+remove the stationary component of the complexity flow, thus proving the saturation of
+the refined OQSL (10) and showing its equivalence with the dispersion bound (56).
+Finally, although the framework of the geometrical QSL requires a finite dimension, it is
+instructive to consider the behavior of the quantities involved in Eq. (64) as D → ∞. In
+particular, we have already stressed above that the velocity VK (65) of the complexity flow
+remains finite, is non-zero for α > 0 and vanishes for α = 0. Moreover, from Eq. (68), with
+analogous steps as for the SU(2), we obtain that for α = 0 the autocorrelation function
+behaves as (K0|Kt) = ∥K∥2 + γ
+2t2. At any finite time, this implies the vanishing of the
+numerator of the QSL (64), since the argument of the arccosine approaches 1 as D → ∞.
+The evaluation of the limit of the full expression yields as a result that τQSL → 0 as D → ∞
+in the case of the HW algebra, i.e., for α = 0. Conversely, the notion of distance employed
+in our QSL (7) is not well defined in the case α > 0, since the normalized autocorrelation
+function diverges exponentially with time, (K0|Kt)/∥K∥2 ∼ exp{√αt}.
+21
+
+5.3.1
+Saturation of the refined OQSL
+The fact that the Krylov complexity operator Kt cannot saturate the OQSL (64) is al-
+ready evident from the observation that Tr Kt ̸= 0, as this condition results in a non-zero
+stationary component P0. In particular, the trace accounts for the stationary component
+along the identity. Removing the trace is sufficient to achieve saturation only if there are
+no other stationary components of Kt, meaning that the zero eigenvalue of the super Li-
+ouvillian S has no degeneracy, such that the corresponding eigenspace is spanned by the
+identity. We explicitly show that this is indeed the case for closed complexity algebras.
+In this sense, the dispersion bound (56) and the OQSL (10) provide a unique constraint
+on the operator growth in Krylov space and the saturation of the former automatically
+implies the saturation of the latter.
+Let us, therefore, consider the operator Kt obtained by subtracting from the Krylov com-
+plexity its component along the identity:
+Kt = Kt − (Kt|1)
+1
+∥1∥2 ,
+(72)
+where (Kt|1) = Tr K and ∥1∥2 = D. The OQSL (7) for Kt reads as
+t ≥
+arccos
+� (K0|Kt)
+∥K∥2
+�
+VK
+,
+(73)
+where V2
+K = ∥B∥2/∥K∥2.
+Now, by using Eq. (66) and that Tr K = D(D − 1)/2, we
+obtain
+∥K∥2 = ∥K∥2 − (Tr K)2
+D
+= D(D2 − 1)
+12
+.
+(74)
+Moreover, in the case of SU(2) complexity algebra, from Eq. (58) with α < 0 and 2γ =
+|α|(D − 1) we find
+∥B∥2 = 2
+D−1
+�
+n=1
+b2
+n = |α|D(D2 − 1)
+12
+.
+(75)
+By taking the ratio of the expressions above, we conclude that the velocity of the Kt flow
+for the SU(2) complexity algebra is VK =
+�
+|α|. On the other hand, the autocorrelation
+function (K0|Kt) can be computed analogously to the one of Kt in Eqs. (68)-(69), with
+the only difference that now Tr K = 0. We thus obtain
+(K0|Kt) = ∥K∥2 cos
+�
+|α|t = ∥K∥2 cos VKt,
+(76)
+which implies that the inequality in the OQSL (73) reduces t an identity at any time. In
+conclusion, the saturation of the dispersion bound (56) in finite dimension implies that
+the Krylov complexity Kt also saturates the refined OQSL (10) with P0 = 1 Tr K/D. We
+illustrate this saturation in Fig. (7). From the comparison between Figs. 6 and (7) we can
+assess the efficiency of the refined OQSL (10) in yielding a tight evolution by removing the
+components that do not contribute dynamically to the flow.
+6
+Conclusions, Discussion and Outlook
+Conventional QSLs bound the minimum time for the completion of a process by quantifying
+the distance traveled by the system along the evolution in state space. OQSLs generalize
+22
+
+a
+0
+10
+20
+30
+40
+50
+-1.0
+-0.5
+0.0
+0.5
+1.0
+t
+SU(2)
+Geodesic
+b
+0
+2
+4
+6
+8
+10
+0
+2
+4
+6
+8
+10
+t
+QSL
+t
+Figure 7: Illustration of the saturation of the OQSL (73) for the SU(2) complexity algebra, with
+Krylov dimension D = 1000 and α = −1. a The complexity autocorrelation function (K0|Kt) (76)
+(red curve) is shown to match the geodesic trajectory (blue dashed curve). b The left-hand and
+right-hand sides of the inequality (73) (blue dashed and red curves, respectively). The OQSL reduces
+to an identity at any time.
+the scope of conventional QSL to account for processes described in terms of operator flows,
+i.e., the change of an operator resulting from a conjugation by a one-parameter unitary [56].
+In this work, we have introduced a geometric OQSL that holds for arbitrary unitaries, i.e.,
+whether the generator of flow is parameter dependent or not. In addition, we have shown
+the bound to be tight and identified the required conditions for its saturation. This has
+led us to introduce a refined OQSL upon identifying the subspace in which the dynamics
+unfolds.
+The usefulness of these OQSLs has been illustrated in the context of a continuous renor-
+malization group formulated as a Wegner Hamiltonian flow for block diagonalization. In
+this context, we have shown that Wegner’s choice of the flow generator leads to a mono-
+tonic decay of the off-diagonal elements of the flowing Hamiltonian towards the target
+block-diagonal one. However, such a choice does not saturate the OQSL. By contrast, an
+alternative choice of the generator associated with the Toda flow can lead to the satura-
+tion of the OQSL for a specific family of initial Hamiltonians. Beyond the case of Wegner
+Hamiltonian flows, we expect our results to apply to other schemes for Hamiltonian diag-
+onalization, such as those relying on the Schrieffer-Wolff transformation [86].
+We have further discussed the implication of our results in the context of operator growth
+in Krylov space. In this representation, the time evolution of an operator is analogous
+to the spreading of a particle in the Krylov lattice, where the mean position is a proxy
+for operator complexity. The conditions for maximal operator growth are then associated
+with the saturation of the dispersion bound [62], which occurs when the Lanczos coeffi-
+cients exhibit a specific dependence on the lattice site index. Here, we have introduced
+a “super-Heisenberg” representation of the Krylov complexity operator generated by a su-
+per Liouvillian.
+Making use of the OQSL in such representation, we have shown that
+the saturation of the dispersion bound implies the saturation of the OQSL for the Krylov
+complexity operator. The application of OQSL to other complexity measures, such as the
+family of q-complexities including out-of-time-order correlators [54], offers an interesting
+prospect.
+Beyond these examples, we expect OQSLs to find manifold applications in the characteri-
+zation of nonequilibrium phenomena, such as the crossing of a quantum phase transition,
+the equilibration and thermalization of isolated many-body systems, quantum thermody-
+23
+
+namic processes, quantum control, and quantum annealing. In addition, OQSL may be
+used in the study of integrable systems, using the zero-curvature representation [87], Lax
+pairs [88], and Hamiltonian deformations [89–91].
+The generalization of our results to
+dissipative quantum systems would be highly desirable, given its prospective applications,
+e.g., to the description of open quantum dynamics in Heisenberg’s representation and the
+quest for fundamental limits to nonunitary operator growth [92, 93].
+7
+Acknowledgements
+It is a pleasure to acknowledge discussions with Léonce Dupays, Íñigo L. Egusquiza and
+Federico Roccati. KT acknowledges support by JSPS KAKENHI grant No. JP20K03781
+and No. JP20H01827.
+Appendices
+A
+Proving bijection between positive semi-definite inner-products and positive semi-
+definite operators
+Lemma 1. Let P ∈ End(B) be a positive semi-definite superoperator. The binary operation
+⟨·, P·⟩h : B × B → R is a positive semi-definite inner product on B.
+Proof. We need to show that the map ⟨·, P·⟩h satisfies linearity, Hermitian symmetry, and
+positive semi-definiteness.
+Linearity
+Consider any triplet of operators A, B and C and a complex number λ. We then have
+⟨A, PλB⟩h = ⟨A, λPB⟩h = λ⟨A, PB⟩h
+(77)
+⟨A, P(B + C)⟩h = ⟨A, PB + PC⟩h = ⟨A, PB⟩h + ⟨A, PC⟩h,
+(78)
+where we have used the linearity of the Hilbert-Schmidt inner product and the superoperator.
+Hermitian symmetry
+For any pair of operators A and B we have
+⟨A, PB⟩h = ⟨PB, A⟩∗
+h = ⟨B, P†(A)⟩∗
+h = ⟨B, PA⟩∗
+h,
+(79)
+where we have used the Hermitian symmetry property of the Hilbert-Schmidt inner product
+and the fact that a positive semi-definite superoperator is self-adjoint.
+Positive semi-definiteness
+From the definition of positive semi-definiteness of a superoperator it follows directly that
+⟨A, PA⟩h ≥ 0,
+(80)
+for any operator A.
+■
+Proposition 2. Given the Hilbert space (B, ⟨·, ·⟩h), the map P �→ ⟨·, P·⟩h is a bijection
+between the set of positive semi-definite operators on (B, ⟨·, ·⟩h) and the set of positive
+semi-definite inner products on B.
+24
+
+Proof. We can prove that the map is a bijection if we can prove that it is injective and
+surjective.
+Injectivity
+Suppose that ⟨·, P·⟩h = ⟨·, η(·)⟩h for some pair of superoperators P and η. It follows that
+⟨·, P·⟩h = ⟨·, η(·)⟩h ⇐⇒ ⟨A, PB⟩h = ⟨A, η(B)⟩h
+∀A, B ∈ B
+⇐⇒ P = η.
+(81)
+Surjectivity
+Given any positive semi-definite inner product (·|·), we want to construct a positive semi-
+definite superoperator P such that (·|·) = ⟨·, P·⟩h. Let M1, M2 . . . Mn2 be an operator basis
+in B and ak and bk be the corresponding components of A and B. Define ⟨Mi, PMj⟩h =
+(Mi|Mj). This superoperator is positive semi-definite since
+⟨A, PB⟩H =
+n2
+�
+i=1
+n2
+�
+j=1
+a∗
+i bj⟨Mi, PMj⟩H =
+n2
+�
+i=1
+n2
+�
+j=1
+a∗
+i bj(Mi|Mj)
+= (A|B)
+=⇒
+⟨A, PA⟩H = (A|A) ≥ 0,
+(82)
+from which it is also clear that P maps to (·|·).
+■
+B
+The kernel of seminorms
+Proposition 3. Let ∥·∥ be the seminorm induced by the positive semi-definite inner product
+⟨·, P·⟩h. It is then the case that ∥A∥ = 0 ⇐⇒ PA = 0.
+Proof. Let {Mk}n2
+k=0 be an orthonormal eigenbasis of P such that λk is the eigenvalue
+corresponding to the eigenvector Mk. Let ak be the components of an operator A. We
+then have
+⟨A, PA⟩H =
+n2
+�
+i=1
+n2
+�
+j=1
+a∗
+i aj⟨Mi, PMj⟩H =
+n2
+�
+i=1
+n2
+�
+j=1
+a∗
+i ajλjδij
+=
+n2
+�
+k=1
+|ak|2λk.
+(83)
+Since λk ≥ 0, this sum can only be zero if ak = 0 for λk > 0, in other words, A lies in the
+kernel of P.
+■
+C
+Proof of equation 4
+Proof. Define ˜A = A− ˆA. We can choose an orthogonal basis M1, M2, . . . Md, N1, N2, . . . Nn−d,
+such that the operators Mk and Nk span im(P) and ker(P) respectively and d is the di-
+mension of im(P). Let ak be the components of A with respect to this basis. We have
+that
+P ˜A = P(A − ˆA) = PA − P ˆA
+=
+d
+�
+k=1
+akPMk +
+n−d
+�
+k=1
+akPNk −
+d
+�
+k=1
+akPMk = 0.
+(84)
+25
+
+Using this together with linearity of (·|·), we get
+(A|B) = ( ˆA| ˆB) + ( ˆA| ˜B) + ( ˜A| ˆB) + ( ˜A| ˜B) = ( ˆA| ˆB) = ⟨ ˆA| ˆB⟩ ,
+(85)
+where the step to the second equality follows from proposition 3 and the last step follows
+from the definition of ⟨·, ·⟩.
+■
+D
+Smallest subspace containing the dynamics
+Let V be a real or complex finite dimensional vector space and let L be a linear endo-
+morphism on V . Assuming that L is diagonalizable, we can write L = �d
+i=1 liPi, where
+li are the d distinct eigenvalues of L and Pi are the projections onto the corresponding
+eigenspaces satisfying �d
+i=1 Pi = I and PiPj = δijPi. Here I is the identity map on V . It
+follows from the definition of the exponential function that eLt = �d
+i=1 elitPi. Consider
+now any initial vector v in V evolving according to v(t) = eLtv. Let us define the subspace
+W = span{vi}i∈I where i ∈ I ⇐⇒ vi := Piv ̸= 0. We then have that v(t) = �
+i∈I elitvi
+and we see that the evolution is entirely contained in W. Given a proper time interval
+T ⊂ R, we now ask whether W is the smallest subspace for which {v(t) : t ∈ T} is con-
+tained in.9 The answer is affirmative. To show this, first, note that the functions elit with
+domain T are linearly independent given that all eigenvalues li are distinct. This implies
+that
+�
+i∈I
+cielit = 0 ∀t ∈ T ⇐⇒ ci = 0 ∀i ∈ I,
+(86)
+where ci ∈ C. We will use proof by contradiction to show that W must be the smallest
+subspace. Assume that there exists a subspace ˜W containing the evolution with a dimen-
+sion strictly smaller than W. We must then have the evolution contained in the subspace
+given by the intersection F = W ∩ ˜W. By our assumption, F must then have a dimen-
+sion strictly smaller than W. This implies that there exists a non-zero linear functional
+w with domain W for which F ⊂ ker(w). We can expand this functional in the basis
+{fi}i∈I defined by fi(vj) = δij so that w = �
+i∈I wifi, where wi = w(vi). We get that
+w
+�v(t)
+� = 0 ∀t ∈ T ⇐⇒ �
+i∈I wielit = 0 ∀t ∈ T. This last expression together with (86)
+implies that wi = 0 ∀i ∈ I ⇐⇒ w = 0. Thus, we have reached a contradiction; hence, W
+is the smallest subspace containing {v(t) : t ∈ T}.
+The proof can be carried out analogously for the case when L is time dependent but
+commutes, i.e., [L(t1), L(t2)] = 0 ∀t1, t2 ∈ T.
+E
+Optimal refinement
+Consider the decomposition ˆA = S + Vt discussed in section 2.3 and assume that the
+subspace ker(L) ∩ HP does not change over time. Suppose Vt has a non-zero projection
+S′ onto ker(L) ∩ HP then S′ is guaranteed to remain unchanged since we have by the
+assumption that ker(L) ∩ HP is time-independent. Let V ′
+t be the orthogonal complement
+so that V = S′ + V ′
+t . It follows that
+⟨V, Vt⟩ = (V |Vt) = (S′ + V ′|S′ + V ′
+t ) = (V ′|V ′
+t ) +
+��S′��2.
+(87)
+9A proper interval is an interval in R excluding the empty set and singletons.
+26
+
+This implies that
+Re(V ′|V ′
+t ) = Re(V |Vt) −
+��S′��2 = Re C(t) − ∥S∥2 −
+��S′��2 = Re C(t) −
+��S + S′��2,
+(88)
+where the last equality follows from the assumption Re⟨S, Vt⟩ = 0. We can thus improve
+the speed limit further whenever S′ ̸= 0 since we would then have that ∥S + S′∥ > ∥S∥ +
+∥S′∥ > ∥S∥. The operator P0 = S + S′ is precisely the orthogonal projection of ˆAt onto
+ker(L) ∩ HP.
+F
+Proving orthogonality from the preservation of norm
+We here want to show that the operators P0, Xω and Yω in (11) are orthogonal and that
+Xω and Yω have the same norm. Using (11), we get that
+∥At∥2 = ∥P0∥2 + ∥Pω∥2 + ∥P−ω∥2 + 2 cos θ(t) Re⟨P0, Xω⟩ + 2 cos(2θ(t)) Re⟨Pω, P−ω⟩
+(89)
+= ∥P0∥2 + ∥Pω∥2 + ∥P−ω∥2 + 2 sin θ(t) Re⟨P0, Yω⟩ + 2 cos(2θ(t)) Re⟨Pω, P−ω⟩.
+(90)
+At time t = 0, we have that θ(0) = 0 and we get from expression (89) and (90) that
+Re⟨P0, Xω⟩ = 0. Assuming that θ(t) is not zero over the whole interval [0, τ], we can
+conclude from Re⟨P0, Xω⟩ = 0, (89) and (90) that Re⟨P0, Yω⟩ = 0 must also hold. This
+in turn implies that Re⟨Pω, P−ω⟩ = 0 since ∥At∥ must be constant. This last equality
+guarantees that the norm of Xω and Yω are equal. Note that in the case when θ(t) = 0
+over the whole interval, we have that the dynamics is stationary.
+References
+[1] P. Pfeifer and J. Fröhlich, “Generalized time-energy uncertainty relations and bounds
+on lifetimes of resonances,” Rev. Mod. Phys. 67, 759–779 (1995).
+[2] P. Busch, “The time–energy uncertainty relation,” in Time in Quantum Mechanics,
+edited by J. G. Muga, R. S. Mayato, and Í. L. Egusquiza (Springer Berlin Heidelberg,
+Berlin, Heidelberg, 2008) pp. 73–105.
+[3] L. S. Schulman, “Jump time and passage time: The duration ofs a quantum transition,”
+in Time in Quantum Mechanics, edited by J. G. Muga, R. Sala Mayato,
+and Í. L.
+Egusquiza (Springer Berlin Heidelberg, Berlin, Heidelberg, 2008) pp. 107–128.
+[4] V. V. Dodonov and A. V. Dodonov, “Energy–time and frequency–time uncertainty
+relations: exact inequalities,” Physica Scripta 90, 074049 (2015).
+[5] L. Mandelstam and I. Tamm, “The uncertainty relation between energy and time
+in non-relativistic quantum mechanics,” in Selected Papers, edited by Boris M. Bolo-
+tovskii, Victor Ya. Frenkel,
+and Rudolf Peierls (Springer Berlin Heidelberg, Berlin,
+Heidelberg, 1991) pp. 115–123.
+[6] S. Deffner and S. Campbell, “Quantum speed limits: from heisenberg’s uncertainty
+principle to optimal quantum control,” Journal of Physics A: Mathematical and The-
+oretical 50, 453001 (2017).
+[7] Z. Gong and R. Hamazaki, “Bounds in nonequilibrium quantum dynamics,” Interna-
+tional Journal of Modern Physics B 36, 2230007 (2022).
+27
+
+[8] N. Margolus and L. B. Levitin, “The maximum speed of dynamical evolution,” Physica
+D: Nonlinear Phenomena 120, 188–195 (1998), proceedings of the Fourth Workshop
+on Physics and Consumption.
+[9] B. Zieliński and M. Zych, “Generalization of the margolus-levitin bound,” Phys. Rev.
+A 74, 034301 (2006).
+[10] N. Margolus, “The finite-state character of physical dynamics,” arXiv e-prints ,
+arXiv:1109.4994 (2011), arXiv:1109.4994 [quant-ph] .
+[11] A. Uhlmann, “An energy dispersion estimate,” Physics Letters A 161, 329–331 (1992).
+[12] S. Deffner and E. Lutz, “Energy–time uncertainty relation for driven quantum sys-
+tems,” Journal of Physics A: Mathematical and Theoretical 46, 335302 (2013).
+[13] M. Okuyama and M. Ohzeki, “Comment on ‘energy-time uncertainty relation for
+driven quantum systems’,” Journal of Physics A: Mathematical and Theoretical 51,
+318001 (2018).
+[14] M. M. Taddei, B. M. Escher, L. Davidovich, and R. L. de Matos Filho, “Quantum
+speed limit for physical processes,” Phys. Rev. Lett. 110, 050402 (2013).
+[15] A. del Campo, I. L. Egusquiza, M. B. Plenio,
+and S. F. Huelga, “Quantum speed
+limits in open system dynamics,” Phys. Rev. Lett. 110, 050403 (2013).
+[16] S. Deffner and E. Lutz, “Quantum speed limit for non-markovian dynamics,” Phys.
+Rev. Lett. 111, 010402 (2013).
+[17] F. Campaioli, F. A. Pollock,
+and K. Modi, “Tight, robust, and feasible quantum
+speed limits for open dynamics,” Quantum 3, 168 (2019).
+[18] L. P. García-Pintos and A. del Campo, “Quantum speed limits under continuous
+quantum measurements,” New Journal of Physics 21, 033012 (2019).
+[19] B. Shanahan, A. Chenu, N. Margolus,
+and A. del Campo, “Quantum speed limits
+across the quantum-to-classical transition,” Phys. Rev. Lett. 120, 070401 (2018).
+[20] M. Okuyama and M. Ohzeki, “Quantum speed limit is not quantum,” Phys. Rev. Lett.
+120, 070402 (2018).
+[21] N. Shiraishi, K. Funo, and K. Saito, “Speed limit for classical stochastic processes,”
+Phys. Rev. Lett. 121, 070601 (2018).
+[22] S. B. Nicholson, L. P. García-Pintos, A. del Campo,
+and J. R. Green, “Time–
+information uncertainty relations in thermodynamics,” Nature Physics 16, 1211–1215
+(2020).
+[23] V. T. Vo, T. Van Vu, and Y. Hasegawa, “Unified approach to classical speed limit
+and thermodynamic uncertainty relation,” Phys. Rev. E 102, 062132 (2020).
+[24] T. Van Vu and Y. Hasegawa, “Geometrical bounds of the irreversibility in markovian
+systems,” Phys. Rev. Lett. 126, 010601 (2021).
+[25] L. P. García-Pintos, S. B. Nicholson, J. R. Green, A. del Campo, and A. V. Gorshkov,
+“Unifying quantum and classical speed limits on observables,” Phys. Rev. X 12, 011038
+(2022).
+[26] I. Bengtsson and K. Życzkowski, Geometry of Quantum States: An Introduction to
+Quantum Entanglement, 2nd ed. (Cambridge University Press, 2017).
+[27] D. P. Pires, M. Cianciaruso, L. C. Céleri, G. Adesso, and D. O. Soares-Pinto, “Gen-
+eralized geometric quantum speed limits,” Phys. Rev. X 6, 021031 (2016).
+[28] F. Campaioli, F. A. Pollock, F. C. Binder, and K. Modi, “Tightening quantum speed
+limits for almost all states,” Phys. Rev. Lett. 120, 060409 (2018).
+28
+
+[29] N. Hörnedal, D. Allan,
+and O. Sönnerborn, “Extensions of the mandelstam–tamm
+quantum speed limit to systems in mixed states,” New Journal of Physics 24, 055004
+(2022).
+[30] M. Bukov, D. Sels, and A. Polkovnikov, “Geometric speed limit of accessible many-
+body state preparation,” Phys. Rev. X 9, 011034 (2019).
+[31] T. Fogarty, S. Deffner, T. Busch, and S. Campbell, “Orthogonality catastrophe as a
+consequence of the quantum speed limit,” Phys. Rev. Lett. 124, 110601 (2020).
+[32] K. Suzuki and K. Takahashi, “Performance evaluation of adiabatic quantum computa-
+tion via quantum speed limits and possible applications to many-body systems,” Phys.
+Rev. Research 2, 032016 (2020).
+[33] A. del Campo, “Probing quantum speed limits with ultracold gases,” Phys. Rev. Lett.
+126, 180603 (2021).
+[34] R. Hamazaki, “Speed limits for macroscopic transitions,” PRX Quantum 3, 020319
+(2022).
+[35] S. L. Braunstein, C. M. Caves, and G. J. Milburn, “Generalized uncertainty relations:
+Theory, examples, and lorentz invariance,” Annals of Physics 247, 135–173 (1996).
+[36] V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nature
+Photonics 5, 222–229 (2011).
+[37] G. Tóth and I. Apellaniz, “Quantum metrology from a quantum information science
+perspective,” Journal of Physics A: Mathematical and Theoretical 47, 424006 (2014).
+[38] M. Beau and A. del Campo, “Nonlinear quantum metrology of many-body open sys-
+tems,” Phys. Rev. Lett. 119, 010403 (2017).
+[39] T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V. Giovannetti,
+and
+G. E. Santoro, “Optimal control at the quantum speed limit,” Phys. Rev. Lett. 103,
+240501 (2009).
+[40] S. An, D. Lv, A. del Campo, and K. Kim, “Shortcuts to adiabaticity by counterdia-
+batic driving for trapped-ion displacement in phase space,” Nature Communications
+7, 12999 (2016).
+[41] K. Funo, J.-N. Zhang, C. Chatou, K. Kim, M. Ueda, and A. del Campo, “Universal
+work fluctuations during shortcuts to adiabaticity by counterdiabatic driving,” Phys.
+Rev. Lett. 118, 100602 (2017).
+[42] S. Campbell and S. Deffner, “Trade-off between speed and cost in shortcuts to adia-
+baticity,” Phys. Rev. Lett. 118, 100601 (2017).
+[43] A. del Campo, J. Goold,
+and M. Paternostro, “More bang for your buck: Super-
+adiabatic quantum engines,” Scientific Reports 4, 6208 (2014).
+[44] F. C. Binder, S. Vinjanampathy, K. Modi,
+and J. Goold, “Quantacell: powerful
+charging of quantum batteries,” New Journal of Physics 17, 075015 (2015).
+[45] F. Wegner, “Flow-equations for hamiltonians,” Annalen der Physik 506, 77–91 (1994).
+[46] S. D. Głazek and K. G. Wilson, “Renormalization of hamiltonians,” Phys. Rev. D 48,
+5863–5872 (1993).
+[47] S. D. Glazek and K. G. Wilson, “Perturbative renormalization group for hamiltonians,”
+Phys. Rev. D 49, 4214–4218 (1994).
+[48] F. J. Wegner, “Flow equations for hamiltonians,” Physics Reports 348, 77–89 (2001).
+[49] S. Kehrein, The Flow Equation Approach to Many-Particle Systems, Springer Tracts
+in Modern Physics (Springer Berlin Heidelberg, 2007).
+29
+
+[50] C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and S. L. Sondhi, “Operator hy-
+drodynamics, otocs, and entanglement growth in systems without conservation laws,”
+Phys. Rev. X 8, 021013 (2018).
+[51] A. Nahum, S. Vijay, and J. Haah, “Operator spreading in random unitary circuits,”
+Phys. Rev. X 8, 021014 (2018).
+[52] T. Rakovszky, F. Pollmann, and C. W. von Keyserlingk, “Diffusive hydrodynamics
+of out-of-time-ordered correlators with charge conservation,” Phys. Rev. X 8, 031058
+(2018).
+[53] V. Khemani, A. Vishwanath, and D. A. Huse, “Operator spreading and the emergence
+of dissipative hydrodynamics under unitary evolution with conservation laws,” Phys.
+Rev. X 8, 031057 (2018).
+[54] D. E. Parker, X. Cao, A. Avdoshkin, T. Scaffidi, and E. Altman, “A universal operator
+growth hypothesis,” Phys. Rev. X 9, 041017 (2019).
+[55] D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, And Correlation Func-
+tions, Advanced Books Classics (CRC Press, 2018).
+[56] Nicoletta Carabba, Niklas Hörnedal, and Adolfo del Campo, “Quantum speed limits
+on operator flows and correlation functions,” Quantum 6, 884 (2022).
+[57] B. Mohan and A. K. Pati, “Quantum speed limits for observables,” Phys. Rev. A 106,
+042436 (2022).
+[58] J. L. F. Barbón, E. Rabinovici, R. Shir, and R. Sinha, “On the evolution of operator
+complexity beyond scrambling,” Journal of High Energy Physics 2019, 264 (2019).
+[59] P. Caputa, J. M. Magan, and D. Patramanis, “Geometry of krylov complexity,” Phys.
+Rev. Research 4, 013041 (2022).
+[60] Anatoly Dymarsky and Alexander Gorsky, “Quantum chaos as delocalization in krylov
+space,” Phys. Rev. B 102, 085137 (2020).
+[61] E. Rabinovici, A. Sánchez-Garrido, R. Shir, and J. Sonner, “Operator complexity: a
+journey to the edge of krylov space,” Journal of High Energy Physics 2021, 62 (2021).
+[62] N. Hörnedal, N. Carabba, A. S. Matsoukas-Roubeas, and A. del Campo, “Ultimate
+speed limits to the growth of operator complexity,” Communications Physics 5, 207
+(2022).
+[63] H. Mori, “A Continued-Fraction Representation of the Time-Correlation Functions,”
+Progress of Theoretical Physics 34, 399–416 (1965).
+[64] R. Kubo, “The fluctuation-dissipation theorem,” Reports on Progress in Physics 29,
+255 (1966).
+[65] G. Müller V. S. Viswanath, The Recursion Method: Application to Many-Body Dy-
+namics (Springer-Verlag, 1994).
+[66] R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Reso-
+nance in One and Two Dimensions, International series of monographs on chemistry
+(Clarendon Press, 1990).
+[67] J. A. Gyamfi, “Fundamentals of quantum mechanics in liouville space,” European
+Journal of Physics 41, 063002 (2020).
+[68] S. H. Friedberg, A. J. Insel, and L. E. Spence, Linear Algebra (Pearson, 2019).
+[69] L. B. Levitin and T. Toffoli, “Fundamental limit on the rate of quantum dynamics:
+The unified bound is tight,” Phys. Rev. Lett. 103, 160502 (2009).
+[70] J. Haegeman, T. J. Osborne, H. Verschelde, and F. Verstraete, “Entanglement renor-
+malization for quantum fields in real space,” Phys. Rev. Lett. 110, 100402 (2013).
+30
+
+[71] M. Nozaki, S. Ryu,
+and T. Takayanagi, “Holographic geometry of entanglement
+renormalization in quantum field theories,” Journal of High Energy Physics 2012, 193
+(2012).
+[72] J. Molina-Vilaplana and A. del Campo, “Complexity functionals and complexity
+growth limits in continuous mera circuits,” Journal of High Energy Physics 2018, 12
+(2018).
+[73] P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi, and K. Watanabe, “Anti–de sitter
+space from optimization of path integrals in conformal field theories,” Phys. Rev. Lett.
+119, 071602 (2017).
+[74] P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi, and K. Watanabe, “Liouville action
+as path-integral complexity: from continuous tensor networks to ads/cft,” Journal of
+High Energy Physics 2017, 97 (2017).
+[75] A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle,
+and Y. Zhao, “Complexity,
+action, and black holes,” Phys. Rev. D 93, 086006 (2016).
+[76] A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle,
+and Y. Zhao, “Holographic
+complexity equals bulk action?” Phys. Rev. Lett. 116, 191301 (2016).
+[77] R. Uzdin and R. Kosloff, “Speed limits in liouville space for open quantum systems,”
+EPL (Europhysics Letters) 115, 40003 (2016).
+[78] D. A. Lidar, A. Shabani,
+and R. Alicki, “Conditions for strictly purity-decreasing
+quantum markovian dynamics,” Chemical Physics 322, 82–86 (2006).
+[79] M. Toda, “Vibration of a chain with nonlinear interaction,” Journal of the Physical
+Society of Japan 22, 431–436 (1967).
+[80] M. Toda, “Wave propagation in anharmonic lattices,” Journal of the Physical Society
+of Japan 23, 501–506 (1967).
+[81] H. Flaschka, “The toda lattice. ii. existence of integrals,” Phys. Rev. B 9, 1924–1925
+(1974).
+[82] J. Moser, Dynamical Systems, Theory and Applications (Springer, 1975).
+[83] C. Monthus, “Flow towards diagonalization for many-body-localization models: adap-
+tation of the toda matrix differential flow to random quantum spin chains,” Journal
+of Physics A: Mathematical and Theoretical 49, 305002 (2016).
+[84] M. Okuyama and K. Takahashi, “From classical nonlinear integrable systems to quan-
+tum shortcuts to adiabaticity,” Phys. Rev. Lett. 117, 070401 (2016).
+[85] D. Chowdhury, A. Georges, O. Parcollet, and S. Sachdev, “Sachdev-ye-kitaev models
+and beyond: Window into non-fermi liquids,” Rev. Mod. Phys. 94, 035004 (2022).
+[86] S. Bravyi, D. P. DiVincenzo, and D. Loss, “Schrieffer–wolff transformation for quan-
+tum many-body systems,” Annals of Physics 326, 2793–2826 (2011).
+[87] L. D. Faddeev and L. A. Takhtajan, Hamiltonian Methods in the Theory of Solitons
+(Springer, Berlin Heidelberg, 2007).
+[88] B. Sutherland, Beautiful Models (World Scientific, 2004).
+[89] D. J. Gross, J. Kruthoff, A. Rolph, and E. Shaghoulian, “tT in ads2 and quantum
+mechanics,” Phys. Rev. D 101, 026011 (2020).
+[90] D. J. Gross, J. Kruthoff, A. Rolph, and E. Shaghoulian, “Hamiltonian deformations
+in quantum mechanics, tT, and the syk model,” Phys. Rev. D 102, 046019 (2020).
+[91] A. S. Matsoukas-Roubeas, F. Roccati, J. Cornelius, Z. Xu, A. Chenu,
+and A. del
+Campo, “Non-hermitian hamiltonian deformations in quantum mechanics,” (2022).
+31
+
+[92] A. Bhattacharya, P. Nandy, P. P. Nath, and H. Sahu, “Operator growth and krylov
+construction in dissipative open quantum systems,” Journal of High Energy Physics
+2022, 81 (2022).
+[93] C. Liu, H. Tang, and H. Zhai, “Krylov complexity in open quantum systems,” (2022).
+32
+
diff --git a/rNE3T4oBgHgl3EQfMQnG/content/tmp_files/load_file.txt b/rNE3T4oBgHgl3EQfMQnG/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0b3515f4952fb5c1ee50e38383721615985a139f
--- /dev/null
+++ b/rNE3T4oBgHgl3EQfMQnG/content/tmp_files/load_file.txt
@@ -0,0 +1,1172 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf,len=1171
+page_content='Geometric Operator Quantum Speed Limit, Wegner  Hamiltonian Flow and Operator Growth  Niklas Hörnedal1, Nicoletta Carabba1, Kazutaka Takahashi1,2, and Adolfo del Campo1,3  1Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Luxembourg  2Department of Physics Engineering, Faculty of Engineering, Mie University, Mie 514–8507, Japan  3Donostia International Physics Center, E-20018 San Sebastián, Spain  Quantum speed limits (QSLs) provide lower bounds on the minimum time  required for a process to unfold by using a distance between quantum states  and identifying the speed of evolution or an upper bound to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We introduce a  generalization of QSL to characterize the evolution of a general operator when  conjugated by a unitary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The resulting operator QSL (OQSL) admits a geomet-  ric interpretation, is shown to be tight, and holds for operator flows induced  by arbitrary unitaries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', with time- or parameter-dependent generators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The  derived OQSL is applied to the Wegner flow equations in Hamiltonian renor-  malization group theory and the operator growth quantified by the Krylov  complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In what time scale does a physical process unfold?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Time-energy uncertainty relations have  long been used to estimate characteristic time scales in physical processes, including life-  times in quantum decay, tunneling times, and the duration of a quantum jump, among  others [1–4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In the quantum domain, Mandelstam and Tamm put the time-energy uncer-  tainty relation on firm ground in their 1945 work [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' They provided its rigorous derivation  by combining the Heisenberg equation of motion and the Robertson uncertainty relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  They went a step further by identifying the minimum time for the quantum state of a  system to evolve into a distinct state, using the energy dispersion of the initial state as an  upper bound to the speed of evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In doing so, they introduced an early example of  a quantum speed limit (QSL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Over the last decades, such an approach has been refined and generalized to a great extent  [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Margolus and Levitin found an alternative bound to the speed of evolution in terms  of the mean energy of the system [8], and ensuing works showed that an infinite family  of bounds exist in terms of other moments of the generator of evolution [9, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' QSLs  have also been derived for time-dependent Hamiltonians [11–13], open systems described  by master equations [14–17], and with a stochastic evolution under continuous quantum  measurements [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' They have been further extended to the classical domain, with appli-  cations ranging from Hamiltonian dynamics to stochastic thermodynamics [19–25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' QSLs  generally involve a notion of distance between quantum states and an upper bound to the  speed of quantum evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' While the Bures angle, defined in terms of the Uhlmann  fidelity [26], is often the default choice for the distance between quantum states, other  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='04372v1  [quant-ph]  11 Jan 2023  alternatives can provide tighter QSLs [17, 27–29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This freedom is particularly important  in the context of many-body systems given the orthogonality catastrophe and the growth  of the Hilbert space with the system size [30–34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The emphasis on quantum state distinguishability was a key stepping stone in developing  QSLs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Today, QSLs find manifold applications in quantum metrology and parameter esti-  mation [35–38], quantum control [39–42], and quantum thermodynamics [43, 44], among  other fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' However, certain phenomena are naturally described in terms of operator  flows, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', the continuous evolution of an operator according to given equations of motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  A typical example is the description of quantum evolution in the Heisenberg picture, but  the relevance of operator flows is not restricted to quantum dynamics in rotating frames.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Operator flows naturally arise in the Wegner flow equations for Hamiltonian renormaliza-  tion [45–49], the study of operator growth and quantum complexity [50–54], and correlation  functions [55], to name some examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Motivated by these applications, we have introduced the notion of QSL for operator flows  in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' [56], which we shall term Operator QSL (OQSL) hereafter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Another approach  pursuing QSLs for observables was proposed in [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' At variance with conventional QSLs,  OQSLs involve a notion of distance between operators (instead of quantum states) and  an upper bound on the corresponding speed of evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' OQSLs have proved useful in  characterizing the time evolution of autocorrelation functions, setting bounds on dynamical  susceptibilities arising in linear response theory, and the precision in parameter estimation  with thermal quantum systems [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' However, in their current form, OQSLs are restricted  to flows associated with a constant generator, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', one that is independent of time or the  relevant parameter characterizing the evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In addition, OQSLs lack in their present  formulation an intuitive geometric description, common in other bounds arising in quantum  information geometry, such as the Mandelstam-Tamm QSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In this work, we introduce an OQSL valid under unitary dynamics generated by a time-  (or parameter-) dependent generator, that can be a generic operator or an observable, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=',  a Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The resulting bound admits a geometric interpretation and is shown to  be tight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We illustrate its usefulness in the study of Wegner flow equations in the theory  of Hamiltonian continuous renormalization group [46–48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We characterize the OQSL for  the Hamiltonian flow in detail and illustrate the possibility of saturating it when the flow  of Hamiltonian parameters is described by the Toda equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We further apply the new  OQSL to the problem of operator growth in unitary quantum dynamics in Krylov space,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', as characterized by the Krylov complexity [54, 58–62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We close with a discussion and  an outlook pointing out directions for further work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  1  Motivation  In quantum physics, a broad class of time-correlation functions is defined through a positive  semi-definite inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Consider any operator A evolving unitarily according to ˙At =  iLAt, where L = [H, ·] is the Liouvillian superoperator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  One class of time-correlation  functions that have been considered in the literature takes the form C(t) = (A|At), defined  with the help of a Hermitian bilinear form in the space of operators,  (A|B) = Tr  �  A†ρ1Bρ2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (1)  2  The operators ρ1 and ρ2 are in general positive semi-definite, commute with the Hamilto-  nian, and need not have unit trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A familiar example of this type of correlation function  is obtained by setting ρ1 = ρ2 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (1) reduces then to the Hilbert-Schmidt inner  product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Another familiar instance corresponds to the choice of the identity ρ1 = 1 and  the canonical Gibbs state ρ2 = e−βH/Z at inverse temperature β, with partition function  Z = Tr e−βH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Note that in general, the bilinear form in (1) is not positive definite, which  means that it does not always define an inner product;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' instead, it will define a positive  semi-definite inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='1  As a result, there might exist cases in which A ̸= 0 and  (A|A) = 0 are simultaneously fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Another example of a correlation function defined  through a positive semi-definite inner product, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' C(t) = (A|At), is given by the so-called  Kubo inner product [55, 63–65]  (A|B) = 1  β  � β  0  dλ⟨eλHA†e−λHB⟩β − ⟨A†⟩β⟨B⟩β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (2)  Here, ⟨·⟩β denote the thermal expectation value and β is once again the inverse tempera-  ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The function ∥A∥ =  �  (A|A) is a seminorm and we note that the condition ∥At∥ = ∥A∥ is  satisfied in the above examples for all t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='2 We might then ask, given a unitary flow induced  by a possibly time-dependent Hamiltonian H, what is the minimal time τ for an initial  observable A to reach some specific value of C(t) provided that ∥At∥ = ∥A∥ is satisfied  during the whole evolution?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' What follows is a derivation of a speed limit that lower bounds  this minimum time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  2  An Operator Quantum Speed Limit  The complex Hilbert space H used to model the system will be assumed throughout this  paper to be finite-dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We define B to be the space of linear operators acting on  this space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Moreover, let End(B) be the space consisting of all vector space endomorphism  of B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This linear space is commonly referred to as the Liouville space in the literature  [66, 67] and its elements are referred to as superoperators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Positive semi-definiteness of (·|·) makes it possible for C(t) to be constant for certain paths  At even though the operator is changing in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We will see that there is a way of “carving  away” the degrees of freedom in H that do not contribute to changes in C(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In doing so,  we obtain an effective Hilbert subspace HP, where the restriction of (·|·) onto this subspace  defines a proper inner-product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We will see that the condition ∥At∥ = ∥A∥ implies that At  will be situated on a sphere centered at the origin in HP with radius ∥A∥ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This observation  will then enable us to derive a geometric OQSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='1  Construction of the effective Hilbert space  We let ⟨·, ·⟩h denote the Hilbert-Schmidt inner product on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' It can be shown that any  positive semi-definite inner product (·|·) can be expressed as (·|·) = ⟨·, P·⟩h, where P is  1We use the convention that an inner product must satisfy positive-definiteness, be linear in the second  argument and conjugate symmetric  2A seminorm fulfills all the properties of regular norm except that non-zero vectors can have norm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  3  a positive semi-definite superoperator with respect to the Hilbert-Schmidt inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  This superoperator will be unique, provided that (·|·) has been specified—see Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  As we prove in Appendix B, a useful relation between (·|·) and P is that  ∥A∥ = 0 ⇐⇒ PA = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (3)  Since P is self-adjoint, it follows from the spectral theorem that the linear space B can  be expressed as a direct sum of the eigenspaces of P [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Consequently, the image of P  will be spanned by the eigenvectors corresponding to non-zero eigenvalues, and we thus  have that B = im(P) ⊕ ker(P), where im(P) and ker(P) are the image and kernel of P  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Relation (3) then implies that the restriction of (·|·) to im(P) will be positive  definite and will thus define an inner product on the Hilbert space defined by HP = im(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We will express this inner product with the usual bracket notation ⟨·, ·⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  For any operator A ∈ B, we will let ˆA ∈ HP denote the orthogonal projection of A onto  HP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='3 More explicitly, given the spectral decomposition P = �  k pkΠk, where pk are the  non-zero eigenvalues of P and Πk are the corresponding eigenprojections, we have that  ˆA = �  k ΠkA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We show in Appendix C that  (A|B) = ⟨ ˆA| ˆB⟩  ∀A, B ∈ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (4)  An important consequence of (4) is that C(t) = ⟨ ˆA| ˆAt⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  This means that if we are  interested in how C(t) changes over time, then we only need to consider the projected  dynamics ˆA(t) of A(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='2  Deriving the speed limit  If d is the complex dimension of the Hilbert space HP, then we can view it as a real vector  space isomorphic to R2d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We endow this space with the Riemannian metric given by the  real part of the inner product ⟨·, ·⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The condition that (A|A) = (At|At) holds for all  t ∈ [0, τ] then means that ˆAt will be situated on the (2d − 1)-dimensional sphere S∥A∥  with radius ∥A∥ centered at the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The shortest path connecting two points on the  sphere lies on a great circle with a distance given by the angle between the points times  the radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In other words, if ˆA and ˆB are two operators on the sphere with radius ∥A∥,  then the geodesic distance is given by  dist( ˆA, ˆB) = ∥A∥ arccos  �  Re(A|B)  ∥A∥2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (5)  The length of any curve ˆAt on the sphere must be greater or equal to the geodesic distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  As a consequence, we obtain an operator quantum speed limit τqsl by noting that  τ = length([ ˆAt])  1  τ length([ ˆAt])  ≥ dist( ˆA0, ˆAτ)  1  τ length([ ˆAt])  ,  (6)  where length([ ˆAt]) =  � τ  0 ∥LtAt∥dt is the length of the evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' More explicitly, the speed  limit can be written in terms of C(t) as  τ ≥ τqsl,  τqsl =  �  C(0) arccos  �  Re C(τ)  C(0)  �  Vτ  ,  (7)  3By orthogonal, we mean orthogonality measured by the Hilbert-Schmidt inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  4  where Vτ = 1  τ  � τ  0 ∥LtAt∥dt is the time averaged speed of the evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' For non-constant  speeds, Vτ needs in practice be replaced by an upper bound on the speed of the evolution  in order to make τqsl independent on the time τ one is trying to estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We stress that the speed limit τ is only guaranteed to hold whenever ∥At∥ is preserved  for the evolving operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This is always satisfied in the case when P = 1 so that (·|·)  becomes the Hilbert-Schmidt inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' For more general choices of P however, norm  preservation will not be guaranteed to hold for all initial operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In fact, the norm is  preserved for all initial operators if and only if [L, P] = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Assuming [L, P] = 0, let Pnm  and ωα = En − Em be the eigenvalues of P and L with respect to a common eigenbasis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Moreover, let Aij be the components of A with respect to this basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Define vα = Pnm|Anm|2  C(0)  ,  where C(0) = �  n,m Pnm|Anm|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We can then express (7) more explicitly, as  τqsl = arccos  �Re �  α vαeiωατ�  ��  γ vγω2γ  ,  (8)  where the indices α and γ runs from 1 to dim(H)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Example 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In the case when C(t) = Tr  �  A†Ate−βH/Z  �  we have that PA = Ae−βH/Z  and a common eigenbasis between L and P is given by the operators |En⟩⟨Em| where the  eigenvalues of P are given by Pnm = e−βEm/Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' For the Kubo inner-product we can view P as the composition P = A ◦ B ◦ C  of the three superoperators defined by A(A) = Ae−βH  Z  , B(A) = 1  β  � β  0 dλe−λHAeλH and  CA = A − Tr(A)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The superoperators A and B commute with a common eigenbasis being  given by the eigenvectors |En⟩⟨Em|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A speed limit for a time-evolving operator At using  the Kubo inner-product can then be obtained by using ˜At = C(At) and ˜P = A ◦ B instead  of At and P and then use that ˜Pnm = e−βEm  βZ  � β  0 eλ(Em−En)dλ and ˜Anm = Anm − �  k Akk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Let us note that the OQSL (7) is saturated by any traceless observable involving solely  the coupling of the ground state and an excited state of a time-independent Hamiltonian,  in the same spirit as the superposition of these eigenstates saturates the standard QSLs  for states [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' To show this, let us consider a time-independent Hamiltonian H and let us  denote by |0⟩ and |E⟩ its ground state and the eigenstate with energy E: H |0⟩ = 0 and  H |E⟩ = E |E⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Then, it is straightforward to see that the operator A =  1  √  2(|0⟩⟨E|+|E⟩⟨0|)  exactly saturates the OQSL (7) with respect to the Hilbert-Schmidt inner product (A|B) =  Tr  �  A†B  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Indeed, the autocorrelation function reduces to C(t) = cos(Et), in natural units,  while the velocity is constant and takes the value V = ∥[H, A]∥ = E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Therefore, being  C(0) = 1 due to the normalization, the OQSL (7) reduces to an identity at any time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  This intuition, that when the operator dynamics is confined to two time-independent Hamil-  tonian eigenspaces the evolution occurs along a geodesic trajectory, can be made more  rigorous and general, as we shall describe below identifying the general conditions for the  saturation of the OQSL (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='3  Refined speed Limit  Suppose we can find a decomposition of ˆAt such that ˆAt = S + Vt, where S and Vt stays  orthogonal with respect to the metric Re⟨·, ·⟩ throughout the evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We then have that  5  the minimal time it takes V to reach the operator Vτ is smaller or equal to the time it takes  ˆA to reach ˆAτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We can thus obtain another speed limit by substituting C(t) with (V |Vt)  in (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Using that S and Vt are orthogonal, one can write Re(V |Vt) = Re C(t)−∥S∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Our  refined speed limit thus takes the form  τ ≥ τref,  τref =  �  C(0) − ∥S∥2 arccos  �  Re C(τ)−∥S∥2  C(0)−∥S∥2  �  Vτ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (9)  This OQSL is a generalization of (7) since we can always trivially consider the case when  S = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Also, since 1 stays invariant throughout the flow generated by the Hamiltonian,  we can always consider the choice S = (1|A)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In the particular case when (·|·) is the  Hilbert-Schmidt inner product, this choice of S reduces (9) to the speed limit, denoted by  TΘ, in [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  What is worth noting is that the speed limit (9) becomes tighter the larger the norm  of S is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We can understand this from a geometrical perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The speed limit is  saturated whenever the traced-out curve of Vt follows a great circle on the sphere S∥V ∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  This means that the evolution will be contained in a two-dimensional subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' If we  then let X and Y be a pair of orthonormal vectors spanning this subspace, we must have  that Vt/∥V ∥ = cos θ(t)X + sin θ(t)Y , where θ(t) is some real-valued function of t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='4 Given  that S is non-zero, the corresponding curve of ˆA must then be situated on an effective  Bloch sphere spanned by the operators X, Y and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  More explicitly, we have that  ˆA = ∥V ∥ cos θ(t)X + ∥V ∥ sin θ(t)Y + S will trace out a curve following a circle centered  at S (see figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Since this circle is not centered at the origin, it will not be a great  circle on the sphere S∥A∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A consequence of this is that the length of this curve must be  strictly larger than the geodesic distance on S∥A∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This length is precisely the numerator  in (9) and we can thus conclude that (9) gives a strictly tighter inequality than (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The  difference between these inequalities becomes greater the larger ∥S∥ is, which can be seen  in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Consider the case when ker(L) ∩ HP is invariant throughout the evolution, for example,  when the Hamiltonian commutes with itself for any two points in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We then have  that the norm of S is maximal when S is equal to the orthogonal projection of ˆA onto the  subspace ker(L) ∩ HP—see Appendix E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='6 Calling this component P0, we thus have that  the tightest possible refinement, in this case, is given by  τ ≥ τoref ≥ τref ≥ τqsl,  τoref =  �  C(0) − ∥P0∥2 arccos  �  Re C(τ)−∥P0∥2  C(0)−∥P0∥2  �  Vτ  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (10)  We will refer to this as the optimal refinement of the OQSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  4In fact, if we choose X and Y so that X = V , then θ is the angle between V and Vt and is given by  θ(t) = arccos  �  Re C(τ)−∥S∥2  C(0)−∥S∥2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  5We emphasize that the operators S, X and Y are orthogonal with respect to Re⟨·, ·⟩ and not necessarily  the Hilbert-Schmidt inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  6The orthogonal projection here is with respect to the inner product ⟨·, ·⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  6  Figure 1: As the evolving operator saturates the refined speed limit, it will move along a circle  that is displaced from the origin by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' As a consequence, the length of the traced-out curve will be  strictly larger than the geodesic distance in S∥A∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The numerator in (9) is exactly the length of this  traced-out curve, and we can thus conclude that the refined speed limit is strictly tighter than the  original one, given that S ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  3  More on the Conditions for Saturation  As discussed in section 2, the part of the evolution that induces a change in the time-  correlation function will be situated on the sphere S∥A∥ in the effective Hilbert space  HP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The OQSL (7) will then be saturated whenever the traced-out curve follows a great  circle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In the case when we could find a decomposition ˆAt = S + Vt, where S and Vt  remain orthogonal, we could consider the refined speed limit (9), which is saturated if and  only if Vt follows a great circle on the sphere S∥V ∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We discussed that for saturation of  (9), there exists a pair of orthonormal vectors X and Y such that ˆA = ∥V ∥ cos θ(t)X +  ∥V ∥ sin θ(t)Y + S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' If we choose X = ˆA/∥A∥, then the function θ(t) is the angle between  V and Vt with respect to the real-valued inner product Re⟨·, ·⟩ and is more explicitly given  by θ(t) = arccos  �  Re C(τ)−∥S∥2  C(0)−∥S∥2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  This section will discuss the conditions for saturation for two particular cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In the  first case, we consider the consequences of the operator ˆA having support in only two of  the eigenspaces of the Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In the second case, we assume ˆA to be Hermitian,  allowing us to draw connections between the saturation of the OQSLs and the dimension  of an underlying Krylov space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='1  Evolution with support in only two eigenspaces of the Hamiltonian  Consider the case when the Hamiltonian commutes with itself at any two points in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We will consider the case when ˆA has non-zero support in only two of the eigenspaces of the  Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='7 Let E and E′ denote the energies of these two eigenspaces through time and  let ω = E−E′ be the energy gap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' If PE and PE′ are the corresponding eigenspace projectors,  then ˆA = PE ˆAPE + PE ˆAPE′ + PE′ ˆAPE + PE′ ˆAPE′ and it is straight forward to check that  7An operator A is said to have non-zero support in a subspace X ⊆ H if ∃ |ψ⟩ ∈ X s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A |ψ⟩ ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  7  SilAll N span[S, X, Y]  V  S  A  Y  XFigure 2: As ∥S∥ grows larger, the center of the circle that ˆAt follows will be closer to the poles of  the sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Consequently, ˆAt moves in a more curved path, as highlighted by the yellow segments  where the right figure shows a top view of the sphere, and have to travel further in order to reach  the same angle θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The result of this is that the refined speed limit becomes increasingly tight the  larger ∥S∥ is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  LPE ˆAPE′ = ωPE ˆAPE′, LPE ˆAPE′ = −ωPE′ ˆAPE and LPE ˆAPE = LPE′ ˆAPE′ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In other  words, ˆA is spanned by the eigenspaces of the Liouvillian with eigenvalues 0, ω, and −ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Let P0, Pω, and P−ω be the corresponding projections of ˆA onto these three eigenspaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  More explicitly, we have in this specific case that P0 = PE ˆAPE + PE′ ˆAPE′, Pω = PE ˆAPE′  and P−ω = PE′ ˆAPE and we can write ˆA = P0 + Pω + P−ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The evolution of ˆA is given  by  ˆAt = P0 + ei� t  0 ω(t′)dt′Pω + e−i� t  0 ω(t′)dt′P−ω  = P0 + cos  �� t  0  ω(t′)dt′  ��Pω + P−ω  � + sin  �� t  0  ω(t′)dt′  ��iPω − iP−ω  �  = P0 + cos θ(t)Xω + sin θ(t)Yω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (11)  Here, we have introduced the non normalized operators Xω = Pω + P−ω and Yω = iPω −  iP−ω and the angle θ(t) =  � t  0 ω(t′)dt′ between ˆA − P0 and ˆAt − P0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The requirement that  ∥At∥ is constant in the interval [0, τ] implies that P0, X and Y are orthogonal and that  X and Y have the same norm—see Appendix F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='8 We can thus conclude that ˆAt − P0  moves along a great arc and thus saturates the optimal refined speed limit (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' One of  the consequences of this is that any qubit system with a commutative Hamiltonian must  satisfy the speed limit (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The above result can be extended to non-commuting Hamiltonians that keep the eigenspaces  corresponding to E and E′ invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' One might wonder whether the Hamiltonian must  keep these eigenspaces invariant for the evolving operator ˆAt to achieve saturation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The  answer is no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' To see this, we can consider the commuting Hamiltonian Ht above and add  to it any non-trivial Hamiltonian ˜Ht that commutes with ˆAt for all times t ∈ [0, τ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The  Hamiltonian Ht + ˜Ht then generates the same path for ˆAt as the Hamiltonian Ht.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The  difference is that Ht + ˜Ht will not keep the eigenspaces of E and E′ invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  8Note that we never need to assume that ˆA is Hermitian in order to conclude this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  8  03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='2  Relation to Krylov dimension for Hermitian operators  When ˆA is Hermitian, it can be illuminating to describe the saturation conditions in terms  of the dimension of the Krylov space of the evolving operator ˆAt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The Krylov space is  defined to be the smallest subspace containing the evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In the Hermitian case, this  is a real vector space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We can then conclude that saturation of (7) happens if and only if  the dimension of the Krylov space is equal to two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Similarly, given that S ̸= 0, we have  that a necessary condition for saturation of (7) is that the dimension of the Krylov space  is equal to three.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In the case when the Liouvillian is time-independent, the Krylov dimension is given by  the number of eigenspaces of L that ˆA has support in—see Appendix D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' If one of these  eigenspaces is the kernel of L, then we can say that the bound will be saturated if and only  if the Krylov dimension is smaller or equal to three.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  4  Hamiltonian Flow Equations in Continuous Renormalization Group  Operator flows are ubiquitous in physics and are not restricted to time evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In this  section, we show that the continuous renormalization group provides an arena in which  Hamiltonian flows naturally occur and where OQSLs are of relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  As a preamble, we note that the continuous renormalization group is also extensively used  in the study of the complexity of quantum states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' For instance, the continuous version of  the Entanglement Renormalization tensor networks, cMERA [70, 71], implements a real  space renormalization in which the flow of a quantum state is described as a function of  a continuous parameter characterizing the length scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A cMERA Hamiltonian generates  translations of the cMERA parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The use of conventional QSL has been explored  in this context to investigate the complexity of states in quantum field theory [72], using  the path integral description of tensor networks [73, 74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' These works result from an effort  to characterize the growth of quantum complexity in quantum field theories, a context in  which conventional QSLs had been applied [75, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Indeed, all these results concern flows  of quantum states and can thus be tackled with conventional QSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In this section, we consider a different framework for the continuous renormalization group  as a paradigmatic example and test bed for our result, the OQSL (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Specifically, we focus  on the Hamiltonian flow formulated by Wegner [45] and Glazek and Wilson [46, 47], as  a method for Hamiltonian block-diagonalization [48, 49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Consider the Hamiltonian flow  H(l) = U(l)H(0)U(l)† with respect to some parameter l, where U(l) is a unitary operator  satisfying U(0) = 1, and H(0) is the Hamiltonian of which the block diagonal form is  desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The flowing Hamiltonian satisfies the differential equation  dH(l)  dl  = [η(l), H(l)],  (12)  where η(l) =  dU(l)  dl U(l)† is the l-dependent generator of the unitary flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  For specific  choices of η(l), the initial Hamiltonian H(0) eventually flows to its (block)-diagonal form,  thus achieving the desired diagonalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' At each point of the flow, let us define the  target Hamiltonian HT (l) as the diagonal part of H(l),  HT (l) =  �  n  ϵn(l) |n⟩ ⟨n| ,  (13)  9  where we have defined ϵn(l) ≡ Hnn(l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' One instance of a generator that achieves this is  η = [HT , H], as originally proposed in [45, 48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We shall refer to this specific choice as  the Wegner flow, for simplicity, even when any Hamiltonian flow described by (12) and  converging to HT (l) is generally referred to as a Wegner flow in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Clearly,  the choice η = [HT , H] is not the only possibility and we shall consider a different choice  in an example below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let us stress that the l-dependent diagonal entries ϵn(l) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (13)  do not correspond to the Hamiltonian eigenvalues unless we have reached the end of the  flow l = lf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In that case, the flowing Hamiltonian has been transformed into its diagonal  form to coincide with the target part, H(lf) = HT (lf).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The final lf is typically reached as  l → ∞, as shown explicitly in the practical example below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  By applying our general result (7) to the evolution (12), with t → l, At → H(l) and  H(t) → −iη(l), we obtain the following OQSL on the Hamiltonian flow  l ≥ lqsl,  lqsl =  ∥H∥ arccos (H(0)|H(l))  ∥H∥2  Vl  ,  (14)  where the speed, averaged over the interval [0, l], is given by  Vl = 1  l  � l  0  ∥[η(t), H(t)]∥dt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (15)  For the rest of this section, we will only consider the case when (·|·) is the Hilbert-Schmidt  inner product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In this case we have that ∥[η, H]∥ = Tr  �[η, H]2�.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='1  Dephasing-like Wegner flow  Before applying the OQSL (14) in an explicit example, we show that the Wegner flow,  although unitary, features formal similarities with a dephasing evolution, under which the  off-diagonal entries of the density matrix ρ(t) decay and the fixed point is set by its diagonal  part only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The crucial difference is that in the Wegner flow, the diagonal part evolves as  well, and it does so in such a way that the total evolution is unitary and the final diagonal  form coincides with the diagonalized initial Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Here we aim to characterize the  decay of the off-diagonal elements Hnm(l) with n ̸= m and reveal its formal analogy with  dephasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' To this end, let us adopt the approach of vectorization [77] and represent an  operator A = �  n,m Anm |n⟩ ⟨m| as a normalized vector  |A⟩ =  1  ∥A∥  �  n,m  Anm |n, m⟩ ,  (16)  where |n, m⟩ = |n⟩ ⊗ |m⟩ and the normalization factor has been introduced to enhance  the comparison with the evolution of a quantum state ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Now, since we are interested in  the decay of the off-diagonal elements, let us introduce the (super)projector Q over the  non-diagonal part of the Hamiltonian,  Q = 1B − PHT ,  (17)  where 1B is the identity on the operator space B and PHT is the (super)projector over the  target Hamiltonian  PHT = |HT ⟩⟨HT | =  1  ∥HT ∥2  �  n,m  ϵnϵm |n, n⟩ ⟨m, m| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (18)  10  From this expression, it follows that PHT |HT ⟩ = |HT ⟩ and Q |HT ⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' To characterize  the dephasing-like decay realized by the Wegner flow, let us consider the overlap between  the flowing Hamiltonian and its non-diagonal part  AQ(l) ≡ ⟨H(l)| Q |H(l)⟩ ,  (19)  which quantifies how far H(l) is from being diagonal and vanishes as l → lf, that is as  H(l) → HT (l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' By substituting Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (17) and (18) we obtain  AQ(l) = 1 − ∥HT ∥2  ∥H∥2 ,  (20)  where we stress that ∥HT ∥2 = �  n ϵ2  n(l) depends on l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The quantity AQ identically van-  ishes at the end of the flow, when the Hamiltonian is diagonalized and H(l) = HT (l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Remarkably, if we choose the Wegner generator to be η = [HT , H] [48], then AQ decays  monotonically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Indeed, its decay rate reads as  d  dlAQ(l) = −  1  ∥H∥2  d  dl  �  n  ϵ2  n =  1  ∥H∥2  d  dl  �  n̸=m  |Hnm|2,  (21)  where the last inequality follows from the conservation of the total norm,  d  dl∥H∥ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' If  η = [HT , H] [48], it is straightforward to compute that  dHnm  dl  =  �  k  (ϵn + ϵm − 2ϵk)HnkHkm  (22)  and therefore  d  dlAQ(l) = −  2  ∥H∥2  �  n,m  (ϵn − ϵm)2|Hnm|2 < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (23)  As a result, the overlap (19), quantifying how far we are from the target, is monotonically  decreasing during the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This feature suggests an analogy with the well-known model of  dephasing, where the purity is found to decrease monotonically [78], in a similar manner  as in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' To show this, let us consider the case of pure dephasing  dρ  dt = −[X, [X, ρ]],  (24)  where X is a time-independent Hermitian operator satisfying X |n⟩ = xn |n⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Then it can  be shown [78] that the purity Tr ρ2 decreases monotonically with time as  d Tr ρ2  dt  = −2  �  nm  (xn − xm)2|ρmn|2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (25)  Now, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (23) can be also expressed as a “purity”-decay of the off-diagonal Hamiltonian  Hoff-diag(l) = H(l) − HT (l) and it reads as  d Tr H2  off-diag  dl  = d  dl  �  i̸=j  |Hij|2 = −2  �  i,j  (ϵi − ϵj)2|(Hoff-diag)ij|2,  (26)  which formally corresponds to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (25) with ρ → Hoff-diag and X → HT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We conclude that  the Wegner flow (12) generated by η = [HT , H],  dH  dl = [[HT , H], H],  (27)  which is unitary, suppresses the off-diagonal part of the Hamiltonian as if it was undergoing  a dephasing evolution under the action of the diagonal part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  11  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='2  Wegner and Toda flows  As already advanced, there are several choices of the generator η for diagonalizing a given  N × N matrix H(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' As a possible form, consider  ηnm(l) = Hnm(l)sgn (m − n),  (28)  for m ̸= n and ηnn = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Equation (12) then reduces to  dHnm(l)  dl  =  �  k  Hnk(l)Hkm(l) [sgn (k − n) − sgn (m − k)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (29)  Further, assume that the matrix H(l) takes a symmetric tridiagonal form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Then, the  equations for diagonal and off-diagonal components are written respectively as  dHnn(l)  dl  = 2(H2  n,n+1(l) − H2  n−1,n(l))  (n = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' , N),  (30)  dHn,n+1(l)  dl  = Hn,n+1(l)(Hn+1,n+1(l) − Hnn(l))  (n = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' , N − 1),  (31)  with H01 = HN,N+1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  This set of equations takes a closed form and is known as  the Toda equations in classical nonlinear integrable systems [79–81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We thus refer to the  Hamiltonian flow generated by (28) as the Toda flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We note that Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (23) is not satisfied in the present choice of η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  However, it is still  guaranteed that the matrix is diagonalized at large l due to the relation  d  dl  k  �  n=1  Hnn(l) = 2H2  k,k+1(l) ≥ 0,  (32)  where k = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' , N [82, 83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The relation for k = 1 denotes that H11(l) is a non-  decreasing function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Since Tr H2(l) is independent of l, each component of H(l) is not di-  vergent, if each component of the original matrix H0 takes a finite value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We conclude that  liml→∞ H11(l) converges to a finite value and liml→∞ H12(l) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Then, we examine the re-  lation for k = 2 to conclude that liml→∞ H22(l) takes a finite value and liml→∞ H23(l) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We can repeat the same consideration for the other values of k to conclude that H(l) is  diagonalized at l → ∞ keeping the eigenvalues of the matrix unchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  A possible realization of the tridiagonal matrix is the one-dimensional XY model with  isotropic interaction [84],  H(l) = 1  2  N−1  �  n=1  vn(l) (XnXn+1 + YnYn+1) + 1  2  N  �  n=1  hn(l)Zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (33)  In the z-basis, the second term represents the diagonal part and the first term represents  the off-diagonal part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The corresponding generator of the time evolution is  η(l) = i  2  N−1  �  n=1  vn(l) (XnYn+1 − YnXn+1) ,  (34)  and the set of coupling functions {v1(l), v2(l), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' , vN(l), h1(l), h2(l), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' , hN−1(l)} satisfies  the Toda equations  dhn(l)  dl  = 2(v2  n(l) − v2  n−1(l)),  (35)  dvn(l)  dl  = vn(l)(hn+1(l) − hn(l)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (36)  12  Figure 3:  OQSLs for the Wegner and Toda flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The upper panels represent θ(l)  =  arccos  �  Tr(H(0)H(l))/∥H(0)∥2�  (bold lines) and its bound  � l  0 ds ||[η(s), H(s)]||/||H|| (thin lines)  for Wegner and Toda flows with N = 3 (left panel) and N = 10 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We set the initial matrix as  a symmetric tridiagonal form and each component is taken from a uniform random number between  −1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In the lower panels, we plot the sum of off-diagonal components �  m̸=n H2  mn(l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  This Hamiltonian commutes with the total magnetization M = �N  n=1 Zn and the matrix  form of the single flip sector with M = ±(N − 2) takes a tridiagonal form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We plot examples of the Wegner and Toda flows in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We take a traceless symmetric  tridiagonal matrix as an initial given Hamiltonian H(0) in which each nonzero component  is taken from a uniform random number between −1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The numerical results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 3  implies that the Toda flow gives a tight bound for a small l and becomes worse for a large  l due to the nonmonotonic decay of the off-diagonal components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 4, we show how the result is dependent on the dimension of the matrix N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' For the  Wegner flow, when N is not considerably large, the angle θ(l) between H(0) and H(l) grows  faster by the l-evolution as N becomes large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In the Wegner flow, even though we start  the time evolution from a tridiagonal form, the matrix breaks the band structure during  the flow, which makes θ a large value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' It does not necessarily give the property that the  overlap (H(0)|H(l)) decays rapidly as a function of N, as we can see in some many-body  systems exhibiting the orthogonality catastrophe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' On the other hand, the Toda flow does  not show any growing behavior as a function of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This is due to the property that the  tridiagonal form is kept throughout the time evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' As for lqsl, a saturating behavior  is seen for the Wegner flow and is not seen for the Toda flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The independence of the Toda flow on the matrix dimension implies that we can find a  tight OQSL for specific initial Hamiltonians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' As we have discussed in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='1, saturation  is possible when the flowing operator has support in only two of the eigenspaces of the  generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In what follows, we will consider the condition that the eigenvectors of the  generator η(l) are l-independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  13  0  0  2  Todabound  2  Toda bound  Wegner bound  元/2  元/2  Wegnerbound  Toda  Wegner  Toda  Wegner  N=3  N=10  0  0  0  10  20  ZmnHmn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Zm≠nHmn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  N=3  4  N=10  Toda  2  Toda  Wegner  Wegner  0  0  0  10  0  20Figure 4: Plot of the θ(l) = arccos  �  Tr(H(0)H(l))/∥H(0)∥2�  (top panels) and lqsl (bottom panels)  for several values of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We set the initial matrix as a symmetric tridiagonal form and each  component is taken from a uniform random number between −1 and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The left panels represent  the Wegner flow, while the right panels correspond to the Toda flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Hereafter, we write Hnn(l) = hn(l) and Hn,n+1(l) = vn(l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The eigenvalue equation  η(l)|ϕ⟩ = iλ(l)|ϕ⟩, with a real eigenvalue λ(l) and the corresponding eigenvector |ϕ⟩ is  written as  �  �  �  �  �  �  �  �  �  ϕ2  0  −ϕ1  ϕ3  0  0  −ϕ2  ϕ4  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  0  −ϕN−2  ϕN  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  �  v1(l)  v2(l)  v3(l)  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  vN−1(l)  �  �  �  �  �  �  �  �  �  = iλ(l)  �  �  �  �  �  �  �  �  �  ϕ1  ϕ2  ϕ3  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  ϕN−1  �  �  �  �  �  �  �  �  �  ,  (37)  and −vN−1(l)ϕN−1 = iλ(l)ϕN, where (ϕ1, ϕ2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' , ϕN) denotes the l-independent eigenvec-  tor |ϕ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' When the diagonal components of the matrix on the left-hand side are nonzero,  the matrix is invertible and vn(l) for any index n is proportional to the same l-dependent  function λ(l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The possibility that some of the components of |ϕ⟩ are identically zero is  excluded since that condition only results in |ϕ⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  As an exceptional case, we can find the eigenvector with λ(l) = 0 when N is odd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In that  case, the eigenvector is written as  |ϕ⟩ ∝  �  1, 0, v1(l)  v2(l), 0, v3(l)v1(l)  v4(l)v2(l), 0, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' , 0, vN−2(l)vN−4(l) · · · v1(l)  vN−1(l)vN−3(l) · · · v2(l)  �T  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (38)  The l-independence of |ϕ⟩ gives the conditions v2k(l) ∝ v2k−1(l) with k = 1, 2, · · · , (N −  1)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We note that the eigenvector with λ(l) = 0 is unique if it exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Therefore, when we impose  the condition that two of the eigenvectors of η(l) are l-independent, the dependence of η(l)  14  0  N=3  N=3  N=10  N=10  Wegner  N=20  Toda  N=20  N=40  N=40  0  N=100  0  N=100  0  10  0  20  40  IQSL  40  N=3  N=3  N=10  IQSL  N=10  N=20  N=20  Toda  10  N=40  N=40  N=100  N=100  20  Wegner  0  0  10  0  20  40on l is described by a single function f(l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Each of the nonzero components is written  as  vn(l) = f(l)vn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (39)  We insert the condition (39) into Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (30) and (31) to find  h′  n(l) = 2f2(l)(v2  n − v2  n−1),  (40)  f′(l) = f(l)(hn+1(l) − hn(l)),  (41)  where the prime symbol denotes the derivative with respect to l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The second equation (41)  shows that hn(l) is a linear function in n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Since the constant shift hn(l) → hn(l) + h0 does  not change Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (30) and (31), we set �N  n=1 hn(l) = 0 and obtain  hn(l) = f′(l)  f(l)  �  n − N + 1  2  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (42)  We use this form for the first equation (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Then, v2  n(l) is a quadratic function of n and  f(l) obeys the differential equation  �f′(l)  f(l)  �′  = −2d1f2(l),  (43)  where d1 represents a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The corresponding form of vn is  v2  n = 1  2d1n(N − n) + d0,  (44)  where d0 represents a constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  To determine d0, we look at the following condition, which follows from the conservation  of the norm  N  �  n=1  h2  n(l) + 2  N−1  �  n=1  v2  n(l) = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (45)  Without losing the generality, we can put the form f(l) = cos θ(l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Using Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (43) and  (45), we find as the possible solution  d0 = 0,  (46)  � θ′(l)  cos θ(l)  �2  = 2d1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (47)  The l dependence of each component is specified as hn(l) = hn sin θ(l) and vn(l) =  vn cos θ(l).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' By representing d1 with respect to h1, we finally obtain  hn(l) = − 2h1  N − 1  �  n − N + 1  2  �  sin θ(l),  (48)  v2  n(l) = n(N − n)  (N − 1)2 h2  1 cos2 θ(l),  (49)  and  θ′(l)  cos θ(l) =  2h1  N − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (50)  15  Figure 5: Left: The parameters of the initial matrix H, {hn}n=1,2,··· ,N and {vn}n=1,2,··· ,N−1, result-  ing in the tight bound in the Toda flow with N = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Right: θ(l) = arccos  �  Tr(H(0)H(l))/∥H(0)∥2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We set l0 = (N − 1)/4h1 and sin θ(0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The differential equation for θ(l) is easily solved as  sin θ(l) =  sinh  �  4h1  N−1l  �  + sin θ(0) cosh  �  4h1  N−1l  �  cosh  �  4h1  N−1l  �  + sin θ(0) sinh  �  4h1  N−1l  �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (51)  In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 5, we plot {hn}n=1,2,··· ,N, {vn}n=1,2,··· ,N−1, and θ(l) for N = 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  All components of the matrix H(l) are parameterized by a single l-dependent function θ(l),  which implies that the time evolution can be denoted by a motion along an arc in the  Bloch space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In fact, we find that θ(l) denotes the operator angle and the dynamics gives  the tight bound:  arccos  ����  Tr(H(l)H(0))  Tr(H(0)2)  ���� =  � l  0  dt  �  Tr([η(t), H(t)]2)  Tr(H(0)2)  = θ(l) − θ(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (52)  5  Operator Growth and Krylov Complexity  In the previous section, we have considered the flow of an observable, the Hamiltonian,  with respect to a parameter different than time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Here we illustrate another application of  the OQSL, pointing out that operator flows need not necessarily concern an observable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In particular, given a Liouvillian operator L = [H, ·], we show that the geometrical OQSL  (7) can also be applied to the unitary flow of a superoperator, generated under the action  of S = [L, ·], which can be accordingly viewed as a “super Liouvillian”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This kind of flow  arises naturally in characterizing the complexity of a given quantum evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Specifi-  cally, in the context of operator growth, the notion of Krylov complexity [54, 58–62] has  recently gained attention as a measure of operator complexity for the Heisenberg evolution  of an observable under the action of a time-independent Hamiltonian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The evolution of  simple, local observables into increasingly complex and nonlocal ones can be described as  the operator spreading in the so-called Krylov space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' As mentioned in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='2, the  latter provides the minimal subspace in which the Heisenberg dynamics unfolds and is  uniquely determined by the Hamiltonian of the system and the initial operator O0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Krylov  complexity can then be understood as the mean position of the evolving operator Ot in  the so-called Krylov basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' It can be expressed as an expectation value (Ot|KOt) of a cor-  responding (super)operator K, known as the complexity operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' At this point, one can  16  Vn/h1  0/(元/2)  0  hn/h1  10  20  0  0  I/lo  10  nagain change representation and let the superoperators, such as K, evolve while keeping the  observable |O) fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We shall call this representation the super-Heisenberg picture from  the evident analogy with the standard Heisenberg representation of the quantum evolution  in the Hilbert space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In this picture, the complexity operator evolves accordingly to the  equation  ˙K = i[L, K]  (53)  and the corresponding unitary flow is constrained by the speed limit (7), upon identifying  A and H with K and L, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We note that our result (7) holds for finite dimensions  and that the dimension of the Krylov space is always finite whenever the Hilbert space  that the observables are defined over is finite [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='1  Quantum dynamics in Krylov space  Let us start by briefly recalling how the Krylov space and the corresponding notion of  complexity are constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' For a more detailed discussion, we refer to [54, 58–62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The  evolution in the Heisenberg picture of an operator Ot = eiHtO0e−iHt can be formally  written in terms of the nested commutators with the Hamiltonian H, that is, the powers  of the Liouvillian L = [H, ·], as Ot = �∞  n=0  (it)n  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' LnO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The space explored during this  evolution is given by the span of the infinite set {LnO}∞  n=0 and is precisely the Krylov  space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' From this infinite set, one can extract an orthonormal, finite basis {On}D−1  n=0 by  applying the so-called Lanczos algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The first element of the basis coincides with the  initial operator O0, which we will assume to be normalized to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Then, at each iterative  step, the next orthogonal vector is constructed as |An+1) = L|On) − bn|On−1), where  bn = ∥An∥ is the n-th Lanczos coefficient, and the corresponding element of the Krylov  basis |On+1) is obtained upon normalization as On = An/bn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Throughout this section, we  will use the Hilbert-Schmidt inner product (A|B) = Tr A†B between operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' By making  use of the Krylov space, the unitary evolution of the operator Ot is effectively mapped to  a hopping problem on the one-dimensional, semi-infinite chain represented by the Krylov  basis {On}D−1  n=0 , where the Lanczos coefficients bn play the role of hopping parameters and  the Liouvillian, which takes the tridiagonal form  L =  D−1  �  n=0  bn+1|On+1)(On| + bn|On−1)(On|,  (54)  with |O−1) = |OD) = 0, acts as an Hamiltonian for the so-called operator wavefunction  |Ot).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The Krylov complexity operator K is then defined as the position operator  K =  D−1  �  n=0  n|On)(On|,  (55)  on this lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The most studied object in this context is the expectation value of the  above (super)-operator with respect to Ot and is simply known as the Krylov complexity:  K = (Ot|KOt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Its rate of growth is constrained by the speed limit  |∂tK(t)| ≤ 2b1∆K,  (56)  introduced in [62] and known as the dispersion bound, given that (∆K)2 = (Ot|K2Ot) −  (Ot|KOt)2 is the variance of K with respect to Ot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The dispersion bound is saturated  17  at any time if and only if the structure of Krylov space features the so-called complexity  algebra (57), which we shall introduce below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  It was pointed out in [59] that the Liouvillian in Krylov space, given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (54), can  be written as the sum L = L+ + L− of raising and lowering operators that act on the  Krylov basis as L+|On) = bn+1|On+1) and L−|On) = bn|On−1), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' It appears  then natural to introduce a super-operator B = L+ − L−, conjugated to the Liouvillian,  and consider their commutator ˜K = [L, B] [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The dispersion bound (56) is identically  saturated if and only if these three operators close an algebra, which can only take the  form [62]  [L, B] = ˜K,  [ ˜K, L] = αB,  [ ˜K, B] = αL  (57)  and implies also that ˜K = αK + γ1, where α, γ ∈ R [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The Krylov complexity growth  rate is then maximal [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' It can be shown that γ is always a positive number and α is a  real number satisfying the condition α = − 2γ  D−1 for finite Krylov dimension D and α ≥ 0  if D = ∞ [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Moreover, the algebraic closure (57), or equivalently the saturation of the  bound (56), implies that the Lanczos coefficients evolve according to [59, 62]  bn =  �1  4αn(n − 1) + 1  2γn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (58)  For α > 0, this dependence captures the asymptotic linear growth bn = √αn conjectured  by Parker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' to hold in generic non-integrable systems, leading to the maximal growth  of Krylov complexity [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A paradigmatic example of this class of systems is the celebrated  Sachdev-Ye-Kitaev (SYK) model [85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='2  Saturation of the OQSL by the complexity algebras  In the “super” Heisenberg picture, the observable operator is kept fixed while the complexity  operator K evolves unitarily according to  Kt = e−iLtK0eiLt =  ∞  �  n=0  (−i)n  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Sn(K0) tn,  (59)  where S = [L, ·] will be referred to as super Liouvillian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In the case of closed complexity  algebras, thanks to the commutation relations (57), all the powers Sn(K0) reduce to terms  proportional to either K0 or B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In particular, if α ̸= 0 one can show that [62]  S2n(K0)  =  (−1)nαn−1(αK0 + γ1),  (60)  S2n+1(K0)  =  (−1)n+1αnB,  (61)  where the first equation clearly holds only for n > 0, being S0(K0) = K0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Conversely,  when α = 0 only S(K0) = −B and S2(K0) = −γ1 survive, being Sn(K0) = 0 for n > 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Thus,  Kt =  �  (1 − α)K0 − γ1 + cosh(√αt)  �K0 + γ  α1  � + i sinh(√αt) 1  αB  α ̸= 0,  K0 + iBt + γ  2t21  α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (62)  Equation (59), together with Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (60)-(61), implies that whenever the dispersion bound  (56) is saturated, the full time-evolution of the Krylov complexity operator Kt must be  18  contained in a 3-dimensional space, spanned by the identity 1, the initial complexity K0  and B = [K0, L]:  Kt ∈ Span{1, K0, B}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (63)  This space defines the “super” Krylov space of Krylov complexity itself and turns out to  be dramatically simplified by the assumption of closed complexity algebra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' From the dis-  cussion in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='2, we can conclude that Kt having a 3-dimensional Krylov space is a  sufficient condition for it to saturate the refined OQSL (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We recall that here At and L  are replaced by Kt and S, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Then Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (63) implies that K has support in only  three eigenspaces of S, one of them corresponding to the eigenvalue 0: Kt = P0+Pω +P−ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Therefore, we conclude that the super operator Kt − P0 saturates the OQSL (10);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' that is,  it evolves along a geodesic trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In other words, the maximal growth rate of Krylov  complexity, leading to the saturation of the dispersion bound (56), is equivalent to the  geodesic evolution of the Krylov complexity operator, provided that we subtract its sta-  tionary component P0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Indeed, we remark that P0 is necessarily different from zero since  Tr K ̸= 0, and must be removed to obtain a tight OQSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' From the explicit computation  performed below, we shall conclude that the identity is indeed the only stationary compo-  nent of the Krylov complexity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', P0 = Tr K  1  ∥1∥2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' By doing so, we shall also explicitly  assess the improvement achieved by replacing the OQSL (7) with its refined counterpart  (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='3  Computation of the OQSL for the complexity algebras  The geometrical OQSL (7) for the Krylov complexity reads as  t ≥ ∥K0∥  arccos  � (K0|Kt)  ∥K0∥2  �  ∥[L, K0]∥  ,  (64)  where, given a time-independent Liouvillian L, the velocity of the flow ∥[L, K0]∥ is constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The initial complexity K0 coincides with the usual Krylov complexity operator (55) in the  standard Heisenberg picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In order to assess its deviation from saturation, we explicitly  evaluate the OQSL (64) in the case of the SU(2) complexity algebra, that is, when the  complexity growth saturates the dispersion bound (56) in finite dimension [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let us  define VK ≡ ∥K0∥−1∥[L, K0]∥ as the (normalized) velocity of the complexity flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  By  explicit computation in the Krylov basis, one can verify that VK, being [L, K0] = −B by  construction, always reduces to  V2  K = ∥B∥2  ∥K0∥2 =  2  ∥K0∥2  D−1  �  n=1  b2  n,  (65)  where the norm of the complexity is fixed by the Krylov dimension as  ∥K0∥2 =  D−1  �  n=0  n2 = D(D − 1)(2D − 1)  6  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (66)  The velocity (65) of the complexity flow is maximized whenever the Lanczos coefficients  growth is maximal, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', linear in n, which is the case for maximally chaotic systems accord-  ing to the universal growth hypothesis [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Indeed, by focusing on the initial scrambling  period and neglecting the role of the following plateau and descent in the bn’s [61], we  19  conclude that a sub-polynomial behavior bn ∝ nδ with 0 < δ < 1 always leads to a smaller  velocity VK than the linear growth bn ∝ n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We stress that this observation also holds for  infinite-dimensional Krylov spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' As shown below, the velocity (65) remains finite in  this limit, and once we fix the proportionality constant, the velocity is maximized by the  linear growth of the bn’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In other words, according to the universal growth hypothesis  [54], complexity flows at the highest speed in maximally chaotic systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Let us now focus on the instances of Krylov dynamics that saturate another notion of the  speed limit for operator growth, namely the above-mentioned dispersion bound (56).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' As  reviewed above, in such cases, the dynamics of Krylov complexity is determined by an  underlying 3-dimensional algebra [62] and the Lanczos coefficients obey Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (58).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' As a  result, the velocity (65) of the complexity flow can be expressed as  V2  K = α(D − 2) + 3γ  2D − 1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (67)  Before restricting the analysis to the finite-dimensional case α < 0, where the geometrical  QSL (7) can be applied, let us stress that this notion of velocity is well defined also in  the limit D → ∞, where α ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In particular, if α > 0, when the Krylov complexity  diverges exponentially with time as K(t) ∼ e  √αt [59, 62], we obtain that VK →  �  α/2:  the speed of the complexity operator flow is proportional to the characteristic time scale  of the exponential divergence of the Krylov complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Instead, if α = 0, which leads to  a quadratic divergence of K [59, 62], the above-defined speed of the flow vanishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This  singular behavior can be understood as the QSL (64), derived under the assumption of  finite dimension D, may not have a well-defined counterpart for D → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In particular,  as we shall see below, the numerator in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (64) also vanishes for α = 0, resulting in  an indeterminate form 0/0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Finally, for the Krylov dynamics to saturate the dispersion  bound (56) over a finite-dimensional space, the underlying complexity algebra must be that  of SU(2), corresponding to the case α < 0 [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In such case, given the condition bD = 0,  the parameters α and γ of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (58) are subject to the further constraint 2γ = |α|(D−1) [62],  which also ensures the expression (67) to be positive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Indeed, the velocity of the complexity  flow generated by the SU(2) algebra reduces to V2  K = |α|(D + 1)/[2(2D − 1)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' For this  class of models, we compute the QSL (64) exactly, thus establishing a direct comparison  between the geometrical OQSL introduced in the present work and the dispersion bound  that constraints the growth of Krylov complexity [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In addition to the velocity of the flow, the other quantity that characterizes the speed limit  is the notion of distance spanned during the evolution, which appears at the numerator of  Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (7) and (64) and is given in terms of the autocorrelation function, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', the operator  overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In the case of closed complexity algebras, the autocorrelation function of the  complexity  (K0|Kt) =  ∞  �  n=0  (−i)n  n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (K0|Sn(K0)) tn  (68)  can be explicitly evaluated by making use of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (60)-(61).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We note that, since (K0|B) = 0,  only the even powers of the super Liouvillian S contribute to the sum in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (68).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Moreover,  the only finite-dimensional case where we can straightforwardly apply the OQSL (64) is  that of the SU(2) complexity algebra, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', when α < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  For this class of models, by  substituting Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (60)-(61) into the expression (68) and recognizing the Taylor expansion  20  a  0  5  10  15  20  25  30  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  t  SU(2)  Geodesic  b  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  t  QSL  t  Figure 6: We illustrate the deviation from the saturation of the OQSL (64) for the SU(2) complexity  algebra, with Krylov dimension D = 1000 and α = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' a We compare the evolution (69) of the  complexity autocorrelation function (K0|Kt) (red curve) with the geodesic trajectory (K0|Kt)|geodesic  (71) (blue dashed curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' b We show the left and right-hand side of the inequality (70) (blue dashed  and red curves, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The OQSL is tight only near t = 0, and the deviation increases with  time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  of the cosine, we obtain  (K0|Kt) = (∥K∥2 + γ  α Tr K) cos  �  |α|t − γ  α Tr K,  (69)  where Tr K = D(D − 1)/2 and ∥K∥2 is given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (66).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Therefore, in the case of the  SU(2) complexity algebra, the autocorrelation function (K0|Kt) oscillates at the frequency  �  |α|, which, we note, is half the frequency of oscillation of the Krylov complexity K itself  [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' By substituting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (69) into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (64) and using that 2γ = |α|(D − 1), we rewrite  the OQSL as  t ≥ 1  VK  arccos  ��  1 − 3(D − 1)  2(2D − 1)  �  cos  �  |α|t + 3(D − 1)  2(2D − 1)  �  ,  (70)  where V2  K = |α|(D + 1)/[2(2D − 1)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' As argued above, we expect this bound not to be  tight due to the presence of a stationary component in the complexity flow given by the  non-vanishing of its trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We illustrate the deviation from the geodesic trajectory  (K0|Kt)|geodesic = ∥K∥2 cos VKt  (71)  and the divergence of the two sides of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (70) in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In what follows, we shall explicitly  remove the stationary component of the complexity flow, thus proving the saturation of  the refined OQSL (10) and showing its equivalence with the dispersion bound (56).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Finally, although the framework of the geometrical QSL requires a finite dimension, it is  instructive to consider the behavior of the quantities involved in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (64) as D → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In  particular, we have already stressed above that the velocity VK (65) of the complexity flow  remains finite, is non-zero for α > 0 and vanishes for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Moreover, from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (68), with  analogous steps as for the SU(2), we obtain that for α = 0 the autocorrelation function  behaves as (K0|Kt) = ∥K∥2 + γ  2t2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' At any finite time, this implies the vanishing of the  numerator of the QSL (64), since the argument of the arccosine approaches 1 as D → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The evaluation of the limit of the full expression yields as a result that τQSL → 0 as D → ∞  in the case of the HW algebra, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', for α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Conversely, the notion of distance employed  in our QSL (7) is not well defined in the case α > 0, since the normalized autocorrelation  function diverges exponentially with time, (K0|Kt)/∥K∥2 ∼ exp{√αt}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  21  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='1  Saturation of the refined OQSL  The fact that the Krylov complexity operator Kt cannot saturate the OQSL (64) is al-  ready evident from the observation that Tr Kt ̸= 0, as this condition results in a non-zero  stationary component P0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In particular, the trace accounts for the stationary component  along the identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Removing the trace is sufficient to achieve saturation only if there are  no other stationary components of Kt, meaning that the zero eigenvalue of the super Li-  ouvillian S has no degeneracy, such that the corresponding eigenspace is spanned by the  identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We explicitly show that this is indeed the case for closed complexity algebras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In this sense, the dispersion bound (56) and the OQSL (10) provide a unique constraint  on the operator growth in Krylov space and the saturation of the former automatically  implies the saturation of the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Let us, therefore, consider the operator Kt obtained by subtracting from the Krylov com-  plexity its component along the identity:  Kt = Kt − (Kt|1)  1  ∥1∥2 ,  (72)  where (Kt|1) = Tr K and ∥1∥2 = D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The OQSL (7) for Kt reads as  t ≥  arccos  � (K0|Kt)  ∥K∥2  �  VK  ,  (73)  where V2  K = ∥B∥2/∥K∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Now, by using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (66) and that Tr K = D(D − 1)/2, we  obtain  ∥K∥2 = ∥K∥2 − (Tr K)2  D  = D(D2 − 1)  12  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (74)  Moreover, in the case of SU(2) complexity algebra, from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (58) with α < 0 and 2γ =  |α|(D − 1) we find  ∥B∥2 = 2  D−1  �  n=1  b2  n = |α|D(D2 − 1)  12  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (75)  By taking the ratio of the expressions above, we conclude that the velocity of the Kt flow  for the SU(2) complexity algebra is VK =  �  |α|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' On the other hand, the autocorrelation  function (K0|Kt) can be computed analogously to the one of Kt in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (68)-(69), with  the only difference that now Tr K = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We thus obtain  (K0|Kt) = ∥K∥2 cos  �  |α|t = ∥K∥2 cos VKt,  (76)  which implies that the inequality in the OQSL (73) reduces t an identity at any time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In  conclusion, the saturation of the dispersion bound (56) in finite dimension implies that  the Krylov complexity Kt also saturates the refined OQSL (10) with P0 = 1 Tr K/D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We  illustrate this saturation in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' From the comparison between Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 6 and (7) we can  assess the efficiency of the refined OQSL (10) in yielding a tight evolution by removing the  components that do not contribute dynamically to the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  6  Conclusions, Discussion and Outlook  Conventional QSLs bound the minimum time for the completion of a process by quantifying  the distance traveled by the system along the evolution in state space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' OQSLs generalize  22  a  0  10  20  30  40  50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='0  t  SU(2)  Geodesic  b  0  2  4  6  8  10  0  2  4  6  8  10  t  QSL  t  Figure 7: Illustration of the saturation of the OQSL (73) for the SU(2) complexity algebra, with  Krylov dimension D = 1000 and α = −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' a The complexity autocorrelation function (K0|Kt) (76)  (red curve) is shown to match the geodesic trajectory (blue dashed curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' b The left-hand and  right-hand sides of the inequality (73) (blue dashed and red curves, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The OQSL reduces  to an identity at any time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  the scope of conventional QSL to account for processes described in terms of operator flows,  i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', the change of an operator resulting from a conjugation by a one-parameter unitary [56].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  In this work, we have introduced a geometric OQSL that holds for arbitrary unitaries, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=',  whether the generator of flow is parameter dependent or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In addition, we have shown  the bound to be tight and identified the required conditions for its saturation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This has  led us to introduce a refined OQSL upon identifying the subspace in which the dynamics  unfolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The usefulness of these OQSLs has been illustrated in the context of a continuous renor-  malization group formulated as a Wegner Hamiltonian flow for block diagonalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In  this context, we have shown that Wegner’s choice of the flow generator leads to a mono-  tonic decay of the off-diagonal elements of the flowing Hamiltonian towards the target  block-diagonal one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' However, such a choice does not saturate the OQSL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' By contrast, an  alternative choice of the generator associated with the Toda flow can lead to the satura-  tion of the OQSL for a specific family of initial Hamiltonians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Beyond the case of Wegner  Hamiltonian flows, we expect our results to apply to other schemes for Hamiltonian diag-  onalization, such as those relying on the Schrieffer-Wolff transformation [86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  We have further discussed the implication of our results in the context of operator growth  in Krylov space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In this representation, the time evolution of an operator is analogous  to the spreading of a particle in the Krylov lattice, where the mean position is a proxy  for operator complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The conditions for maximal operator growth are then associated  with the saturation of the dispersion bound [62], which occurs when the Lanczos coeffi-  cients exhibit a specific dependence on the lattice site index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Here, we have introduced  a “super-Heisenberg” representation of the Krylov complexity operator generated by a su-  per Liouvillian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Making use of the OQSL in such representation, we have shown that  the saturation of the dispersion bound implies the saturation of the OQSL for the Krylov  complexity operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The application of OQSL to other complexity measures, such as the  family of q-complexities including out-of-time-order correlators [54], offers an interesting  prospect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Beyond these examples, we expect OQSLs to find manifold applications in the characteri-  zation of nonequilibrium phenomena, such as the crossing of a quantum phase transition,  the equilibration and thermalization of isolated many-body systems, quantum thermody-  23  namic processes, quantum control, and quantum annealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' In addition, OQSL may be  used in the study of integrable systems, using the zero-curvature representation [87], Lax  pairs [88], and Hamiltonian deformations [89–91].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The generalization of our results to  dissipative quantum systems would be highly desirable, given its prospective applications,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', to the description of open quantum dynamics in Heisenberg’s representation and the  quest for fundamental limits to nonunitary operator growth [92, 93].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  7  Acknowledgements  It is a pleasure to acknowledge discussions with Léonce Dupays, Íñigo L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Egusquiza and  Federico Roccati.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' KT acknowledges support by JSPS KAKENHI grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' JP20K03781  and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' JP20H01827.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Appendices  A  Proving bijection between positive semi-definite inner-products and positive semi-  definite operators  Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let P ∈ End(B) be a positive semi-definite superoperator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The binary operation  ⟨·, P·⟩h : B × B → R is a positive semi-definite inner product on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We need to show that the map ⟨·, P·⟩h satisfies linearity, Hermitian symmetry, and  positive semi-definiteness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Linearity  Consider any triplet of operators A, B and C and a complex number λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We then have  ⟨A, PλB⟩h = ⟨A, λPB⟩h = λ⟨A, PB⟩h  (77)  ⟨A, P(B + C)⟩h = ⟨A, PB + PC⟩h = ⟨A, PB⟩h + ⟨A, PC⟩h,  (78)  where we have used the linearity of the Hilbert-Schmidt inner product and the superoperator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Hermitian symmetry  For any pair of operators A and B we have  ⟨A, PB⟩h = ⟨PB, A⟩∗  h = ⟨B, P†(A)⟩∗  h = ⟨B, PA⟩∗  h,  (79)  where we have used the Hermitian symmetry property of the Hilbert-Schmidt inner product  and the fact that a positive semi-definite superoperator is self-adjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Positive semi-definiteness  From the definition of positive semi-definiteness of a superoperator it follows directly that  ⟨A, PA⟩h ≥ 0,  (80)  for any operator A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  ■  Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Given the Hilbert space (B, ⟨·, ·⟩h), the map P �→ ⟨·, P·⟩h is a bijection  between the set of positive semi-definite operators on (B, ⟨·, ·⟩h) and the set of positive  semi-definite inner products on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  24  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We can prove that the map is a bijection if we can prove that it is injective and  surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Injectivity  Suppose that ⟨·, P·⟩h = ⟨·, η(·)⟩h for some pair of superoperators P and η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' It follows that  ⟨·, P·⟩h = ⟨·, η(·)⟩h ⇐⇒ ⟨A, PB⟩h = ⟨A, η(B)⟩h  ∀A, B ∈ B  ⇐⇒ P = η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (81)  Surjectivity  Given any positive semi-definite inner product (·|·), we want to construct a positive semi-  definite superoperator P such that (·|·) = ⟨·, P·⟩h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let M1, M2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Mn2 be an operator basis  in B and ak and bk be the corresponding components of A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Define ⟨Mi, PMj⟩h =  (Mi|Mj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This superoperator is positive semi-definite since  ⟨A, PB⟩H =  n2  �  i=1  n2  �  j=1  a∗  i bj⟨Mi, PMj⟩H =  n2  �  i=1  n2  �  j=1  a∗  i bj(Mi|Mj)  = (A|B)  =⇒  ⟨A, PA⟩H = (A|A) ≥ 0,  (82)  from which it is also clear that P maps to (·|·).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  ■  B  The kernel of seminorms  Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let ∥·∥ be the seminorm induced by the positive semi-definite inner product  ⟨·, P·⟩h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' It is then the case that ∥A∥ = 0 ⇐⇒ PA = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let {Mk}n2  k=0 be an orthonormal eigenbasis of P such that λk is the eigenvalue  corresponding to the eigenvector Mk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let ak be the components of an operator A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We  then have  ⟨A, PA⟩H =  n2  �  i=1  n2  �  j=1  a∗  i aj⟨Mi, PMj⟩H =  n2  �  i=1  n2  �  j=1  a∗  i ajλjδij  =  n2  �  k=1  |ak|2λk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (83)  Since λk ≥ 0, this sum can only be zero if ak = 0 for λk > 0, in other words, A lies in the  kernel of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  ■  C  Proof of equation 4  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Define ˜A = A− ˆA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We can choose an orthogonal basis M1, M2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Md, N1, N2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Nn−d,  such that the operators Mk and Nk span im(P) and ker(P) respectively and d is the di-  mension of im(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let ak be the components of A with respect to this basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We have  that  P ˜A = P(A − ˆA) = PA − P ˆA  =  d  �  k=1  akPMk +  n−d  �  k=1  akPNk −  d  �  k=1  akPMk = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (84)  25  Using this together with linearity of (·|·), we get  (A|B) = ( ˆA| ˆB) + ( ˆA| ˜B) + ( ˜A| ˆB) + ( ˜A| ˜B) = ( ˆA| ˆB) = ⟨ ˆA| ˆB⟩ ,  (85)  where the step to the second equality follows from proposition 3 and the last step follows  from the definition of ⟨·, ·⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  ■  D  Smallest subspace containing the dynamics  Let V be a real or complex finite dimensional vector space and let L be a linear endo-  morphism on V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Assuming that L is diagonalizable, we can write L = �d  i=1 liPi, where  li are the d distinct eigenvalues of L and Pi are the projections onto the corresponding  eigenspaces satisfying �d  i=1 Pi = I and PiPj = δijPi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Here I is the identity map on V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' It  follows from the definition of the exponential function that eLt = �d  i=1 elitPi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Consider  now any initial vector v in V evolving according to v(t) = eLtv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let us define the subspace  W = span{vi}i∈I where i ∈ I ⇐⇒ vi := Piv ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We then have that v(t) = �  i∈I elitvi  and we see that the evolution is entirely contained in W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Given a proper time interval  T ⊂ R, we now ask whether W is the smallest subspace for which {v(t) : t ∈ T} is con-  tained in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='9 The answer is affirmative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' To show this, first, note that the functions elit with  domain T are linearly independent given that all eigenvalues li are distinct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This implies  that  �  i∈I  cielit = 0 ∀t ∈ T ⇐⇒ ci = 0 ∀i ∈ I,  (86)  where ci ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We will use proof by contradiction to show that W must be the smallest  subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Assume that there exists a subspace ˜W containing the evolution with a dimen-  sion strictly smaller than W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We must then have the evolution contained in the subspace  given by the intersection F = W ∩ ˜W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' By our assumption, F must then have a dimen-  sion strictly smaller than W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This implies that there exists a non-zero linear functional  w with domain W for which F ⊂ ker(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We can expand this functional in the basis  {fi}i∈I defined by fi(vj) = δij so that w = �  i∈I wifi, where wi = w(vi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We get that  w  �v(t)  � = 0 ∀t ∈ T ⇐⇒ �  i∈I wielit = 0 ∀t ∈ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This last expression together with (86)  implies that wi = 0 ∀i ∈ I ⇐⇒ w = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Thus, we have reached a contradiction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' hence, W  is the smallest subspace containing {v(t) : t ∈ T}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  The proof can be carried out analogously for the case when L is time dependent but  commutes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=', [L(t1), L(t2)] = 0 ∀t1, t2 ∈ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  E  Optimal refinement  Consider the decomposition ˆA = S + Vt discussed in section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='3 and assume that the  subspace ker(L) ∩ HP does not change over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Suppose Vt has a non-zero projection  S′ onto ker(L) ∩ HP then S′ is guaranteed to remain unchanged since we have by the  assumption that ker(L) ∩ HP is time-independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Let V ′  t be the orthogonal complement  so that V = S′ + V ′  t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' It follows that  ⟨V, Vt⟩ = (V |Vt) = (S′ + V ′|S′ + V ′  t ) = (V ′|V ′  t ) +  ��S′��2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (87)  9A proper interval is an interval in R excluding the empty set and singletons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  26  This implies that  Re(V ′|V ′  t ) = Re(V |Vt) −  ��S′��2 = Re C(t) − ∥S∥2 −  ��S′��2 = Re C(t) −  ��S + S′��2,  (88)  where the last equality follows from the assumption Re⟨S, Vt⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' We can thus improve  the speed limit further whenever S′ ̸= 0 since we would then have that ∥S + S′∥ > ∥S∥ +  ∥S′∥ > ∥S∥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' The operator P0 = S + S′ is precisely the orthogonal projection of ˆAt onto  ker(L) ∩ HP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  F  Proving orthogonality from the preservation of norm  We here want to show that the operators P0, Xω and Yω in (11) are orthogonal and that  Xω and Yω have the same norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Using (11), we get that  ∥At∥2 = ∥P0∥2 + ∥Pω∥2 + ∥P−ω∥2 + 2 cos θ(t) Re⟨P0, Xω⟩ + 2 cos(2θ(t)) Re⟨Pω, P−ω⟩  (89)  = ∥P0∥2 + ∥Pω∥2 + ∥P−ω∥2 + 2 sin θ(t) Re⟨P0, Yω⟩ + 2 cos(2θ(t)) Re⟨Pω, P−ω⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  (90)  At time t = 0, we have that θ(0) = 0 and we get from expression (89) and (90) that  Re⟨P0, Xω⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Assuming that θ(t) is not zero over the whole interval [0, τ], we can  conclude from Re⟨P0, Xω⟩ = 0, (89) and (90) that Re⟨P0, Yω⟩ = 0 must also hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This  in turn implies that Re⟨Pω, P−ω⟩ = 0 since ∥At∥ must be constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' This last equality  guarantees that the norm of Xω and Yω are equal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Note that in the case when θ(t) = 0  over the whole interval, we have that the dynamics is stationary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  References  [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Pfeifer and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Fröhlich, “Generalized time-energy uncertainty relations and bounds  on lifetimes of resonances,” Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 67, 759–779 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [2] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Busch, “The time–energy uncertainty relation,” in Time in Quantum Mechanics,  edited by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Muga, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Mayato, and Í.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Egusquiza (Springer Berlin Heidelberg,  Berlin, Heidelberg, 2008) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 73–105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [3] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Schulman, “Jump time and passage time: The duration ofs a quantum transition,”  in Time in Quantum Mechanics, edited by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Muga, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sala Mayato,  and Í.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Egusquiza (Springer Berlin Heidelberg, Berlin, Heidelberg, 2008) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 107–128.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [4] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Dodonov and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Dodonov, “Energy–time and frequency–time uncertainty  relations: exact inequalities,” Physica Scripta 90, 074049 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [5] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Mandelstam and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Tamm, “The uncertainty relation between energy and time  in non-relativistic quantum mechanics,” in Selected Papers, edited by Boris M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Bolo-  tovskii, Victor Ya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Frenkel,  and Rudolf Peierls (Springer Berlin Heidelberg, Berlin,  Heidelberg, 1991) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 115–123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [6] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Deffner and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Campbell, “Quantum speed limits: from heisenberg’s uncertainty  principle to optimal quantum control,” Journal of Physics A: Mathematical and The-  oretical 50, 453001 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [7] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Gong and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Hamazaki, “Bounds in nonequilibrium quantum dynamics,” Interna-  tional Journal of Modern Physics B 36, 2230007 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  27  [8] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Margolus and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Levitin, “The maximum speed of dynamical evolution,” Physica  D: Nonlinear Phenomena 120, 188–195 (1998), proceedings of the Fourth Workshop  on Physics and Consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [9] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Zieliński and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Zych, “Generalization of the margolus-levitin bound,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  A 74, 034301 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [10] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Margolus, “The finite-state character of physical dynamics,” arXiv e-prints ,  arXiv:1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='4994 (2011), arXiv:1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='4994 [quant-ph] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Uhlmann, “An energy dispersion estimate,” Physics Letters A 161, 329–331 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Deffner and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lutz, “Energy–time uncertainty relation for driven quantum sys-  tems,” Journal of Physics A: Mathematical and Theoretical 46, 335302 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [13] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Okuyama and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Ohzeki, “Comment on ‘energy-time uncertainty relation for  driven quantum systems’,” Journal of Physics A: Mathematical and Theoretical 51,  318001 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Taddei, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Escher, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Davidovich, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' de Matos Filho, “Quantum  speed limit for physical processes,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 110, 050402 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Egusquiza, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Plenio,  and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Huelga, “Quantum speed  limits in open system dynamics,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 110, 050403 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Deffner and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lutz, “Quantum speed limit for non-markovian dynamics,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 111, 010402 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [17] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Campaioli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Pollock,  and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Modi, “Tight, robust, and feasible quantum  speed limits for open dynamics,” Quantum 3, 168 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [18] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' García-Pintos and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, “Quantum speed limits under continuous  quantum measurements,” New Journal of Physics 21, 033012 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [19] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Shanahan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Chenu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Margolus,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, “Quantum speed limits  across the quantum-to-classical transition,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 120, 070401 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [20] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Okuyama and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Ohzeki, “Quantum speed limit is not quantum,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  120, 070402 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [21] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Shiraishi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Funo, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Saito, “Speed limit for classical stochastic processes,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 121, 070601 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [22] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Nicholson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' García-Pintos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Green, “Time–  information uncertainty relations in thermodynamics,” Nature Physics 16, 1211–1215  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [23] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Vo, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Van Vu, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Hasegawa, “Unified approach to classical speed limit  and thermodynamic uncertainty relation,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' E 102, 062132 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [24] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Van Vu and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Hasegawa, “Geometrical bounds of the irreversibility in markovian  systems,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 126, 010601 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [25] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' García-Pintos, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Nicholson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Green, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Gorshkov,  “Unifying quantum and classical speed limits on observables,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' X 12, 011038  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [26] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Bengtsson and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Życzkowski, Geometry of Quantum States: An Introduction to  Quantum Entanglement, 2nd ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' (Cambridge University Press, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [27] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Pires, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Cianciaruso, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Céleri, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Adesso, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Soares-Pinto, “Gen-  eralized geometric quantum speed limits,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' X 6, 021031 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [28] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Campaioli, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Pollock, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Binder, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Modi, “Tightening quantum speed  limits for almost all states,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 120, 060409 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  28  [29] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Hörnedal, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Allan,  and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sönnerborn, “Extensions of the mandelstam–tamm  quantum speed limit to systems in mixed states,” New Journal of Physics 24, 055004  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Bukov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sels, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Polkovnikov, “Geometric speed limit of accessible many-  body state preparation,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' X 9, 011034 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [31] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Fogarty, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Deffner, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Busch, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Campbell, “Orthogonality catastrophe as a  consequence of the quantum speed limit,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 124, 110601 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [32] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Suzuki and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Takahashi, “Performance evaluation of adiabatic quantum computa-  tion via quantum speed limits and possible applications to many-body systems,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Research 2, 032016 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, “Probing quantum speed limits with ultracold gases,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  126, 180603 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [34] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Hamazaki, “Speed limits for macroscopic transitions,” PRX Quantum 3, 020319  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [35] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Braunstein, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Caves, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Milburn, “Generalized uncertainty relations:  Theory, examples, and lorentz invariance,” Annals of Physics 247, 135–173 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [36] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Giovannetti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lloyd, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Maccone, “Advances in quantum metrology,” Nature  Photonics 5, 222–229 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [37] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Tóth and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Apellaniz, “Quantum metrology from a quantum information science  perspective,” Journal of Physics A: Mathematical and Theoretical 47, 424006 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [38] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Beau and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, “Nonlinear quantum metrology of many-body open sys-  tems,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 119, 010403 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [39] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Caneva, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Murphy, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Calarco, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Fazio, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Montangero, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Giovannetti,  and  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Santoro, “Optimal control at the quantum speed limit,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 103,  240501 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [40] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' An, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lv, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Kim, “Shortcuts to adiabaticity by counterdia-  batic driving for trapped-ion displacement in phase space,” Nature Communications  7, 12999 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [41] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Funo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Chatou, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Kim, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Ueda, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, “Universal  work fluctuations during shortcuts to adiabaticity by counterdiabatic driving,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 118, 100602 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [42] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Campbell and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Deffner, “Trade-off between speed and cost in shortcuts to adia-  baticity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 118, 100601 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Goold,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Paternostro, “More bang for your buck: Super-  adiabatic quantum engines,” Scientific Reports 4, 6208 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [44] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Binder, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Vinjanampathy, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Modi,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Goold, “Quantacell: powerful  charging of quantum batteries,” New Journal of Physics 17, 075015 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [45] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Wegner, “Flow-equations for hamiltonians,” Annalen der Physik 506, 77–91 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [46] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Głazek and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Wilson, “Renormalization of hamiltonians,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' D 48,  5863–5872 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Glazek and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Wilson, “Perturbative renormalization group for hamiltonians,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' D 49, 4214–4218 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [48] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Wegner, “Flow equations for hamiltonians,” Physics Reports 348, 77–89 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [49] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Kehrein, The Flow Equation Approach to Many-Particle Systems, Springer Tracts  in Modern Physics (Springer Berlin Heidelberg, 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  29  [50] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' von Keyserlingk, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rakovszky, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Pollmann, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sondhi, “Operator hy-  drodynamics, otocs, and entanglement growth in systems without conservation laws,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' X 8, 021013 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [51] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Nahum, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Vijay, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Haah, “Operator spreading in random unitary circuits,”  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' X 8, 021014 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [52] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rakovszky, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Pollmann, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' von Keyserlingk, “Diffusive hydrodynamics  of out-of-time-ordered correlators with charge conservation,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' X 8, 031058  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [53] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Khemani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Vishwanath, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Huse, “Operator spreading and the emergence  of dissipative hydrodynamics under unitary evolution with conservation laws,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' X 8, 031057 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [54] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Parker, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Cao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Avdoshkin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Scaffidi, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Altman, “A universal operator  growth hypothesis,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' X 9, 041017 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [55] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Forster, Hydrodynamic Fluctuations, Broken Symmetry, And Correlation Func-  tions, Advanced Books Classics (CRC Press, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [56] Nicoletta Carabba, Niklas Hörnedal, and Adolfo del Campo, “Quantum speed limits  on operator flows and correlation functions,” Quantum 6, 884 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [57] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Mohan and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Pati, “Quantum speed limits for observables,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A 106,  042436 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [58] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Barbón, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rabinovici, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Shir, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sinha, “On the evolution of operator  complexity beyond scrambling,” Journal of High Energy Physics 2019, 264 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [59] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Caputa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Magan, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Patramanis, “Geometry of krylov complexity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Research 4, 013041 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [60] Anatoly Dymarsky and Alexander Gorsky, “Quantum chaos as delocalization in krylov  space,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' B 102, 085137 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [61] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rabinovici, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sánchez-Garrido, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Shir, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sonner, “Operator complexity: a  journey to the edge of krylov space,” Journal of High Energy Physics 2021, 62 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [62] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Hörnedal, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Carabba, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Matsoukas-Roubeas, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, “Ultimate  speed limits to the growth of operator complexity,” Communications Physics 5, 207  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [63] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Mori, “A Continued-Fraction Representation of the Time-Correlation Functions,”  Progress of Theoretical Physics 34, 399–416 (1965).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [64] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Kubo, “The fluctuation-dissipation theorem,” Reports on Progress in Physics 29,  255 (1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [65] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Müller V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Viswanath, The Recursion Method: Application to Many-Body Dy-  namics (Springer-Verlag, 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [66] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Ernst, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Bodenhausen, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Wokaun, Principles of Nuclear Magnetic Reso-  nance in One and Two Dimensions, International series of monographs on chemistry  (Clarendon Press, 1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [67] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Gyamfi, “Fundamentals of quantum mechanics in liouville space,” European  Journal of Physics 41, 063002 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [68] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Friedberg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Insel, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Spence, Linear Algebra (Pearson, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [69] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Levitin and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Toffoli, “Fundamental limit on the rate of quantum dynamics:  The unified bound is tight,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 103, 160502 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [70] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Haegeman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Osborne, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Verschelde, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Verstraete, “Entanglement renor-  malization for quantum fields in real space,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 110, 100402 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  30  [71] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Nozaki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Ryu,  and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Takayanagi, “Holographic geometry of entanglement  renormalization in quantum field theories,” Journal of High Energy Physics 2012, 193  (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [72] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Molina-Vilaplana and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del Campo, “Complexity functionals and complexity  growth limits in continuous mera circuits,” Journal of High Energy Physics 2018, 12  (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [73] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Caputa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Kundu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Takayanagi, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Watanabe, “Anti–de sitter  space from optimization of path integrals in conformal field theories,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  119, 071602 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [74] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Caputa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Kundu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Miyaji, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Takayanagi, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Watanabe, “Liouville action  as path-integral complexity: from continuous tensor networks to ads/cft,” Journal of  High Energy Physics 2017, 97 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [75] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Brown, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Roberts, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Susskind, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Swingle,  and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Zhao, “Complexity,  action, and black holes,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' D 93, 086006 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [76] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Brown, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Roberts, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Susskind, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Swingle,  and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Zhao, “Holographic  complexity equals bulk action?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 116, 191301 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [77] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Uzdin and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Kosloff, “Speed limits in liouville space for open quantum systems,”  EPL (Europhysics Letters) 115, 40003 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [78] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lidar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Shabani,  and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Alicki, “Conditions for strictly purity-decreasing  quantum markovian dynamics,” Chemical Physics 322, 82–86 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [79] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Toda, “Vibration of a chain with nonlinear interaction,” Journal of the Physical  Society of Japan 22, 431–436 (1967).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [80] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Toda, “Wave propagation in anharmonic lattices,” Journal of the Physical Society  of Japan 23, 501–506 (1967).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [81] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Flaschka, “The toda lattice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' existence of integrals,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' B 9, 1924–1925  (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [82] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Moser, Dynamical Systems, Theory and Applications (Springer, 1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [83] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Monthus, “Flow towards diagonalization for many-body-localization models: adap-  tation of the toda matrix differential flow to random quantum spin chains,” Journal  of Physics A: Mathematical and Theoretical 49, 305002 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [84] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Okuyama and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Takahashi, “From classical nonlinear integrable systems to quan-  tum shortcuts to adiabaticity,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 117, 070401 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [85] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Chowdhury, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Georges, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Parcollet, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sachdev, “Sachdev-ye-kitaev models  and beyond: Window into non-fermi liquids,” Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' 94, 035004 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [86] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Bravyi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' DiVincenzo, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Loss, “Schrieffer–wolff transformation for quan-  tum many-body systems,” Annals of Physics 326, 2793–2826 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [87] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Faddeev and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Takhtajan, Hamiltonian Methods in the Theory of Solitons  (Springer, Berlin Heidelberg, 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [88] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sutherland, Beautiful Models (World Scientific, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [89] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Gross, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Kruthoff, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rolph, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Shaghoulian, “tT in ads2 and quantum  mechanics,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' D 101, 026011 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [90] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Gross, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Kruthoff, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rolph, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Shaghoulian, “Hamiltonian deformations  in quantum mechanics, tT, and the syk model,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' D 102, 046019 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [91] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Matsoukas-Roubeas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Roccati, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Cornelius, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Xu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Chenu,  and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' del  Campo, “Non-hermitian hamiltonian deformations in quantum mechanics,” (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  31  [92] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Bhattacharya, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Nandy, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Nath, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Sahu, “Operator growth and krylov  construction in dissipative open quantum systems,” Journal of High Energy Physics  2022, 81 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  [93] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Tang, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content=' Zhai, “Krylov complexity in open quantum systems,” (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
+page_content='  32' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rNE3T4oBgHgl3EQfMQnG/content/2301.04372v1.pdf'}
diff --git a/sdAyT4oBgHgl3EQfZvfd/content/tmp_files/2301.00231v1.pdf.txt b/sdAyT4oBgHgl3EQfZvfd/content/tmp_files/2301.00231v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6d95f51ed2ef520c8d259172608264b93287c043
--- /dev/null
+++ b/sdAyT4oBgHgl3EQfZvfd/content/tmp_files/2301.00231v1.pdf.txt
@@ -0,0 +1,2108 @@
+Democratic three Higgs-doublet models:
+the custodial limit and wrong-sign Yukawa
+Dipankar Dasa,∗, Miguel Levyb,†, Palash B. Palc,‡,
+Anugrah M. Prasada,§, Ipsita Sahad,¶, Ayushi Srivastavaa,‖
+aIndian Institute of Technology (Indore), Khandwa Road, Simrol, Indore 453 552, India
+b Centro de F´ısica Te´orica de Part´ıculas-CFTP and Departamento de F´ısica, Instituto Superior T´ecnico,
+Universidade de Lisboa, Av Rovisco Pais, 1, P-1049-001 Lisboa, Portugal
+cDepartment of Physics, University of Calcutta, 92 A. P. C. Road, Calcutta 700009, India
+dDepartment of Physics, Faculty of Science, University of Allahabad, Old Katra, Prayagraj 211002, India
+Abstract
+We study two novel aspects of democratic 3HDMs – the custodial limit and the possibility of
+wrong-sign Yukawa couplings. In the custodial limit, the democratic 3HDMs can easily negotiate
+the constraints from the electroweak T-parameter. We also uncover the possibility of having wrong-
+sign Yukawa couplings in democratic 3HDMs, as in the case of 2HDMs. We show that a democratic
+3HDM encompasses all the wrong-sign possibilities entertained by 2HDMs, and has considerably
+more leeway in the wrong-sign limit as compared to the 2HDM case. Our study underscores the
+importance of reporting analysis in the kappa-formalism without any implicit assumptions on the
+signs of the kappas.
+1
+Introduction
+The Standard Model (SM) of particle physics remains consistent in accommodating the experimental
+tests designed to measure its properties. The discovery of a scalar particle at the LHC has further
+vindicated the SM. This discovery has also intensified the interest in scalar extensions of the SM, which
+feature more than one fundamental scalars. In fact, the phenomenological evidences of dark matter
+and neutrino masses quite regularly motivate us to pursue physics beyond the SM (BSM). More often
+than not, these BSM scenarios come with an extension of the scalar sector of the SM. Although there
+are many different ways to extend the SM scalar sector, extensions with additional SU(2)L doublets
+are particularly attractive because they preserve the tree-level value of the ρ-parameter [1].
+The SM being reliant on the minimal scalar sector containing only one SU(2)L doublet, is free
+from flavour-changing neutral currents (FCNCs) at the tree-level. This feature is not guaranteed to
+be preserved when one extends the SM scalar sector. In fact, BSM with multiple scalar doublets, in
+∗d.das@iiti.ac.in
+†miguelplevy@tecnico.ulisboa.pt
+‡palashbaran.pal@saha.ac.in
+§anugrahmprasad@gmail.com
+¶ipsita@allduniv.ac.in
+‖srivastavaayushi860@gmail.com
+1
+arXiv:2301.00231v1  [hep-ph]  31 Dec 2022
+
+general, lead to the presence of tree-level FCNCs mediated by neutral scalars. However, experimental
+data suggest that the FCNC processes are strongly suppressed [1], which makes the absence of tree-
+level FCNCs a desirable property of any BSM scenario. A common way to achieve this is to impose a
+symmetry which ensures that fermions of a particular charge couple to only one scalar doublet. Con-
+sequently, the fermionic mass matrices and the corresponding Yukawa matrices are simultaneously
+diagonalizable, thereby preventing the appearance of scalar-mediated FCNCs at the tree-level, just
+as in the SM. Such a possibility, in the context of multi Higgs-doublet models, is known as natural
+flavour conservation (NFC) [2]. The two Higgs-doublet model (2HDM) entertains four types of flavour
+universal NFC models (type-I, type-II, type-X, and type-Y), which have been extensively studied in
+the literature [3]. Beyond these four possibilities, there is one more attractive option where a partic-
+ular scalar doublet is reserved exclusively for each type of massive fermion, and the up-type quarks,
+the down-type quarks, and the charged-leptons couple to separate dedicated scalar doublets. Quite
+clearly, such an arrangement of Yukawa couplings is impossible within the 2HDM framework and one
+needs at least three scalar doublets to achieve it. It should be mentioned that this particular compo-
+sition of Yukawa couplings is commonly dubbed as ‘democratic’ [4] or ‘type-Z’ [5] Yukawa structure.
+In this paper, we choose to refer to this possibility as ‘democratic Yukawa’ and subsequently, the
+three Higgs-doublet models (3HDMs) that feature a democratic Yukawa structure will be collectively
+called ‘democratic 3HDMs’. These democratic 3HDMs have received a lot of attention in the recent
+past. Theoretical constraints from unitarity and boundedness from below (BFB) have been studied
+in refs. [6,7], the alignment limit in democratic 3HDMs is studied in refs. [8,9], and more recently, the
+phenomenological studies involving the flavour and Higgs data have been performed in refs. [10,11].
+In this paper, we turn our attention to a couple of unexplored aspects of democratic 3HDMs,
+namely, the custodial limit and the possibility of ‘wrong-sign’ Yukawa couplings. Keeping in mind the
+surging popularity of democratic 3HDMs, this study is quite timely and relevant. To highlight the
+importance of the custodial limit, we recall that in the SM, the custodial symmetry (CS) ensures ρ = 1
+at the tree-level. The custodial symmetry is only an approximate symmetry of the SM since it is broken
+by the U(1)Y gauge coupling, as well as the Yukawa couplings [12]. Because of this, at the loop level,
+the ρ-parameter deviates slightly from unity and the deviation is quite accurately predicted by the
+SM. As it happens, the experimental measurement is compatible with this SM prediction, leaving very
+little room for new physics (NP) to give an extra contribution. Such NP contributions are sometimes
+conveniently expressed in terms of the T-parameter, which has the following experimental limit [1]
+∆T = 0.03 ± 0.12 .
+One noteworthy aspect is that the SM scalar sector respects CS perfectly. However, this is no longer
+guaranteed once the scalar sector is extended. Therefore, it is expected that the additional scalars
+will give rise to extra contributions to the T-parameter. The limit on the T-parameter will place
+constraints on the NP contributions, sometimes requiring a fine-tuned scalar spectrum to keep the
+value under control. Thus, models with n Higgs-doublets (nHDMs), although respecting ρ = 1 at the
+tree-level, can potentially drive the T-parameter away from the experimental bounds, if the scalar
+masses are arbitrarily chosen [13–16]. Therefore, it can be very attractive if we can systematically
+construct democratic 3HDMs which respect the CS in the scalar sector by design. Admittedly, such
+studies have been performed earlier in the context of nHDMs [17–21], resulting in relations between the
+quartic parameters of the scalar potential. But, unlike the earlier studies, which directly implement
+the custodial symmetry in the scalar potential, our analysis conveniently starts with the scalar kinetic
+terms, following ref. [22]. This alternative approach enables us to intuitively identify the different
+custodial multiplets and at the end, the conditions for CS in nHDMs are concisely expressed in a
+single equation, in terms of the physical masses and mixings of the scalar sector. Note that such
+2
+
+a condition does not depend on the explicit structure of the scalar potential. Being related to the
+mass matrices of the scalar sector, the condition for respecting CS in nHDMs becomes quite easily
+implemented in practical analysis. As a simple cross-check, we will also show how the conditions
+in terms of the quartic parameters of the scalar sector in earlier references follow from this single
+condition in a straightforward manner.
+The scalar extensions of the SM also face severe constraints from the measurements of the
+Higgs signal strengths [23]. For nHDMs, these constraints can be greatly alleviated by staying in the
+proximity of the ‘alignment limit’ [8,9,24–29], where the lightest CP-even scalar has the same couplings
+as the SM Higgs boson at the tree-level. However, an intriguing possibility may arise if we keep in
+mind that the current Higgs data is not very sensitive to the sign of the down quark and charged lepton
+Yukawa. Such an exotic possibility can be accommodated in a 2HDM framework with e.g. a type-II
+Yukawa structure and is quite well studied in the literature [30–33]. In this paper, we want to point
+out that democratic 3HDMs can also accommodate this possibility, with much more freedom, due to
+the increased number of parameters. These possibilities should encourage our experimental colleagues
+to report the results of the analysis of the Higgs data in the kappa framework [34, 35] without any
+implicit assumption on the sign of the kappas.
+This article will be organized as follows. In Sec. 2 we lay down our methodology to study the
+CS starting from the scalar kinetic terms. We then apply this in the case of the SM and recover
+the essential features of CS in the SM. Later in this section, we extend our analysis to the nHDM
+case and retrieve the 2HDM result as a special example. In Sec. 3 we explicitly demonstrate how
+the custodial limit neutralizes the constraint arising from the electroweak T-parameter. We define
+democratic 3HDMs in Sec. 4, and present the custodial limit for the two usual incarnations in Sec. 4.1.
+Afterwards, in Sec. 4.2 we investigate the possibility of wrong-sign Yukawa couplings in democratic
+3HDMs. Finally, we summarize our findings in Sec. 5.
+2
+Custodial Symmetry in multi Higgs-doublet models
+The CS is an accidental global SU(2) symmetry (hereafter denoted as SU(2)C) which prevails even
+after the spontaneous breaking of the electroweak symmetry in the SM. In the case of the SM gauge
+group, SU(2)L × U(1)Y , the CS is responsible for the value of the ρ-parameter to be equal to unity at
+the tree-level. In this paper, we follow the formulation of CS as in ref. [22], and confine ourselves to
+the SU(2)L part of the electroweak gauge symmetry, that is, we work in the limit where the U(1)Y
+gauge coupling goes to zero (g′ = 0). In this section, we will build our intuition first, by considering
+the simple example of the SM scalar sector. Then, we will extend our formalism to the case of a
+general nHDM and obtain conditions such that the scalar sector obeys the CS.
+2.1
+Recap of the custodial symmetry in the SM
+In the SM, there is a single complex scalar doublet, φ, which drives the electroweak symmetry breaking
+(EWSB). The scalar Lagragian of the SM is given by
+Lscalar = (Dµφ)† (Dµφ) − V (φ) ,
+(1)
+where V (φ) is the scalar potential. In the limit g′ = 0, the gauge-covariant derivative for φ is given by
+Dµφ
+=
+�
+∂µ + igτa
+2 W a
+µ
+�
+φ,
+(2)
+where g is the SU(2)L gauge coupling, W a
+µ are the SU(2)L gauge bosons, and τa are the Pauli matrices.
+After the EWSB, the scalar doublet φ can be explicitly expressed in terms of the component fields, as
+3
+
+follows
+φ =
+1
+√
+2
+� √
+2 ω+
+v + h + iζ
+�
+,
+(3)
+where v is the vacuum expectation value (VEV). Subsequently, the scalar kinetic terms can be conve-
+niently decomposed as [22]
+Lkin = (Dµφ)†(Dµφ) = Lmass + Lquad + Lmixed + Lderiv + Lcubic + Lquartic .
+(4)
+Collectively denoting the gauge bosons as Ga,b,...
+µ
+and the component scalar fields as si,j,..., the meaning
+of the individual terms introduced in the above equation are given below
+Lmass :
+these are the mass terms for the guage bosons of the form v2Ga
+µ
+†Gaµ ,
+Lquad :
+these are the kinetic terms of the component scalar fields, (∂µsi)†(∂µsi) ,
+Lmixed :
+terms of the form (∂µsi)†(ivGµ) + h.c. ,
+Lderiv :
+terms of the form (∂µsi)†(iGµsj) + h.c. ,
+Lcubic :
+terms of the form (Ga,µsi)†(vGb
+µ) + h.c. ,
+Lquartic :
+terms of the form (Ga,µsi)†(Gb
+µsj) .
+To identify the custodial multiplets, we begin with Lmass which, in the SM, is given by
+Lmass
+=
+g2v2
+8
+�
+W µ+W −
+µ + W µ−W +
+µ + W 3µW 3
+µ
+�
+.
+(5)
+where
+W ±
+µ = W 1
+µ ∓ iW 2
+µ
+√
+2
+.
+(6)
+We can see from the above equation that the SU(2)L gauge bosons have the same mass. This motivates
+us to identify a custodial multiplet of the gauge bosons as1
+W =
+�
+�
+−W +
+W3
+W −
+�
+� .
+(7)
+Note that the Lorentz indices have been suppressed here for simplicity as it has no bearing on the
+SU(2)C transformations. In terms of the SU(2)C triplet of Eq. (7), Lmass can be rewritten as
+Lmass = g2v2
+8
+(W · W) ,
+(8)
+which is manifestly invariant under SU(2)C. To identify the SU(2)C multiplets of the scalar fields, let
+us turn our attention to Lcubic and Lmixed. First, in terms of the triplet W, Lcubic can be expressed
+as
+Lcubic = g2v
+4 h (W · W) .
+(9)
+1the minus sign in the first entry of W comes from the details of SU(2) group theory, which are explained in
+Appendix A.
+4
+
+Thus, Lcubic will also be SU(2)C invariant if we identify the physical scalar, h, as a singlet of SU(2)C.
+Next, we look into Lmixed, which is given by
+Lmixed = gv
+2
+�
+i
+�
+∂µw−�
+W +
+µ − i
+�
+∂µw+�
+W −
+µ − (∂µζ) W 3
+µ
+�
+.
+(10)
+Given the identification of W in Eq. (7), the above equation encourages us to define an SU(2)C triplet
+of scalar fields as follows:
+T =
+�
+�
+iω+
+−ζ
+iω−
+�
+� .
+(11)
+In terms of W and T, Eq. (10) can be written as
+Lmixed = gv
+2 (W · ∂T) ,
+(12)
+which explicitly demonstrates the SU(2)C invariance of Lmixed. The other terms, Lquad, Lderiv, and
+Lquartic, when expressed in terms of W and T, can also be shown to be invariant under SU(2)C.
+All these terms will be considered in detail in the next subsection, when we consider the nHDM
+generalisation of the above prescription.
+Now, let us take a look at the SU(2)C invariance of the scalar potential, which is given by
+V (φ) = µ2 �
+φ†φ
+�
++ λ
+�
+φ†φ
+�2
+.
+(13)
+After the EWSB, φ†φ can be expressed as
+φ†φ
+=
+1
+2(T · T) + v2
+2 + h2
+2 + vh .
+(14)
+We can see that, our previous multiplet identifications of T and h are compatible with the SU(2)C
+invariance of the scalar potential. In other words, no additional conditions need to be imposed on the
+SM scalar potential to make it SU(2)C invariant. It should be noted that, the SU(2)C invariance of
+the scalar potential mandates that the scalars which are in the same SU(2)C multiplet should have
+the same mass. This condition is trivially satisfied here in the SM as all the components of T are
+Goldstone bosons with zero masses. This will no longer be true in nHDMs, where we will need to
+impose additional restrictions on the parameters of the scalar potential to ensure custodial invariance.
+2.2
+Generalization to nHDM
+We will now look at the scalar kinetic Lagrangian for a model with n complex scalar doublets φk
+(k = 1, . . . , n) and identify the different SU(2)C multiplets. Thus we begin with
+Lkin =
+n
+�
+k=1
+(Dµφk)†(Dµφk) ,
+(15)
+where, under the assumption of g′ = 0, the gauge covariant derivative of φk is given by
+Dµφk =
+�
+∂µ + igτa
+2 W a
+µ
+�
+φk .
+(16)
+5
+
+After the EWSB, the k-th scalar doublet is decomposed as
+φk =
+1
+√
+2
+�
+√
+2w+
+k
+vk + hk + izk
+�
+,
+(17)
+where vk is the VEV of φk, assumed to be real. Borrowing the terminology introduced in Eq. (4), we
+still have
+Lmass = g2v2
+8
+(W · W) ,
+(18)
+where v =
+�
+v2
+1 + v2
+2 + ... + v2n is the total electroweak VEV, and we have used Eq. (7) for the definiton
+of W. This implies that Lmass will still respect SU(2)C once we identify the custodial triplet of the
+gauge bosons, as in the case of the SM. Similarly, for Lcubic we have
+Lcubic = g2
+4 (W · W)
+n
+�
+k=1
+vkhk .
+(19)
+Evidently, Lcubic will also be custodially invariant if we identify hk (k = 1, ..., n) as singlets of SU(2)C.
+Next, we turn our attention to Lmixed, which has the following form
+Lmixed = g
+2
+n
+�
+k=1
+vk
+�
+i(∂µw−
+k )W +
+µ − i(∂µw+
+k )W −
+µ − (∂µzk)W 3
+µ
+�
+.
+(20)
+Taking inspiration from Eq. (10), we now proceed to define a set of SU(2)C triplets involving the
+scalar component fields as
+Tk ≡
+�
+�
+iw+
+k
+−zk
+iw−
+k
+�
+� ,
+k = 1, ..., n .
+(21)
+Following this identification, we can express Lmixed as the sum of SU(2)C invariants, given by
+Lmixed
+=
+g
+2
+n
+�
+k=1
+vk (W · ∂Tk) .
+(22)
+For the sake of completeness, we also express Lquad, Lquartic, and Lderiv, in terms of W, Tk, and hk,
+as follows
+Lquad
+=
+1
+2
+n
+�
+k=1
+[(∂Tk · ∂Tk) + (∂µhk)(∂µhk)] ,
+(23a)
+Lquartic
+=
+g2
+8 (W · W)
+n
+�
+k=1
+(Tk · Tk + h2
+k) ,
+(23b)
+Lderiv
+=
+g
+2
+n
+�
+k=1
+{hk(W · ∂Tk) + ∂hk(Tk · W) + (Tk × ∂Tk) · W} ,
+(23c)
+where (r1 × r2) · r3 is the singlet combination of the SU(2) product of three triplets, r1,2,3, for which
+the explicit expression is given in appendix A.
+6
+
+Thus, we can see that all the terms in the scalar kinetic Lagrangian are custodially invariant.
+However, the triplets Tk are not expressed in terms of physical fields. Rotation of these fields from
+the Lagrangian basis to the physical basis will give rise to the Goldstone bosons, the physical charged
+scalars, and pseudoscalars2. We would like to transfer the SU(2)C invariance into the physical basis
+as well. For this, we need to rotate each triplet as a whole object, that is,
+Pj =
+n
+�
+k=1
+OjkTk
+j = 1, 2, . . . n ,
+(24)
+where Pj denotes the j-th triplet of SU(2)C in the physical basis, and Ojk are the elements of an
+orthogonal matrix. Note that, each triplet Tk, contained a pseudoscalar field and a pair of charged
+fields. Consequently, Eq. (24) implies that the charged and pseudoscalar mass matrices should be
+rotated into the physical basis by means of the same rotation matrix, in order to preserve the SU(2)C
+invariance of Lkin in the physical basis as well. Now, for a charged scalar and a pseudoscalar in the
+physical basis to be placed in the same triplet Pj, they should have a common mass so that the mass
+terms for the members of Pj can be concisely expressed in an SU(2)C invariant form as M2
+j (Pj · Pj).
+Thus, we can conclude that, in the physical basis, the diagonal mass matrices in the charged and
+pseudoscalar sectors must be equal. Also, from Eq. (24), we should recall that the rotations that bring
+the mass matrices of the charged and pseudoscalar sectors to their respective diagonal forms should
+also be the same. Putting this together, we can conclude that the mass matrix of the charged and
+pseudoscalar sectors should be equal in the Lagrangian basis as well, that is
+M2
+C = M2
+P .
+(25)
+Since the information about the scalar masses and the mixings come from the scalar potential, the
+parameters of the scalar potential should adjust themselves so that Eq. (25) is satisfied (for arbitrary
+values of the VEVs), and consequently, the scalar potential also comes under the umbrella of SU(2)C
+invariance.
+2.3
+Examples with 2HDMs
+We will now explicitly demonstrate how Eq. (25) manifests itself for the simple case of a 2HDM scalar
+potential.
+At first, let us consider the 2HDM scalar potential with a softly-broken Z2 symmetry
+(φ1 → φ1, φ2 → −φ2), which is commonly used in NFC models [3]:
+V (φ1, φ2)
+=
+m2
+11φ†
+1φ1 + m2
+22φ†
+2φ2 − m2
+12(φ†
+1φ2 + φ†
+2φ1) + λ1
+2 (φ†
+1φ1)2 + λ2
+2 (φ†
+2φ2)2
++λ3(φ†
+1φ1)(φ†
+2φ2) + λ4(φ†
+1φ2)(φ†
+2φ1) + λ5
+2
+�
+(φ†
+1φ2)2 + (φ†
+2φ1)2�
+.
+(26)
+The charged and pseudoscalar mass matrices which transpire from the above scalar potential are given
+by
+M2
+C
+=
+�
+m2
+12v2
+v1
+− 1
+2λ4v2
+2 − 1
+2λ5v2
+2
+−m2
+12 + 1
+2λ4v1v2 + 1
+2λ5v1v2
+−m2
+12 + 1
+2λ4v1v2 + 1
+2λ5v1v2
+m2
+12v1
+v2
+− 1
+2λ4v2
+1 − 1
+2λ5v2
+1
+�
+,
+(27a)
+M2
+P
+=
+�
+m2
+12v2
+v1
+− λ5v2
+2
+−m2
+12 + λ5v1v2
+−m2
+12 + λ5v1v2
+m2
+12v1
+v2
+− λ5v2
+1
+�
+.
+(27b)
+2Throughout the paper, we are implicitly assuming CP conservation in the scalar potential, so that such a classification
+of the scalar spectrum is possible.
+7
+
+Thus, imposition of Eq. (25) will lead to the following relation
+λ4 = λ5 ,
+(28)
+which agrees with earlier results [13,14,21]. In passing, we wish to point out that even if we consider
+the general 2HDM potential [3]
+V (φ1, φ2)
+=
+m2
+11φ†
+1φ1 + m2
+22φ†
+2φ2 − (m2
+12φ†
+1φ2 + h.c.) + λ1
+2 (φ†
+1φ1)2 + λ2
+2 (φ†
+2φ2)2 + λ3(φ†
+1φ1)(φ†
+2φ2)
++λ4(φ†
+1φ2)(φ†
+2φ1) +
+�λ5
+2 (φ†
+1φ2)2 + λ6(φ†
+1φ1)(φ†
+1φ2) + λ7(φ†
+2φ2)(φ†
+1φ2) + h.c.
+�
+,
+(29)
+the condition for custodial invariance is still given by Eq. (28). The reason for this will be discussed
+in more detail in Appendix B.
+3
+Validation of the custodial limit by explicit calculation
+In SU(2)C invariant models, we expect that no additional contribution to the T-parameter comes
+from the scalar sector. It would be rather reassuring to explicitly verify that this is indeed the case for
+nHDMs in the limit of Eq. (25). For this purpose, we use the one-loop formula for the NP contribution
+to the T-parameter for nHDMs given in refs. [15,16]:
+αT =
+g2
+64π2M2
+W
+�
+n
+�
+a=2
+2n
+�
+b=2
+���
+�
+U †V
+�
+ab
+���
+2
+F
+�
+m2
+a, µ2
+b
+�
+−
+2n−1
+�
+b=2
+2n
+�
+b′=b+1
+���
+�
+V †V
+�
+bb′
+���
+2
+F
+�
+µ2
+b, µ2
+b′
+�
++3
+n
+�
+b=2
+���
+�
+V †V
+�
+1b
+���
+2 �
+F
+�
+M2
+Z, µ2
+b
+�
+− F
+�
+M2
+W , µ2
+b
+� ��
+,
+(30)
+where
+F(x, y) ≡
+�
+�
+�
+x + y
+2
+−
+xy
+x − y ln x
+y ,
+x ̸= y
+0,
+x = y
+,
+(31)
+and α is the fine-structure constant.
+The masses of the charged-scalars are denoted by ma, and
+µa are the masses of the physical neutral scalars, defined in such a way that a ≤ n refers to the
+pseudoscalars, and a > n are the CP-even fields. Lastly, U † and V † are n × n and 2n × n matrices
+that rotate the charged and neutral components (w±
+k and ϕ0
+k ≡ hk + izk) into the physical basis (S±
+and S0), respectively, in such a way that the Goldstone bosons are located in the first row,
+w±
+k =
+n
+�
+a=1
+UkaS±
+a ,
+ϕ0
+k =
+2n
+�
+b=1
+VkbS0
+b .
+(32)
+We give the explicit structure of S± and S0 as follows
+S± =
+�
+ω±, H±
+1 , . . . , H±
+n−1
+�T ,
+S0 =
+�
+ζ, A1, . . . , An−1, h, H1, . . . , Hn−1
+�T ,
+(33)
+where ω± and ζ are the charged and neutral unphysical Goldstone bosons, respectively, H±
+k is the
+k-th charged scalar, and Ak the k-th pseudoscalar. For the CP-even scalars, h is the lightest scalar
+8
+
+usually identified as the SM-like Higgs, and Hk denotes the k-th physical CP-even scalar. Following
+the definition of Eq. (24), and comparing with Eq. (32), we can relate the U and V matrices with the
+scalar rotation matrices as follows
+U = OT
+C ,
+V =
+�
+iOT
+P
+OT
+S
+�
+,
+(34)
+where the subscripts C, P, S refer to the charged, pseudoscalar, and scalar sectors respectively. The
+relevant combinations can be expressed as
+U †V =
+�
+i OC OT
+P
+OC OT
+S
+�
+,
+V †V =
+� 1n×n
+−i OP OT
+S
+i OS OT
+P
+1n×n
+�
+.
+(35)
+We must note that the last term of Eq. (30) vanishes in the limit g′ → 0, that is, MZ = MW . Therefore,
+we will focus on the first two terms in Eq. (30), and convince ourselves that they also vanish in the
+custodial limit of Eq. (25). Taking advantage of Eq. (35), we can rewrite the first two terms of Eq. (30)
+as
+αT =
+g2
+64π2M2
+W
+�
+n
+�
+a=2
+n
+�
+b=2
+���
+iOCOT
+P
+�
+ab
+��2 F
+�
+m2
+a, µ2
+b
+�
++
+n
+�
+a=2
+n
+�
+b=1
+���
+OCOT
+S
+�
+ab
+��2 F
+�
+m2
+a, µ2
+n+b
+�
+−
+n
+�
+a=2
+n
+�
+b=1
+���
+− iOP OT
+S
+�
+ab
+��2 F
+�
+µ2
+a, µ2
+n+b
+� �
+.
+(36)
+In the custodial limit, we must have M2
+P = M2
+C, and thus OP = OC, as well as m2
+a = µ2
+a (with a < n).
+In this way, the second and third terms of Eq. (36) cancel out, and OCOT
+P = OP OT
+P = 1n×n leads to
+a zero contribution from the first term, because of Eq. (31).
+4
+Democratic 3HDMs
+The Yukawa Lagrangian for a democratic 3HDM, as discussed in the introduction, has the following
+form
+LY = −YdQLφ2nR − YuQL�φ3pR − YℓLLφ1ℓR ,
+(37)
+where Yd.u.ℓ are the Yukawa couplings in the down-quark, up-quark, and charged-lepton sectors.
+The up-type, down-type, and charged-lepton right-handed fields are denoted as pR, nR, and ℓR,
+respectively. The left-handed SU(2)L doublets for the quarks and leptons are QL = (pL, nL)T and
+LL = (νL, eL)T . Finally, �φ3 = iτ2φ∗
+3 is the SU(2)L doublet responsible for the up-quark masses. There
+are two common ways to arrive at the above Lagrangian. The first is to impose a Z3 symmetry as
+follows [8]
+φ1 → ω φ1 ,
+φ2 → ω2φ2 ,
+ℓR → ω2ℓR ,
+nR → ω nR .
+(38)
+The second possibility relies on a Z2 × Z′
+2 symmetry under which the fields transform as [5]
+Z2 :
+φ1 → −φ1 ,
+ℓR → −ℓR
+(39a)
+Z′
+2 :
+φ2 → −φ2 ,
+nR → −nR
+(39b)
+Both in Eqs. (38) and (39), only the nontrivial transformations are explicitly displayed. In the follow-
+ing, we will discuss the implications of these symmetries on the scalar potential in the context of the
+custodial limit.
+9
+
+4.1
+Custodial Limit of Democratic 3HDMs
+In this subsection, we will write down the explicit forms of the scalar potential which follow from
+the symmetry of Eqs. (38) and (39). Then, we will proceed to calculate the detailed structure of the
+charged and pseudoscalar mass matrices. Finally, we will impose Eq. (25) to extract the implications
+in terms of the parameters of the scalar potential.
+4.1.1
+The case with a Z3 symmetry
+The scalar potential for this case will be given by [36]
+VZ3
+=
+m2
+11φ†
+1φ1 + m2
+22φ†
+2φ2 + m2
+33φ†
+3φ3 − m2
+12(φ†
+1φ2 + φ†
+2φ1) − m2
+13(φ†
+1φ3 + φ†
+3φ1) − m2
+23(φ†
+2φ3 + φ†
+3φ2)
++λ1(φ†
+1φ1)2 + λ2(φ†
+2φ2)2 + λ3(φ†
+3φ3)2 + λ4(φ†
+1φ1)(φ†
+2φ2) + λ5 (φ†
+1φ1)(φ†
+3φ3) + λ6(φ†
+2φ2)(φ†
+3φ3)
++λ7(φ†
+1φ2)(φ†
+2φ1) + λ8(φ†
+1φ3)(φ†
+3φ1) + λ9(φ†
+2φ3)(φ†
+3φ2) + λ10
+�
+(φ†
+1φ2)(φ†
+1φ3) + (φ†
+2φ1)(φ†
+3φ1)
+�
++λ11
+�
+(φ†
+2φ1)(φ†
+2φ3) + (φ†
+1φ2)(φ†
+3φ2)
+�
++ λ12
+�
+(φ†
+3φ1)(φ†
+3φ2) + (φ†
+1φ3)(φ†
+2φ3)
+�
+,
+(40)
+where soft-breaking terms have also been allowed. The explicit expressions for the elements of the
+3 × 3 symmetric mass matrix in the charged scalar sector are given below3
+(M2
+C)11
+=
+m2
+12v2
+v1
++ m2
+13v3
+v1
+− λ10v2v3 − λ11v2
+2v3
+2v1
+− λ12v2v2
+3
+2v1
+− λ7v2
+2
+2
+− λ8v2
+3
+2
+,
+(41a)
+(M2
+C)22
+=
+m2
+12v1
+v2
++ m2
+23v3
+v2
+− λ10v2
+1v3
+2v2
+− λ11v1v3 − λ12v1v2
+3
+2v2
+− λ7v2
+1
+2
+− λ9v2
+3
+2
+,
+(41b)
+(M2
+C)33
+=
+m2
+13v1
+v3
++ m2
+23v2
+v3
+− λ10v2
+1v2
+2v3
+− λ11v1v2
+2
+2v3
+− λ12v1v2 − λ8v2
+1
+2
+− λ9v2
+2
+2
+,
+(41c)
+(M2
+C)12
+=
+(M2
+C)21 = −m2
+12 + 1
+2λ10v1v3 + 1
+2λ11v2v3 + 1
+2λ7v1v2 ,
+(41d)
+(M2
+C)13
+=
+(M2
+C)31 = −m2
+13 + 1
+2λ10v1v2 + 1
+2λ12v2v3 + 1
+2λ8v1v3 ,
+(41e)
+(M2
+C)23
+=
+(M2
+C)32 = −m2
+23 + 1
+2λ11v1v2 + 1
+2λ12v1v3 + 1
+2λ9v2v3 .
+(41f)
+Similarly, for the pseudoscalar mass matrix we have
+(M2
+P )11
+=
+m2
+12v2
+v1
++ m2
+13v3
+v1
+− 2λ10v2v3 − λ11v2
+2v3
+2v1
+− λ12v2v2
+3
+2v1
+,
+(42a)
+(M2
+P )22
+=
+m2
+12v1
+v2
++ m2
+23v3
+v2
+− λ10v2
+1v3
+2v2
+− 2λ11v1v3 − λ12v1v2
+3
+2v2
+,
+(42b)
+(M2
+P )33
+=
+m2
+13v1
+v3
++ m2
+23v2
+v3
+− λ10v2
+1v2
+2v3
+− λ11v1v2
+2
+2v3
+− 2λ12v1v2 ,
+(42c)
+(M2
+P )12
+=
+(M2
+P )21 = −m2
+12 + λ10v1v3 + λ11v2v3 − λ12v2
+3
+2
+,
+(42d)
+(M2
+P )13
+=
+(M2
+P )31 = −m2
+13 + λ10v1v2 + λ12v2v3 − λ11v2
+2
+2
+,
+(42e)
+(M2
+P )23
+=
+(M2
+P )32 = −m2
+23 + λ11v1v2 + λ12v1v3 − λ10v2
+1
+2
+.
+(42f)
+3We have used the minimization conditions to trade m2
+11, m2
+22, and m2
+33 in favor of the VEVs.
+10
+
+For Eq. (25) to hold for any arbitrary values of the VEVs, we should have
+λ7 = λ8 = λ9 = λ10 = λ11 = λ12 = 0 ,
+(43)
+which should be read as the conditions for custodial invariance in a Z3 symmetric 3HDM potential.
+4.1.2
+The case with a Z2 × Z′
+2 symmetry
+The scalar potential in this case can be written as [37]
+VZ2×Z2
+=
+m2
+11φ†
+1φ1 + m2
+22φ†
+2φ2 + m2
+33φ†
+3φ3
+−m2
+12(φ†
+1φ2 + φ†
+2φ1) − m2
+13(φ†
+1φ3 + φ†
+3φ1) − m2
+23(φ†
+2φ3 + φ†
+3φ2)
++λ1(φ†
+1φ1)2 + λ2(φ†
+2φ2)2 + λ3(φ†
+3φ3)2 + λ4(φ†
+1φ1)(φ†
+2φ2) + λ5(φ†
+1φ1)(φ†
+3φ3)
++λ6(φ†
+2φ2)(φ†
+3φ3) + λ7(φ†
+1φ2)(φ†
+2φ1) + λ8(φ†
+1φ3)(φ†
+3φ1) + λ9(φ†
+2φ3)(φ†
+3φ2)
++λ10
+�
+(φ†
+1φ2)2 + (φ†
+2φ1)2�
++ λ11
+�
+(φ†
+1φ3)2 + (φ†
+3φ1)2�
++ λ12
+�
+(φ†
+2φ3)2 + (φ†
+3φ2)2�
+, (44)
+where, again, we have allowed terms that softly-break the symmetry. The elements of the charged-
+scalar mass matrix are given below:
+(M2
+C)11
+=
+m2
+12v2
+v1
++ m2
+13v3
+v1
+− λ10v2
+2 − λ7v2
+2
+2
+− λ11v2
+3 − λ8v2
+3
+2
+,
+(45a)
+(M2
+C)22
+=
+m2
+12v1
+v2
++ m2
+23v3
+v2
+− λ10v2
+1 − λ7v2
+1
+2
+− λ12v2
+3 − λ9v2
+3
+2
+,
+(45b)
+(M2
+C)33
+=
+m2
+13v1
+v3
++ m2
+23v2
+v3
+− λ11v2
+1 − λ8v2
+1
+2
+− λ12v2
+2 − λ9v2
+2
+2
+,
+(45c)
+(M2
+C)12
+=
+(M2
+C)21 = −m2
+12 + λ10v1v2 + 1
+2λ7v1v2 ,
+(45d)
+(M2
+C)13
+=
+(M2
+C)31 = −m2
+13 + λ11v1v3 + 1
+2λ8v1v3 ,
+(45e)
+(M2
+C)23
+=
+(M2
+C)32 = −m2
+23 + λ12v2v3 + 1
+2λ9v2v3 .
+(45f)
+For the case of the pseudoscalar mass matrix elements, we find
+(M2
+P )11
+=
+m2
+12v2
+v1
++ m2
+13v3
+v1
+− 2λ10v2
+2 − 2λ11v2
+3 ,
+(46a)
+(M2
+P )22
+=
+m2
+12v1
+v2
++ m3
+23v3
+v2
+− 2λ10v2
+1 − 2λ12v2
+3 ,
+(46b)
+(M2
+P )33
+=
+m2
+13v1
+v3
++ m2
+23v2
+v3
+− 2λ11v2
+1 − 2λ12v2
+2 ,
+(46c)
+(M2
+P )12
+=
+(M2
+P )21 = −m2
+12 + 2λ10v1v2 ,
+(46d)
+(M2
+P )13
+=
+(M2
+P )31 = −m2
+13 + 2λ11v1v3 ,
+(46e)
+(M2
+P )23
+=
+(M2
+P )32 = −m2
+23 + 2λ12v2v3 .
+(46f)
+Following the reasoning presented for the Z3 case, the conditions for custodial invariance can be found
+using Eq. (25), which read
+λ7 = 2λ10, λ8 = 2λ11, λ9 = 2λ12.
+(47)
+11
+
+4.2
+Wrong-sign Yukawas in democratic 3HDMs
+Now we turn our attention to the Yukawa sector phenomenology that follows from Eq. (37). To begin
+with, we parametrize the VEVs of the three doublets as follows
+v1 = v cos β1 cos β2,
+v2 = v cos β1 sin β2,
+v3 = v sin β1,
+(48)
+which, by design, satisfies the relation
+v2
+1 + v2
+2 + v2
+3 = v2,
+(49)
+with v = 246 GeV being the total electroweak VEV. The range of values of β1 and β2 allowed from
+the perturbativity of the fermionic Yukawa couplings can be found in refs. [10,11].
+The current LHC Higgs data usually serves as a motivation to stay close to the so-called align-
+ment limit [8]. However, as explained in the introduction, here we are after a relatively less-explored
+possibility where the sign of the down-type Yukawa couplings is opposite to what has been predicted
+by the SM. To prepare ourselves for what comes next, we define the Higgs coupling modifiers as
+follows [34,35]
+κx = ghxx
+gSM
+hxx
+,
+(50)
+where the field h, in the context of nHDMs, denotes the lightest CP-even scalar, and ‘x’ can represent
+the massive vector bosons or fermions.
+To illustrate the details of the wrong-sign limit, we briefly revisit the example of a type-II 2HDM
+where the coupling modifiers have the expression given in Table 1.4 These coupling modifiers can be
+conveniently rewritten as follows
+κII
+V = sin (β − α) ,
+(51a)
+κII
+u = sin (β − α) + cot β cos (β − α) ,
+(51b)
+κII
+d = κII
+ℓ = sin (β − α) − tan β cos (β − α) .
+(51c)
+Model
+κV
+κu
+κd
+κℓ
+type-II 2HDM
+sin (α − β)
+cos α
+sin β
+− sin α
+cos β
+− sin α
+cos β
+democratic 3HDMs
+cos α2 cos β2 cos (α1 − β1)
++ sin α2 sin β2
+sin α2
+sin β2
+sin α1
+sin β1
+cos α2
+cos β2
+cos α1
+cos β1
+cos α2
+cos β2
+Table 1:
+The coupling modifiers for the type-II 2HDM and democratic 3HDMs. In the 2HDM case,
+tan β = v2/v1 and α is a suitably defined rotation angle in the CP-even scalar sector [3]. Similarly, in
+the case of 3HDMs, α1 and α2 are two suitably defined rotation angles in the CP-even scalar sector [8].
+Now let us consider the limit
+cos (β − α) =
+r
+tan β ,
+(52)
+4We note here that for the 2HDM case we are using the standard convention for α, such that the alignment limit is
+given by cos (β − α) = 0. However, for the case of democratic 3HDMs, the angles α1,2 are defined in a way such that
+the alignment conditions read sin (αi − βi) = 0, with i = 1, 2 [8].
+12
+
+Figure 1:
+Allowed region at 95% CL from the current data on Higgs signal strengths in the type-II
+2HDM. It should be noted that when considering the h → γγ decay, the charged-Higgs contribu-
+tion has been neglected with the understanding that it can be safely decoupled in the presence of the
+soft-breaking parameter in the scalar potential [38–40].
+For illustration, the line corresponding to
+cos(β − α) = 2/tan β has also been plotted in the same graph, which reinforces our intuitions from
+Eq. (52).
+where r is a real number and tan β ≫ |r|. In such a scenario, Eq. (51) can be approximated as
+κII
+V ≈ 1,
+κII
+u ≈ 1,
+κII
+d,ℓ ≈ 1 − r.
+(53)
+The wrong-sign limit, in particular, arises for r = 2, in which case Eq. (53) takes the following
+form
+κII
+V ≈ 1,
+κII
+u ≈ 1,
+κII
+d,ℓ ≈ −1.
+(54)
+Such a possibility is allowed because the current LHC Higgs data is not sensitive enough to probe
+the sign of the bottom-quark Yukawa coupling in the loop-induced vertices such as hgg and hγγ. To
+demonstrate this explicitly, we use the current Higgs data [23], and display the 2σ-allowed region in
+the cos (β − α) vs tan β plane in Fig. 1. The thin dark-blue region corresponds to the wrong-sign limit
+in the type-II 2HDM.5
+Now, we will demonstrate that such wrong-sign scenarios are also entertained in democratic
+3HDMs with much greater flexibility in terms of the number of free parameters. To illustrate this, we
+again purposefully rewrite the Higgs coupling modifiers in Table 1 for democratic 3HDMs as follows
+κV
+=
+cos (α1 − β1)
+1 + tan2 β2
+�
+cos (α2 − β2) − sin (α2 − β2) tan β2
+�
++
+tan2 β2
+1 + tan2 β2
+�
+cos (α2 − β2) + sin (α2 − β2) cot β2
+�
+,
+(55a)
+5In a recent 2HDM fit [41], it was claimed that the wrong-sign limit is disfavoured by the current Higgs data at 2σ,
+and only allowed within 3σ. However, we have used a more updated dataset and our result for 2HDM agrees with the
+most updated fit from ATLAS [23] (in Fig. 20b, we can see the wrong-sign limit is still allowed).
+13
+
+40
+Kd=K
+0.9
+30
+0.3
+-0.3
+tanβ
+20
+-0.9
+2
+cos (β-α) =
+tanβ
+10
+0.2
+0.0
+0.2
+0.4
+cos(β-α)κu
+=
+cos (α2 − β2) + sin (α2 − β2) cot β2,
+(55b)
+κd
+=
+�
+cos (α1 − β1) + sin (α1 − β1) cot β1
+��
+cos (α2 − β2) − tan β2 sin (α2 − β2)
+�
+,
+(55c)
+κℓ
+=
+�
+cos (α1 − β1) − sin (α1 − β1) tan β1
+��
+cos (α2 − β2) − tan β2 sin (α2 − β2)
+�
+.
+(55d)
+In a similar way to the 2HDM scenario, we focus our attention to the limit
+sin (α2 − β2) =
+r2
+tan β2
+,
+(56)
+where r2 is a real number, and tan β2 ≫ |r2|. In this limit, κV ≈ κu ≈ 1, but κd and κℓ take the
+following form
+κd
+=
+(1 − r2)
+�
+cos (α1 − β1) + sin (α1 − β1) cot β1
+�
+= (1 − r2)sin α1
+sin β1
+,
+(57a)
+κℓ
+=
+(1 − r2)
+�
+cos (α1 − β1) − sin (α1 − β1) tan β1
+�
+= (1 − r2)cos α1
+cos β1
+.
+(57b)
+If we further consider the limit
+sin (α1 − β1) =
+r1
+tan β1
+,
+(58)
+where, again, r1 is a real number, and tan β1 ≫ |r1|, then Eq. (57) can be further simplified to
+κd
+=
+(1 − r2),
+(59a)
+κℓ
+=
+(1 − r2)(1 − r1).
+(59b)
+The limits that can be obtained for different values of r1 and r2 have been listed in Table 2, where
+we can see that all the wrong-sign possibilities that can be obtained from 2HDMs with NFC are
+encompassed by a democratic 3HDM. All these features have been clearly depicted in Figs. 2 and 3,
+where the darker shade correspond to the wrong-sign limit. Thus, we can see that the democratic
+3HDM gives more leeway for the wrong-sign limit, when compared to the 2HDM.
+r1 = 0
+r1 = 2
+r2 = 0
+κd = 1
+κℓ = 1
+(alignment limit)
+κd ≈ 1
+κℓ ≈ −1
+(wrong-sign limit in the type-X 2HDM)
+r2 = 2
+κd ≈ −1
+κℓ ≈ −1
+(wrong-sign limit in the type-II 2HDM)
+κd ≈ −1
+κℓ ≈ 1
+(wrong-sign limit in the type-Y 2HDM)
+Table 2:
+Wrong-sign possibilities in democratic 3HDMs. It should be noted that κu ≈ κV ≈ 1 in all
+the cases.
+So far, we have obtained the wrong-sign limit in the democratic 3HDM following the 2HDM
+prescription. However, a democratic Yukawa structure can entertain more exotic possibilities. As
+usual, we start by investigating how to impose κu ≈ 1. One possibility is to set tan β2 ≫ 1 together
+with cos (α2 − β2) ≈ 1, as was done in Eq. (56), leading to Eq. (57). Now, instead of going to the
+limit of Eq. (58), one can choose
+sin (α1 − β1) ≈ ±1 ,
+tan β1 ≈ 1 .
+(60)
+14
+
+Figure 2:
+Allowed region at 95% CL from the current data on Higgs signal strengths in democratic
+3HDM. As before, the charged-Higgs contribution to h → γγ decay is neglected with the understanding
+that it can be safely decoupled in the presence of the soft-breaking parameter in the scalar potential [38–
+40]. The contour corresponding to Eqs. (56) and (58), for r1 = r2 = 2 are also displayed for easy
+comparison.
+In this way, using cos (α1 − β1) ≈ 0, we get
+κV ≈ κu
+≈
+1,
+(61a)
+κd ≈ −κℓ
+≈
+± (1 − r2) ,
+(61b)
+where, as before, r2 ≈ 0 and r2 ≈ 2 can give us two different possibilities. As such, we see that it
+is possible to achieve a wrong-sign limit in the democratic 3HDMs without the requirement of large
+tan β1. If we follow the usual path to the wrong-sign limit, we see that sin (α1 − β1) ≈ 1 is allowed in
+Fig. 2. The possibility with sin (α1 − β1) ≈ −1 is separately showcased in Fig. 3 for better visibility.
+At this point it will be quite natural to wonder how such wrong-sign possibilities can be probed
+in experiments. An obvious way to sense the wrong-sign limit will be to measure the Higgs signal
+strengths that involve hgg and hγγ effective vertices with increasing precision to the extent that the
+interference terms from the lighter fermions in the loop start to become relevant. Alternatively, the
+decay h → Υγ was suggested as a probe for the sign of κb [42, 43]. Similarly h → τ +τ −γ [44] may
+serve as a probe for the sign of κτ. Additionally, if we know the UV complete model responsible for
+the wrong-sign Yukawas, then we can perform a targeted search for the nonstandard particles. For
+instance, in this case the wrong-sign limit is arising within an nHDM framework. Thus, one can look
+for nonstandard scalars whose phenomenologies in the wrong-sign limit will be presumably different
+from the corresponding alignment limit counterparts [45].
+But the crucial point is, even if we stay agnostic about the origin of the wrong-sign Yukawas,
+we should still remember that any departure from the SM couplings will introduce an energy scale
+beyond which unitarity will be violated [46]. Therefore, the wrong-sign limits as described in, e.g., Eq.
+(54) will inevitably call for NP below the unitarity violation scale. For the arrangement of couplings
+appearing in Eq. (54), the earliest onset of unitarity violation will occur in the bb → WLWL scattering
+15
+
+40
+py
+35
+0.9
+30
+0.6
+0.3
+25
+0
+-0.3
+tan
+20
+-0.6
+-0.9
+15
+2
+sin (α2-β2)
+tan β2
+10
+5
+-0.4
+-0.2
+0.0
+0.2
+0.4
+0.6
+0.8
+sin(α2-β2)40
+ly* Py
+35
+0.9
+30
+0.6
+0.3
+25
+0
+-0.3
+B
+tan
+20
+-0.6
+-0.9
+15
+2
+sin (α1-β1) :
+tan βi
+10
+5
+1.0
+-0.5
+0.0
+0.5
+1.0
+sin(α1-β1)Figure 3:
+Allowed region at 95% CL from the current data on Higgs signal strengths for
+sin(α1 − β1) ≈ −1 is displayed separately in this plot. All the points shown in the left panel in the
+sin(α2 − β2) vs. tan β2 plane are sampled from the sin(α1 − β1) ≈ −1 region as displayed in the right
+panel. The contour corresponding to Eq. (56) for r2 = 2 is displayed for easy comparison.
+and the maximum energy cut-off before which the NP must intervene, will be given by [47],
+Emax = 2
+√
+2π
+GF mb
+≈ 180 TeV .
+(62)
+5
+Summary
+In this article we have studied two new aspects of democratic 3HDMs, namely, the impact of custodial
+symmetry and the wrong-sign Yukawa couplings.
+As such, our goal is to provide the ingredients
+for constructing democratic 3HDMs which is safeguarded against the T-parameter constraints, while
+showcasing the interesting Yukawa structure allowed by the Higgs data. The custodial limit serves
+as a systematic guideline for alleviating the stringent constraints arising from the electroweak T-
+parameter. We have followed an alternative approach to find the general condition for the custodial
+symmetry to be prevalent in scalar sector of an nHDM. We used these results to extract the model
+specific conditions for democratic 3HDMs which usually comes in two different avatars – one with a Z3
+symmetry and the other with a Z2 × Z′
+2 symmetry. We then turn our attention to the Yukawa sector
+of democratic 3HDMs and showed that the democratic 3HDMs also accommodate the possibility of
+wrong-sign limit where the signs of the down-type Yukawa couplings are opposite to the corresponding
+SM predictions. We find that a democratic 3HDM covers all the wrong-sign scenarios that can possibly
+arise from a 2HDM framework with NFC. In the recent fits of the Higgs couplings [23,48,49] in the
+kappa formalism [34, 35], the results are often reported with an implicit assumption about the signs
+of the kappas. Our discussion on the wrong-sign limit highlights the importance of presenting the fit
+results without any inherent assumptions about the signs of the kappas because, otherwise we can
+miss potentially interesting and unconventional limits brought in by many different BSM scenarios.
+16
+
+40
+py
+35
+0.9
+30
+0.6
+0.3
+25
+0
+-0.3
+tan
+20
+-0.6
+-0.9
+15
+2
+sin (α2-β2)
+tan β2
+10
+5
+-0.4
+-0.2
+0.0
+0.2
+0.4
+0.6
+0.8
+sin(α2-β2)1.20
+ly×Py
+0.9
+1.15
+0.6
+0.3
+0
+tan β1
+1.10
+-0.3
+-0.6
+-0.9
+1.05
+1.00
+1.00
+-0.99
+-0.98
+-0.97
+-0.96
+-0.95
+sin(α1-β1)To emphasize the last point, we have also argued how the wrong-sign limit inevitably leads to an
+upper limit on the energy scale for the onset of NP.
+Acknowledgments
+DD and AS thank the Science and Engineering Research Board, India for financial support
+through grant no.
+SRG/2020/000006.
+ML acknowledges funding from Funda¸c˜ao para a Ciˆencia
+e a Tecnologia (FCT) through Grant No.PD/BD/150488/2019, in the framework of the Doc-
+toral Programme IDPASC-PT, and was supported in part by FCT projects CFTP-FCT Unit 777
+(UID/FIS/00777/2019), CERN/FIS-PAR/0008/2019 and CERN/FIS-PAR/0002/2021 which are par-
+tially funded through POCTI (FEDER), COMPETE, QREN and EU. DD and IS also thank ICTS,
+Bengaluru for the warm hospitality while the final stages of this work were being completed.
+A
+Brief note on SU(2) triplets
+A real triplet of SU(2) in the cartesian basis is expressed as follows:
+ACar =
+�
+�
+A1
+A2
+A3
+�
+�
+(63)
+The generators of SU(2) in this basis are given by
+T1 =
+�
+�
+0
+0
+0
+0
+0
+−i
+0
+i
+0
+�
+� ,
+T2 =
+�
+�
+0
+0
+i
+0
+0
+0
+−i
+0
+0
+�
+� ,
+T3 =
+�
+�
+0
+−i
+0
+i
+0
+0
+0
+0
+0
+�
+� .
+(64)
+which make the transformation real. Now we want to migrate to a basis where T3 is diagonal. We
+will call this the spherical basis and the SU(2) triplet in this basis will be denoted by ASph. We note
+that the unitary matrix
+U =
+1
+√
+2
+�
+�
+−1
+i
+0
+0
+0
+√
+2
+1
+i
+0
+�
+� ,
+(65)
+diagonalizes T3 as follows
+U · T3 · U† =
+�
+�
+1
+0
+0
+0
+0
+0
+0
+0
+−1
+�
+� = T ′
+3 .
+(66)
+This implies that ASph will be related to ACar via the following relation
+ASph = UACar =
+�
+�
+�
+1
+√
+2(−A1 + iA2)
+A3
+1
+√
+2(A1 + iA2)
+�
+�
+� .
+(67)
+where we have used Eq. (63). Now let us define
+A± =
+1
+√
+2(A1 ∓ iA2) ,
+(68)
+17
+
+where A+ and A− are implicitly understood to be the complex conjugates of each other. In terms of
+these we can write the SU(2) triplet in the spherical basis as follows
+ASph =
+�
+�
+−A+
+A3
+A−
+�
+� .
+(69)
+Thus, the SU(2) invariant combination of two triplets, in these two bases, will be given by
+A · B
+=
+A1B1 + A2B2 + A3B3
+(70a)
+=
+A+B− + A−B+ + A3B3 .
+(70b)
+In a similar manner, the SU(2) invariant combination of three triplets is expressed as
+(A × B) · C
+=
+(A2B3 − B2A3)C1 + (A3B1 − B3A1)C2 + (A1B2 − B1A2)C3
+(71a)
+=
+i [A3(B−C+ − C−B+) + B3(C−A+ − A−C+) + C3(A−B+ − B−A+)] . (71b)
+B
+Custodially invariant scalar potential
+In this Appendix, we try to enumerate the terms in the scalar potential of a CS-invariant nHDM. Since
+we have doublets only, the renormalizable scalar potential can contain only quadratic and quartic
+terms.
+In n doublets, there are 4n real fields. After the symmetry breaking, there will be n triplets
+of the CS, including one that contains the unphysical Goldstone modes. In addition, there will be n
+singlets. The real parts of the neutral components of φk will be CS singlets. It is then easy to see that
+φ†
+kφk
+=
+1
+2Tk · Tk + CS singlets,
+(72a)
+φ†
+jφk + φ†
+kφj
+=
+Tj · Tk + CS singlets,
+(72b)
+with j ̸= k. These are the quadratic forms which are CS invariant [13, 17, 19]. The total number of
+terms of the first kind is n, and of the second kind is 1
+2n(n − 1), making a total of 1
+2n(n + 1), which
+is also exactly the number of different quadratic terms of the form Tj · Tk that we can get, with
+unrestricted j and k. In fact, if we insist on only real parameters in the scalar potential, there is no
+additional restriction arising from the CS: the terms shown in Eq. (72) are the only ones that are
+Hermitian and gauge invariant.
+The quartic CS invariants are combinations of the quadratics. Thus, we can enumerate the
+kinds of terms that are possible, with N = 1
+2n(n − 1), as follows:
+(φ†
+iφi)2
+:
+:
+n terms,
+(73a)
+(φ†
+iφi)(φ†
+jφj)
+: (i ̸= j) :
+N terms,
+(73b)
+(φ†
+iφj + φ†
+jφi)2
+: (i ̸= j) :
+N terms,
+(73c)
+(φ†
+iφj + φ†
+jφi)(φ†
+kφl + φ†
+l φk)
+: ({i.j} ̸= {k, l}) :
+1
+2N(N − 1) terms,
+(73d)
+(φ†
+iφi)(φ†
+kφl + φ†
+l φk)
+: (k ̸= l) :
+nN terms.
+(73e)
+The total number of such terms is 1
+8n(n+1)(n2 +n+2). The number of terms coming from n triplets
+of CS comes out to be exactly the same, confirming that these are the only possible gauge invariant
+18
+
+combinations. However, it should be noted that in the most general gauge invariant potential, many
+more quartic terms are possible. Thus, the quartic coefficients, λi, need to be correlated in such a way
+so that the terms in the quartic part of the scalar potential can be expressed in terms of the SU(2)C
+invariant quantities listed in Eq. (73).
+To elucidate the implications, let us go back to the example of the 2HDM scalar potential. From
+the general 2HDM potential of Eq. (29), we can see that the only terms that are not expressible in
+terms of the SU(2)C bilinear invariants of Eq. (73) are the terms proportional to λ4 and λ5. But in
+the custodial limit of Eq. (28), these two terms can be combined as
+λ4(φ†
+1φ2)(φ†
+2φ1) + λ5
+2
+�
+(φ†
+1φ2)2 + (φ†
+2φ1)2� λ4=λ5
+−−−−→ λ4
+2 (φ†
+1φ2 + φ†
+2φ1)2
+(74)
+which, in view of Eq. (73), is SU(2)C invariant.
+The above discussion can easily be extended to the case of nHDMs, especially to the democratic
+3HDMs, discussed in section 4.1. The conditions obtained using Eq. (25) thus rearrange the quartic
+part of the scalar potential in such a way that it can be expressed as combinations of the terms listed
+in Eq. (73).
+References
+[1] Particle Data Group Collaboration, R. L. Workman et al., Review of Particle Physics, PTEP
+2022 (2022) 083C01.
+[2] S. L. Glashow and S. Weinberg, Natural Conservation Laws for Neutral Currents, Phys. Rev. D
+15 (1977) 1958.
+[3] G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher, and J. P. Silva, Theory and
+phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1–102, [arXiv:1106.0034].
+[4] G. Cree and H. E. Logan, Yukawa alignment from natural flavor conservation, Phys. Rev. D 84
+(2011) 055021, [arXiv:1106.4039].
+[5] A. G. Akeroyd, S. Moretti, K. Yagyu, and E. Yildirim, Light charged Higgs boson scenario in
+3-Higgs doublet models, Int. J. Mod. Phys. A 32 (2017), no. 23n24 1750145,
+[arXiv:1605.05881].
+[6] M. P. Bento, J. C. Rom˜ao, and J. a. P. Silva, Unitarity bounds for all symmetry-constrained
+3HDMs, JHEP 08 (2022) 273, [arXiv:2204.13130].
+[7] R. Boto, J. C. Rom˜ao, and J. a. P. Silva, BFB conditions on a class of symmetry constrained
+3HDM, arXiv:2208.01068.
+[8] D. Das and I. Saha, Alignment limit in three Higgs-doublet models, Phys. Rev. D 100 (2019),
+no. 3 035021, [arXiv:1904.03970].
+[9] A. Pilaftsis, Symmetries for standard model alignment in multi-Higgs doublet models, Phys. Rev.
+D 93 (2016), no. 7 075012, [arXiv:1602.02017].
+[10] M. Chakraborti, D. Das, M. Levy, S. Mukherjee, and I. Saha, Prospects for light charged scalars
+in a three-Higgs-doublet model with Z3 symmetry, Phys. Rev. D 104 (2021), no. 7 075033,
+[arXiv:2104.08146].
+19
+
+[11] R. Boto, J. C. Rom˜ao, and J. a. P. Silva, Current bounds on the type-Z Z3 three-Higgs-doublet
+model, Phys. Rev. D 104 (2021), no. 9 095006, [arXiv:2106.11977].
+[12] S. Willenbrock, Symmetries of the standard model, in Theoretical Advanced Study Institute in
+Elementary Particle Physics: Physics in D ≧ 4, pp. 3–38, 10, 2004. hep-ph/0410370.
+[13] A. Pomarol and R. Vega, Constraints on CP violation in the Higgs sector from the rho
+parameter, Nucl. Phys. B 413 (1994) 3–15, [hep-ph/9305272].
+[14] H. E. Haber and D. O’Neil, Basis-independent methods for the two-Higgs-doublet model III: The
+CP-conserving limit, custodial symmetry, and the oblique parameters S, T, U, Phys. Rev. D 83
+(2011) 055017, [arXiv:1011.6188].
+[15] W. Grimus, L. Lavoura, O. M. Ogreid, and P. Osland, A Precision constraint on
+multi-Higgs-doublet models, J. Phys. G 35 (2008) 075001, [arXiv:0711.4022].
+[16] W. Grimus, L. Lavoura, O. M. Ogreid, and P. Osland, The Oblique parameters in
+multi-Higgs-doublet models, Nucl. Phys. B 801 (2008) 81–96, [arXiv:0802.4353].
+[17] K. Olaussen, P. Osland, and M. A. Solberg, Symmetry and Mass Degeneration in
+Multi-Higgs-Doublet Models, JHEP 07 (2011) 020, [arXiv:1007.1424].
+[18] C. C. Nishi, Custodial SO(4) symmetry and CP violation in N-Higgs-doublet potentials, Phys.
+Rev. D 83 (2011) 095005, [arXiv:1103.0252].
+[19] M. A. Solberg, Conditions for the custodial symmetry in multi-Higgs-doublet models, JHEP 05
+(2018) 163, [arXiv:1801.00519].
+[20] B. Grzadkowski, M. Maniatis, and J. Wudka, The bilinear formalism and the custodial
+symmetry in the two-Higgs-doublet model, JHEP 11 (2011) 030, [arXiv:1011.5228].
+[21] N. Darvishi and A. Pilaftsis, Classifying Accidental Symmetries in Multi-Higgs Doublet Models,
+Phys. Rev. D 101 (2020), no. 9 095008, [arXiv:1912.00887].
+[22] A. Kundu, P. Mondal, and P. B. Pal, Custodial symmetry, the Georgi-Machacek model, and
+other scalar extensions, Phys. Rev. D 105 (2022), no. 11 115026, [arXiv:2111.14195].
+[23] ATLAS Collaboration, Combined measurements of Higgs boson production and decay using up
+to 139 fb−1 of proton-proton collision data at √s = 13 TeV collected with the ATLAS
+experiment, .
+[24] D. Das and I. Saha, Search for a stable alignment limit in two-Higgs-doublet models, Phys. Rev.
+D 91 (2015), no. 9 095024, [arXiv:1503.02135].
+[25] J. F. Gunion and H. E. Haber, The CP conserving two Higgs doublet model: The Approach to
+the decoupling limit, Phys. Rev. D 67 (2003) 075019, [hep-ph/0207010].
+[26] G. Bhattacharyya, D. Das, P. B. Pal, and M. N. Rebelo, Scalar sector properties of
+two-Higgs-doublet models with a global U(1) symmetry, JHEP 10 (2013) 081,
+[arXiv:1308.4297].
+20
+
+[27] P. S. Bhupal Dev and A. Pilaftsis, Maximally Symmetric Two Higgs Doublet Model with Natural
+Standard Model Alignment, JHEP 12 (2014) 024, [arXiv:1408.3405]. [Erratum: JHEP 11, 147
+(2015)].
+[28] M. Carena, I. Low, N. R. Shah, and C. E. M. Wagner, Impersonating the Standard Model Higgs
+Boson: Alignment without Decoupling, JHEP 04 (2014) 015, [arXiv:1310.2248].
+[29] N. Darvishi, M. R. Masouminia, and A. Pilaftsis, Maximally symmetric three-Higgs-doublet
+model, Phys. Rev. D 104 (2021), no. 11 115017, [arXiv:2106.03159].
+[30] D. Fontes, J. C. Rom˜ao, and J. a. P. Silva, A reappraisal of the wrong-sign hbb coupling and the
+study of h → Zγ, Phys. Rev. D 90 (2014), no. 1 015021, [arXiv:1406.6080].
+[31] A. Biswas and A. Lahiri, Alignment, reverse alignment, and wrong sign Yukawa couplings in
+two Higgs doublet models, Phys. Rev. D 93 (2016), no. 11 115017, [arXiv:1511.07159].
+[32] P. M. Ferreira, R. Guedes, M. O. P. Sampaio, and R. Santos, Wrong sign and symmetric limits
+and non-decoupling in 2HDMs, JHEP 12 (2014) 067, [arXiv:1409.6723].
+[33] P. M. Ferreira, R. Guedes, J. F. Gunion, H. E. Haber, M. O. P. Sampaio, and R. Santos, The
+Wrong Sign limit in the 2HDM, in 2nd Large Hadron Collider Physics Conference, 10, 2014.
+arXiv:1410.1926.
+[34] LHC Higgs Cross Section Working Group Collaboration, A. David, A. Denner,
+M. Duehrssen, M. Grazzini, C. Grojean, G. Passarino, M. Schumacher, M. Spira, G. Weiglein,
+and M. Zanetti, LHC HXSWG interim recommendations to explore the coupling structure of a
+Higgs-like particle, arXiv:1209.0040.
+[35] LHC Higgs Cross Section Working Group Collaboration, J. R. Andersen et al., Handbook
+of LHC Higgs Cross Sections: 3. Higgs Properties, arXiv:1307.1347.
+[36] M. P. Bento, H. E. Haber, J. C. Rom˜ao, and J. a. P. Silva, Multi-Higgs doublet models: physical
+parametrization, sum rules and unitarity bounds, JHEP 11 (2017) 095, [arXiv:1708.09408].
+[37] V. Keus, S. F. King, and S. Moretti, Three-Higgs-doublet models: symmetries, potentials and
+Higgs boson masses, JHEP 01 (2014) 052, [arXiv:1310.8253].
+[38] G. Bhattacharyya and D. Das, Nondecoupling of charged scalars in Higgs decay to two photons
+and symmetries of the scalar potential, Phys. Rev. D 91 (2015) 015005, [arXiv:1408.6133].
+[39] S. Carrolo, J. C. Rom˜ao, J. a. P. Silva, and F. Vaz˜ao, Symmetry and decoupling in multi-Higgs
+boson models, Phys. Rev. D 103 (2021), no. 7 075026, [arXiv:2102.11303].
+[40] F. Faro, J. C. Romao, and J. P. Silva, Nondecoupling in Multi-Higgs doublet models, Eur. Phys.
+J. C 80 (2020), no. 7 635, [arXiv:2002.10518].
+[41] O. Atkinson, M. Black, A. Lenz, A. Rusov, and J. Wynne, Cornering the Two Higgs Doublet
+Model Type II, JHEP 04 (2022) 172, [arXiv:2107.05650].
+[42] T. Modak, J. C. Rom˜ao, S. Sadhukhan, J. a. P. Silva, and R. Srivastava, Constraining
+wrong-sign hbb couplings with h → Υγ, Phys. Rev. D 94 (2016), no. 7 075017,
+[arXiv:1607.07876].
+21
+
+[43] A. Batra, S. Mandal, and R. Srivastava, h → Υγ Decay: Smoking Gun Signature of Wrong-Sign
+hbb Coupling, arXiv:2209.01200.
+[44] I. Galon, A. Rajaraman, and T. M. P. Tait, H → τ +τ −γ as a probe of the τ magnetic dipole
+moment, JHEP 12 (2016) 111, [arXiv:1610.01601].
+[45] S. Kanemura, T. Mondal, and K. Yagyu, Exploring Wrong Sign Scenarios in the
+Yukawa-Aligned 2HDM, arXiv:2211.08803.
+[46] S. D. Joglekar, S matrix derivation of the Weinberg model, Annals Phys. 83 (1974) 427.
+[47] G. Bhattacharyya, D. Das, and P. B. Pal, Modified Higgs couplings and unitarity violation,
+Phys. Rev. D 87 (2013) 011702, [arXiv:1212.4651].
+[48] ATLAS Collaboration, G. Aad et al., Combined measurements of Higgs boson production and
+decay using up to 80 fb−1 of proton-proton collision data at √s = 13 TeV collected with the
+ATLAS experiment, Phys. Rev. D 101 (2020), no. 1 012002, [arXiv:1909.02845].
+[49] CMS Collaboration, Measurement of Higgs boson decay to a pair of muons in proton-proton
+collisions at √s = 13 TeV, CMS-PAS-HIG-19-006 (2020).
+22
+
diff --git a/sdAyT4oBgHgl3EQfZvfd/content/tmp_files/load_file.txt b/sdAyT4oBgHgl3EQfZvfd/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f364e534f62637861709de97fec2c28ea7990528
--- /dev/null
+++ b/sdAyT4oBgHgl3EQfZvfd/content/tmp_files/load_file.txt
@@ -0,0 +1,976 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf,len=975
+page_content='Democratic three Higgs-doublet models:  the custodial limit and wrong-sign Yukawa  Dipankar Dasa,∗, Miguel Levyb,†, Palash B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Palc,‡,  Anugrah M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Prasada,§, Ipsita Sahad,¶, Ayushi Srivastavaa,‖  aIndian Institute of Technology (Indore), Khandwa Road, Simrol, Indore 453 552, India  b Centro de F´ısica Te´orica de Part´ıculas-CFTP and Departamento de F´ısica, Instituto Superior T´ecnico,  Universidade de Lisboa, Av Rovisco Pais, 1, P-1049-001 Lisboa, Portugal  cDepartment of Physics, University of Calcutta, 92 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Road, Calcutta 700009, India  dDepartment of Physics, Faculty of Science, University of Allahabad, Old Katra, Prayagraj 211002, India  Abstract  We study two novel aspects of democratic 3HDMs – the custodial limit and the possibility of  wrong-sign Yukawa couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In the custodial limit, the democratic 3HDMs can easily negotiate  the constraints from the electroweak T-parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We also uncover the possibility of having wrong-  sign Yukawa couplings in democratic 3HDMs, as in the case of 2HDMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We show that a democratic  3HDM encompasses all the wrong-sign possibilities entertained by 2HDMs, and has considerably  more leeway in the wrong-sign limit as compared to the 2HDM case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Our study underscores the  importance of reporting analysis in the kappa-formalism without any implicit assumptions on the  signs of the kappas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  1  Introduction  The Standard Model (SM) of particle physics remains consistent in accommodating the experimental  tests designed to measure its properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The discovery of a scalar particle at the LHC has further  vindicated the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' This discovery has also intensified the interest in scalar extensions of the SM, which  feature more than one fundamental scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In fact, the phenomenological evidences of dark matter  and neutrino masses quite regularly motivate us to pursue physics beyond the SM (BSM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' More often  than not, these BSM scenarios come with an extension of the scalar sector of the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Although there  are many different ways to extend the SM scalar sector, extensions with additional SU(2)L doublets  are particularly attractive because they preserve the tree-level value of the ρ-parameter [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  The SM being reliant on the minimal scalar sector containing only one SU(2)L doublet, is free  from flavour-changing neutral currents (FCNCs) at the tree-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' This feature is not guaranteed to  be preserved when one extends the SM scalar sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In fact, BSM with multiple scalar doublets, in  ∗d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='das@iiti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='in  †miguelplevy@tecnico.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='ulisboa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='pt  ‡palashbaran.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='pal@saha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='in  §anugrahmprasad@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='com  ¶ipsita@allduniv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='in  ‖srivastavaayushi860@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='com  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='00231v1  [hep-ph]  31 Dec 2022  general, lead to the presence of tree-level FCNCs mediated by neutral scalars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' However, experimental  data suggest that the FCNC processes are strongly suppressed [1], which makes the absence of tree-  level FCNCs a desirable property of any BSM scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' A common way to achieve this is to impose a  symmetry which ensures that fermions of a particular charge couple to only one scalar doublet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Con-  sequently, the fermionic mass matrices and the corresponding Yukawa matrices are simultaneously  diagonalizable, thereby preventing the appearance of scalar-mediated FCNCs at the tree-level, just  as in the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Such a possibility, in the context of multi Higgs-doublet models, is known as natural  flavour conservation (NFC) [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The two Higgs-doublet model (2HDM) entertains four types of flavour  universal NFC models (type-I, type-II, type-X, and type-Y), which have been extensively studied in  the literature [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Beyond these four possibilities, there is one more attractive option where a partic-  ular scalar doublet is reserved exclusively for each type of massive fermion, and the up-type quarks,  the down-type quarks, and the charged-leptons couple to separate dedicated scalar doublets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Quite  clearly, such an arrangement of Yukawa couplings is impossible within the 2HDM framework and one  needs at least three scalar doublets to achieve it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' It should be mentioned that this particular compo-  sition of Yukawa couplings is commonly dubbed as ‘democratic’ [4] or ‘type-Z’ [5] Yukawa structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  In this paper, we choose to refer to this possibility as ‘democratic Yukawa’ and subsequently, the  three Higgs-doublet models (3HDMs) that feature a democratic Yukawa structure will be collectively  called ‘democratic 3HDMs’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' These democratic 3HDMs have received a lot of attention in the recent  past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Theoretical constraints from unitarity and boundedness from below (BFB) have been studied  in refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' [6,7], the alignment limit in democratic 3HDMs is studied in refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' [8,9], and more recently, the  phenomenological studies involving the flavour and Higgs data have been performed in refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' [10,11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  In this paper, we turn our attention to a couple of unexplored aspects of democratic 3HDMs,  namely, the custodial limit and the possibility of ‘wrong-sign’ Yukawa couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Keeping in mind the  surging popularity of democratic 3HDMs, this study is quite timely and relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' To highlight the  importance of the custodial limit, we recall that in the SM, the custodial symmetry (CS) ensures ρ = 1  at the tree-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The custodial symmetry is only an approximate symmetry of the SM since it is broken  by the U(1)Y gauge coupling, as well as the Yukawa couplings [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Because of this, at the loop level,  the ρ-parameter deviates slightly from unity and the deviation is quite accurately predicted by the  SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' As it happens, the experimental measurement is compatible with this SM prediction, leaving very  little room for new physics (NP) to give an extra contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Such NP contributions are sometimes  conveniently expressed in terms of the T-parameter, which has the following experimental limit [1]  ∆T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='03 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='12 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  One noteworthy aspect is that the SM scalar sector respects CS perfectly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' However, this is no longer  guaranteed once the scalar sector is extended.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Therefore, it is expected that the additional scalars  will give rise to extra contributions to the T-parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The limit on the T-parameter will place  constraints on the NP contributions, sometimes requiring a fine-tuned scalar spectrum to keep the  value under control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Thus, models with n Higgs-doublets (nHDMs), although respecting ρ = 1 at the  tree-level, can potentially drive the T-parameter away from the experimental bounds, if the scalar  masses are arbitrarily chosen [13–16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Therefore, it can be very attractive if we can systematically  construct democratic 3HDMs which respect the CS in the scalar sector by design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Admittedly, such  studies have been performed earlier in the context of nHDMs [17–21], resulting in relations between the  quartic parameters of the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' But, unlike the earlier studies, which directly implement  the custodial symmetry in the scalar potential, our analysis conveniently starts with the scalar kinetic  terms, following ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' This alternative approach enables us to intuitively identify the different  custodial multiplets and at the end, the conditions for CS in nHDMs are concisely expressed in a  single equation, in terms of the physical masses and mixings of the scalar sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Note that such  2  a condition does not depend on the explicit structure of the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Being related to the  mass matrices of the scalar sector, the condition for respecting CS in nHDMs becomes quite easily  implemented in practical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' As a simple cross-check, we will also show how the conditions  in terms of the quartic parameters of the scalar sector in earlier references follow from this single  condition in a straightforward manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  The scalar extensions of the SM also face severe constraints from the measurements of the  Higgs signal strengths [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' For nHDMs, these constraints can be greatly alleviated by staying in the  proximity of the ‘alignment limit’ [8,9,24–29], where the lightest CP-even scalar has the same couplings  as the SM Higgs boson at the tree-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' However, an intriguing possibility may arise if we keep in  mind that the current Higgs data is not very sensitive to the sign of the down quark and charged lepton  Yukawa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Such an exotic possibility can be accommodated in a 2HDM framework with e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' a type-II  Yukawa structure and is quite well studied in the literature [30–33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In this paper, we want to point  out that democratic 3HDMs can also accommodate this possibility, with much more freedom, due to  the increased number of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' These possibilities should encourage our experimental colleagues  to report the results of the analysis of the Higgs data in the kappa framework [34, 35] without any  implicit assumption on the sign of the kappas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  This article will be organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 2 we lay down our methodology to study the  CS starting from the scalar kinetic terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We then apply this in the case of the SM and recover  the essential features of CS in the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Later in this section, we extend our analysis to the nHDM  case and retrieve the 2HDM result as a special example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 3 we explicitly demonstrate how  the custodial limit neutralizes the constraint arising from the electroweak T-parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We define  democratic 3HDMs in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 4, and present the custodial limit for the two usual incarnations in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  Afterwards, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2 we investigate the possibility of wrong-sign Yukawa couplings in democratic  3HDMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Finally, we summarize our findings in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  2  Custodial Symmetry in multi Higgs-doublet models  The CS is an accidental global SU(2) symmetry (hereafter denoted as SU(2)C) which prevails even  after the spontaneous breaking of the electroweak symmetry in the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In the case of the SM gauge  group, SU(2)L × U(1)Y , the CS is responsible for the value of the ρ-parameter to be equal to unity at  the tree-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In this paper, we follow the formulation of CS as in ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' [22], and confine ourselves to  the SU(2)L part of the electroweak gauge symmetry, that is, we work in the limit where the U(1)Y  gauge coupling goes to zero (g′ = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In this section, we will build our intuition first, by considering  the simple example of the SM scalar sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Then, we will extend our formalism to the case of a  general nHDM and obtain conditions such that the scalar sector obeys the CS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1  Recap of the custodial symmetry in the SM  In the SM, there is a single complex scalar doublet, φ, which drives the electroweak symmetry breaking  (EWSB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The scalar Lagragian of the SM is given by  Lscalar = (Dµφ)† (Dµφ) − V (φ) ,  (1)  where V (φ) is the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In the limit g′ = 0, the gauge-covariant derivative for φ is given by  Dµφ  =  �  ∂µ + igτa  2 W a  µ  �  φ,  (2)  where g is the SU(2)L gauge coupling, W a  µ are the SU(2)L gauge bosons, and τa are the Pauli matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  After the EWSB, the scalar doublet φ can be explicitly expressed in terms of the component fields, as  3  follows  φ =  1  √  2  � √  2 ω+  v + h + iζ  �  ,  (3)  where v is the vacuum expectation value (VEV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Subsequently, the scalar kinetic terms can be conve-  niently decomposed as [22]  Lkin = (Dµφ)†(Dµφ) = Lmass + Lquad + Lmixed + Lderiv + Lcubic + Lquartic .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (4)  Collectively denoting the gauge bosons as Ga,b,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  µ  and the component scalar fields as si,j,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=', the meaning  of the individual terms introduced in the above equation are given below  Lmass :  these are the mass terms for the guage bosons of the form v2Ga  µ  †Gaµ ,  Lquad :  these are the kinetic terms of the component scalar fields, (∂µsi)†(∂µsi) ,  Lmixed :  terms of the form (∂µsi)†(ivGµ) + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' ,  Lderiv :  terms of the form (∂µsi)†(iGµsj) + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' ,  Lcubic :  terms of the form (Ga,µsi)†(vGb  µ) + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' ,  Lquartic :  terms of the form (Ga,µsi)†(Gb  µsj) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  To identify the custodial multiplets, we begin with Lmass which, in the SM, is given by  Lmass  =  g2v2  8  �  W µ+W −  µ + W µ−W +  µ + W 3µW 3  µ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (5)  where  W ±  µ = W 1  µ ∓ iW 2  µ  √  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (6)  We can see from the above equation that the SU(2)L gauge bosons have the same mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' This motivates  us to identify a custodial multiplet of the gauge bosons as1  W =  �  �  −W +  W3  W −  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (7)  Note that the Lorentz indices have been suppressed here for simplicity as it has no bearing on the  SU(2)C transformations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In terms of the SU(2)C triplet of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (7), Lmass can be rewritten as  Lmass = g2v2  8  (W · W) ,  (8)  which is manifestly invariant under SU(2)C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' To identify the SU(2)C multiplets of the scalar fields, let  us turn our attention to Lcubic and Lmixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' First, in terms of the triplet W, Lcubic can be expressed  as  Lcubic = g2v  4 h (W · W) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (9)  1the minus sign in the first entry of W comes from the details of SU(2) group theory, which are explained in  Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  4  Thus, Lcubic will also be SU(2)C invariant if we identify the physical scalar, h, as a singlet of SU(2)C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  Next, we look into Lmixed, which is given by  Lmixed = gv  2  �  i  �  ∂µw−�  W +  µ − i  �  ∂µw+�  W −  µ − (∂µζ) W 3  µ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (10)  Given the identification of W in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (7), the above equation encourages us to define an SU(2)C triplet  of scalar fields as follows:  T =  �  �  iω+  −ζ  iω−  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (11)  In terms of W and T, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (10) can be written as  Lmixed = gv  2 (W · ∂T) ,  (12)  which explicitly demonstrates the SU(2)C invariance of Lmixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The other terms, Lquad, Lderiv, and  Lquartic, when expressed in terms of W and T, can also be shown to be invariant under SU(2)C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  All these terms will be considered in detail in the next subsection, when we consider the nHDM  generalisation of the above prescription.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  Now, let us take a look at the SU(2)C invariance of the scalar potential, which is given by  V (φ) = µ2 �  φ†φ  �  + λ  �  φ†φ  �2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (13)  After the EWSB, φ†φ can be expressed as  φ†φ  =  1  2(T · T) + v2  2 + h2  2 + vh .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (14)  We can see that, our previous multiplet identifications of T and h are compatible with the SU(2)C  invariance of the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In other words, no additional conditions need to be imposed on the  SM scalar potential to make it SU(2)C invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' It should be noted that, the SU(2)C invariance of  the scalar potential mandates that the scalars which are in the same SU(2)C multiplet should have  the same mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' This condition is trivially satisfied here in the SM as all the components of T are  Goldstone bosons with zero masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' This will no longer be true in nHDMs, where we will need to  impose additional restrictions on the parameters of the scalar potential to ensure custodial invariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2  Generalization to nHDM  We will now look at the scalar kinetic Lagrangian for a model with n complex scalar doublets φk  (k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' , n) and identify the different SU(2)C multiplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Thus we begin with  Lkin =  n  �  k=1  (Dµφk)†(Dµφk) ,  (15)  where, under the assumption of g′ = 0, the gauge covariant derivative of φk is given by  Dµφk =  �  ∂µ + igτa  2 W a  µ  �  φk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (16)  5  After the EWSB, the k-th scalar doublet is decomposed as  φk =  1  √  2  �  √  2w+  k  vk + hk + izk  �  ,  (17)  where vk is the VEV of φk, assumed to be real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Borrowing the terminology introduced in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (4), we  still have  Lmass = g2v2  8  (W · W) ,  (18)  where v =  �  v2  1 + v2  2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' + v2n is the total electroweak VEV, and we have used Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (7) for the definiton  of W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' This implies that Lmass will still respect SU(2)C once we identify the custodial triplet of the  gauge bosons, as in the case of the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Similarly, for Lcubic we have  Lcubic = g2  4 (W · W)  n  �  k=1  vkhk .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (19)  Evidently, Lcubic will also be custodially invariant if we identify hk (k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=', n) as singlets of SU(2)C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  Next, we turn our attention to Lmixed, which has the following form  Lmixed = g  2  n  �  k=1  vk  �  i(∂µw−  k )W +  µ − i(∂µw+  k )W −  µ − (∂µzk)W 3  µ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (20)  Taking inspiration from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (10), we now proceed to define a set of SU(2)C triplets involving the  scalar component fields as  Tk ≡  �  �  iw+  k  −zk  iw−  k  �  � ,  k = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=', n .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (21)  Following this identification, we can express Lmixed as the sum of SU(2)C invariants, given by  Lmixed  =  g  2  n  �  k=1  vk (W · ∂Tk) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (22)  For the sake of completeness, we also express Lquad, Lquartic, and Lderiv, in terms of W, Tk, and hk,  as follows  Lquad  =  1  2  n  �  k=1  [(∂Tk · ∂Tk) + (∂µhk)(∂µhk)] ,  (23a)  Lquartic  =  g2  8 (W · W)  n  �  k=1  (Tk · Tk + h2  k) ,  (23b)  Lderiv  =  g  2  n  �  k=1  {hk(W · ∂Tk) + ∂hk(Tk · W) + (Tk × ∂Tk) · W} ,  (23c)  where (r1 × r2) · r3 is the singlet combination of the SU(2) product of three triplets, r1,2,3, for which  the explicit expression is given in appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  6  Thus, we can see that all the terms in the scalar kinetic Lagrangian are custodially invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  However, the triplets Tk are not expressed in terms of physical fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rotation of these fields from  the Lagrangian basis to the physical basis will give rise to the Goldstone bosons, the physical charged  scalars, and pseudoscalars2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We would like to transfer the SU(2)C invariance into the physical basis  as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' For this, we need to rotate each triplet as a whole object, that is,  Pj =  n  �  k=1  OjkTk  j = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' n ,  (24)  where Pj denotes the j-th triplet of SU(2)C in the physical basis, and Ojk are the elements of an  orthogonal matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Note that, each triplet Tk, contained a pseudoscalar field and a pair of charged  fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Consequently, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (24) implies that the charged and pseudoscalar mass matrices should be  rotated into the physical basis by means of the same rotation matrix, in order to preserve the SU(2)C  invariance of Lkin in the physical basis as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Now, for a charged scalar and a pseudoscalar in the  physical basis to be placed in the same triplet Pj, they should have a common mass so that the mass  terms for the members of Pj can be concisely expressed in an SU(2)C invariant form as M2  j (Pj · Pj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  Thus, we can conclude that, in the physical basis, the diagonal mass matrices in the charged and  pseudoscalar sectors must be equal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Also, from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (24), we should recall that the rotations that bring  the mass matrices of the charged and pseudoscalar sectors to their respective diagonal forms should  also be the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Putting this together, we can conclude that the mass matrix of the charged and  pseudoscalar sectors should be equal in the Lagrangian basis as well, that is  M2  C = M2  P .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (25)  Since the information about the scalar masses and the mixings come from the scalar potential, the  parameters of the scalar potential should adjust themselves so that Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (25) is satisfied (for arbitrary  values of the VEVs), and consequently, the scalar potential also comes under the umbrella of SU(2)C  invariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  Examples with 2HDMs  We will now explicitly demonstrate how Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (25) manifests itself for the simple case of a 2HDM scalar  potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  At first, let us consider the 2HDM scalar potential with a softly-broken Z2 symmetry  (φ1 → φ1, φ2 → −φ2), which is commonly used in NFC models [3]:  V (φ1, φ2)  =  m2  11φ†  1φ1 + m2  22φ†  2φ2 − m2  12(φ†  1φ2 + φ†  2φ1) + λ1  2 (φ†  1φ1)2 + λ2  2 (φ†  2φ2)2  +λ3(φ†  1φ1)(φ†  2φ2) + λ4(φ†  1φ2)(φ†  2φ1) + λ5  2  �  (φ†  1φ2)2 + (φ†  2φ1)2�  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (26)  The charged and pseudoscalar mass matrices which transpire from the above scalar potential are given  by  M2  C  =  �  m2  12v2  v1  − 1  2λ4v2  2 − 1  2λ5v2  2  −m2  12 + 1  2λ4v1v2 + 1  2λ5v1v2  −m2  12 + 1  2λ4v1v2 + 1  2λ5v1v2  m2  12v1  v2  − 1  2λ4v2  1 − 1  2λ5v2  1  �  ,  (27a)  M2  P  =  �  m2  12v2  v1  − λ5v2  2  −m2  12 + λ5v1v2  −m2  12 + λ5v1v2  m2  12v1  v2  − λ5v2  1  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (27b)  2Throughout the paper, we are implicitly assuming CP conservation in the scalar potential, so that such a classification  of the scalar spectrum is possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  7  Thus, imposition of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (25) will lead to the following relation  λ4 = λ5 ,  (28)  which agrees with earlier results [13,14,21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In passing, we wish to point out that even if we consider  the general 2HDM potential [3]  V (φ1, φ2)  =  m2  11φ†  1φ1 + m2  22φ†  2φ2 − (m2  12φ†  1φ2 + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=') + λ1  2 (φ†  1φ1)2 + λ2  2 (φ†  2φ2)2 + λ3(φ†  1φ1)(φ†  2φ2)  +λ4(φ†  1φ2)(φ†  2φ1) +  �λ5  2 (φ†  1φ2)2 + λ6(φ†  1φ1)(φ†  1φ2) + λ7(φ†  2φ2)(φ†  1φ2) + h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  �  ,  (29)  the condition for custodial invariance is still given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (28).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The reason for this will be discussed  in more detail in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  3  Validation of the custodial limit by explicit calculation  In SU(2)C invariant models, we expect that no additional contribution to the T-parameter comes  from the scalar sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' It would be rather reassuring to explicitly verify that this is indeed the case for  nHDMs in the limit of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' For this purpose, we use the one-loop formula for the NP contribution  to the T-parameter for nHDMs given in refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' [15,16]:  αT =  g2  64π2M2  W  �  n  �  a=2  2n  �  b=2  ���  �  U †V  �  ab  ���  2  F  �  m2  a, µ2  b  �  −  2n−1  �  b=2  2n  �  b′=b+1  ���  �  V †V  �  bb′  ���  2  F  �  µ2  b, µ2  b′  �  +3  n  �  b=2  ���  �  V †V  �  1b  ���  2 �  F  �  M2  Z, µ2  b  �  − F  �  M2  W , µ2  b  � ��  ,  (30)  where  F(x, y) ≡  �  �  �  x + y  2  −  xy  x − y ln x  y ,  x ̸= y  0,  x = y  ,  (31)  and α is the fine-structure constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  The masses of the charged-scalars are denoted by ma, and  µa are the masses of the physical neutral scalars, defined in such a way that a ≤ n refers to the  pseudoscalars, and a > n are the CP-even fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Lastly, U † and V † are n × n and 2n × n matrices  that rotate the charged and neutral components (w±  k and ϕ0  k ≡ hk + izk) into the physical basis (S±  and S0), respectively, in such a way that the Goldstone bosons are located in the first row,  w±  k =  n  �  a=1  UkaS±  a ,  ϕ0  k =  2n  �  b=1  VkbS0  b .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (32)  We give the explicit structure of S± and S0 as follows  S± =  �  ω±, H±  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' , H±  n−1  �T ,  S0 =  �  ζ, A1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' , An−1, h, H1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' , Hn−1  �T ,  (33)  where ω± and ζ are the charged and neutral unphysical Goldstone bosons, respectively, H±  k is the  k-th charged scalar, and Ak the k-th pseudoscalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' For the CP-even scalars, h is the lightest scalar  8  usually identified as the SM-like Higgs, and Hk denotes the k-th physical CP-even scalar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Following  the definition of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (24), and comparing with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (32), we can relate the U and V matrices with the  scalar rotation matrices as follows  U = OT  C ,  V =  �  iOT  P  OT  S  �  ,  (34)  where the subscripts C, P, S refer to the charged, pseudoscalar, and scalar sectors respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The  relevant combinations can be expressed as  U †V =  �  i OC OT  P  OC OT  S  �  ,  V †V =  � 1n×n  −i OP OT  S  i OS OT  P  1n×n  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (35)  We must note that the last term of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (30) vanishes in the limit g′ → 0, that is, MZ = MW .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Therefore,  we will focus on the first two terms in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (30), and convince ourselves that they also vanish in the  custodial limit of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (25).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Taking advantage of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (35), we can rewrite the first two terms of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (30)  as  αT =  g2  64π2M2  W  �  n  �  a=2  n  �  b=2  ���  iOCOT  P  �  ab  ��2 F  �  m2  a, µ2  b  �  +  n  �  a=2  n  �  b=1  ���  OCOT  S  �  ab  ��2 F  �  m2  a, µ2  n+b  �  −  n  �  a=2  n  �  b=1  ���  − iOP OT  S  �  ab  ��2 F  �  µ2  a, µ2  n+b  � �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (36)  In the custodial limit, we must have M2  P = M2  C, and thus OP = OC, as well as m2  a = µ2  a (with a < n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  In this way, the second and third terms of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (36) cancel out, and OCOT  P = OP OT  P = 1n×n leads to  a zero contribution from the first term, because of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (31).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  4  Democratic 3HDMs  The Yukawa Lagrangian for a democratic 3HDM, as discussed in the introduction, has the following  form  LY = −YdQLφ2nR − YuQL�φ3pR − YℓLLφ1ℓR ,  (37)  where Yd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='ℓ are the Yukawa couplings in the down-quark, up-quark, and charged-lepton sectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  The up-type, down-type, and charged-lepton right-handed fields are denoted as pR, nR, and ℓR,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The left-handed SU(2)L doublets for the quarks and leptons are QL = (pL, nL)T and  LL = (νL, eL)T .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Finally, �φ3 = iτ2φ∗  3 is the SU(2)L doublet responsible for the up-quark masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' There  are two common ways to arrive at the above Lagrangian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The first is to impose a Z3 symmetry as  follows [8]  φ1 → ω φ1 ,  φ2 → ω2φ2 ,  ℓR → ω2ℓR ,  nR → ω nR .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (38)  The second possibility relies on a Z2 × Z′  2 symmetry under which the fields transform as [5]  Z2 :  φ1 → −φ1 ,  ℓR → −ℓR  (39a)  Z′  2 :  φ2 → −φ2 ,  nR → −nR  (39b)  Both in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (38) and (39), only the nontrivial transformations are explicitly displayed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In the follow-  ing, we will discuss the implications of these symmetries on the scalar potential in the context of the  custodial limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  9  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1  Custodial Limit of Democratic 3HDMs  In this subsection, we will write down the explicit forms of the scalar potential which follow from  the symmetry of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (38) and (39).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Then, we will proceed to calculate the detailed structure of the  charged and pseudoscalar mass matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Finally, we will impose Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (25) to extract the implications  in terms of the parameters of the scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='The case with a Z3 symmetry  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='The scalar potential for this case will be given by [36]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='VZ3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='=  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='11φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ1 + m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='22φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ2 + m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='33φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ3 − m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='12(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ2 + φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ1) − m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='13(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ3 + φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ1) − m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='23(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ3 + φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='+λ1(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ1)2 + λ2(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ2)2 + λ3(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ3)2 + λ4(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ1)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ2) + λ5 (φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ1)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ3) + λ6(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ2)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ3)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='+λ7(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ2)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ1) + λ8(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ3)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ1) + λ9(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ3)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ2) + λ10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ2)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ3) + (φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ1)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='+λ11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ1)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ3) + (φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ2)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='+ λ12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ1)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ2) + (φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ3)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ3)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (40)  where soft-breaking terms have also been allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The explicit expressions for the elements of the  3 × 3 symmetric mass matrix in the charged scalar sector are given below3  (M2  C)11  =  m2  12v2  v1  + m2  13v3  v1  − λ10v2v3 − λ11v2  2v3  2v1  − λ12v2v2  3  2v1  − λ7v2  2  2  − λ8v2  3  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (41a)  (M2  C)22  =  m2  12v1  v2  + m2  23v3  v2  − λ10v2  1v3  2v2  − λ11v1v3 − λ12v1v2  3  2v2  − λ7v2  1  2  − λ9v2  3  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (41b)  (M2  C)33  =  m2  13v1  v3  + m2  23v2  v3  − λ10v2  1v2  2v3  − λ11v1v2  2  2v3  − λ12v1v2 − λ8v2  1  2  − λ9v2  2  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (41c)  (M2  C)12  =  (M2  C)21 = −m2  12 + 1  2λ10v1v3 + 1  2λ11v2v3 + 1  2λ7v1v2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (41d)  (M2  C)13  =  (M2  C)31 = −m2  13 + 1  2λ10v1v2 + 1  2λ12v2v3 + 1  2λ8v1v3 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (41e)  (M2  C)23  =  (M2  C)32 = −m2  23 + 1  2λ11v1v2 + 1  2λ12v1v3 + 1  2λ9v2v3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (41f)  Similarly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' for the pseudoscalar mass matrix we have  (M2  P )11  =  m2  12v2  v1  + m2  13v3  v1  − 2λ10v2v3 − λ11v2  2v3  2v1  − λ12v2v2  3  2v1  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (42a)  (M2  P )22  =  m2  12v1  v2  + m2  23v3  v2  − λ10v2  1v3  2v2  − 2λ11v1v3 − λ12v1v2  3  2v2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (42b)  (M2  P )33  =  m2  13v1  v3  + m2  23v2  v3  − λ10v2  1v2  2v3  − λ11v1v2  2  2v3  − 2λ12v1v2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (42c)  (M2  P )12  =  (M2  P )21 = −m2  12 + λ10v1v3 + λ11v2v3 − λ12v2  3  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (42d)  (M2  P )13  =  (M2  P )31 = −m2  13 + λ10v1v2 + λ12v2v3 − λ11v2  2  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (42e)  (M2  P )23  =  (M2  P )32 = −m2  23 + λ11v1v2 + λ12v1v3 − λ10v2  1  2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (42f)  3We have used the minimization conditions to trade m2  11, m2  22, and m2  33 in favor of the VEVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  10  For Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (25) to hold for any arbitrary values of the VEVs, we should have  λ7 = λ8 = λ9 = λ10 = λ11 = λ12 = 0 ,  (43)  which should be read as the conditions for custodial invariance in a Z3 symmetric 3HDM potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='The case with a Z2 × Z′  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2 symmetry  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='The scalar potential in this case can be written as [37]  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='VZ2×Z2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='=  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='11φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ1 + m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='22φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ2 + m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='33φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='−m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='12(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ2 + φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ1) − m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='13(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ3 + φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ1) − m2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='23(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ3 + φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='+λ1(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ1)2 + λ2(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ2)2 + λ3(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ3)2 + λ4(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ1)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ2) + λ5(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ1)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ3)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='+λ6(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ2)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ3) + λ7(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ2)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ1) + λ8(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ3)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ1) + λ9(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ3)(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ2)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='+λ10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ2)2 + (φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ1)2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='+ λ11  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1φ3)2 + (φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ1)2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='+ λ12  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='(φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2φ3)2 + (φ†  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3φ2)2�  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (44)  where,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' again,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' we have allowed terms that softly-break the symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The elements of the charged-  scalar mass matrix are given below:  (M2  C)11  =  m2  12v2  v1  + m2  13v3  v1  − λ10v2  2 − λ7v2  2  2  − λ11v2  3 − λ8v2  3  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (45a)  (M2  C)22  =  m2  12v1  v2  + m2  23v3  v2  − λ10v2  1 − λ7v2  1  2  − λ12v2  3 − λ9v2  3  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (45b)  (M2  C)33  =  m2  13v1  v3  + m2  23v2  v3  − λ11v2  1 − λ8v2  1  2  − λ12v2  2 − λ9v2  2  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (45c)  (M2  C)12  =  (M2  C)21 = −m2  12 + λ10v1v2 + 1  2λ7v1v2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (45d)  (M2  C)13  =  (M2  C)31 = −m2  13 + λ11v1v3 + 1  2λ8v1v3 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (45e)  (M2  C)23  =  (M2  C)32 = −m2  23 + λ12v2v3 + 1  2λ9v2v3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (45f)  For the case of the pseudoscalar mass matrix elements, we find  (M2  P )11  =  m2  12v2  v1  + m2  13v3  v1  − 2λ10v2  2 − 2λ11v2  3 ,  (46a)  (M2  P )22  =  m2  12v1  v2  + m3  23v3  v2  − 2λ10v2  1 − 2λ12v2  3 ,  (46b)  (M2  P )33  =  m2  13v1  v3  + m2  23v2  v3  − 2λ11v2  1 − 2λ12v2  2 ,  (46c)  (M2  P )12  =  (M2  P )21 = −m2  12 + 2λ10v1v2 ,  (46d)  (M2  P )13  =  (M2  P )31 = −m2  13 + 2λ11v1v3 ,  (46e)  (M2  P )23  =  (M2  P )32 = −m2  23 + 2λ12v2v3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (46f)  Following the reasoning presented for the Z3 case, the conditions for custodial invariance can be found  using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (25), which read  λ7 = 2λ10, λ8 = 2λ11, λ9 = 2λ12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (47)  11  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2  Wrong-sign Yukawas in democratic 3HDMs  Now we turn our attention to the Yukawa sector phenomenology that follows from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (37).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' To begin  with, we parametrize the VEVs of the three doublets as follows  v1 = v cos β1 cos β2,  v2 = v cos β1 sin β2,  v3 = v sin β1,  (48)  which, by design, satisfies the relation  v2  1 + v2  2 + v2  3 = v2,  (49)  with v = 246 GeV being the total electroweak VEV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The range of values of β1 and β2 allowed from  the perturbativity of the fermionic Yukawa couplings can be found in refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' [10,11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  The current LHC Higgs data usually serves as a motivation to stay close to the so-called align-  ment limit [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' However, as explained in the introduction, here we are after a relatively less-explored  possibility where the sign of the down-type Yukawa couplings is opposite to what has been predicted  by the SM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' To prepare ourselves for what comes next, we define the Higgs coupling modifiers as  follows [34,35]  κx = ghxx  gSM  hxx  ,  (50)  where the field h, in the context of nHDMs, denotes the lightest CP-even scalar, and ‘x’ can represent  the massive vector bosons or fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  To illustrate the details of the wrong-sign limit, we briefly revisit the example of a type-II 2HDM  where the coupling modifiers have the expression given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4 These coupling modifiers can be  conveniently rewritten as follows  κII  V = sin (β − α) ,  (51a)  κII  u = sin (β − α) + cot β cos (β − α) ,  (51b)  κII  d = κII  ℓ = sin (β − α) − tan β cos (β − α) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (51c)  Model  κV  κu  κd  κℓ  type-II 2HDM  sin (α − β)  cos α  sin β  − sin α  cos β  − sin α  cos β  democratic 3HDMs  cos α2 cos β2 cos (α1 − β1)  + sin α2 sin β2  sin α2  sin β2  sin α1  sin β1  cos α2  cos β2  cos α1  cos β1  cos α2  cos β2  Table 1:  The coupling modifiers for the type-II 2HDM and democratic 3HDMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In the 2HDM case,  tan β = v2/v1 and α is a suitably defined rotation angle in the CP-even scalar sector [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Similarly, in  the case of 3HDMs, α1 and α2 are two suitably defined rotation angles in the CP-even scalar sector [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  Now let us consider the limit  cos (β − α) =  r  tan β ,  (52)  4We note here that for the 2HDM case we are using the standard convention for α, such that the alignment limit is  given by cos (β − α) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' However, for the case of democratic 3HDMs, the angles α1,2 are defined in a way such that  the alignment conditions read sin (αi − βi) = 0, with i = 1, 2 [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  12  Figure 1:  Allowed region at 95% CL from the current data on Higgs signal strengths in the type-II  2HDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' It should be noted that when considering the h → γγ decay, the charged-Higgs contribu-  tion has been neglected with the understanding that it can be safely decoupled in the presence of the  soft-breaking parameter in the scalar potential [38–40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  For illustration, the line corresponding to  cos(β − α) = 2/tan β has also been plotted in the same graph, which reinforces our intuitions from  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (52).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  where r is a real number and tan β ≫ |r|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In such a scenario, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (51) can be approximated as  κII  V ≈ 1,  κII  u ≈ 1,  κII  d,ℓ ≈ 1 − r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (53)  The wrong-sign limit, in particular, arises for r = 2, in which case Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (53) takes the following  form  κII  V ≈ 1,  κII  u ≈ 1,  κII  d,ℓ ≈ −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (54)  Such a possibility is allowed because the current LHC Higgs data is not sensitive enough to probe  the sign of the bottom-quark Yukawa coupling in the loop-induced vertices such as hgg and hγγ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' To  demonstrate this explicitly, we use the current Higgs data [23], and display the 2σ-allowed region in  the cos (β − α) vs tan β plane in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The thin dark-blue region corresponds to the wrong-sign limit  in the type-II 2HDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='5  Now, we will demonstrate that such wrong-sign scenarios are also entertained in democratic  3HDMs with much greater flexibility in terms of the number of free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' To illustrate this, we  again purposefully rewrite the Higgs coupling modifiers in Table 1 for democratic 3HDMs as follows  κV  =  cos (α1 − β1)  1 + tan2 β2  �  cos (α2 − β2) − sin (α2 − β2) tan β2  �  +  tan2 β2  1 + tan2 β2  �  cos (α2 − β2) + sin (α2 − β2) cot β2  �  ,  (55a)  5In a recent 2HDM fit [41], it was claimed that the wrong-sign limit is disfavoured by the current Higgs data at 2σ,  and only allowed within 3σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' However, we have used a more updated dataset and our result for 2HDM agrees with the  most updated fit from ATLAS [23] (in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 20b, we can see the wrong-sign limit is still allowed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  13  40  Kd=K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  tanβ  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  2  cos (β-α) =  tanβ  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4  cos(β-α)κu  =  cos (α2 − β2) + sin (α2 − β2) cot β2,  (55b)  κd  =  �  cos (α1 − β1) + sin (α1 − β1) cot β1  ��  cos (α2 − β2) − tan β2 sin (α2 − β2)  �  ,  (55c)  κℓ  =  �  cos (α1 − β1) − sin (α1 − β1) tan β1  ��  cos (α2 − β2) − tan β2 sin (α2 − β2)  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (55d)  In a similar way to the 2HDM scenario, we focus our attention to the limit  sin (α2 − β2) =  r2  tan β2  ,  (56)  where r2 is a real number, and tan β2 ≫ |r2|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In this limit, κV ≈ κu ≈ 1, but κd and κℓ take the  following form  κd  =  (1 − r2)  �  cos (α1 − β1) + sin (α1 − β1) cot β1  �  = (1 − r2)sin α1  sin β1  ,  (57a)  κℓ  =  (1 − r2)  �  cos (α1 − β1) − sin (α1 − β1) tan β1  �  = (1 − r2)cos α1  cos β1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (57b)  If we further consider the limit  sin (α1 − β1) =  r1  tan β1  ,  (58)  where, again, r1 is a real number, and tan β1 ≫ |r1|, then Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (57) can be further simplified to  κd  =  (1 − r2),  (59a)  κℓ  =  (1 − r2)(1 − r1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (59b)  The limits that can be obtained for different values of r1 and r2 have been listed in Table 2, where  we can see that all the wrong-sign possibilities that can be obtained from 2HDMs with NFC are  encompassed by a democratic 3HDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' All these features have been clearly depicted in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 2 and 3,  where the darker shade correspond to the wrong-sign limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Thus, we can see that the democratic  3HDM gives more leeway for the wrong-sign limit, when compared to the 2HDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  r1 = 0  r1 = 2  r2 = 0  κd = 1  κℓ = 1  (alignment limit)  κd ≈ 1  κℓ ≈ −1  (wrong-sign limit in the type-X 2HDM)  r2 = 2  κd ≈ −1  κℓ ≈ −1  (wrong-sign limit in the type-II 2HDM)  κd ≈ −1  κℓ ≈ 1  (wrong-sign limit in the type-Y 2HDM)  Table 2:  Wrong-sign possibilities in democratic 3HDMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' It should be noted that κu ≈ κV ≈ 1 in all  the cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  So far, we have obtained the wrong-sign limit in the democratic 3HDM following the 2HDM  prescription.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' However, a democratic Yukawa structure can entertain more exotic possibilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' As  usual, we start by investigating how to impose κu ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' One possibility is to set tan β2 ≫ 1 together  with cos (α2 − β2) ≈ 1, as was done in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (56), leading to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (57).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Now, instead of going to the  limit of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (58), one can choose  sin (α1 − β1) ≈ ±1 ,  tan β1 ≈ 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (60)  14  Figure 2:  Allowed region at 95% CL from the current data on Higgs signal strengths in democratic  3HDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' As before, the charged-Higgs contribution to h → γγ decay is neglected with the understanding  that it can be safely decoupled in the presence of the soft-breaking parameter in the scalar potential [38–  40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The contour corresponding to Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (56) and (58), for r1 = r2 = 2 are also displayed for easy  comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  In this way, using cos (α1 − β1) ≈ 0, we get  κV ≈ κu  ≈  1,  (61a)  κd ≈ −κℓ  ≈  ± (1 − r2) ,  (61b)  where, as before, r2 ≈ 0 and r2 ≈ 2 can give us two different possibilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' As such, we see that it  is possible to achieve a wrong-sign limit in the democratic 3HDMs without the requirement of large  tan β1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' If we follow the usual path to the wrong-sign limit, we see that sin (α1 − β1) ≈ 1 is allowed in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The possibility with sin (α1 − β1) ≈ −1 is separately showcased in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 3 for better visibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  At this point it will be quite natural to wonder how such wrong-sign possibilities can be probed  in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' An obvious way to sense the wrong-sign limit will be to measure the Higgs signal  strengths that involve hgg and hγγ effective vertices with increasing precision to the extent that the  interference terms from the lighter fermions in the loop start to become relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Alternatively, the  decay h → Υγ was suggested as a probe for the sign of κb [42, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Similarly h → τ +τ −γ [44] may  serve as a probe for the sign of κτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Additionally, if we know the UV complete model responsible for  the wrong-sign Yukawas, then we can perform a targeted search for the nonstandard particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' For  instance, in this case the wrong-sign limit is arising within an nHDM framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Thus, one can look  for nonstandard scalars whose phenomenologies in the wrong-sign limit will be presumably different  from the corresponding alignment limit counterparts [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  But the crucial point is, even if we stay agnostic about the origin of the wrong-sign Yukawas,  we should still remember that any departure from the SM couplings will introduce an energy scale  beyond which unitarity will be violated [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Therefore, the wrong-sign limits as described in, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=', Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (54) will inevitably call for NP below the unitarity violation scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' For the arrangement of couplings  appearing in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (54), the earliest onset of unitarity violation will occur in the bb → WLWL scattering  15  40  py  35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  25  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  tan  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  15  2  sin (α2-β2)  tan β2  10  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='8  sin(α2-β2)40  ly* Py  35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  25  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  B  tan  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  15  2  sin (α1-β1) :  tan βi  10  5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='0  sin(α1-β1)Figure 3:  Allowed region at 95% CL from the current data on Higgs signal strengths for  sin(α1 − β1) ≈ −1 is displayed separately in this plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' All the points shown in the left panel in the  sin(α2 − β2) vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' tan β2 plane are sampled from the sin(α1 − β1) ≈ −1 region as displayed in the right  panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The contour corresponding to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (56) for r2 = 2 is displayed for easy comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  and the maximum energy cut-off before which the NP must intervene, will be given by [47],  Emax = 2  √  2π  GF mb  ≈ 180 TeV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (62)  5  Summary  In this article we have studied two new aspects of democratic 3HDMs, namely, the impact of custodial  symmetry and the wrong-sign Yukawa couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  As such, our goal is to provide the ingredients  for constructing democratic 3HDMs which is safeguarded against the T-parameter constraints, while  showcasing the interesting Yukawa structure allowed by the Higgs data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The custodial limit serves  as a systematic guideline for alleviating the stringent constraints arising from the electroweak T-  parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We have followed an alternative approach to find the general condition for the custodial  symmetry to be prevalent in scalar sector of an nHDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We used these results to extract the model  specific conditions for democratic 3HDMs which usually comes in two different avatars – one with a Z3  symmetry and the other with a Z2 × Z′  2 symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We then turn our attention to the Yukawa sector  of democratic 3HDMs and showed that the democratic 3HDMs also accommodate the possibility of  wrong-sign limit where the signs of the down-type Yukawa couplings are opposite to the corresponding  SM predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We find that a democratic 3HDM covers all the wrong-sign scenarios that can possibly  arise from a 2HDM framework with NFC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In the recent fits of the Higgs couplings [23,48,49] in the  kappa formalism [34, 35], the results are often reported with an implicit assumption about the signs  of the kappas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Our discussion on the wrong-sign limit highlights the importance of presenting the fit  results without any inherent assumptions about the signs of the kappas because, otherwise we can  miss potentially interesting and unconventional limits brought in by many different BSM scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  16  40  py  35  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  30  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  25  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  tan  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  15  2  sin (α2-β2)  tan β2  10  5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='8  sin(α2-β2)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='20  ly×Py  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  0  tan β1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='9  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='00  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='00  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='97  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='96  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='95  sin(α1-β1)To emphasize the last point, we have also argued how the wrong-sign limit inevitably leads to an  upper limit on the energy scale for the onset of NP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  Acknowledgments  DD and AS thank the Science and Engineering Research Board, India for financial support  through grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  SRG/2020/000006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  ML acknowledges funding from Funda¸c˜ao para a Ciˆencia  e a Tecnologia (FCT) through Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='PD/BD/150488/2019, in the framework of the Doc-  toral Programme IDPASC-PT, and was supported in part by FCT projects CFTP-FCT Unit 777  (UID/FIS/00777/2019), CERN/FIS-PAR/0008/2019 and CERN/FIS-PAR/0002/2021 which are par-  tially funded through POCTI (FEDER), COMPETE, QREN and EU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' DD and IS also thank ICTS,  Bengaluru for the warm hospitality while the final stages of this work were being completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  A  Brief note on SU(2) triplets  A real triplet of SU(2) in the cartesian basis is expressed as follows:  ACar =  �  �  A1  A2  A3  �  �  (63)  The generators of SU(2) in this basis are given by  T1 =  �  �  0  0  0  0  0  −i  0  i  0  �  � ,  T2 =  �  �  0  0  i  0  0  0  −i  0  0  �  � ,  T3 =  �  �  0  −i  0  i  0  0  0  0  0  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (64)  which make the transformation real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Now we want to migrate to a basis where T3 is diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We  will call this the spherical basis and the SU(2) triplet in this basis will be denoted by ASph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' We note  that the unitary matrix  U =  1  √  2  �  �  −1  i  0  0  0  √  2  1  i  0  �  � ,  (65)  diagonalizes T3 as follows  U · T3 · U† =  �  �  1  0  0  0  0  0  0  0  −1  �  � = T ′  3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (66)  This implies that ASph will be related to ACar via the following relation  ASph = UACar =  �  �  �  1  √  2(−A1 + iA2)  A3  1  √  2(A1 + iA2)  �  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (67)  where we have used Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (63).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Now let us define  A± =  1  √  2(A1 ∓ iA2) ,  (68)  17  where A+ and A− are implicitly understood to be the complex conjugates of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In terms of  these we can write the SU(2) triplet in the spherical basis as follows  ASph =  �  �  −A+  A3  A−  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (69)  Thus, the SU(2) invariant combination of two triplets, in these two bases, will be given by  A · B  =  A1B1 + A2B2 + A3B3  (70a)  =  A+B− + A−B+ + A3B3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (70b)  In a similar manner, the SU(2) invariant combination of three triplets is expressed as  (A × B) · C  =  (A2B3 − B2A3)C1 + (A3B1 − B3A1)C2 + (A1B2 − B1A2)C3  (71a)  =  i [A3(B−C+ − C−B+) + B3(C−A+ − A−C+) + C3(A−B+ − B−A+)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (71b)  B  Custodially invariant scalar potential  In this Appendix, we try to enumerate the terms in the scalar potential of a CS-invariant nHDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Since  we have doublets only, the renormalizable scalar potential can contain only quadratic and quartic  terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  In n doublets, there are 4n real fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' After the symmetry breaking, there will be n triplets  of the CS, including one that contains the unphysical Goldstone modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In addition, there will be n  singlets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The real parts of the neutral components of φk will be CS singlets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' It is then easy to see that  φ†  kφk  =  1  2Tk · Tk + CS singlets,  (72a)  φ†  jφk + φ†  kφj  =  Tj · Tk + CS singlets,  (72b)  with j ̸= k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' These are the quadratic forms which are CS invariant [13, 17, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The total number of  terms of the first kind is n, and of the second kind is 1  2n(n − 1), making a total of 1  2n(n + 1), which  is also exactly the number of different quadratic terms of the form Tj · Tk that we can get, with  unrestricted j and k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' In fact, if we insist on only real parameters in the scalar potential, there is no  additional restriction arising from the CS: the terms shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (72) are the only ones that are  Hermitian and gauge invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  The quartic CS invariants are combinations of the quadratics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Thus, we can enumerate the  kinds of terms that are possible, with N = 1  2n(n − 1), as follows:  (φ†  iφi)2  :  :  n terms,  (73a)  (φ†  iφi)(φ†  jφj)  : (i ̸= j) :  N terms,  (73b)  (φ†  iφj + φ†  jφi)2  : (i ̸= j) :  N terms,  (73c)  (φ†  iφj + φ†  jφi)(φ†  kφl + φ†  l φk)  : ({i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='j} ̸= {k, l}) :  1  2N(N − 1) terms,  (73d)  (φ†  iφi)(φ†  kφl + φ†  l φk)  : (k ̸= l) :  nN terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  (73e)  The total number of such terms is 1  8n(n+1)(n2 +n+2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The number of terms coming from n triplets  of CS comes out to be exactly the same, confirming that these are the only possible gauge invariant  18  combinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' However, it should be noted that in the most general gauge invariant potential, many  more quartic terms are possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Thus, the quartic coefficients, λi, need to be correlated in such a way  so that the terms in the quartic part of the scalar potential can be expressed in terms of the SU(2)C  invariant quantities listed in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (73).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  To elucidate the implications, let us go back to the example of the 2HDM scalar potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' From  the general 2HDM potential of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (29), we can see that the only terms that are not expressible in  terms of the SU(2)C bilinear invariants of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (73) are the terms proportional to λ4 and λ5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' But in  the custodial limit of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (28), these two terms can be combined as  λ4(φ†  1φ2)(φ†  2φ1) + λ5  2  �  (φ†  1φ2)2 + (φ†  2φ1)2� λ4=λ5  −−−−→ λ4  2 (φ†  1φ2 + φ†  2φ1)2  (74)  which, in view of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (73), is SU(2)C invariant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  The above discussion can easily be extended to the case of nHDMs, especially to the democratic  3HDMs, discussed in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' The conditions obtained using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (25) thus rearrange the quartic  part of the scalar potential in such a way that it can be expressed as combinations of the terms listed  in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' (73).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  References  [1] Particle Data Group Collaboration, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Workman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=', Review of Particle Physics, PTEP  2022 (2022) 083C01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Glashow and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Weinberg, Natural Conservation Laws for Neutral Currents, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D  15 (1977) 1958.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Branco, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Ferreira, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Lavoura, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rebelo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Sher, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Silva, Theory and  phenomenology of two-Higgs-doublet models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 516 (2012) 1–102, [arXiv:1106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='0034].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [4] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Cree and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Logan, Yukawa alignment from natural flavor conservation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 84  (2011) 055021, [arXiv:1106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4039].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Akeroyd, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Moretti, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Yagyu, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Yildirim, Light charged Higgs boson scenario in  3-Higgs doublet models, Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' A 32 (2017), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 23n24 1750145,  [arXiv:1605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='05881].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Bento, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rom˜ao, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Silva, Unitarity bounds for all symmetry-constrained  3HDMs, JHEP 08 (2022) 273, [arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='13130].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [7] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Boto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rom˜ao, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Silva, BFB conditions on a class of symmetry constrained  3HDM, arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='01068.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [8] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Das and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Saha, Alignment limit in three Higgs-doublet models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 100 (2019),  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 3 035021, [arXiv:1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='03970].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Pilaftsis, Symmetries for standard model alignment in multi-Higgs doublet models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  D 93 (2016), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 7 075012, [arXiv:1602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='02017].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Chakraborti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Das, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Levy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Mukherjee, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Saha, Prospects for light charged scalars  in a three-Higgs-doublet model with Z3 symmetry, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 104 (2021), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 7 075033,  [arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='08146].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  19  [11] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Boto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rom˜ao, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Silva, Current bounds on the type-Z Z3 three-Higgs-doublet  model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 104 (2021), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 9 095006, [arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='11977].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Willenbrock, Symmetries of the standard model, in Theoretical Advanced Study Institute in  Elementary Particle Physics: Physics in D ≧ 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 3–38, 10, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' hep-ph/0410370.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Pomarol and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Vega, Constraints on CP violation in the Higgs sector from the rho  parameter, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' B 413 (1994) 3–15, [hep-ph/9305272].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [14] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Haber and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' O’Neil, Basis-independent methods for the two-Higgs-doublet model III: The  CP-conserving limit, custodial symmetry, and the oblique parameters S, T, U, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 83  (2011) 055017, [arXiv:1011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6188].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [15] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Grimus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Lavoura, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Ogreid, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Osland, A Precision constraint on  multi-Higgs-doublet models, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' G 35 (2008) 075001, [arXiv:0711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [16] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Grimus, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Lavoura, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Ogreid, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Osland, The Oblique parameters in  multi-Higgs-doublet models, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' B 801 (2008) 81–96, [arXiv:0802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4353].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [17] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Olaussen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Osland, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Solberg, Symmetry and Mass Degeneration in  Multi-Higgs-Doublet Models, JHEP 07 (2011) 020, [arXiv:1007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1424].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [18] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Nishi, Custodial SO(4) symmetry and CP violation in N-Higgs-doublet potentials, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 83 (2011) 095005, [arXiv:1103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='0252].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [19] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Solberg, Conditions for the custodial symmetry in multi-Higgs-doublet models, JHEP 05  (2018) 163, [arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='00519].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [20] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Grzadkowski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Maniatis, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Wudka, The bilinear formalism and the custodial  symmetry in the two-Higgs-doublet model, JHEP 11 (2011) 030, [arXiv:1011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='5228].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [21] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Darvishi and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Pilaftsis, Classifying Accidental Symmetries in Multi-Higgs Doublet Models,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 101 (2020), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 9 095008, [arXiv:1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='00887].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Kundu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Mondal, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Pal, Custodial symmetry, the Georgi-Machacek model, and  other scalar extensions, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 105 (2022), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 11 115026, [arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='14195].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [23] ATLAS Collaboration, Combined measurements of Higgs boson production and decay using up  to 139 fb−1 of proton-proton collision data at √s = 13 TeV collected with the ATLAS  experiment, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [24] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Das and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Saha, Search for a stable alignment limit in two-Higgs-doublet models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  D 91 (2015), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 9 095024, [arXiv:1503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='02135].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [25] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Gunion and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Haber, The CP conserving two Higgs doublet model: The Approach to  the decoupling limit, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 67 (2003) 075019, [hep-ph/0207010].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [26] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Bhattacharyya, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Das, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Pal, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rebelo, Scalar sector properties of  two-Higgs-doublet models with a global U(1) symmetry, JHEP 10 (2013) 081,  [arXiv:1308.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4297].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  20  [27] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Bhupal Dev and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Pilaftsis, Maximally Symmetric Two Higgs Doublet Model with Natural  Standard Model Alignment, JHEP 12 (2014) 024, [arXiv:1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='3405].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' [Erratum: JHEP 11, 147  (2015)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Carena, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Low, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Shah, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Wagner, Impersonating the Standard Model Higgs  Boson: Alignment without Decoupling, JHEP 04 (2014) 015, [arXiv:1310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='2248].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [29] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Darvishi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Masouminia, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Pilaftsis, Maximally symmetric three-Higgs-doublet  model, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 104 (2021), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 11 115017, [arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='03159].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [30] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Fontes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rom˜ao, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Silva, A reappraisal of the wrong-sign hbb coupling and the  study of h → Zγ, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 90 (2014), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 1 015021, [arXiv:1406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6080].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [31] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Biswas and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Lahiri, Alignment, reverse alignment, and wrong sign Yukawa couplings in  two Higgs doublet models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 93 (2016), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 11 115017, [arXiv:1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='07159].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [32] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Ferreira, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Guedes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Sampaio, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Santos, Wrong sign and symmetric limits  and non-decoupling in 2HDMs, JHEP 12 (2014) 067, [arXiv:1409.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6723].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [33] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Ferreira, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Guedes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Gunion, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Haber, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Sampaio, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Santos, The  Wrong Sign limit in the 2HDM, in 2nd Large Hadron Collider Physics Conference, 10, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  arXiv:1410.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1926.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [34] LHC Higgs Cross Section Working Group Collaboration, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' David, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Denner,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Duehrssen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Grazzini, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Grojean, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Passarino, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Schumacher, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Spira, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Weiglein,  and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Zanetti, LHC HXSWG interim recommendations to explore the coupling structure of a  Higgs-like particle, arXiv:1209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='0040.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [35] LHC Higgs Cross Section Working Group Collaboration, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Andersen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=', Handbook  of LHC Higgs Cross Sections: 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Higgs Properties, arXiv:1307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='1347.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [36] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Bento, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Haber, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rom˜ao, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Silva, Multi-Higgs doublet models: physical  parametrization, sum rules and unitarity bounds, JHEP 11 (2017) 095, [arXiv:1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='09408].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [37] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Keus, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' King, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Moretti, Three-Higgs-doublet models: symmetries, potentials and  Higgs boson masses, JHEP 01 (2014) 052, [arXiv:1310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='8253].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [38] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Bhattacharyya and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Das, Nondecoupling of charged scalars in Higgs decay to two photons  and symmetries of the scalar potential, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 91 (2015) 015005, [arXiv:1408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='6133].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [39] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Carrolo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rom˜ao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Silva, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Vaz˜ao, Symmetry and decoupling in multi-Higgs  boson models, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 103 (2021), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 7 075026, [arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='11303].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [40] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Faro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Romao, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Silva, Nondecoupling in Multi-Higgs doublet models, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C 80 (2020), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 7 635, [arXiv:2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='10518].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [41] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Atkinson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Black, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Lenz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rusov, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Wynne, Cornering the Two Higgs Doublet  Model Type II, JHEP 04 (2022) 172, [arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='05650].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [42] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Modak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rom˜ao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Sadhukhan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Silva, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Srivastava, Constraining  wrong-sign hbb couplings with h → Υγ, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 94 (2016), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 7 075017,  [arXiv:1607.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='07876].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  21  [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Batra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Mandal, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Srivastava, h → Υγ Decay: Smoking Gun Signature of Wrong-Sign  hbb Coupling, arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='01200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [44] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Galon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rajaraman, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Tait, H → τ +τ −γ as a probe of the τ magnetic dipole  moment, JHEP 12 (2016) 111, [arXiv:1610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='01601].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [45] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Kanemura, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Mondal, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Yagyu, Exploring Wrong Sign Scenarios in the  Yukawa-Aligned 2HDM, arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='08803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [46] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Joglekar, S matrix derivation of the Weinberg model, Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 83 (1974) 427.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [47] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Bhattacharyya, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Das, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Pal, Modified Higgs couplings and unitarity violation,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 87 (2013) 011702, [arXiv:1212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='4651].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [48] ATLAS Collaboration, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Aad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=', Combined measurements of Higgs boson production and  decay using up to 80 fb−1 of proton-proton collision data at √s = 13 TeV collected with the  ATLAS experiment, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' D 101 (2020), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content=' 1 012002, [arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='02845].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  [49] CMS Collaboration, Measurement of Higgs boson decay to a pair of muons in proton-proton  collisions at √s = 13 TeV, CMS-PAS-HIG-19-006 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
+page_content='  22' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdAyT4oBgHgl3EQfZvfd/content/2301.00231v1.pdf'}
diff --git a/sdE3T4oBgHgl3EQf9Qs1/content/tmp_files/2301.04814v1.pdf.txt b/sdE3T4oBgHgl3EQf9Qs1/content/tmp_files/2301.04814v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cd001aa151f1e72799d0fd8d56345785881b445c
--- /dev/null
+++ b/sdE3T4oBgHgl3EQf9Qs1/content/tmp_files/2301.04814v1.pdf.txt
@@ -0,0 +1,1627 @@
+Multi-Constraint Molecular Generation using Sparsely 
+Labelled Training Data for Localized High-Concentration 
+Electrolyte Diluent Screening 
+Jonathan P. Mailoa,1* Xin Li,1 Jiezhong Qiu,1 and Shengyu Zhang2* 
+ 
+1) Tencent Quantum Laboratory, Tencent, Shenzhen, Guangdong, China 
+2) Tencent Quantum Laboratory, Tencent, Hong Kong SAR, China 
+ 
+* corresponding author: jpmailoa@alum.mit.edu, shengyzhang@tencent.com 
+ 
+ 
+
+Multi-Constraint Molecular Generation using Sparsely 
+Labelled Training Data for Localized High-Concentration 
+Electrolyte Diluent Screening 
+ 
+Abstract 
+Recently, machine learning methods have been used to propose molecules with desired 
+properties, which is especially useful for exploring large chemical spaces efficiently. However, these 
+methods rely on fully labelled training data, and are not practical in situations where molecules with 
+multiple property constraints are required. There is often insufficient training data for all those 
+properties from publicly available databases, especially when ab-initio simulation or experimental 
+property data is also desired for training the conditional molecular generative model. In this work, we 
+show how to modify a semi-supervised variational auto-encoder (SSVAE) model which only works with 
+fully labelled and fully unlabelled molecular property training data into the ConGen model, which also 
+works on training data that have sparsely populated labels. We evaluate ConGen’s performance in 
+generating molecules with multiple constraints when trained on a dataset combined from multiple 
+publicly available molecule property databases, and demonstrate an example application of building 
+the virtual chemical space for potential Lithium-ion battery localized high-concentration electrolyte 
+(LHCE) diluents. 
+ 
+ 
+
+Introduction 
+Conditional molecular generation capability is a topic of strong interest for the purpose of 
+chemical space exploration in the material virtual screening effort. Efforts in the field of conditional 
+molecular generative model either takes no conditional constraint on the generation approach1–5 or 
+fail to introduce a cost function based on the generated molecules’ property accuracy, making the 
+models’ generated molecular properties vary over a large range far from the desired property range.6  
+This difficulty arises because in a model, molecular properties are typically the output of some 
+regression model using the molecular structure as input. This makes it more challenging to use 
+molecular properties as the input to conditionally constrain the chemical space of the generated 
+molecules. Recent work based on reinforcement learning has enabled a conditional molecule 
+generator which generates good molecular candidates after thousands of training iterations, assuming 
+that a molecule property evaluator (cheminformatics library or computational material simulation 
+tool) can continuously be utilized on the generated molecules during training.7 In this work, we are 
+interested in a specific practical task more commonly encountered in the virtual screening of chemical 
+space relevant to industry: given a limited and often incomplete set of molecular property training 
+labels from multiple sources, develop a generative model to generate a molecular chemical space 
+which satisfies multiple property constraints so that it can be used as the high-quality input for a virtual 
+screening pipeline in a low-cost and relatively accurate manner, without requiring additional 
+simulations or experiments to further refine the generative model. 
+Recent work such as the semi-supervised variational auto encoder (SSVAE) model developed by 
+Kang, et al8,9 solves a part of this problem by employing a dual-track architecture where the molecular 
+property ������������ is simultaneously the output from a molecule regression predictor sub-model and the 
+input to a molecule generation decoder sub-model, in addition to also being the input for a separate 
+molecule encoder sub-model. Because ������������ is an output of the predictor sub-model, it can still be used 
+to construct a useful cost function for the entire model even though it is also being used as the input 
+
+to control the decoder’s generated molecule structures. The resulting combined model has a relatively 
+good control over the generated molecules’ property, making it attractive for efficiently generating 
+conditionally constrained molecular chemical space of interest. In addition to that, the SSVAE model 
+is capable of utilizing both fully labelled molecules and fully unlabelled molecules during the training 
+process, making it somewhat attractive for practical usage as there are many cases where we have no 
+access to the molecule properties due to a lack of simulation or experimental data. Nevertheless, the 
+model is still impractical because in practice there are a lot of molecules where the data is only partially 
+labelled and the SSVAE model is not equipped to handle such cases. A practical example of this 
+problem is a situation in battery electrolyte molecule screening where ‘easy’ molecular properties 
+such as molecular weight (Mol.Wt) and the number of fluorine atoms (nF) are easily obtainable from 
+cheminformatics libraries, while simulation data such as ionization energy (IE) and experimental data 
+such as the viscosity (Log.Vis, or the logarithm of viscosity) are not widely available. If we are 
+interested in generating a chemical space satisfying a number of of these constraints, many of the 
+molecules found in publicly available databases cannot be used as the fully labelled training data for 
+the SSVAE model. Removing the labels completely and turning them into fully unlabelled SSVAE 
+training data is detrimental as we then lose significant valuable label information from our training 
+dataset. 
+In this work, we show how to enable a generative model which fully utilizes molecules with 
+incomplete labels as the training data for a generative model without having to request additional 
+training data label during training. This model improvement is enabled by modifying the SSVAE model 
+to stop differentiating between fully labelled or unlabelled molecules. The model now relies on a 
+molecular property mask instead, which tells the model which property can be used for training from 
+a given molecule and which cannot. We name this modified SSVAE approach as the ConGen model, 
+and the major modifications needed to enable these practical capabilities will be outlined in the next 
+section. When the supplied molecule training data is either fully labelled or fully unlabelled, the 
+ConGen model’s data workflow will look identical to that of the SSVAE model’s fully labelled and fully 
+
+unlabelled data workflow. However, when the ConGen model is supplied with molecules with sparsely 
+populated property labels as the training data, its components and cost functions are appropriately 
+modified such that it only uses the relevant property labels based on the property mask. We first 
+benchmark the usage of this model on a training dataset used by the original SSVAE model, which 
+contains just labelled and unlabelled molecules. We then demonstrate several use cases which cannot 
+be done using the SSVAE model, including the generation of virtual screening chemical space for 
+Lithium-ion battery localized high concentration electrolyte diluent (LHCE) candidates. This is achieved 
+by combining five publicly available molecular property databases, comprising different properties 
+such as Mol.Wt, number of fluorine and oxygen atoms (nF and nO), ionization energy and electron 
+affinity (IE and EA), and Log.Vis. The availability of these properties are very different, with the first 
+three being fully available (‘easy’), the next two with availability of approximately 3% (‘medium’ 
+property, obtainable from quantum chemistry simulations), and the last one with availability of 
+approximately 0.03% (‘hard’ property, obtainable from experimental measurements). 
+ 
+ 
+
+Baseline SSVAE Model 
+We first describe the inner workings of the baseline SSVAE model developed by S. Kang, et al,8 
+which forms the foundation of this work. The main idea of the SSVAE model is simple: 
+1. Encode the input molecule structure ������������  from the training dataset into a latent space 
+representation ������������ using an encoder sub-model. 
+2. Predict the property label of the input molecule structure ������������ from the training dataset into 
+predicted property  ������������������������ using a predictor sub-model. If an actual molecule property label ������������������������ 
+exists in the training database, ������������������������ is discarded and the model uses the internal molecule 
+property label ������������ = ������������������������. Otherwise, ������������ = ������������������������ is used. 
+3. Use the internal molecule property label ������������ and the latent space representation ������������ as input 
+to the decoder sub-model to generate the output molecule structure ������������������������. 
+In order to handle different types of training data (labeled vs unlabeled), the SSVAE model treats 
+the two types of data differently. The training dataset in an epoch’s minibatch is split into two different 
+minibatch (labeled vs unlabeled). The SSVAE workflow is then run twice, in a slightly different manner 
+depending on whether the molecule minibatch is fully labeled or fully unlabeled (Figure 1). 
+ 
+Figure 1 | High-level labelled / unlabelled data & model differentiation within Kang et al’s original SSVAE model.8 The 
+variational auto-encoder (VAE) cost is calculated separately for the unlabeled and the labeled dataset, while regression cost 
+is only calculated for the labeled dataset. The three costs are then summed up to calculate the total minibatch training cost. 
+ 
+
+Labelled
+Unlabelled
+Minibatch Labelled Samples
+Property
+Labelled
+(In)
+Data
+yp
+yL
+SMILES
+RNN
+np property
+(Predictor)
+y=yl
+(In)
+y
+Total Training Cost
+x
+=
+RNN
+RNN
+SMILES
+sample
+Labelled Regression Cost
+(Encoder)
+(Decoder)
+XD
+(Out)
++
+Labelled VAE Cost
+Unlabelled VAE Cost
+SMILES
+RNN
+y=yp
+(In)
+(Predictor)
+Yp
+x
+Unlabelled
+RNN
+RNN
+SMILES
+Data
+(Encoder)
+Z
+(Decoder)
+X
+(Out)
+Minibatch Unlabelled SamplesIn SSVAE approach, a molecule entry’s training cost function needs to be split into three parts 
+(Equation 1-3). The cost function is written in verbose detail below for clarity, as we need to 
+subsequently explain in the following section how the modifications need to be done for the dirty 
+(partially labelled) data in the ConGen model: 
+a. VAE cost function for completely labeled entries in the minibatch (Equation 1): 
+������������(������������, ������������) = − � ��������������������������,������������ ln ������������������������,������������,������������ + �1 − ������������������������,������������� ln�1 − ������������������������,������������,��������������
+������������������������
+������������=1
+������������������������
+������������=1
+ 
++ � 1
+2 ������������������������� ln 2������������ + ln�������������������������������������(������������)� + ��������������������������,������������,������������ − ������������������������� ��������������������������,������������,������������ − �������������������������������������������������,������������
+−1
+������������������������
+������������=1
+������������������������
+������������=1
+�
+������������������������
+������������=1
+ 
+− � � 1
+2 �1 + ln �������������������������������������,�������������
+2 − �������������������������������������,�������������
+2 − �������������������������������������,�������������
+2�
+������������������������
+������������=1
+������������������������
+������������=1
+ 
+b. VAE cost function for completely unlabeled entries in the minibatch (Equation 2): 
+������������(������������) = − � ��������������������������,������������ ln ������������������������,������������,������������ + �1 − ������������������������,������������� ln�1 − ������������������������,������������,��������������
+������������������������
+������������=1
+������������������������
+������������=1
+ 
++ � 1
+2 �� ������������������������,������������
+−1�������������������������������������,������������,�������������
+2
+������������������������
+������������=1
++ ��������������������������,������������,������������ − ������������������������� ��������������������������,������������,������������ − �������������������������������������������������,������������
+−1
+������������������������
+������������=1
+������������������������
+������������=1
+− ������������������������ + ln�������������������������������������(������������)� − � ln �������������������������������������,������������,�������������
+2
+������������������������
+������������=1
+�
+������������������������
+������������=1
+ 
+− � � 1
+2 �1 + ln �������������������������������������,�������������
+2 − �������������������������������������,�������������
+2 − �������������������������������������,�������������
+2�
+������������������������
+������������=1
+������������������������
+������������=1
+ 
+c. Regression cost function for completely labeled entries (Equation 3): 
+������������������������������������������������������������������������(������������, ������������) = ������������ � � �������������������������,������������,������������ − �������������������������������������,������������,��������������
+2
+������������������������
+������������=1
+������������������������
+������������=1
+ 
+where ������������ = ������������������������������������(������������������������) and ������������ = ������������(������������������������) are the label covariance matrix and mean values constructed 
+from the entire fully labelled training set, ������������ is the mean function, ������������ is the standard deviation function, 
+������������ is the tradeoff hyperparameter between generative and supervised learning, while ������������������������, ������������������������, ������������������������, ������������������������, 
+and ������������������������ represent the number of minibatch’s completely labeled entries, completely unlabeled entries, 
+and dimensions of ������������, ������������, and ������������ respectively. Finally, the total minibatch cost function is simply 
+������������������������������������������������������������������������������������������������������������ = ������������ + ������������ + ������������������������������������������������������������������������. 
+
+Finally, once the training is finished, the decoder sub-model can be extracted and be run 
+independently by specifying the conditional property input ������������ and the randomly sampled latent space 
+input ������������ to conditionally generate the desired molecule outputs, where a beam search algorithm is 
+used for converting output ������������������������ to a molecule SMILES. The primary disadvantage of this approach is 
+that the training dataset must be either fully labelled or fully unlabelled. The reason the SSVAE model 
+splits the problem as specified in Figure 1 above is because it simplifies the model dataflow, math, and 
+behaviour tremendously. In practice, training datasets of interest likely consist of molecules with 
+incomplete labels, in addition to the completely labelled or unlabelled molecules. This is especially so, 
+if the training molecule database is either taken from a publicly available database (like PubChem 
+experimental data10) or combined from several different databases. Neither of these practical types 
+of “dirty” datasets will work for training the baseline SSVAE model, thereby severely limiting the type 
+of conditional molecule generation which can be done, especially when multi-property conditional 
+molecule generation is desired. This is typically the case for battery electrolyte or pharmaceutical drug 
+molecule virtual screening. 
+ 
+
+Enabling Sparse Labelled Data Utilization using ConGen Model 
+We modify the SSVAE model into the ConGen model, which is explicitly designed to work with 
+“dirty” training data, thereby enabling the usage of significantly larger number of training data sources 
+including those merged from different public and private sources. This enables us to perform 
+conditional molecule generation tasks which are previously not possible using the SSVAE model. For 
+example, given a large labeled molecule dataset from ZINC11 (containing Mol.Wt, hydrophobicity LogP, 
+and drug-likeness QED) and another similarly large molecule dataset from Materials Project 
+Electrolyte Genome12 (containing Mol.Wt, EA, and IP), we can train a conditional generative model 
+which can generate molecules with multiple simultaneous constraints on the Mol.Wt, LogP, and EA 
+values (known useful properties for screening lithium battery electrolytes). Given these diverse 
+sources of training data, the original SSVAE model cannot be trained on the combined database of 
+Mol.Wt, LogP, and EA labels because the training data label is sparse. ConGen on the other hand has 
+no such limitation, allowing users to mix non-ideal practical data from multiple sources as desired. 
+The primary idea of the ConGen model is to take the general high-level architecture of the 
+SSVAE model, but then modify all its components as needed in order to enable the usage of dirty 
+training data. We have re-written the entire SSVAE model from the original TensorFlow 1.0 version 
+into a PyTorch version to enable better model flexibility, before further implementing the necessary 
+modifications to enable the usage of sparse training data labels. When this PyTorch version is trained 
+on the original SSVAE training data (only fully labelled and fully unlabelled molecules) using the same 
+hyperparameter training settings (ntrn = 285k training molecules with 50:50 labelled/unlabelled 
+molecule split, nval = 15k validation molecules, ntst = 10k test molecules, ������������ = 104, Adam optimizer 
+learning rate ������������������������ = 10−4), we obtain accuracy metrics for property prediction, unconditional and 
+single-property conditional molecule generation tasks (only Mol.Wt = 250 Da constraint is used, 
+because the original SSVAE code only allows single-property constraint) equivalent to the TensorFlow 
+version (Table 1). 100 molecules are generated on both unconditional & conditional generation tasks. 
+
+Task 
+Property 
+SSVAE 
+ConGen 
+Predictor 
+Regression 
+MAE 
+Mol.Wt (Da) 
+0.95 
+1.22 
+LogP 
+0.06 
+0.08 
+QED 
+0.013 
+0.014 
+Decoder 
+Unconditional 
+Generation 
+Mol.Wt (Da) 
+360 ± 65 
+363 ± 64 
+LogP 
+2.95 ± 1.06 
+3.01 ± 1.07 
+QED 
+0.723 ± 0.142 
+0.713 ± 0.154 
+Decoder 
+Conditional 
+Generation 
+Mol.Wt (Da) 
+249 ± 6 
+251 ± 5 
+LogP 
+2.38 ± 0.89 
+2.13 ± 0.91 
+QED 
+0.810 ± 0.072 
+0.816 ± 0.095 
+Table 1 | Comparison between SSVAE (TensorFlow 1.0) and baseline ConGen (PyTorch) model on the original SSVAE model 
+tasks. The baseline ConGen is equivalent to SSVAE, except that it is implemented in PyTorch. This comparison is performed 
+on SSVAE ‘clean’ original training dataset, which only contains fully labelled and fully unlabelled molecules. Identical training 
+hyperparameter settings are used, and relatively equivalent performance metrics are obtained. The slight differences can be 
+attributed to the high aggressivity of the original model’s training hyperparameter settings. For the property prediction task, 
+predictor sub-model is utilized to calculate mean absolute error (MAE) with respect to the training labels. For the 
+unconditional / conditional generation tasks, the decoder sub-model is used to generate the molecules and the molecules 
+property labels are calculated using RDKit cheminformatics library. 
+ 
+Once we have confirmed that the two models are equivalent, the input data preprocessing and 
+molecule data workflow inside the ConGen sub-models are modified (Figure 2). First, we enable the 
+ability to merge molecule training data labels with different types of property labels into a new 
+property label matrix ������������������������. This will cause a significant fraction of the merged database to contain 
+missing [molecule, property] entry labels. For entries with no label available from all the databases, 
+we designate the property label as invalid. This can be done by generating a mask matrix ������������ containing 
+‘0’ for invalid entries and ‘1’ for entries with available property values. For entries where multiple 
+property labels are available from different databases, we choose the available label from the latest 
+database being merged. Both ������������������������ and ������������ matrices are now required as inputs into the ConGen model. 
+ConGen no longer differentiates data workflow based on whether the molecule is fully labelled or fully 
+unlabelled. ConGen instead implements a selector for the intermediate label ������������ which choose whether 
+to utilize existing label ������������������������ or the predicted property label  ������������������������ generated by the predictor sub-model 
+depending on the value of the mask ������������ (Equation 4): 
+������������(������������, ������������) = �������������������������(������������, ������������)   ������������������������  ������������(������������, ������������) == 1 
+������������������������(������������, ������������)   ������������������������  ������������(������������, ������������) == 0 
+
+where ������������ and ������������ denote the molecule and property type indices, respectively. With this modification, a 
+unified data workflow can be utilized for fully labelled, fully unlabelled, and partially unlabelled 
+molecules. Furthermore, when the molecule in the minibatch is either fully labelled or fully unlabelled 
+the mathematical operations performed on them within the ConGen model will be identical to those 
+performed in the SSVAE model.  
+ 
+Figure 2 | Dirty training label data merging and high-level dirty data workflow within the ConGen model. ConGen model 
+no longer differentiates between fully labelled, fully unlabelled, and partially labelled molecule inputs. The unified data 
+workflow is controlled by the mask matrix ������������. ������������������������,1, ������������������������,2, and ������������������������,1+2 denote the number of samples within the first, the second, 
+and the merged property databases respectively. 
+ 
+However, it is not as straightforward with respect to the training cost function and subsequent 
+molecule generation. It is important to recognize that the implementation of the training cost function 
+within the SSVAE model is heavily dependent on whether the molecule is fully labelled or fully 
+unlabelled. The SSVAE cost function consists of three major elements, designed to ensure that the 
+predictor, encoder, and decoder are all accurate (Equation 1-3) and we need to design the dirty data 
+VAE cost function substitute for ������������ and ������������ because we no longer have fully labelled and fully unlabelled 
+molecules. It is worth noting that during the execution of the original SSVAE model, there is no 
+interaction between molecule inputs within a minibatch (e.g. if molecule A and B are processed 
+
+Labelled
+Invalid
+Unlabelled
+Property 1
+Property 2-3
+Property 1-3
+Property 1-3
+ns,1 sample
+0
+0
+1
+0
+0
+sample
+0
+0
+0
+sample
+0
+0
+0
+1
+1
+1
+ns,1+2
+0
+0
+0
+1
+0
+0
+0
+1
+L
+0
+0
+0
+0
+1
+Mixture of Multiple
+Label matrix
+Mask matrix
+Incomplete Database Labels
+YL
+M
+yp
+Total Training Cost
+SMILES
+X
+RNN
+Selector
+All Sample Regression Cost
+(In)
+(Predictor)
+y
+All Sample VAE Cost
+x
+RNN
+RNN
+SMILES
+Minibatch Partially
+(Encoder)
+Z
+(Decoder)
+XD
+(ano)
+Labelled Samplessimultaneously, the model output ������������������������ for both molecules are not influenced by the fact that the other 
+molecule is also simultaneously processed. This ensures that any intermediate values for a molecule 
+( ������������������������ , ������������������������ , ������������ , ������������������������ , etc) are solely determined by that molecule input ������������ . Because of this, the 
+implementation of a new cost function for the ConGen model becomes less complicated. There is a 
+significant overlap of terms between ������������ and ������������, enabling us to design a new VAE cost function ������������ for the 
+ConGen model which takes partially labeled entries utilizing our mask matrix ������������ (Equation 5). When 
+the entries are all completely labeled, the entries of ������������ will all be 1, and ������������ should be converted to ������������, 
+except for some constant terms that do not affect the training. When the entries are all completely 
+unlabeled, the entries of ������������ will all be 0, and ������������ should be converted to ������������, again, except for some 
+constant terms. Similarly, our new regression cost function ������������������������������������������������������������������������������������ should only sum over labeled 
+entries in the minibatch. By ensuring this behavior, the subsequent ConGen cost function 
+differentiation and model parameter optimization will work exactly like the SSVAE versions when 
+completely labeled / unlabeled data are supplied. However, it will also now work for dirty sparsely 
+labelled training data. Henceforth, we define new cost functions for the ConGen minibatch, especially 
+meant for dirty data: 
+a. VAE cost function for dirty labeled entries in the minibatch (Equation 5): 
+������������(������������, ������������) = − � ��������������������������,������������ ln ������������������������,������������,������������ + �1 − ������������������������,������������� ln�1 − ������������������������,������������,��������������
+������������������������
+������������=1
+������������������������
+������������=1
+ 
++ � 1
+2 ������������������������� ln 2������������ + � ������������������������,�������������������������������������,������������ − ������������������������� � ������������������������,�������������������������������������,������������ − �������������������������������������������������,������������
+−1
+������������������������
+������������=1
+������������������������
+������������=1
+�
+������������������������
+������������=1
+ 
++ � 1
+2 �� ������������������������,������������
+−1�1 − ������������������������,��������������������������������������������������,�������������
+2
+������������������������
+������������=1
++ ��1 − ������������������������,��������������������������������������,������������ − ������������������������� ��1 − ������������������������,��������������������������������������,������������ − �������������������������������������������������,������������
+−1
+������������������������
+������������=1
+������������������������
+������������=1
+− ������������������������ − ��1 − ������������������������,������������� ln �������������������������������������,�������������
+2
+������������������������
+������������=1
+�
+������������������������
+������������=1
+ 
+− � � 1
+2 �1 + ln �������������������������������������,�������������
+2 − �������������������������������������,�������������
+2 − �������������������������������������,�������������
+2�
+������������������������
+������������=1
+������������������������
+������������=1
+ 
+b. Regression cost function for dirty labeled entries in the minibatch (Equation 6): 
+������������������������������������������������������������������������������������(������������, ������������) = ������������ � � ������������������������,������������ �������������������������,������������ − �������������������������������������,������������,��������������
+2
+������������������������
+������������=1
+������������������������
+������������=1
+ 
+
+where ������������������������ refers to the number of all samples in the dirty data minibatch. It is straightforward to prove 
+that under this scheme, ������������ is converted to either ������������ or ������������ depending on the values of ������������, except for 
+constant terms which do not have any impact on the model parameter optimization process. Note 
+that, compared to the SSVAE cost functions, we have intentionally removed the constant terms 
+ln�������������������������������������(������������)� from the cost function above for numerical reasons we will describe in the following 
+paragraph related to the dirty data covariance matrix ������������. Crucially, under this new cost function only 
+the corresponding labeled / unlabeled matrix elements from ������������ and ������������ contributes to the summation 
+over ������������������������  and ������������������������  forming ������������ . The total minibatch cost function is now simply ������������������������������������������������������������������������������������������������������������������������ = ������������ +
+������������������������������������������������������������������������������������. 
+It is important to note that because we only have partially labeled entries, we do not have 
+complete entries for ������������������������ and correspondingly ������������ = ������������������������������������(������������������������) and ������������ = ������������(������������������������) can only be calculated 
+using the incomplete entries, making these matrices ill-defined especially ������������������������������������(������������������������). For an SSVAE 
+model, ������������ is well-defined because it is straightforward to completely discard the unlabelled molecule 
+entries from the training set and calculate ������������ and ������������ directly from the completely labelled molecule 
+entries (this will be a good approximation as long as there is a large number of fully labelled molecules 
+which is a good chemical representation of the full training dataset). This can be done once during the 
+model construction and be set at those values throughout the entire model training. However, this 
+strategy does not work for ConGen because the training data is dirty. In this case, it only makes sense 
+to calculate the label mean ������������ from the valid entries and ignore the invalid values in the ������������������������ matrix. 
+Similarly, it makes more sense to calculate covariance matrix ������������ entries from the available ������������������������ matrix 
+entries while ignoring the invalid entries. In other words, we have the following situation for ������������ and ������������ 
+calculation (Equation 7-8): 
+������������������������ = ������������(������������������������)������������ =
+∑
+������������������������,������������,������������������������������������,������������
+������������������������
+������������=1
+∑
+������������������������,������������
+������������������������
+������������=1
+ 
+������������������������,������������ = ������������������������������������(������������������������)������������,������������ =
+∑
+�������������������������,������������,������������ − ��������������������������������������������������,������������,������������ − �������������������������������������������������,������������������������������������,������������
+������������������������
+������������=1
+�∑
+������������������������,������������������������������������,������������
+������������������������
+������������=1
+� − 1
+ 
+
+In a clean training data like the ones being used in the SSVAE model, all entries of the mask matrix ������������ 
+are all 1’s, and it can then mathematically be proven that the covariance matrix ������������ will always be a 
+positive semi-definite (PSD) matrix. Correspondingly, in SSVAE the log-determinant term ln�������������������������������������(������������)� 
+in the cost function above will always be well-defined. The mathematical guarantee breaks down 
+when the entries of mask matrix ������������ are no longer all 1’s, however.13 Consequently, we can get training 
+errors due to attempting log operations on negative numbers. Nevertheless, because the term 
+ln�������������������������������������(������������)�  is just a constant, we can remove it from the ConGen cost function without any 
+mathematical training consequences as we have done in Equation 5. 
+The real physical issue arises from the quality of ������������ and ������������ themselves. When we have low 
+availability of training data label (a lot of 0 entries in the mask matrix ������������), we will have significant 
+problems because the ������������ and ������������ matrices do not accurately represent the real molecule property labels, 
+especially when we have many invalid labels in the training dataset. Keeping the values of ������������ and ������������ the 
+same throughout the training iterations mean we will have poor control on the conditionally 
+generated molecules’ properties after subsequent model training and conditional generation 
+processes. We can mitigate this problem by using imputation technique13 to re-calculate ������������ and ������������ 
+using predicted molecule property labels from the predictor sub-model when there is no valid label in 
+������������������������. In other words, we track minibatch ������������ from the selector (Equation 4, Figure 2) throughout a training 
+epoch, and re-calculate ������������ and ������������ using ������������ instead of using ������������������������ after each training and validation cycle in 
+the epoch has been completed. This update is performed iteratively throughout the training, and it is 
+important to store the final ������������ and ������������ as part of the ConGen model parameter because subsequent 
+molecule generation tasks need to be performed using these higher quality ������������ and ������������ parameters 
+(Equation 8-9): 
+������������������������ = ������������(������������)������������ =
+∑
+������������������������,������������
+������������������������
+������������=1
+������������������������ − 1  
+������������������������,������������ = ������������������������������������(������������)������������,������������ =
+∑
+�������������������������,������������ − ��������������������������������������������������,������������ − �������������������������
+������������������������
+������������=1
+������������������������ − 1
+ 
+
+where ������������������������ is the number of all molecules in the training dataset. The quality of ������������ and ������������ are not very 
+good in the beginning of the training. However, as the predictor sub-model gets more accurate during 
+subsequent training iterations, ������������ and ������������ will represent the real sample population better and we 
+correspondingly achieve better molecule property prediction and conditional generation accuracy in 
+the end. 
+We also take advantage of the modular nature of the ConGen model (inherited from the 
+modularity of SSVAE) to further improve model performance on dataset with rare training property 
+labels (such as ab-initio simulation or experimental properties). It is straightforward to implement 
+transfer learning in ConGen by replacing the recurrent neural networks (RNN) in the predictor and 
+encoder sub-models with a bidirectional encoder representations from transformer (BERT) model pre-
+trained on a much larger (but ‘cheaper’) molecule property dataset. Here we use the ChemBERTa 
+model, which is a large-scale self-supervised transformer-based pretraining model which only requires 
+molecule SMILES as input and has been thoroughly evaluated.14 During the sub-model construction, 
+we add a fully connected network linear layer on top of the transferred ChemBERTa model. We 
+nickname this type of transferred model ‘BERT’ from here onward. When BERT is used to substitute 
+the RNN encoder, the entire ChemBERTa layers’ parameters are frozen. However, when BERT is used 
+to substitute the RNN predictor, the last ChemBERTa layer’s parameters can be fine-tuned by the 
+PyTorch optimizer. While we do not substitute the RNN decoder with other types of decoder sub-
+model, in principle it is straightforward to do so as well if desired. For the standard ConGen model 
+training with just RNN sub-models, we set the Adam optimizer ������������������������ = 10−4 and clip the gradients 
+absolute value to a maximum of 102. For the ConGen model training with BERT predictor and decoder 
+sub-model substitutions, we have significantly lower Adam optimizer ������������������������ = 3 × 10−5 for the BERT-
+based sub-models, and ������������������������ = 10−3 is used for optimizing the decoder sub-model parameters. 
+Finally, we demonstrate the resulting capability of the ConGen model on dirty dataset in Table 
+2. The training data labels are mixed from two different databases: 1) ZINC database containing 
+properties such as Mol.Wt, LogP, and QED11 used in the SSVAE publication,8 2) Materials Project 
+
+Electrolyte Genome database containing properties such as IE and EA.12 The ConGen model is trained 
+on all 5 of these properties, which cannot be done by the SSVAE model. As an example of multi-
+property conditional generation, we query the models to generate molecules with 3 simultaneous 
+properties: Mol.Wt = 250 Da, LogP = 2.5, and IE = 5 eV. The corresponding regression and conditional 
+generation results are given below in Table 2. We validate the properties of the generated molecules 
+using RDKit15 (for Mol.Wt and LogP) and quantum chemistry (for IE, see Methods). We see that overall, 
+the BERT-based ConGen has worse performance than the RNN-based ConGen model on property 
+prediction tasks, but is relatively equivalent to the RNN-based ConGen on conditional generation tasks 
+(good on Mol.Wt and LogP, but less accurate on IE). We have expected the transferred BERT-based 
+ConGen to perform worse than the RNN-based ConGen on abundant property label such as Mol.Wt 
+and LogP  and better than RNN-based ConGen on rare property label such as IE. The fact that both 
+RNN and BERT-based ConGen shows relatively equivalent performance for molecular conditional 
+generation tasks merits further future investigation. We hypothesize that we still have insufficient 
+number of quantum chemistry property training labels from just the Materials Project Electrolyte 
+Genome database,12 and that a more accurate and data-efficient predictor sub-model is still needed. 
+Currently the BERT-based ConGen is computationally more expensive while offering no significant 
+improvement over the RNN-based ConGen, so we focus solely on using RNN-based ConGen in the 
+following large-scale electrolyte diluent screening section. 
+Task 
+Model 
+Mol.Wt (Da) 
+LogP 
+QED 
+EA (eV) 
+IE (eV) 
+Predictor Regression 
+Test Set MAE 
+RNN 
+2.70 
+0.05 
+0.009 
+0.20 
+0.16 
+BERT 
+ 6.07 
+0.15 
+0.017 
+0.22 
+0.19  
+Decoder Unconditional 
+Generation 
+RNN 
+312 ± 95 
+2.07 ± 1.28 
+0.677 ± 0.124 
+1.79 ± 0.84 
+5.99 ± 0.44 
+BERT 
+271 ± 145 
+2.15 ± 1.11 
+0.583 ± 0.138 
+1.72 ± 0.82 
+6.40 ± 0.34 
+Decoder Conditional 
+Generation 
+RNN 
+248 ± 4 
+2.55 ± 0.23 
+0.672 ± 0.082 
+2.06 ± 0.55 
+6.53 ± 0.62 
+BERT 
+252 ± 3 
+2.45 ± 0.36 
+0.756 ± 0.127 
+1.80 ± 0.64 
+6.36 ± 0.41 
+Table 2 | ConGen model performance comparison on ‘dirty data’ tasks, including both RNN-based ConGen and BERT-based 
+ConGen. This ‘dirty data’ task cannot be done with the original SSVAE model but is useful in practice for conditional 
+generative model training because molecule property labels are often unavailable or incomplete. Including a pre-trained 
+BERT can increase the predictor sub-model’s ability on ‘rare’ properties such as EA and IE, even though in some cases it may 
+reduce the predictor sub-model’s performance on ‘common’ properties (Mol.Wt, LogP, and QED in this case). The conditional 
+generation co-constraints are Mol.Wt = 250 Da, LogP = 2.5, and IE = 5 eV. Regression MAE is calculated using property labels 
+from the database, while generated molecules’ properties are validated using either RDKit library or ab-initio simulation. 
+ 
+
+Use Case Example: Lithium-Ion Battery Localized High Concentration 
+Electrolyte Diluent Screening 
+Finally, we demonstrate the usage of the ConGen model on a practical example: generating the 
+chemical space for further virtual screening of Li-ion battery localized high concentration electrolyte 
+(LHCE) diluent molecules. Recent progress in the development of Li-ion battery electrolytes have led 
+to the discovery of LHCE-type of electrolytes, which microscopically look like that of high salt 
+concentration electrolyte (HCE), but macroscopically look more like a conventional electrolyte.16 The 
+LHCE is useful because it is stable over a wide electrochemical window, in addition to forming stable 
+solid electrolyte interphase (SEI) layer which is important for the long-term stability of the battery.17,18 
+From a cost perspective, the LHCE is also important because it can reduce the required amount of Li-
+salt used, versus that of HCE which requires a large amount of expensive Li-salt.19 Finally, LHCE can 
+have significantly lower solution viscosity than HCE, which is useful not just for improving the 
+electrolyte’s lithium ion transport properties, but also for enabling better electrode wetting which 
+helps to better optimize the energy capacity of Li-ion battery cells.20 Chemically, what differentiates 
+LHCE from HCE and conventional electrolytes is the addition of small molecules which act as a diluent 
+in the electrolyte.16 These diluent molecules are typically hydrofluoroether (HFE) such as bis(2,2,2-
+trifluoroethyl) ether (BTFE) and 1,1,2,2-tetrafluoroethyl-2,2,3,3-tetrafluoropropyl ether (TTE), or 
+fluorinated orthoformate such as tris(2,2,2-trifluoroethyl) orthoformate (TFEO).16–18 The unique trait 
+of these types of compound is that while they are sufficiently polar, they are less polar than the Li-salt 
+anions being used in the LHCE. Consequently, at the right concentration range the Li+ cations will 
+primarily coordinate with the polar salt anions in the first Li+ solvation shell. The diluent molecules will 
+then mostly coordinate with these salt clusters from the second shell onward using their polar oxygen 
+atoms. Furthermore, the fluorinated components of the diluent molecules will tend to form their own 
+non-polar network in the LHCE. Consequently, the addition of diluents into LHCE ensures that locally 
+the salt cluster looks like that of HCE (more stable), while macroscopically the diluents separate these 
+
+salt clusters and ensure that the solution is less viscous, ionically conductive, and ideally inflammable 
+(due to the proportion reduction of flammable solvent molecules in LHCE).  
+Many criteria need to be satisfied by these LHCE diluent molecules such as electrochemical 
+stability, inflammability, and low viscosity. While there are several known working LHCE diluents, it is 
+important to find more relevant compounds in this field to enrich the diluent chemical space suitable 
+for the optimization of specific types of Li-ion batteries. We apply the ConGen model to generate 
+candidate molecules for LHCE diluents through structural chemical properties such as: Mol.Wt, nF, nO, 
+IE, EA, and Log.Vis. To achieve this, we train ConGen model on a mixture of 5 publicly available 
+datasets: 
+• 
+Mol.Wt database from ZINC8,11 (310,000 unique entries) 
+• 
+Mol.Wt, simulated IE, EA database from the Materials Project Electrolyte Genome12 (62,274 
+unique entries) 
+• 
+Mol.Wt, simulated IE, EA database from Austin Apple Github21 (26,394 unique entries) 
+• 
+Oxyfluorocarbon nF, nO database from PubChem10 (200,000 unique entries) 
+• 
+Experimental Log.Vis database from literature22 (322 unique entries) 
+Where applicable, each of these databases are supplemented with the corresponding molecule 
+Mol.Wt, nF, and nO missing property labels because it is computationally efficient and inexpensive to 
+do so using RDKit.15 The combined database has 571,023 unique molecules. Finally, we evaluate the 
+model’s performance. Based on known existing LHCE diluents, we hypothesize that we need the 
+following properties for the LHCE diluent molecules: 
+• 
+Electrochemical properties: 
+EA <= 0.5 eV, IE >= 7.0 eV 
+• 
+Viscosity property: 
+ 
+Log.Vis <= 0.0 
+• 
+Structural properties:  
+Mol.Wt <= 300, nF >= 4, nO = 1-2 
+Within the framework of ConGen, we can implement this multi-condition molecular structure 
+generation task by simply deploying simultaneous property label ‘anchors’ as the decoder input during 
+
+the generation cycle. For example, we may choose the following label anchors to satisfy the conditions 
+stated above: 
+1. 
+EA = 0 or 0.5 eV 
+2. 
+IE = 7.0 or 7.5 eV 
+3. 
+Log.Vis = -0.1 or 0.0 
+4. 
+Mol.Wt = 250 or 300 Da. 
+5. 
+nF = 4 or 6 
+6. 
+nO = 1 or 2 
+We correspondingly have 26 = 64 combinations of multi-constraint property anchors we can use for 
+the conditional generation in the example above. For each set of anchors, we generate 5 molecule 
+samples resulting in 320 conditionally sampled molecules using our RNN-based ConGen model (Query 
+1). The training data label distributions, based on just available property labels, is shown below in 
+Figure 3. 
+ 
+Figure 3 | Training data molecular property label distribution. The dashed lines indicate the property label ‘anchors’ we will 
+use for subsequent conditional molecular generation. The arrows indicate the preferred generated molecules’ property 
+range. The anchors are respectively: EA = [0,0.5], IE = [7.0,7.5], Log.Vis = [-0.1,0.0], Mol.Wt = [250,300], nF = [4,6], nO = [1,2]. 
+
+4000
+3000
+40
+3500
+35
+2500
+3000
+30
+2000
+2500
+25
+Count
+2000
+1500
+15
+1000
+1000
+10
+500
+500
+5
+0+
+2
+0
+-2
+0
+1
+234
+5
+6
+0
+4
+6
+8
+10
+0.5
+0.0
+0.5
+1.0
+1.5
+EA (eV)
+IE (eV)
+Log.Vis
+30000
+350000
+200000
+300000
+175000
+25000
+150000
+250000
+20000
+125000
+200000
+15000
+150000
+75000
+10000
+100000
+50000
+5000
+50000
+25000
+0 +
+0+
++0
+100
+200
+300
+400
+500
+0
+2
+4
+6
+8
+10
+12
+0
+2
+4
+6
+8
+10
+Mol.Wt (Da)
+nF
+ouRegression on the test set, unconditional molecule generation, as well as conditional molecule 
+generation results are shown below in Figure 4 and Table 3. In order to calculate the ground truth 
+property label values for the generated molecules, several methods are employed. For Mol.Wt, nF, 
+and nO, simple cheminformatics tool such as RDKit can be used to quickly calculate their true values. 
+For EA and IE, we used quantum chemistry calculations with identical calculation settings to the prior 
+work12 to calculate the true values. We see that we have excellent control over the generated 
+molecules’ structural properties (Mol.Wt, nF, and nO) and IE, although we observe a positive shift of 
+approximately 2.0 eV on the generated molecules’ EA compared to the mean of the anchors’ EA (0.25 
+eV). We hypothesize that this systemic shift may be caused by the slight difference in our adiabatic EA 
+calculation workflow compared to the procedure utilized by the Materials Project Electrolyte Genome 
+team, as well as the fact that we query the ConGen model to generate molecules with EA label anchors 
+at the extreme left end of the training dataset EA label distribution (making this the most difficult 
+constraint out of the 6 co-constraints we have employed). 
+We currently have no experimental validation capability to measure Log.Vis for the generated 
+molecules, so unfortunately no accuracy metric can be displayed for these molecules’ Log.Vis property. 
+Nevertheless, we have listed all the molecules that the ConGen model has generated based on their 
+property label input anchors in Table 4 for future validation by other research groups with 
+experimental capabilities. Additional molecular property criteria are likely needed to further improve 
+the quality of the generated LHCE diluent candidate molecules. Inclusion of further molecular property 
+constraints to help refine this generated LHCE diluent chemical space further should be 
+straightforward, as it can be done by simply adding a new comma-separated-value (CSV) file 
+containing the desired molecular properties for training. Out of the 320 generated molecule SMILES, 
+6 are invalid molecules, 3 are duplicates, and 5 are within the training set. We have correspondingly 
+generated 306 new unique candidate molecules from this query for computational validation 
+purposes. We further generate 64,000 candidate molecules using the RNN-based ConGen model 
+(1,000 queries for each of the anchor combinations, see Figure 4) although neither EA nor IE ab-initio 
+
+computational validation is done for these additional molecules due to the high computation costs 
+(Query 2). Out of this new query for 64,000 molecules, 1,486 are invalid, 41,117 are duplicates, and 
+356 are within the training set. Correspondingly, Query 2 generates 21,041 new unique candidate 
+LHCE diluent molecules. Future work is needed to reduce the number of large-scale-query duplicates. 
+ 
+Figure 4 | ConGen unconditional and multi-constraint conditional molecular generation property distributions. (a) 
+Unconditional molecule generation showing property distribution without constraints. When multiple co-constraints are 
+utilized for the conditional generation, we have very targeted molecule generation. Structural and electrochemical stability 
+properties validation for Query 1 with 320 molecules is shown in (b), while structural property validation for Query 2 with 
+64k molecules is shown in (c). We can see that the molecules generated with simultaneous multi-property constraints still 
+obey their conditional property anchors quite well (simultaneously, although the hardest property EA distribution is slightly 
+shifted), and that the generated molecules’ property distribution is very different from molecules generated with no property 
+constraint. Conditional generation property anchor inputs are shown as dashed lines. 
+ 
+Task 
+Mol.Wt (Da) 
+nF 
+nO 
+EA (eV) 
+IE (eV) 
+Log.Vis 
+Predictor Regression 
+Test Set MAE 
+1.60 
+0.01 
+0.02 
+0.20 
+0.21 
+0.14 
+Decoder Unconditional 
+Generation 
+302 ± 110 
+1.50 ± 1.12 
+2.30 ± 1.42 
+1.71 ± 0.54 
+6.58 ± 0.75 
+N/A 
+Decoder Conditional 
+Generation (Query 1) 
+275 ± 26 
+5.02 ± 1.08 
+1.50 ± 0.50 
+1.99 ± 0.73 
+7.04 ± 0.61 
+N/A 
+Decoder Conditional 
+Generation (Query 2) 
+274 ± 26 
+5.02 ± 1.05 
+1.49 ± 0.50 
+N/A 
+N/A 
+N/A 
+Table 3 | Molecular property prediction accuracy and the generated molecule’s property distribution statistics for LHCE 
+diluent molecules. From the regression test result, we can see the predictor sub-model is reasonably accurate in predicting 
+molecular property. In addition to that, the discrepancy in distributed molecules’ properties for unconditional vs conditional 
+
+Unconditonal Generation (m = 10)
+4,
+3
+Co:
+3
+3
+5
+3
+6
+Conditional Generation (Query 1, m = 320)
+OXOG
+200
+35
+80
+55
+(600
+125:
+1725
+ron
+20
+40
+75
+55
+751
+50
+:10
+50
+25:
+51
+00 150 00350 300 350400 450
+0i2
+5
+A
+Conditional Generation (Query 2, m = 64,000)
+20000
+AOX0XXO
+A.O0X00
+1500
+35000
+35000
+EL500O
+3000
+3000
+12500
+25000
+25000
+Not validated due to high
+20xxx0
+20000
+5L5000
+L5X0X00
+computational cost
+50X00
+25600
+5000
+T001505002503005504 00450
+3
+8
+4kl.A: (ba
+ngeneration cases show that the conditional generator is generating the right molecules, based on the property label input 
+anchors we have chosen. Regression MAE is calculated using property labels from the database, while generated molecules’ 
+properties are validated using either RDKit library or ab-initio simulation. 
+Table 4 | Candidate Li-ion battery LHCE diluent molecules generated with multi-constraint ConGen model (Query 1). 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, 0.0, 250, 4.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, 0.0, 250, 4.0, 1.0] 
+Cc1ccc(OCC(F)(F)C(F)(F)Cl)cc1 
+CN(C)C(=O)Nc1cc(F)cc(C(F)(F)F)c1 
+Nc1c(F)cc(OC(F)(F)F)cc1CCl 
+CC(C)(C)OC(c1cc(F)cc(F)c1)C(F)F 
+CC(C)C(=O)Nc1ccc(F)c(C(F)(F)F)c1 
+CCOC(=N)c1c(F)cccc1CC(F)(F)F 
+CN(C)C(=O)Nc1c(F)c(F)cc(F)c1CF 
+Nc1cc(C(F)(F)F)ccc1OCCC(F)C 
+OCc1nc(C(F)(F)F)nc2c(F)cccc12 
+Fc1cc(OC(F)(F)F)cc(C2CCNC2)c1 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, 0.0, 250, 4.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, 0.0, 250, 4.0, 2.0] 
+CN(C)C(=O)OC1(C(F)(F)F)CCC(F)C1 
+Oc1cc(OC(F)(F)F)cc(F)c1CCl 
+CCOC(=O)c1cc(C(F)(F)F)nc(F)c1C 
+OC(OCC(F)(F)C(F)F)c1ccsc1 
+CC(=O)NCC(O)c1c(F)c(F)cc(F)c1F 
+COC(=O)CC(CC(F)(F)F)c1ccccc1 
+OCc1c(OC(F)(F)F)ccc(F)c1C1CC1 
+Cc1cc(OCC(F)(F)C(F)(F)CO)ccn1 
+COc1ccc(OCC(F)(F)C(F)F)c(C)c1 
+COC(=O)Cc1c(F)cnc(C(F)F)c1CF 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, 0.0, 250, 6.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, 0.0, 250, 6.0, 1.0] 
+Oc1nc(F)cc(CC(F)(F)C(F)(F)F)n1 
+CC(OC(F)(F)F)c1ccccc1C(F)(F)F 
+FC(C(F)(F)F)C(F)(F)COC1CCCC1 
+Cc1ncc(OC(F)(F)F)nc1C(F)(F)F 
+FC(F)(F)C(F)(F)COc1ccccc1F 
+OC(CCC(F)(F)C(F)(F)C(F)F)C1CC1 
+OC(CCC(F)(C(F)(F)F)C(F)F)C1CC1 
+Fc1ccc(OCC(F)(F)F)cc1C(F)F 
+Cn1nc(C(F)(F)F)c(C(F)(F)F)c1CO 
+NC(c1ccoc1)C(C(F)(F)F)C(F)(F)F 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, 0.0, 250, 6.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, 0.0, 250, 6.0, 2.0] 
+COC(=O)CCCC(F)(F)C(F)(F)C(F)F 
+OC(O)(CCCC(F)(F)F)CC(F)(F)F 
+OC(O)c1cc(C(F)(F)F)c(F)c(F)c1F 
+CC(=O)NCC(O)(C(F)(F)F)C(F)(F)F 
+Oc1cc(C(F)(F)F)cc(C(F)(F)F)c1O 
+CCOc1ccc(C(F)(F)F)c(C(F)(F)F)c1 
+COC(=O)CCC(F)(C(F)(F)F)C(F)(F)F 
+OC(OCC(F)(F)F)c1cccc(F)c1F 
+-- invalid-- 
+Oc1c(OC(F)(F)F)cccc1C(F)(F)F 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, 0.0, 300, 4.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, 0.0, 300, 4.0, 1.0] 
+Cc1noc(-c2ccc(C(F)(F)F)cc2Cl)c1C(F)F 
+Fc1cnc(OC(F)(F)F)c(I)c1 
+Cc1cc(OC(F)(F)F)cc(F)c1I 
+O=C(Nc1ncc(C(F)(F)F)cc1Cl)c1ccccc1 
+COc1cnc(C(F)(F)F)c(F)c1CBr 
+Cn1cc(-c2noc(-c3cc(F)c(F)c(F)c3F)n2)s1 
+Nc1c(F)cc(Oc2ccc(C(F)(F)F)cc2)c(Cl)c1 
+NC(=O)c1c(F)cccc1Nc1cc(C(F)(F)F)ccn1 
+COc1cnc(-c2ccc(C(F)(F)F)c(F)c2)c(Cl)c1 
+OC(Cc1ccc(C(F)(F)F)c(F)c1)c1cccs1 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, 0.0, 300, 4.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, 0.0, 300, 4.0, 2.0] 
+OC(Cc1cc(F)c(Br)cc1F)C(F)(F)O 
+NC(=O)COc1ccccc1-c1c(F)c(F)cc(F)c1F 
+COC(=O)CCc1ccc(Cl)cc1C(F)(F)C(F)F 
+OC(O)(c1cc(F)c(F)c(F)c1)c1ccc(F)cc1Cl 
+CCOC(=O)Nc1c(C(F)(F)F)cc(F)nc1CCl 
+NCc1cnc(OC(F)(F)F)nc1Oc1c(F)cccc1 
+N[C@@H](Cc1cc(F)c(F)c(F)c1F)c1ccc(O)cc1O 
+COc1ccc(CNc2cc(F)c(F)c(F)c2F)cc1O 
+CCC(=O)NCC(=O)Nc1cc(C(F)(F)F)cc(F)c1C 
+FC(F)(F)Oc1cccc(Oc2cc(F)cc(Cl)c2)c1 
+ 
+ 
+
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, 0.0, 300, 6.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, 0.0, 300, 6.0, 1.0] 
+COC(c1cc(C(F)(F)F)nc(C(F)(F)F)c1)C1CC1 
+COc1c(C(F)(F)F)ncc(C(F)(F)F)c1CCl 
+Nc1ccc(C(=O)NCC(F)(F)C(F)(F)C(F)F)cc1 
+OC(c1ccc(F)cc1)c1c(F)c(F)c(F)c(F)c1F 
+NCc1cc(OC(F)(F)F)c(Cl)cc1C(F)(F)F 
+Nc1cc(C(F)(F)F)cc(OC(F)(F)F)c1CCl 
+NC(=O)c1cc(C(F)(F)F)cc(C(F)(F)F)c1CCl 
+FC(F)(F)c1cccc(-c2ccc(OC(F)(F)F)cc2)c1 
+CC(C)C(=O)Nc1cc(C(F)(F)F)cc(C(F)(F)F)c1 
+Nc1c(F)cccc1Oc1cc(F)c(F)c(C(F)(F)F)c1 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, 0.0, 300, 6.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, 0.0, 300, 6.0, 2.0] 
+OCc1ccc(C(F)(F)F)cc1OCCC(F)(F)CF 
+COc1cc(C(F)(F)F)c(C(F)(F)F)c(CC(N)=O)c1 
+OB(O)c1c(C(F)(F)F)ccc(Cl)c1C(F)(F)F 
+Cc1cc(OC(F)(F)F)nc(OC(F)(F)F)c1CC#N 
+COc1ccc(OC(C(F)(F)F)C(F)(F)C(F)F)nc1 
+Cc1ccc(COCC(F)(F)C(F)(F)C(F)F)cc1O 
+OCc1c(OC(F)(F)F)ncc(C(F)(F)F)c1C1CC1 
+O=C(O)Cc1cc(C(F)(F)F)nc(C(F)(F)F)c1CN 
+CS(=O)(=O)Nc1cc(C(F)(F)F)cc(C(F)(F)F)c1 
+OC(c1cccc(OC(F)(F)F)c1)c1ccc(F)cc1F 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, -0.1, 250, 4.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, -0.1, 250, 4.0, 1.0] 
+Oc1ccc(-c2ccc(F)c(F)c2)c(F)c1F 
+Cc1nc(-c2cccc(C(F)(F)F)c2F)c(C)o1 
+COC(c1c(F)c(F)nc(F)c1F)C1CCC1 
+CC(NC(=O)C(F)(F)C(F)F)c1ccccc1 
+NCc1cn(CC(F)(F)F)nc1CC(=O)F 
+CC(CO)Nc1ccccc1C(F)(F)C(F)F 
+NCc1cc(OC(F)(F)F)cc(Cl)c1F 
+CC(C)Oc1nc(C(F)(F)F)c(F)cc1CN 
+Cn1cnc(OC(F)(F)F)c1-c1ccc(F)cc1 
+OCC1Cc2cc(C(F)(F)F)cc(F)c2S1 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, -0.1, 250, 4.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, -0.1, 250, 4.0, 2.0] 
+COc1cc(C(F)(F)F)nc(OC)c1CCF 
+OCC(O)Cc1ncc(C(F)(F)F)cc1CF 
+CC(O)c1c(OC(F)(F)F)cc(F)cc1CN 
+O=C(O)CC(CC(F)(F)C(F)F)c1ccc[nH]1 
+OCCC(=O)Nc1ccc(F)c(C(F)(F)F)c1 
+CCC(NCC(F)(F)C(F)F)C(=O)OCC 
+CC(N)(C(=O)O)c1nc(C(F)(F)F)ccc1F 
+COc1ccc2c(F)c(F)c(F)c(F)c2c1O 
+O=C(O)c1ccn(CCC(F)(F)C(F)F)c1F 
+NCc1cc(OC(F)(F)F)c(O)c(CF)c1C 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, -0.1, 250, 6.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, -0.1, 250, 6.0, 1.0] 
+OCc1nc(C(F)(F)F)c(C(F)(F)F)s1 
+N[C@@H](CO)c1c(F)c(F)c(F)c(F)c1CF 
+OCCc1c(F)c(F)c(C(F)(F)F)c(F)c1 
+CCc1ccc(OC(F)(F)F)c(C(F)(F)F)c1 
+C[C@@H](O)c1c(F)c(F)c(C(F)(F)F)c(F)c1 
+Nc1cnc(OC(F)(F)F)c(C(F)(F)F)c1 
+OC(c1cc(F)cc(F)c1)C(F)(F)C(F)F 
+OC[C@@H](c1cc(F)c(F)c(F)c1)C(F)(F)F 
+CCc1c(OC(F)(F)F)n[nH]c1C(F)(F)F 
+COc1ncc(C(F)(F)F)c(C(F)(F)F)n1 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, -0.1, 250, 6.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, -0.1, 250, 6.0, 2.0] 
+C=C(O)CC(=O)C(C(F)(F)F)C(F)(F)CF 
+C[Si](C)(O)OC(F)(F)C(F)(F)C(F)(F)F 
+OC(F)(F)C(F)(F)Oc1ccc(F)c(F)c1 
+COCC(O)CN(C(F)(F)F)C(F)(F)F 
+OC[C@@H](O)CCC(F)(F)C(F)(F)C(F)(F)F 
+CCOC(C)C(O)(C(F)(F)F)C(F)(F)CF 
+OCCOCCC(F)(F)C(F)(F)C(F)(F)F 
+O=C(O)CCCC(F)(F)C(F)CC(F)(F)F 
+OCc1c(O)c(F)c(F)c(F)c1C(F)(F)F 
+--invalid-- 
+ 
+ 
+
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, -0.1, 300, 4.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, -0.1, 300, 4.0, 1.0] 
+O=C(Cn1nc(C(F)(F)F)cc1Cl)c1ccccc1F 
+Cc1ccc(CC(=O)Nc2cc(F)cc(F)c2)c(F)c1F 
+CC1CCN(C(=O)Nc2cc(F)cc(C(F)(F)F)c2)CC1 
+Cc1cc(C(F)(F)F)nc(Oc2cc(F)cc(Cl)c2)n1 
+OC(c1cc(F)cc(F)c1)c1ccc(C(F)(F)Cl)cc1 
+CCCc1ncc(C(F)(F)F)c(Oc2ccc(F)cc2)n1 
+OC(c1cc(F)cc(F)c1)c1cnc(C(F)(F)Cl)cc1 
+CC(OCC(F)(F)C(F)F)c1ccc(Cl)cc1Cl 
+CCc1nc(-c2ccc(OC(F)(F)F)cc2)nc(C)c1F 
+N#Cc1ccc(OCC(F)(F)C(F)F)cc1Br 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, -0.1, 300, 4.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, -0.1, 300, 4.0, 2.0] 
+Cc1cc(OC(F)(F)C(F)(F)C(=O)NC2CC2)cs1 
+NC(=O)COc1ccc(C(F)(F)F)c(F)c1Br 
+COC(=O)c1ncc(C(F)(F)F)c(F)c1Br 
+COC(=O)c1ccc(C(F)(F)F)c(-c2ccc(F)cc2)c1 
+COC(=O)Cc1nc(C(F)(F)F)c(F)cc1CCl 
+FC(F)(F)Oc1ccc(OCc2ccncc2)c(F)c1C 
+CCOC(=O)Cc1cc(C(F)(F)F)cc(F)c1CCl 
+CCOc1cc(OC(F)(F)F)c(F)cc1Br 
+FC(F)(F)Oc1cc(OC(F)F)cc(Br)n1 
+N[C@@H](CC(=O)O)c1c(C(F)(F)F)cc(F)cc1CCl 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, -0.1, 300, 6.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, -0.1, 300, 6.0, 1.0] 
+FC(F)C(F)(F)Oc1cc(C(F)(F)F)cnc1CCl 
+Nc1ccc(OCC(F)(F)C(F)(F)C(F)F)cc1C#N 
+OCc1c(C(F)(F)F)ccc(C(F)(F)F)c1CCl 
+Oc1cc(F)c(-c2ccc(C(F)(F)F)cc2)c(F)c1F 
+CCc1nc(OC(F)(F)F)c(C(F)(F)F)cc1CC#N 
+CCN(CC(F)(F)C(F)(F)C(F)(F)F)C(=O)NC1CC1 
+OC(c1nc2ccccc2s1)C(F)(F)C(F)(F)CF 
+Fc1ccc(C(F)(F)F)c(Oc2cccc(F)c2)c1F 
+Fc1ccc(-c2ccc(OC(F)(F)F)cc2)c(F)c1F 
+Fc1cc(OC(F)(F)F)ccc1-c1ccc(F)c(F)c1 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.0, -0.1, 300, 6.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.0, -0.1, 300, 6.0, 2.0] 
+Cc1c(OC(F)(F)F)cnc(C(F)(F)F)c1CC(N)=O 
+Oc1ccc(COCC(F)(F)C(F)(F)C(F)F)cc1F 
+O=C(O)C(CC(F)(F)C(F)(F)C(F)F)c1ccccc1 
+OC(O)(Cc1ccc(C(F)(F)F)cc1)CC(F)(F)CF 
+OCc1cc(OC(F)(F)F)c(Cl)cc1C(F)(F)F 
+OC(O)(c1cc(C(F)(F)F)cc(C(F)(F)F)c1)C1CC1 
+C[C@@](N)(C(=O)O)c1nc(C(F)(F)F)c(C(F)(F)F)n1C O=C(NCC(F)(F)C(F)(F)C(F)F)c1ccc(O)cc1 
+CCOC(=O)c1cc(C(F)(F)F)ccc1C(F)(F)CF 
+FC(F)(F)COCCOc1c(F)cc(C(F)F)cc1N 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, 0.0, 250, 4.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, 0.0, 250, 4.0, 1.0] 
+Cc1ccc(CNC(=O)C(F)(F)C(F)F)cc1 
+Cc1c(OC(F)(F)F)cc(F)cc1CCl 
+Cc1cc(CC(=O)NCC(F)(F)F)ccc1F 
+OC(CC(F)(F)F)c1ccc(F)c(Cl)c1 
+O=C(c1cccnc1)c1cc(F)c(F)c(F)c1F 
+COc1cc(C(F)(F)F)c(F)cc1CCl 
+FC(F)(F)c1cccc(Oc2ccccc2)c1F 
+OCc1cnc(C(F)F)c(Cl)c1C(F)(F)F 
+CCNC(=O)Nc1ccc(F)c(C(F)(F)F)c1 
+Nc1cc(OCC(F)(F)C(F)F)ccc1C#N 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, 0.0, 250, 4.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, 0.0, 250, 4.0, 2.0] 
+OCCC(=O)Nc1c(F)cccc1C(F)(F)F 
+OCc1cc(OCCC(F)(F)F)cc(F)c1C 
+O=C(Cc1ccc(OC(F)(F)F)cc1)C1CC1 
+OCc1c(C(F)F)ncc(OC(F)F)c1CC 
+CCOc1c(OC(F)(F)F)cc(F)cc1C#N 
+COc1nc(OC(F)(F)F)c(F)cc1CC#N 
+CCOC1(C(F)(F)F)Oc2ccc(F)cc2C1 
+Cc1ccc(C(F)(F)C(F)(F)C(=O)O)cc1C 
+CC(C)CC(=O)NCC(O)CC(F)(F)C(F)F 
+Cc1nc(C(F)(F)F)c(CC(=O)O)cc1CF 
+ 
+ 
+
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, 0.0, 250, 6.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, 0.0, 250, 6.0, 1.0] 
+O=C(NCC(F)(F)C(F)CF)CC(F)(F)F 
+OC(c1cc(F)c(F)c(F)c1)CC(F)(F)F 
+Cc1cnc(OC(F)(F)F)c(C(F)(F)F)c1 
+FCOc1cc(C(F)(F)F)ccc1C(F)(F)F 
+O=C(Nc1cc(F)cc(F)c1F)C(F)(F)F 
+Cc1ncc(C(F)(F)F)c(OC(F)(F)F)n1 
+NCC(O)CCC(C(F)(F)F)C(F)(F)F 
+OC(c1c(F)c(F)c(F)c(F)c1F)C(F)F 
+Fc1cc(OCC(F)(F)F)ccc1C(F)F 
+OCCc1c(F)c(F)c(C(F)(F)F)c(F)c1 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, 0.0, 250, 6.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, 0.0, 250, 6.0, 2.0] 
+O=C(O)CCCCC(F)(F)C(F)(F)C(F)F 
+FC(F)(F)C1(C(F)(F)F)OCCCCOC1 
+CCOC(=O)CC(C(F)(F)F)C(F)(F)CF 
+COC(=O)CCC(C(F)(F)F)C(F)(F)CF 
+Fc1cccc(OC(F)(F)OC(F)(F)F)c1 
+Cc1c(O)cc(C(F)(F)F)cc1OC(F)(F)F 
+Oc1cc(OC(F)(F)F)cc(C(F)(F)F)c1 
+O=C(OCCCCC(F)(F)F)CC(F)(F)F 
+CCC(=O)OCC(C(F)(F)F)C(F)(F)CF 
+CC(O)CCC(O)(C(F)(F)F)C(F)(F)F 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, 0.0, 300, 4.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, 0.0, 300, 4.0, 1.0] 
+O=C(NCC(F)(F)C(F)F)c1ccc(Cl)cc1Cl 
+CN(C)c1cc(C(F)(F)F)nc(Oc2ccc(F)cc2)n1 
+CCc1ncc(OC(F)(F)F)c(F)c1CBr 
+OC(c1cccc(C(F)(F)F)c1)c1c(F)cccc1Cl 
+FC(F)(F)c1ccc(Oc2ncccc2Cl)c(F)c1 
+Cc1cnc(C(F)(F)F)c(Oc2ccc(F)c(Cl)c2)n1 
+Nc1ncc(F)cc1C(=O)Nc1ccc(C(F)(F)F)cc1 
+N#Cc1ccc(COc2ccccc2C(F)(F)F)c(F)c1 
+CCCc1nc(OC(F)(F)F)nc(F)c1Br 
+CNc1ccc(Oc2ccc(C(F)(F)F)nc2)c(F)c1C 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, 0.0, 300, 4.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, 0.0, 300, 4.0, 2.0] 
+CC(Oc1cccc(C(F)(F)F)c1)C(=O)c1ccccc1 
+CS(=O)(=O)N1CCN(c2c(F)c(F)cc(F)c2F)C1 
+COCc1nc(OC(F)(F)F)c(F)cc1Br 
+Oc1cc(OC(F)(F)F)ccc1CBr 
+O=C(NCC(F)(F)CO)c1c(F)cc(F)cc1CCl 
+CS(=O)(=O)Nc1ccc(SC(F)(F)C(F)F)cc1 
+FC(F)(F)Oc1cc(F)c(OCc2cccnc2)c(C)c1 
+O=S(=O)(c1cccc(C(F)(F)F)c1)c1ccc(F)cc1 
+CS(=O)(=O)Nc1ccc(C(F)(F)C(F)F)c(Cl)c1 
+CC(Nc1cc(C(F)(F)F)cc(F)c1)C(=O)OC(C)(C)C 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, 0.0, 300, 6.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, 0.0, 300, 6.0, 1.0] 
+Cc1c(C(F)(F)F)cc(OC(F)(F)F)nc1CCl 
+Oc1c(F)cccc1-c1cc(C(F)(F)F)cc(F)c1F 
+Nc1cc(OC(F)(F)F)cc(C(F)(F)F)c1CCl 
+OC(c1cccc(C(F)(F)F)c1)c1cccc(F)c1F 
+FC(F)(F)Oc1ccc(-c2ccc(C(F)(F)F)cc2)cc1 
+CC(=O)Nc1c(C(F)(F)F)cnc(C(F)(F)F)c1CN 
+O=Cc1ccc(C(F)(F)F)c(C(F)(F)F)c1CCl 
+OCc1cc(C(F)(F)F)cc(C(F)(F)F)c1CCl 
+--invalid-- 
+OC(c1ccc(C(F)(F)F)nc1)c1c(F)cc(F)cc1F 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, 0.0, 300, 6.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, 0.0, 300, 6.0, 2.0] 
+OCC(Oc1cccc(C(F)(F)F)c1)CC(F)(F)CF 
+C[C@@H](NC(=O)O)c1cc(C(F)(F)F)cc(C(F)(F)F)c1 
+O=Cc1cc(OCC(F)(F)C(F)(F)C(F)F)ccc1N 
+CCOC(=O)Cc1c(F)cc(C(F)(F)F)cc1C(F)F 
+OCc1c(OC(F)(F)F)ncc(C(F)(F)F)c1Cl 
+NC(=O)c1c(OC(F)(F)F)cnc(C(F)(F)F)c1CN 
+NC(COCC(F)(F)F)c1cccc(OC(F)(F)F)c1 
+O=C(NCC(F)(F)F)N1CCC(O)(C(F)(F)F)CC1 
+OCc1ccccc1OCCC(F)(F)C(F)(F)C(F)F 
+FC(F)(F)Oc1ccc(OC(F)(F)C(F)Cl)cc1 
+ 
+ 
+
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, -0.1, 250, 4.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, -0.1, 250, 4.0, 1.0] 
+CNCC(=O)Nc1cc(F)c(C(F)(F)F)cc1 
+OC(c1cc(F)cc(C(F)(F)F)c1)C1CCC1 
+OC(CC(F)(F)F)c1ccc(F)c(Cl)c1 
+OCCc1cc(C(F)(F)F)c(Cl)cc1F 
+Fc1ccc(COc2ccccc2F)c(F)c1F 
+OCCc1nc(C(F)(F)F)c(F)cc1Cl 
+OCc1cc(C(F)(F)F)c(F)cc1CCl 
+Nc1cnc(OCCCC(F)(F)F)c(F)c1F 
+COc1c(C(F)(F)F)ccc(F)c1CCl 
+Nc1ccc(OCCC(F)(F)C(F)F)c(C)c1 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, -0.1, 250, 4.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, -0.1, 250, 4.0, 2.0] 
+CN(C(=O)O)c1cc(C(F)(F)F)cc(F)c1C 
+CCCC(=O)OCCCCC(F)(F)C(F)(F)F 
+CS(=O)(=O)CCSCC(F)(F)C(F)F 
+O=Cc1cc(OCC(F)(F)C(F)F)cs1 
+CCC(=O)NCC(=O)NCC(F)(F)C(F)F 
+OC(COCC(F)(F)F)c1ccc(F)c(C)c1 
+CNC1CC(C(F)(F)C(F)(F)C(=O)O)CC1 
+CCCOC(=O)Nc1c(F)c(F)cc(F)c1F 
+COC(=O)Nc1cccc(C(F)(F)C(F)F)c1 
+CCOC(=O)Nc1nc(C(F)(F)F)ccc1F 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, -0.1, 250, 6.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, -0.1, 250, 6.0, 1.0] 
+C[C@H](O)c1cc(C(F)(F)F)cc(C(F)(F)F)c1 
+Cc1c(OC(F)(F)F)cccc1C(F)(F)F 
+OCC(F)(F)C(F)(F)c1cc(F)cc(F)c1 
+Nc1ncc(F)c(OC(F)(F)F)c1C(F)F 
+C[C@H](N)CC(=O)NC(C(F)(F)F)C(F)(F)F 
+CNCC(=O)NCC(F)(F)C(F)(F)C(F)F 
+Cc1cc(OC(F)(F)F)nc(C(F)(F)F)c1 
+Fc1cc(F)c(OCCC(F)(F)F)c(F)c1 
+--invalid--  
+FC(F)(F)CCOc1cc(F)c(F)c(F)c1 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, -0.1, 250, 6.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, -0.1, 250, 6.0, 2.0] 
+OCc1c(F)c(F)c(OC(F)(F)F)c(F)c1 
+COC(=O)CCC(C(F)(F)F)C(F)(F)CF 
+C=CCOC(=O)CC(F)(F)C(F)(F)C(F)F 
+CC(CC(F)(F)C(F)(F)C(F)F)CC(=O)O 
+OCc1cc(C(F)(F)F)cc(C(F)(F)F)c1O 
+CC(C)(CC(F)(F)C(F)(F)C(F)F)C(=O)O 
+Cc1c(OC(F)(F)F)[nH]c(C(F)(F)F)c1O 
+Cc1ccc(OC(F)(F)F)c(OC(F)(F)F)c1 
+C=CCOC(=O)C(C(F)(F)F)C(F)(F)CF 
+FCOc1c(C(F)(F)F)[nH]c(C(F)F)c1O 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, -0.1, 300, 4.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, -0.1, 300, 4.0, 1.0] 
+OC(c1c(F)c(F)c(F)c(F)c1Br)C1CC1 
+OC(c1cccc(C(F)(F)F)c1)c1ccc(F)cc1Cl 
+Oc1nc(F)c(C(F)(F)F)cc1I 
+CC1CC(c2ccc(C(F)(F)F)cc2)NC(=O)NC1F 
+OC(Cc1ccc(F)c(Br)c1)CC(F)(F)F 
+CC(NC(=O)CC(F)(F)C(F)F)c1ccc(Cl)cc1 
+COc1nc(C(F)(F)F)ccc1CBr 
+COc1cc(Br)cc(CC(F)(F)C(F)F)c1 
+O=C(Cc1nc(C(F)(F)F)ns1)c1ccc(F)cc1C 
+Cn1nc(C(F)(F)F)cc1C(=O)Nc1ccc(F)cc1C 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, -0.1, 300, 4.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, -0.1, 300, 4.0, 2.0] 
+CC(=O)Nc1nc(-c2ccc(C(F)(F)F)c(F)c2)c(C)o1 
+CC(Oc1cccc(C(F)(F)F)c1)c1cccc(F)c1O 
+Oc1cccc(Oc2c(F)c(F)c(F)c(F)c2Cl)c1C 
+COc1nc(C(F)(F)F)ccc1OCc1ccc(F)cc1 
+O=S(=O)(Cc1ccc(F)cc1)c1c(F)cc(F)cc1F 
+OC(COCC(F)(F)C(F)F)Cc1ncccc1Cl 
+OC(O)(c1c(F)cccc1F)c1cc(F)c(Cl)cc1F 
+FC(F)C(F)(F)Oc1ccccc1COc1ccccc1 
+--invalid--  
+COC(=O)c1ncc(C(F)(F)F)cc1-c1ccc(F)cc1 
+ 
+ 
+
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, -0.1, 300, 6.0, 1.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, -0.1, 300, 6.0, 1.0] 
+OC(C(F)(F)C(F)(F)C(F)(F)F)C(Cl)(Cl)Cl 
+OCC(c1ccc(C(F)(F)F)c(C(F)(F)F)c1)C1CC1 
+OCC(c1c(F)cc(F)cc1Cl)C(F)(F)C(F)(F)F 
+FC(F)(F)Oc1cc(C(F)(F)F)c(Cl)cc1Cl 
+FC(F)(F)Oc1ccnc(-c2ccc(C(F)(F)F)cc2)c1 
+Cc1ccc(OCC(F)(F)C(F)(F)C(F)(F)Cl)cc1 
+CS(=O)c1cc(C(F)(F)F)cc(C(F)(F)F)c1C#N 
+Fc1cc(OC(F)(F)F)ccc1-c1cc(F)cc(F)c1 
+OC(F)(C(F)(F)F)C(F)(F)I 
+--invalid--  
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.5, 7.5, -0.1, 300, 6.0, 2.0] 
+['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  
+[0.0, 7.5, -0.1, 300, 6.0, 2.0] 
+FC(F)(F)c1cc2c(cc1C(F)(F)F)OCCCCO2 
+OC(Cc1ccc(OC(F)(F)F)cc1)CC(F)(F)CF 
+CCCC(=O)OCCCCC(F)(F)C(F)(F)C(F)(F)F 
+OCc1ccc(COCC(F)(F)C(F)(F)C(F)F)cc1 
+COC(=O)Cc1cc(C(F)(F)F)cc(C(F)(F)F)c1C 
+Oc1cc(OC(F)(F)F)ccc1SCC(F)(F)F 
+O=C(Cc1cc(C(F)(F)F)cc(C(F)(F)F)c1)C(N)=O 
+NC(=O)Cc1cc(C(F)(F)F)nc(OC(F)(F)F)c1C 
+CCc1cc(C(F)(F)F)cc(C(F)(F)F)c1CC(=O)O 
+OC(c1c(F)c(F)c(F)c(F)c1F)c1ccc(F)cc1O 
+ 
+ 
+ 
+ 
+ 
+ 
+
+Conclusion 
+In summary, we demonstrate a novel conditional molecule generation algorithm ConGen, 
+which is based on semi-supervised variational auto-encoder (SSVAE) technology. However, unlike the 
+SSVAE model, the ConGen model is explicitly designed such that it can work with dirty training data 
+with incomplete labels. This is important because in practice, the molecules we can find from publicly 
+available databases or characterized by in-house simulations and experiments will have incomplete 
+sets of properties available, due to various factors (intellectual property, commercial secret, etc) as 
+well as experimental or computational cost considerations. A user of the baseline SSVAE model will 
+need to remove molecules with incomplete labels or assign dummy labels on the molecules at the 
+cost of lower model accuracy. On the other hand, the ConGen model can easily mix dirty training 
+datasets from multiple sources. ConGen is also designed with flexibility for substituting its sub-models 
+with other types of models, enabling the user to include pre-trained models which can be helpful, 
+especially in cases where there is limited training data availability. Finally, we demonstrate the 
+practical use of our model for generating the virtual screening chemical space for Li-ion battery LHCE 
+diluent candidates with multiple co-constraint requirements. 
+ 
+ 
+
+Experimental methods 
+Ab-initio EA and IA validation 
+These molecule EA and IE calculations are conducted with PySCF’s implementation23,24 of the 
+DFT Kohn-Sham method at the PBE6-31+G* level25 with Grimme’s dispersion correction26 for 
+geometry optimizations on the gas-phase and B3LYP/6-31+G* level of theory with the solvation 
+energy corrections of tetrahydrofuran (THF) using the integral equation formalism polarizable 
+continuum model (IEF-PCM)27 implicit solvation model for single point energies. The vibrational 
+frequencies were computed at the same level of theory at 298.15K as for the geometry optimizations 
+to confirm whether each optimized stationary point is an energy minimum. Here, we optimize the 
+geometry at different charge states (cation, anion, neutral) to calculate the adiabatic IE/EA. 
+Data availability 
+All the training data sources, as well as all the structural and computational validation of the 
+unconditionally and conditionally generated molecules are available in the ESI.  
+Author contributions 
+J.P.M. conceptualized this project, developed the ConGen model, and performed and analysed 
+the model training and molecule generation experiments. S.Z. supervised the project. X.L. performed 
+ab-initio computational validation for the generated molecules. J.Q. supported model training 
+optimization efforts. The manuscript was drafted by J.P.M., and reviewed by all the authors. 
+Conflicts of interest 
+There are no conflicts to declare. 
+Acknowledgements 
+The computation efforts in this work were performed in Tencent Cloud platform. 
+ 
+ 
+
+References 
+ 
+1. 
+Skinnider, M. A. et al. A deep generative model enables automated structure elucidation of 
+novel psychoactive substances. Nat. Mach. Intell. 3, 973–984 (2021). 
+2. 
+Li, Y., Pei, J. & Lai, L. Structure-based de novo drug design using 3D deep generative models. 
+Chem. Sci. 12, 13664–13675 (2021). 
+3. 
+Peng, H., Liu, Z., Yan, X., Ren, J. & Xu, J. A de novo substructure generation algorithm for 
+identifying the privileged chemical fragments of liver X receptorβ agonists. Sci. Rep. 7, 11121 
+(2017). 
+4. 
+Prykhodko, O. et al. A de novo molecular generation method using latent vector based 
+generative adversarial network. J. Cheminform. 11, 74 (2019). 
+5. 
+Walters, W. P. & Barzilay, R. Applications of deep learning in molecule generation and 
+molecular property prediction. Acc. Chem. Res. 54, 263–270 (2021). 
+6. 
+Gebauer, N. W. A., Gastegger, M., Hessmann, S. S. P., Müller, K. R. & Schütt, K. T. Inverse 
+design of 3d molecular structures with conditional generative neural networks. Nat. 
+Commun. 13, 973 (2022). 
+7. 
+Tan, Y., Dai, L., Zheng, S., Chen, H. & Yang, Y. DRlinker: Deep reinforcement learning for 
+optimization in fragment linking design. J. Chem. Inf. Model. (2022) 
+doi:10.1021/acs.jcim.2c00982. 
+8. 
+Kang, S. & Cho, K. Conditional molecular design with deep generative models. J. Chem. Inf. 
+Model. 59, 43–52 (2018). 
+9. 
+Elton, D. C., Boukouvalas, Z., Fuge, M. D. & Chung, P. W. Deep learning for molecular design - 
+A review of the state of the art. Mol. Syst. Des. Eng. 4, 828–849 (2019). 
+10. 
+Kim, S. et al. PubChem in 2021: New data content and improved web interfaces. Nucleic Acids 
+Res. 49, D1388–D1395 (2021). 
+11. 
+Irwin, J. J. & Shoichet, B. K. ZINC - A free database of commercially available compounds for 
+virtual screening. J. Chem. Inf. Model. 45, 177–182 (2005). 
+12. 
+Qu, X. et al. The Electrolyte Genome project: A big data approach in battery materials 
+discovery. Comput. Mater. Sci. 103, 56–67 (2015). 
+13. 
+Lorenzo-Seva, U. & Ferrando, P. J. Not positive definite correlation matrices in exploratory 
+item factor analysis: Causes, consequences and a proposed solution. Struct. Equ. Model. 28, 
+138–147 (2021). 
+14. 
+Chithrananda, S., Grand, G. & Ramsundar, B. ChemBERTa: Large-scale self-supervised 
+pretraining for molecular property prediction. Proc. 34th Neural Inf. Process. Syst. (2020). 
+15. 
+RDKit: Open-Source cheminformatics. http://www.rdkit.org/ (2020). 
+16. 
+Cao, X., Jia, H., Xu, W. & Zhang, J.-G. Review—Localized high-concentration electrolytes for 
+lithium batteries. J. Electrochem. Soc. 168, 010522 (2021). 
+17. 
+Ren, X. et al. Enabling high-voltage Lithium-metal batteries under practical conditions. Joule 
+3, 1662–1676 (2019). 
+
+18. 
+Chen, S. et al. High-efficiency Lithium metal batteries with fire-retardant electrolytes. Joule 2, 
+1548–1558 (2018). 
+19. 
+Yamada, Y. & Yamada, A. Review—Superconcentrated electrolytes for Lithium batteries. J. 
+Electrochem. Soc. 162, A2406–A2423 (2015). 
+20. 
+Giffin, G. A. The role of concentration in electrolyte solutions for non-aqueous lithium-based 
+batteries. Nat. Commun. 13, 5250 (2022). 
+21. 
+Austin Apple Github. https://github.com/AustinApple/SSVAE-for-electrolyte-molecule-design 
+(2020). 
+22. 
+Goussard, V. et al. A new machine-learning tool for fast estimation of liquid viscosity. 
+Application to cosmetic oils. J. Chem. Inf. Model. 60, 2012–2023 (2020). 
+23. 
+Sun, Q. et al. Recent developments in the PySCF program package. J. Chem. Phys. 153, 
+024109 (2020). 
+24. 
+Sun, Q. Libcint: An efficient general integral library for Gaussian basis functions. J. Comput. 
+Chem. 36, 1664–1671 (2015). 
+25. 
+Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. 
+Phys. Rev. Lett. 77, 3865–3868 (1996). 
+26. 
+Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio 
+parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. 
+J. Chem. Phys. 132, 154104 (2010). 
+27. 
+Tomasi, J., Mennucci, B. & Cancès, E. The IEF version of the PCM solvation method: An 
+overview of a new method addressed to study molecular solutes at the QM ab initio level. J. 
+Mol. Struct. THEOCHEM 464, 211–226 (1999). 
+ 
+
diff --git a/sdE3T4oBgHgl3EQf9Qs1/content/tmp_files/load_file.txt b/sdE3T4oBgHgl3EQf9Qs1/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7466aebfc30039845b8bf782b0b8e50a830ce940
--- /dev/null
+++ b/sdE3T4oBgHgl3EQf9Qs1/content/tmp_files/load_file.txt
@@ -0,0 +1,1095 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf,len=1094
+page_content='Multi-Constraint Molecular Generation using Sparsely  Labelled Training Data for Localized High-Concentration  Electrolyte Diluent Screening  Jonathan P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Mailoa,1* Xin Li,1 Jiezhong Qiu,1 and Shengyu Zhang2*  1) Tencent Quantum Laboratory, Tencent, Shenzhen, Guangdong, China  2) Tencent Quantum Laboratory, Tencent, Hong Kong SAR, China  corresponding author: jpmailoa@alum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='mit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='edu, shengyzhang@tencent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='com  Multi-Constraint Molecular Generation using Sparsely  Labelled Training Data for Localized High-Concentration  Electrolyte Diluent Screening  Abstract  Recently, machine learning methods have been used to propose molecules with desired  properties, which is especially useful for exploring large chemical spaces efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' However, these  methods rely on fully labelled training data, and are not practical in situations where molecules with  multiple property constraints are required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' There is often insufficient training data for all those  properties from publicly available databases, especially when ab-initio simulation or experimental  property data is also desired for training the conditional molecular generative model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' In this work, we  show how to modify a semi-supervised variational auto-encoder (SSVAE) model which only works with  fully labelled and fully unlabelled molecular property training data into the ConGen model, which also  works on training data that have sparsely populated labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We evaluate ConGen’s performance in  generating molecules with multiple constraints when trained on a dataset combined from multiple  publicly available molecule property databases, and demonstrate an example application of building  the virtual chemical space for potential Lithium-ion battery localized high-concentration electrolyte  (LHCE) diluents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Introduction  Conditional molecular generation capability is a topic of strong interest for the purpose of  chemical space exploration in the material virtual screening effort.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Efforts in the field of conditional  molecular generative model either takes no conditional constraint on the generation approach1–5 or  fail to introduce a cost function based on the generated molecules’ property accuracy, making the  models’ generated molecular properties vary over a large range far from the desired property range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='6  This difficulty arises because in a model, molecular properties are typically the output of some  regression model using the molecular structure as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This makes it more challenging to use  molecular properties as the input to conditionally constrain the chemical space of the generated  molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Recent work based on reinforcement learning has enabled a conditional molecule  generator which generates good molecular candidates after thousands of training iterations, assuming  that a molecule property evaluator (cheminformatics library or computational material simulation  tool) can continuously be utilized on the generated molecules during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='7 In this work,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' we are  interested in a specific practical task more commonly encountered in the virtual screening of chemical  space relevant to industry: given a limited and often incomplete set of molecular property training  labels from multiple sources,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' develop a generative model to generate a molecular chemical space  which satisfies multiple property constraints so that it can be used as the high-quality input for a virtual  screening pipeline in a low-cost and relatively accurate manner,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' without requiring additional  simulations or experiments to further refine the generative model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Recent work such as the semi-supervised variational auto encoder (SSVAE) model developed by  Kang, et al8,9 solves a part of this problem by employing a dual-track architecture where the molecular  property ������������ is simultaneously the output from a molecule regression predictor sub-model and the  input to a molecule generation decoder sub-model, in addition to also being the input for a separate  molecule encoder sub-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Because ������������ is an output of the predictor sub-model, it can still be used  to construct a useful cost function for the entire model even though it is also being used as the input  to control the decoder’s generated molecule structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The resulting combined model has a relatively  good control over the generated molecules’ property, making it attractive for efficiently generating  conditionally constrained molecular chemical space of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' In addition to that, the SSVAE model  is capable of utilizing both fully labelled molecules and fully unlabelled molecules during the training  process, making it somewhat attractive for practical usage as there are many cases where we have no  access to the molecule properties due to a lack of simulation or experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Nevertheless, the  model is still impractical because in practice there are a lot of molecules where the data is only partially  labelled and the SSVAE model is not equipped to handle such cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A practical example of this  problem is a situation in battery electrolyte molecule screening where ‘easy’ molecular properties  such as molecular weight (Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt) and the number of fluorine atoms (nF) are easily obtainable from  cheminformatics libraries, while simulation data such as ionization energy (IE) and experimental data  such as the viscosity (Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis, or the logarithm of viscosity) are not widely available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' If we are  interested in generating a chemical space satisfying a number of of these constraints, many of the  molecules found in publicly available databases cannot be used as the fully labelled training data for  the SSVAE model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Removing the labels completely and turning them into fully unlabelled SSVAE  training data is detrimental as we then lose significant valuable label information from our training  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  In this work, we show how to enable a generative model which fully utilizes molecules with  incomplete labels as the training data for a generative model without having to request additional  training data label during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This model improvement is enabled by modifying the SSVAE model  to stop differentiating between fully labelled or unlabelled molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The model now relies on a  molecular property mask instead, which tells the model which property can be used for training from  a given molecule and which cannot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We name this modified SSVAE approach as the ConGen model,  and the major modifications needed to enable these practical capabilities will be outlined in the next  section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' When the supplied molecule training data is either fully labelled or fully unlabelled, the  ConGen model’s data workflow will look identical to that of the SSVAE model’s fully labelled and fully  unlabelled data workflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' However, when the ConGen model is supplied with molecules with sparsely  populated property labels as the training data, its components and cost functions are appropriately  modified such that it only uses the relevant property labels based on the property mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We first  benchmark the usage of this model on a training dataset used by the original SSVAE model, which  contains just labelled and unlabelled molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We then demonstrate several use cases which cannot  be done using the SSVAE model, including the generation of virtual screening chemical space for  Lithium-ion battery localized high concentration electrolyte diluent (LHCE) candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This is achieved  by combining five publicly available molecular property databases, comprising different properties  such as Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, number of fluorine and oxygen atoms (nF and nO), ionization energy and electron  affinity (IE and EA), and Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The availability of these properties are very different, with the first  three being fully available (‘easy’), the next two with availability of approximately 3% (‘medium’  property, obtainable from quantum chemistry simulations), and the last one with availability of  approximately 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='03% (‘hard’ property, obtainable from experimental measurements).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Baseline SSVAE Model  We first describe the inner workings of the baseline SSVAE model developed by S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Kang, et al,8  which forms the foundation of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The main idea of the SSVAE model is simple:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Encode the input molecule structure ������������  from the training dataset into a latent space  representation ������������ using an encoder sub-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Predict the property label of the input molecule structure ������������ from the training dataset into  predicted property  ������������������������ using a predictor sub-model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' If an actual molecule property label ������������������������  exists in the training database, ������������������������ is discarded and the model uses the internal molecule  property label ������������ = ������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Otherwise, ������������ = ������������������������ is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Use the internal molecule property label ������������ and the latent space representation ������������ as input  to the decoder sub-model to generate the output molecule structure ������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  In order to handle different types of training data (labeled vs unlabeled), the SSVAE model treats  the two types of data differently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The training dataset in an epoch’s minibatch is split into two different  minibatch (labeled vs unlabeled).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The SSVAE workflow is then run twice, in a slightly different manner  depending on whether the molecule minibatch is fully labeled or fully unlabeled (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Figure 1 | High-level labelled / unlabelled data & model differentiation within Kang et al’s original SSVAE model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='8 The  variational auto-encoder (VAE) cost is calculated separately for the unlabeled and the labeled dataset, while regression cost  is only calculated for the labeled dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The three costs are then summed up to calculate the total minibatch training cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Labelled  Unlabelled  Minibatch Labelled Samples  Property  Labelled  (In)  Data  yp  yL  SMILES  RNN  np property  (Predictor)  y=yl  (In)  y  Total Training Cost  x  =  RNN  RNN  SMILES  sample  Labelled Regression Cost  (Encoder)  (Decoder)  XD  (Out)  +  Labelled VAE Cost  Unlabelled VAE Cost  SMILES  RNN  y=yp  (In)  (Predictor)  Yp  x  Unlabelled  RNN  RNN  SMILES  Data  (Encoder)  Z  (Decoder)  X  (Out)  Minibatch Unlabelled SamplesIn SSVAE approach,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' a molecule entry’s training cost function needs to be split into three parts  (Equation 1-3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The cost function is written in verbose detail below for clarity, as we need to  subsequently explain in the following section how the modifications need to be done for the dirty  (partially labelled) data in the ConGen model:  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' VAE cost function for completely labeled entries in the minibatch (Equation 1):  ������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������) = − � ��������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ ln ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ + �1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������� ln�1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='��������������  ������������������������  ������������=1  ������������������������  ������������=1  + � 1  2 ������������������������� ln 2������������ + ln�������������������������������������(������������)� + ��������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − ������������������������� ��������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − �������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  −1  ������������������������  ������������=1  ������������������������  ������������=1  �  ������������������������  ������������=1  − � � 1  2 �1 + ln �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2 − �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2 − �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2�  ������������������������  ������������=1  ������������������������  ������������=1  b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' VAE cost function for completely unlabeled entries in the minibatch (Equation 2):  ������������(������������) = − � ��������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ ln ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ + �1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������� ln�1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='��������������  ������������������������  ������������=1  ������������������������  ������������=1  + � 1  2 �� ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  −1�������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2  ������������������������  ������������=1  + ��������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − ������������������������� ��������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − �������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  −1  ������������������������  ������������=1  ������������������������  ������������=1  − ������������������������ + ln�������������������������������������(������������)� − � ln �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2  ������������������������  ������������=1  �  ������������������������  ������������=1  − � � 1  2 �1 + ln �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2 − �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2 − �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2�  ������������������������  ������������=1  ������������������������  ������������=1  c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Regression cost function for completely labeled entries (Equation 3):  ������������������������������������������������������������������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������) = ������������ � � �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='��������������  2  ������������������������  ������������=1  ������������������������  ������������=1  where ������������ = ������������������������������������(������������������������) and ������������ = ������������(������������������������) are the label covariance matrix and mean values constructed  from the entire fully labelled training set,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������ is the mean function,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������ is the standard deviation function,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  ������������ is the tradeoff hyperparameter between generative and supervised learning,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' while ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  and ������������������������ represent the number of minibatch’s completely labeled entries,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' completely unlabeled entries,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  and dimensions of ������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' and ������������ respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Finally, the total minibatch cost function is simply  ������������������������������������������������������������������������������������������������������������ = ������������ + ������������ + ������������������������������������������������������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Finally, once the training is finished, the decoder sub-model can be extracted and be run  independently by specifying the conditional property input ������������ and the randomly sampled latent space  input ������������ to conditionally generate the desired molecule outputs, where a beam search algorithm is  used for converting output ������������������������ to a molecule SMILES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The primary disadvantage of this approach is  that the training dataset must be either fully labelled or fully unlabelled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The reason the SSVAE model  splits the problem as specified in Figure 1 above is because it simplifies the model dataflow, math, and  behaviour tremendously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' In practice, training datasets of interest likely consist of molecules with  incomplete labels, in addition to the completely labelled or unlabelled molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This is especially so,  if the training molecule database is either taken from a publicly available database (like PubChem  experimental data10) or combined from several different databases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Neither of these practical types  of “dirty” datasets will work for training the baseline SSVAE model, thereby severely limiting the type  of conditional molecule generation which can be done, especially when multi-property conditional  molecule generation is desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This is typically the case for battery electrolyte or pharmaceutical drug  molecule virtual screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Enabling Sparse Labelled Data Utilization using ConGen Model  We modify the SSVAE model into the ConGen model, which is explicitly designed to work with  “dirty” training data, thereby enabling the usage of significantly larger number of training data sources  including those merged from different public and private sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This enables us to perform  conditional molecule generation tasks which are previously not possible using the SSVAE model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For  example, given a large labeled molecule dataset from ZINC11 (containing Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, hydrophobicity LogP,  and drug-likeness QED) and another similarly large molecule dataset from Materials Project  Electrolyte Genome12 (containing Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, EA, and IP), we can train a conditional generative model  which can generate molecules with multiple simultaneous constraints on the Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, LogP, and EA  values (known useful properties for screening lithium battery electrolytes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Given these diverse  sources of training data, the original SSVAE model cannot be trained on the combined database of  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, LogP, and EA labels because the training data label is sparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ConGen on the other hand has  no such limitation, allowing users to mix non-ideal practical data from multiple sources as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  The primary idea of the ConGen model is to take the general high-level architecture of the  SSVAE model, but then modify all its components as needed in order to enable the usage of dirty  training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We have re-written the entire SSVAE model from the original TensorFlow 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0 version  into a PyTorch version to enable better model flexibility, before further implementing the necessary  modifications to enable the usage of sparse training data labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' When this PyTorch version is trained  on the original SSVAE training data (only fully labelled and fully unlabelled molecules) using the same  hyperparameter training settings (ntrn = 285k training molecules with 50:50 labelled/unlabelled  molecule split,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' nval = 15k validation molecules,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ntst = 10k test molecules,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������ = 104,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Adam optimizer  learning rate ������������������������ = 10−4),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' we obtain accuracy metrics for property prediction,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' unconditional and  single-property conditional molecule generation tasks (only Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt = 250 Da constraint is used,  because the original SSVAE code only allows single-property constraint) equivalent to the TensorFlow  version (Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 100 molecules are generated on both unconditional & conditional generation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Task  Property  SSVAE  ConGen  Predictor  Regression  MAE  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt (Da)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='95  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='22  LogP  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='06  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='08  QED  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='013  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='014  Decoder  Unconditional  Generation  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt (Da)  360 ± 65  363 ± 64  LogP  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='95 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='06  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='01 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='07  QED  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='723 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='142  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='713 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='154  Decoder  Conditional  Generation  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt (Da)  249 ± 6  251 ± 5  LogP  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='38 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='89  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='13 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='91  QED  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='810 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='072  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='816 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='095  Table 1 | Comparison between SSVAE (TensorFlow 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0) and baseline ConGen (PyTorch) model on the original SSVAE model  tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The baseline ConGen is equivalent to SSVAE, except that it is implemented in PyTorch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This comparison is performed  on SSVAE ‘clean’ original training dataset, which only contains fully labelled and fully unlabelled molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Identical training  hyperparameter settings are used, and relatively equivalent performance metrics are obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The slight differences can be  attributed to the high aggressivity of the original model’s training hyperparameter settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For the property prediction task,  predictor sub-model is utilized to calculate mean absolute error (MAE) with respect to the training labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For the  unconditional / conditional generation tasks, the decoder sub-model is used to generate the molecules and the molecules  property labels are calculated using RDKit cheminformatics library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Once we have confirmed that the two models are equivalent, the input data preprocessing and  molecule data workflow inside the ConGen sub-models are modified (Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' First, we enable the  ability to merge molecule training data labels with different types of property labels into a new  property label matrix ������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This will cause a significant fraction of the merged database to contain  missing [molecule, property] entry labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For entries with no label available from all the databases,  we designate the property label as invalid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This can be done by generating a mask matrix ������������ containing  ‘0’ for invalid entries and ‘1’ for entries with available property values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For entries where multiple  property labels are available from different databases, we choose the available label from the latest  database being merged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Both ������������������������ and ������������ matrices are now required as inputs into the ConGen model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  ConGen no longer differentiates data workflow based on whether the molecule is fully labelled or fully  unlabelled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ConGen instead implements a selector for the intermediate label ������������ which choose whether  to utilize existing label ������������������������ or the predicted property label  ������������������������ generated by the predictor sub-model  depending on the value of the mask ������������ (Equation 4):  ������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������) = �������������������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������)   ������������������������  ������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������) == 1  ������������������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������)   ������������������������  ������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������) == 0  where ������������ and ������������ denote the molecule and property type indices,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' With this modification, a  unified data workflow can be utilized for fully labelled, fully unlabelled, and partially unlabelled  molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Furthermore, when the molecule in the minibatch is either fully labelled or fully unlabelled  the mathematical operations performed on them within the ConGen model will be identical to those  performed in the SSVAE model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Figure 2 | Dirty training label data merging and high-level dirty data workflow within the ConGen model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ConGen model  no longer differentiates between fully labelled, fully unlabelled, and partially labelled molecule inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The unified data  workflow is controlled by the mask matrix ������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������������������,1, ������������������������,2, and ������������������������,1+2 denote the number of samples within the first, the second,  and the merged property databases respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  However, it is not as straightforward with respect to the training cost function and subsequent  molecule generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' It is important to recognize that the implementation of the training cost function  within the SSVAE model is heavily dependent on whether the molecule is fully labelled or fully  unlabelled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The SSVAE cost function consists of three major elements, designed to ensure that the  predictor, encoder, and decoder are all accurate (Equation 1-3) and we need to design the dirty data  VAE cost function substitute for ������������ and ������������ because we no longer have fully labelled and fully unlabelled  molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' It is worth noting that during the execution of the original SSVAE model, there is no  interaction between molecule inputs within a minibatch (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' if molecule A and B are processed  Labelled  Invalid  Unlabelled  Property 1  Property 2-3  Property 1-3  Property 1-3  ns,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1 sample  0  0  1  0  0  sample  0  0  0  sample  0  0  0  1  1  1  ns,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1+2  0  0  0  1  0  0  0  1  L  0  0  0  0  1  Mixture of Multiple  Label matrix  Mask matrix  Incomplete Database Labels  YL  M  yp  Total Training Cost  SMILES  X  RNN  Selector  All Sample Regression Cost  (In)  (Predictor)  y  All Sample VAE Cost  x  RNN  RNN  SMILES  Minibatch Partially  (Encoder)  Z  (Decoder)  XD  (ano)  Labelled Samplessimultaneously,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' the model output ������������������������ for both molecules are not influenced by the fact that the other  molecule is also simultaneously processed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This ensures that any intermediate values for a molecule  ( ������������������������ , ������������������������ , ������������ , ������������������������ , etc) are solely determined by that molecule input ������������ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Because of this, the  implementation of a new cost function for the ConGen model becomes less complicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' There is a  significant overlap of terms between ������������ and ������������, enabling us to design a new VAE cost function ������������ for the  ConGen model which takes partially labeled entries utilizing our mask matrix ������������ (Equation 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' When  the entries are all completely labeled, the entries of ������������ will all be 1, and ������������ should be converted to ������������,  except for some constant terms that do not affect the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' When the entries are all completely  unlabeled, the entries of ������������ will all be 0, and ������������ should be converted to ������������, again, except for some  constant terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Similarly, our new regression cost function ������������������������������������������������������������������������������������ should only sum over labeled  entries in the minibatch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' By ensuring this behavior, the subsequent ConGen cost function  differentiation and model parameter optimization will work exactly like the SSVAE versions when  completely labeled / unlabeled data are supplied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' However, it will also now work for dirty sparsely  labelled training data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Henceforth, we define new cost functions for the ConGen minibatch, especially  meant for dirty data:  a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' VAE cost function for dirty labeled entries in the minibatch (Equation 5):  ������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������) = − � ��������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ ln ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ + �1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������� ln�1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='��������������  ������������������������  ������������=1  ������������������������  ������������=1  + � 1  2 ������������������������� ln 2������������ + � ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − ������������������������� � ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − �������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  −1  ������������������������  ������������=1  ������������������������  ������������=1  �  ������������������������  ������������=1  + � 1  2 �� ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  −1�1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='��������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2  ������������������������  ������������=1  + ��1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='��������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − ������������������������� ��1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='��������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − �������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  −1  ������������������������  ������������=1  ������������������������  ������������=1  − ������������������������ − ��1 − ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������� ln �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2  ������������������������  ������������=1  �  ������������������������  ������������=1  − � � 1  2 �1 + ln �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2 − �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2 − �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='�������������  2�  ������������������������  ������������=1  ������������������������  ������������=1  b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Regression cost function for dirty labeled entries in the minibatch (Equation 6):  ������������������������������������������������������������������������������������(������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ������������) = ������������ � � ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − �������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='��������������  2  ������������������������  ������������=1  ������������������������  ������������=1  where ������������������������ refers to the number of all samples in the dirty data minibatch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' It is straightforward to prove  that under this scheme, ������������ is converted to either ������������ or ������������ depending on the values of ������������, except for  constant terms which do not have any impact on the model parameter optimization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Note  that, compared to the SSVAE cost functions, we have intentionally removed the constant terms  ln�������������������������������������(������������)� from the cost function above for numerical reasons we will describe in the following  paragraph related to the dirty data covariance matrix ������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Crucially, under this new cost function only  the corresponding labeled / unlabeled matrix elements from ������������ and ������������ contributes to the summation  over ������������������������  and ������������������������  forming ������������ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The total minibatch cost function is now simply ������������������������������������������������������������������������������������������������������������������������ = ������������ +  ������������������������������������������������������������������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  It is important to note that because we only have partially labeled entries, we do not have  complete entries for ������������������������ and correspondingly ������������ = ������������������������������������(������������������������) and ������������ = ������������(������������������������) can only be calculated  using the incomplete entries, making these matrices ill-defined especially ������������������������������������(������������������������).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For an SSVAE  model, ������������ is well-defined because it is straightforward to completely discard the unlabelled molecule  entries from the training set and calculate ������������ and ������������ directly from the completely labelled molecule  entries (this will be a good approximation as long as there is a large number of fully labelled molecules  which is a good chemical representation of the full training dataset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This can be done once during the  model construction and be set at those values throughout the entire model training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' However, this  strategy does not work for ConGen because the training data is dirty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' In this case, it only makes sense  to calculate the label mean ������������ from the valid entries and ignore the invalid values in the ������������������������ matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Similarly, it makes more sense to calculate covariance matrix ������������ entries from the available ������������������������ matrix  entries while ignoring the invalid entries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' In other words,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' we have the following situation for ������������ and ������������  calculation (Equation 7-8):  ������������������������ = ������������(������������������������)������������ =  ∑  ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  ������������������������  ������������=1  ∑  ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  ������������������������  ������������=1  ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ = ������������������������������������(������������������������)������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ =  ∑  �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − ��������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − �������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  ������������������������  ������������=1  �∑  ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  ������������������������  ������������=1  � − 1  In a clean training data like the ones being used in the SSVAE model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' all entries of the mask matrix ������������  are all 1’s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' and it can then mathematically be proven that the covariance matrix ������������ will always be a  positive semi-definite (PSD) matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Correspondingly, in SSVAE the log-determinant term ln�������������������������������������(������������)�  in the cost function above will always be well-defined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The mathematical guarantee breaks down  when the entries of mask matrix ������������ are no longer all 1’s, however.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='13 Consequently, we can get training  errors due to attempting log operations on negative numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Nevertheless, because the term  ln�������������������������������������(������������)�  is just a constant, we can remove it from the ConGen cost function without any  mathematical training consequences as we have done in Equation 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  The real physical issue arises from the quality of ������������ and ������������ themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' When we have low  availability of training data label (a lot of 0 entries in the mask matrix ������������), we will have significant  problems because the ������������ and ������������ matrices do not accurately represent the real molecule property labels,  especially when we have many invalid labels in the training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Keeping the values of ������������ and ������������ the  same throughout the training iterations mean we will have poor control on the conditionally  generated molecules’ properties after subsequent model training and conditional generation  processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We can mitigate this problem by using imputation technique13 to re-calculate ������������ and ������������  using predicted molecule property labels from the predictor sub-model when there is no valid label in  ������������������������.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' In other words, we track minibatch ������������ from the selector (Equation 4, Figure 2) throughout a training  epoch, and re-calculate ������������ and ������������ using ������������ instead of using ������������������������ after each training and validation cycle in  the epoch has been completed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This update is performed iteratively throughout the training,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' and it is  important to store the final ������������ and ������������ as part of the ConGen model parameter because subsequent  molecule generation tasks need to be performed using these higher quality ������������ and ������������ parameters  (Equation 8-9):  ������������������������ = ������������(������������)������������ =  ∑  ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������  ������������������������  ������������=1  ������������������������ − 1  ������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ = ������������������������������������(������������)������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ =  ∑  �������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − ��������������������������������������������������,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='������������ − �������������������������  ������������������������  ������������=1  ������������������������ − 1  where ������������������������ is the number of all molecules in the training dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The quality of ������������ and ������������ are not very  good in the beginning of the training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' However, as the predictor sub-model gets more accurate during  subsequent training iterations, ������������ and ������������ will represent the real sample population better and we  correspondingly achieve better molecule property prediction and conditional generation accuracy in  the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  We also take advantage of the modular nature of the ConGen model (inherited from the  modularity of SSVAE) to further improve model performance on dataset with rare training property  labels (such as ab-initio simulation or experimental properties).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' It is straightforward to implement  transfer learning in ConGen by replacing the recurrent neural networks (RNN) in the predictor and  encoder sub-models with a bidirectional encoder representations from transformer (BERT) model pre-  trained on a much larger (but ‘cheaper’) molecule property dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Here we use the ChemBERTa  model, which is a large-scale self-supervised transformer-based pretraining model which only requires  molecule SMILES as input and has been thoroughly evaluated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='14 During the sub-model construction,  we add a fully connected network linear layer on top of the transferred ChemBERTa model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We  nickname this type of transferred model ‘BERT’ from here onward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' When BERT is used to substitute  the RNN encoder, the entire ChemBERTa layers’ parameters are frozen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' However, when BERT is used  to substitute the RNN predictor, the last ChemBERTa layer’s parameters can be fine-tuned by the  PyTorch optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' While we do not substitute the RNN decoder with other types of decoder sub-  model, in principle it is straightforward to do so as well if desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For the standard ConGen model  training with just RNN sub-models, we set the Adam optimizer ������������������������ = 10−4 and clip the gradients  absolute value to a maximum of 102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For the ConGen model training with BERT predictor and decoder  sub-model substitutions, we have significantly lower Adam optimizer ������������������������ = 3 × 10−5 for the BERT-  based sub-models, and ������������������������ = 10−3 is used for optimizing the decoder sub-model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Finally, we demonstrate the resulting capability of the ConGen model on dirty dataset in Table  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The training data labels are mixed from two different databases: 1) ZINC database containing  properties such as Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, LogP, and QED11 used in the SSVAE publication,8 2) Materials Project  Electrolyte Genome database containing properties such as IE and EA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='12 The ConGen model is trained  on all 5 of these properties, which cannot be done by the SSVAE model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' As an example of multi-  property conditional generation, we query the models to generate molecules with 3 simultaneous  properties: Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt = 250 Da, LogP = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, and IE = 5 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The corresponding regression and conditional  generation results are given below in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We validate the properties of the generated molecules  using RDKit15 (for Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt and LogP) and quantum chemistry (for IE, see Methods).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We see that overall,  the BERT-based ConGen has worse performance than the RNN-based ConGen model on property  prediction tasks, but is relatively equivalent to the RNN-based ConGen on conditional generation tasks  (good on Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt and LogP, but less accurate on IE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We have expected the transferred BERT-based  ConGen to perform worse than the RNN-based ConGen on abundant property label such as Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt  and LogP  and better than RNN-based ConGen on rare property label such as IE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The fact that both  RNN and BERT-based ConGen shows relatively equivalent performance for molecular conditional  generation tasks merits further future investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We hypothesize that we still have insufficient  number of quantum chemistry property training labels from just the Materials Project Electrolyte  Genome database,12 and that a more accurate and data-efficient predictor sub-model is still needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Currently the BERT-based ConGen is computationally more expensive while offering no significant  improvement over the RNN-based ConGen, so we focus solely on using RNN-based ConGen in the  following large-scale electrolyte diluent screening section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Task  Model  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt (Da)  LogP  QED  EA (eV)  IE (eV)  Predictor Regression  Test Set MAE  RNN  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='70  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='05  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='009  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='16  BERT  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='07  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='15  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='017  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='22  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='19  Decoder Unconditional  Generation  RNN  312 ± 95  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='07 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='28  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='677 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='124  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='79 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='84  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='99 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='44  BERT  271 ± 145  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='15 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='11  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='583 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='138  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='72 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='82  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='40 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='34  Decoder Conditional  Generation  RNN  248 ± 4  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='55 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='23  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='672 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='082  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='06 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='55  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='53 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='62  BERT  252 ± 3  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='45 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='36  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='756 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='127  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='80 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='64  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='36 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='41  Table 2 | ConGen model performance comparison on ‘dirty data’ tasks, including both RNN-based ConGen and BERT-based  ConGen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This ‘dirty data’ task cannot be done with the original SSVAE model but is useful in practice for conditional  generative model training because molecule property labels are often unavailable or incomplete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Including a pre-trained  BERT can increase the predictor sub-model’s ability on ‘rare’ properties such as EA and IE, even though in some cases it may  reduce the predictor sub-model’s performance on ‘common’ properties (Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, LogP, and QED in this case).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The conditional  generation co-constraints are Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt = 250 Da, LogP = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, and IE = 5 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Regression MAE is calculated using property labels  from the database, while generated molecules’ properties are validated using either RDKit library or ab-initio simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Use Case Example: Lithium-Ion Battery Localized High Concentration  Electrolyte Diluent Screening  Finally, we demonstrate the usage of the ConGen model on a practical example: generating the  chemical space for further virtual screening of Li-ion battery localized high concentration electrolyte  (LHCE) diluent molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Recent progress in the development of Li-ion battery electrolytes have led  to the discovery of LHCE-type of electrolytes, which microscopically look like that of high salt  concentration electrolyte (HCE), but macroscopically look more like a conventional electrolyte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='16 The  LHCE is useful because it is stable over a wide electrochemical window, in addition to forming stable  solid electrolyte interphase (SEI) layer which is important for the long-term stability of the battery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='17,18  From a cost perspective, the LHCE is also important because it can reduce the required amount of Li-  salt used, versus that of HCE which requires a large amount of expensive Li-salt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='19 Finally, LHCE can  have significantly lower solution viscosity than HCE, which is useful not just for improving the  electrolyte’s lithium ion transport properties, but also for enabling better electrode wetting which  helps to better optimize the energy capacity of Li-ion battery cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='20 Chemically, what differentiates  LHCE from HCE and conventional electrolytes is the addition of small molecules which act as a diluent  in the electrolyte.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='16 These diluent molecules are typically hydrofluoroether (HFE) such as bis(2,2,2-  trifluoroethyl) ether (BTFE) and 1,1,2,2-tetrafluoroethyl-2,2,3,3-tetrafluoropropyl ether (TTE), or  fluorinated orthoformate such as tris(2,2,2-trifluoroethyl) orthoformate (TFEO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='16–18 The unique trait  of these types of compound is that while they are sufficiently polar, they are less polar than the Li-salt  anions being used in the LHCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Consequently, at the right concentration range the Li+ cations will  primarily coordinate with the polar salt anions in the first Li+ solvation shell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The diluent molecules will  then mostly coordinate with these salt clusters from the second shell onward using their polar oxygen  atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Furthermore, the fluorinated components of the diluent molecules will tend to form their own  non-polar network in the LHCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Consequently, the addition of diluents into LHCE ensures that locally  the salt cluster looks like that of HCE (more stable), while macroscopically the diluents separate these  salt clusters and ensure that the solution is less viscous, ionically conductive, and ideally inflammable  (due to the proportion reduction of flammable solvent molecules in LHCE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Many criteria need to be satisfied by these LHCE diluent molecules such as electrochemical  stability, inflammability, and low viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' While there are several known working LHCE diluents, it is  important to find more relevant compounds in this field to enrich the diluent chemical space suitable  for the optimization of specific types of Li-ion batteries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We apply the ConGen model to generate  candidate molecules for LHCE diluents through structural chemical properties such as: Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, nF, nO,  IE, EA, and Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' To achieve this, we train ConGen model on a mixture of 5 publicly available  datasets: Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt database from ZINC8,11 (310,000 unique entries) Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, simulated IE, EA database from the Materials Project Electrolyte Genome12 (62,274  unique entries) Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, simulated IE, EA database from Austin Apple Github21 (26,394 unique entries) Oxyfluorocarbon nF, nO database from PubChem10 (200,000 unique entries) Experimental Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis database from literature22 (322 unique entries)  Where applicable, each of these databases are supplemented with the corresponding molecule  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, nF, and nO missing property labels because it is computationally efficient and inexpensive to  do so using RDKit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='15 The combined database has 571,023 unique molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Finally, we evaluate the  model’s performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Based on known existing LHCE diluents, we hypothesize that we need the  following properties for the LHCE diluent molecules: Electrochemical properties:  EA <= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5 eV, IE >= 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0 eV Viscosity property:  Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis <= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0 Structural properties:  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt <= 300, nF >= 4, nO = 1-2  Within the framework of ConGen, we can implement this multi-condition molecular structure  generation task by simply deploying simultaneous property label ‘anchors’ as the decoder input during  the generation cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For example, we may choose the following label anchors to satisfy the conditions  stated above:  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  EA = 0 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5 eV  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  IE = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0 or 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5 eV  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis = -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1 or 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt = 250 or 300 Da.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  nF = 4 or 6  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  nO = 1 or 2  We correspondingly have 26 = 64 combinations of multi-constraint property anchors we can use for  the conditional generation in the example above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For each set of anchors, we generate 5 molecule  samples resulting in 320 conditionally sampled molecules using our RNN-based ConGen model (Query  1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The training data label distributions, based on just available property labels, is shown below in  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Figure 3 | Training data molecular property label distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The dashed lines indicate the property label ‘anchors’ we will  use for subsequent conditional molecular generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The arrows indicate the preferred generated molecules’ property  range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The anchors are respectively: EA = [0,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5], IE = [7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0,7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5], Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis = [-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0], Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt = [250,300], nF = [4,6], nO = [1,2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  4000  3000  40  3500  35  2500  3000  30  2000  2500  25  Count  2000  1500  15  1000  1000  10  500  500  5  0+  2  0  2  0  1  234  5  6  0  4  6  8  10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5  EA (eV)  IE (eV)  Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis  30000  350000  200000  300000  175000  25000  150000  250000  20000  125000  200000  15000  150000  75000  10000  100000  50000  5000  50000  25000  0 +  0+  +0  100  200  300  400  500  0  2  4  6  8  10  12  0  2  4  6  8  10  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt (Da)  nF  ouRegression on the test set, unconditional molecule generation, as well as conditional molecule  generation results are shown below in Figure 4 and Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' In order to calculate the ground truth  property label values for the generated molecules, several methods are employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' For Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, nF,  and nO, simple cheminformatics tool such as RDKit can be used to quickly calculate their true values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  For EA and IE, we used quantum chemistry calculations with identical calculation settings to the prior  work12 to calculate the true values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We see that we have excellent control over the generated  molecules’ structural properties (Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt, nF, and nO) and IE, although we observe a positive shift of  approximately 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0 eV on the generated molecules’ EA compared to the mean of the anchors’ EA (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='25  eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We hypothesize that this systemic shift may be caused by the slight difference in our adiabatic EA  calculation workflow compared to the procedure utilized by the Materials Project Electrolyte Genome  team, as well as the fact that we query the ConGen model to generate molecules with EA label anchors  at the extreme left end of the training dataset EA label distribution (making this the most difficult  constraint out of the 6 co-constraints we have employed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  We currently have no experimental validation capability to measure Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis for the generated  molecules, so unfortunately no accuracy metric can be displayed for these molecules’ Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Nevertheless, we have listed all the molecules that the ConGen model has generated based on their  property label input anchors in Table 4 for future validation by other research groups with  experimental capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Additional molecular property criteria are likely needed to further improve  the quality of the generated LHCE diluent candidate molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Inclusion of further molecular property  constraints to help refine this generated LHCE diluent chemical space further should be  straightforward, as it can be done by simply adding a new comma-separated-value (CSV) file  containing the desired molecular properties for training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Out of the 320 generated molecule SMILES,  6 are invalid molecules, 3 are duplicates, and 5 are within the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We have correspondingly  generated 306 new unique candidate molecules from this query for computational validation  purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We further generate 64,000 candidate molecules using the RNN-based ConGen model  (1,000 queries for each of the anchor combinations, see Figure 4) although neither EA nor IE ab-initio  computational validation is done for these additional molecules due to the high computation costs  (Query 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Out of this new query for 64,000 molecules, 1,486 are invalid, 41,117 are duplicates, and  356 are within the training set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Correspondingly, Query 2 generates 21,041 new unique candidate  LHCE diluent molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Future work is needed to reduce the number of large-scale-query duplicates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Figure 4 | ConGen unconditional and multi-constraint conditional molecular generation property distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' (a)  Unconditional molecule generation showing property distribution without constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' When multiple co-constraints are  utilized for the conditional generation, we have very targeted molecule generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Structural and electrochemical stability  properties validation for Query 1 with 320 molecules is shown in (b), while structural property validation for Query 2 with  64k molecules is shown in (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' We can see that the molecules generated with simultaneous multi-property constraints still  obey their conditional property anchors quite well (simultaneously, although the hardest property EA distribution is slightly  shifted), and that the generated molecules’ property distribution is very different from molecules generated with no property  constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Conditional generation property anchor inputs are shown as dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Task  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Wt (Da)  nF  nO  EA (eV)  IE (eV)  Log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Vis  Predictor Regression  Test Set MAE  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='60  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='01  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='02  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='14  Decoder Unconditional  Generation  302 ± 110  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='50 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='12  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='30 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='42  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='71 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='54  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='58 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='75  N/A  Decoder Conditional  Generation (Query 1)  275 ± 26  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='02 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='08  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='50 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='50  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='99 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='73  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='04 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='61  N/A  Decoder Conditional  Generation (Query 2)  274 ± 26  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='02 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='05  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='49 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='50  N/A  N/A  N/A  Table 3 | Molecular property prediction accuracy and the generated molecule’s property distribution statistics for LHCE  diluent molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' From the regression test result, we can see the predictor sub-model is reasonably accurate in predicting  molecular property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' In addition to that, the discrepancy in distributed molecules’ properties for unconditional vs conditional  Unconditonal Generation (m = 10)  4,  3  Co:  3  3  5  3  6  Conditional Generation (Query 1, m = 320)  OXOG  200  35  80  55  (600  125:  1725  ron  20  40  75  55  751  50  :10  50  25:  51  00 150 00350 300 350400 450  0i2  5  A  Conditional Generation (Query 2, m = 64,000)  20000  AOX0XXO  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='O0X00  1500  35000  35000  EL500O  3000  3000  12500  25000  25000  Not validated due to high  20xxx0  20000  5L5000  L5X0X00  computational cost  50X00  25600  5000  T001505002503005504 00450  3  8  4kl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='A: (ba  ngeneration cases show that the conditional generator is generating the right molecules, based on the property label input  anchors we have chosen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Regression MAE is calculated using property labels from the database, while generated molecules’  properties are validated using either RDKit library or ab-initio simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Table 4 | Candidate Li-ion battery LHCE diluent molecules generated with multi-constraint ConGen model (Query 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  Cc1ccc(OCC(F)(F)C(F)(F)Cl)cc1  CN(C)C(=O)Nc1cc(F)cc(C(F)(F)F)c1  Nc1c(F)cc(OC(F)(F)F)cc1CCl  CC(C)(C)OC(c1cc(F)cc(F)c1)C(F)F  CC(C)C(=O)Nc1ccc(F)c(C(F)(F)F)c1  CCOC(=N)c1c(F)cccc1CC(F)(F)F  CN(C)C(=O)Nc1c(F)c(F)cc(F)c1CF  Nc1cc(C(F)(F)F)ccc1OCCC(F)C  OCc1nc(C(F)(F)F)nc2c(F)cccc12  Fc1cc(OC(F)(F)F)cc(C2CCNC2)c1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  CN(C)C(=O)OC1(C(F)(F)F)CCC(F)C1  Oc1cc(OC(F)(F)F)cc(F)c1CCl  CCOC(=O)c1cc(C(F)(F)F)nc(F)c1C  OC(OCC(F)(F)C(F)F)c1ccsc1  CC(=O)NCC(O)c1c(F)c(F)cc(F)c1F  COC(=O)CC(CC(F)(F)F)c1ccccc1  OCc1c(OC(F)(F)F)ccc(F)c1C1CC1  Cc1cc(OCC(F)(F)C(F)(F)CO)ccn1  COc1ccc(OCC(F)(F)C(F)F)c(C)c1  COC(=O)Cc1c(F)cnc(C(F)F)c1CF  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  Oc1nc(F)cc(CC(F)(F)C(F)(F)F)n1  CC(OC(F)(F)F)c1ccccc1C(F)(F)F  FC(C(F)(F)F)C(F)(F)COC1CCCC1  Cc1ncc(OC(F)(F)F)nc1C(F)(F)F  FC(F)(F)C(F)(F)COc1ccccc1F  OC(CCC(F)(F)C(F)(F)C(F)F)C1CC1  OC(CCC(F)(C(F)(F)F)C(F)F)C1CC1  Fc1ccc(OCC(F)(F)F)cc1C(F)F  Cn1nc(C(F)(F)F)c(C(F)(F)F)c1CO  NC(c1ccoc1)C(C(F)(F)F)C(F)(F)F  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  COC(=O)CCCC(F)(F)C(F)(F)C(F)F  OC(O)(CCCC(F)(F)F)CC(F)(F)F  OC(O)c1cc(C(F)(F)F)c(F)c(F)c1F  CC(=O)NCC(O)(C(F)(F)F)C(F)(F)F  Oc1cc(C(F)(F)F)cc(C(F)(F)F)c1O  CCOc1ccc(C(F)(F)F)c(C(F)(F)F)c1  COC(=O)CCC(F)(C(F)(F)F)C(F)(F)F  OC(OCC(F)(F)F)c1cccc(F)c1F  -- invalid--  Oc1c(OC(F)(F)F)cccc1C(F)(F)F  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  Cc1noc(-c2ccc(C(F)(F)F)cc2Cl)c1C(F)F  Fc1cnc(OC(F)(F)F)c(I)c1  Cc1cc(OC(F)(F)F)cc(F)c1I  O=C(Nc1ncc(C(F)(F)F)cc1Cl)c1ccccc1  COc1cnc(C(F)(F)F)c(F)c1CBr  Cn1cc(-c2noc(-c3cc(F)c(F)c(F)c3F)n2)s1  Nc1c(F)cc(Oc2ccc(C(F)(F)F)cc2)c(Cl)c1  NC(=O)c1c(F)cccc1Nc1cc(C(F)(F)F)ccn1  COc1cnc(-c2ccc(C(F)(F)F)c(F)c2)c(Cl)c1  OC(Cc1ccc(C(F)(F)F)c(F)c1)c1cccs1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  OC(Cc1cc(F)c(Br)cc1F)C(F)(F)O  NC(=O)COc1ccccc1-c1c(F)c(F)cc(F)c1F  COC(=O)CCc1ccc(Cl)cc1C(F)(F)C(F)F  OC(O)(c1cc(F)c(F)c(F)c1)c1ccc(F)cc1Cl  CCOC(=O)Nc1c(C(F)(F)F)cc(F)nc1CCl  NCc1cnc(OC(F)(F)F)nc1Oc1c(F)cccc1  N[C@@H](Cc1cc(F)c(F)c(F)c1F)c1ccc(O)cc1O  COc1ccc(CNc2cc(F)c(F)c(F)c2F)cc1O  CCC(=O)NCC(=O)Nc1cc(C(F)(F)F)cc(F)c1C  FC(F)(F)Oc1cccc(Oc2cc(F)cc(Cl)c2)c1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  COC(c1cc(C(F)(F)F)nc(C(F)(F)F)c1)C1CC1  COc1c(C(F)(F)F)ncc(C(F)(F)F)c1CCl  Nc1ccc(C(=O)NCC(F)(F)C(F)(F)C(F)F)cc1  OC(c1ccc(F)cc1)c1c(F)c(F)c(F)c(F)c1F  NCc1cc(OC(F)(F)F)c(Cl)cc1C(F)(F)F  Nc1cc(C(F)(F)F)cc(OC(F)(F)F)c1CCl  NC(=O)c1cc(C(F)(F)F)cc(C(F)(F)F)c1CCl  FC(F)(F)c1cccc(-c2ccc(OC(F)(F)F)cc2)c1  CC(C)C(=O)Nc1cc(C(F)(F)F)cc(C(F)(F)F)c1  Nc1c(F)cccc1Oc1cc(F)c(F)c(C(F)(F)F)c1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  OCc1ccc(C(F)(F)F)cc1OCCC(F)(F)CF  COc1cc(C(F)(F)F)c(C(F)(F)F)c(CC(N)=O)c1  OB(O)c1c(C(F)(F)F)ccc(Cl)c1C(F)(F)F  Cc1cc(OC(F)(F)F)nc(OC(F)(F)F)c1CC#N  COc1ccc(OC(C(F)(F)F)C(F)(F)C(F)F)nc1  Cc1ccc(COCC(F)(F)C(F)(F)C(F)F)cc1O  OCc1c(OC(F)(F)F)ncc(C(F)(F)F)c1C1CC1  O=C(O)Cc1cc(C(F)(F)F)nc(C(F)(F)F)c1CN  CS(=O)(=O)Nc1cc(C(F)(F)F)cc(C(F)(F)F)c1  OC(c1cccc(OC(F)(F)F)c1)c1ccc(F)cc1F  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  Oc1ccc(-c2ccc(F)c(F)c2)c(F)c1F  Cc1nc(-c2cccc(C(F)(F)F)c2F)c(C)o1  COC(c1c(F)c(F)nc(F)c1F)C1CCC1  CC(NC(=O)C(F)(F)C(F)F)c1ccccc1  NCc1cn(CC(F)(F)F)nc1CC(=O)F  CC(CO)Nc1ccccc1C(F)(F)C(F)F  NCc1cc(OC(F)(F)F)cc(Cl)c1F  CC(C)Oc1nc(C(F)(F)F)c(F)cc1CN  Cn1cnc(OC(F)(F)F)c1-c1ccc(F)cc1  OCC1Cc2cc(C(F)(F)F)cc(F)c2S1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  COc1cc(C(F)(F)F)nc(OC)c1CCF  OCC(O)Cc1ncc(C(F)(F)F)cc1CF  CC(O)c1c(OC(F)(F)F)cc(F)cc1CN  O=C(O)CC(CC(F)(F)C(F)F)c1ccc[nH]1  OCCC(=O)Nc1ccc(F)c(C(F)(F)F)c1  CCC(NCC(F)(F)C(F)F)C(=O)OCC  CC(N)(C(=O)O)c1nc(C(F)(F)F)ccc1F  COc1ccc2c(F)c(F)c(F)c(F)c2c1O  O=C(O)c1ccn(CCC(F)(F)C(F)F)c1F  NCc1cc(OC(F)(F)F)c(O)c(CF)c1C  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  OCc1nc(C(F)(F)F)c(C(F)(F)F)s1  N[C@@H](CO)c1c(F)c(F)c(F)c(F)c1CF  OCCc1c(F)c(F)c(C(F)(F)F)c(F)c1  CCc1ccc(OC(F)(F)F)c(C(F)(F)F)c1  C[C@@H](O)c1c(F)c(F)c(C(F)(F)F)c(F)c1  Nc1cnc(OC(F)(F)F)c(C(F)(F)F)c1  OC(c1cc(F)cc(F)c1)C(F)(F)C(F)F  OC[C@@H](c1cc(F)c(F)c(F)c1)C(F)(F)F  CCc1c(OC(F)(F)F)n[nH]c1C(F)(F)F  COc1ncc(C(F)(F)F)c(C(F)(F)F)n1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  C=C(O)CC(=O)C(C(F)(F)F)C(F)(F)CF  C[Si](C)(O)OC(F)(F)C(F)(F)C(F)(F)F  OC(F)(F)C(F)(F)Oc1ccc(F)c(F)c1  COCC(O)CN(C(F)(F)F)C(F)(F)F  OC[C@@H](O)CCC(F)(F)C(F)(F)C(F)(F)F  CCOC(C)C(O)(C(F)(F)F)C(F)(F)CF  OCCOCCC(F)(F)C(F)(F)C(F)(F)F  O=C(O)CCCC(F)(F)C(F)CC(F)(F)F  OCc1c(O)c(F)c(F)c(F)c1C(F)(F)F  --invalid--  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  O=C(Cn1nc(C(F)(F)F)cc1Cl)c1ccccc1F  Cc1ccc(CC(=O)Nc2cc(F)cc(F)c2)c(F)c1F  CC1CCN(C(=O)Nc2cc(F)cc(C(F)(F)F)c2)CC1  Cc1cc(C(F)(F)F)nc(Oc2cc(F)cc(Cl)c2)n1  OC(c1cc(F)cc(F)c1)c1ccc(C(F)(F)Cl)cc1  CCCc1ncc(C(F)(F)F)c(Oc2ccc(F)cc2)n1  OC(c1cc(F)cc(F)c1)c1cnc(C(F)(F)Cl)cc1  CC(OCC(F)(F)C(F)F)c1ccc(Cl)cc1Cl  CCc1nc(-c2ccc(OC(F)(F)F)cc2)nc(C)c1F  N#Cc1ccc(OCC(F)(F)C(F)F)cc1Br  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  Cc1cc(OC(F)(F)C(F)(F)C(=O)NC2CC2)cs1  NC(=O)COc1ccc(C(F)(F)F)c(F)c1Br  COC(=O)c1ncc(C(F)(F)F)c(F)c1Br  COC(=O)c1ccc(C(F)(F)F)c(-c2ccc(F)cc2)c1  COC(=O)Cc1nc(C(F)(F)F)c(F)cc1CCl  FC(F)(F)Oc1ccc(OCc2ccncc2)c(F)c1C  CCOC(=O)Cc1cc(C(F)(F)F)cc(F)c1CCl  CCOc1cc(OC(F)(F)F)c(F)cc1Br  FC(F)(F)Oc1cc(OC(F)F)cc(Br)n1  N[C@@H](CC(=O)O)c1c(C(F)(F)F)cc(F)cc1CCl  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  FC(F)C(F)(F)Oc1cc(C(F)(F)F)cnc1CCl  Nc1ccc(OCC(F)(F)C(F)(F)C(F)F)cc1C#N  OCc1c(C(F)(F)F)ccc(C(F)(F)F)c1CCl  Oc1cc(F)c(-c2ccc(C(F)(F)F)cc2)c(F)c1F  CCc1nc(OC(F)(F)F)c(C(F)(F)F)cc1CC#N  CCN(CC(F)(F)C(F)(F)C(F)(F)F)C(=O)NC1CC1  OC(c1nc2ccccc2s1)C(F)(F)C(F)(F)CF  Fc1ccc(C(F)(F)F)c(Oc2cccc(F)c2)c1F  Fc1ccc(-c2ccc(OC(F)(F)F)cc2)c(F)c1F  Fc1cc(OC(F)(F)F)ccc1-c1ccc(F)c(F)c1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  Cc1c(OC(F)(F)F)cnc(C(F)(F)F)c1CC(N)=O  Oc1ccc(COCC(F)(F)C(F)(F)C(F)F)cc1F  O=C(O)C(CC(F)(F)C(F)(F)C(F)F)c1ccccc1  OC(O)(Cc1ccc(C(F)(F)F)cc1)CC(F)(F)CF  OCc1cc(OC(F)(F)F)c(Cl)cc1C(F)(F)F  OC(O)(c1cc(C(F)(F)F)cc(C(F)(F)F)c1)C1CC1  C[C@@](N)(C(=O)O)c1nc(C(F)(F)F)c(C(F)(F)F)n1C O=C(NCC(F)(F)C(F)(F)C(F)F)c1ccc(O)cc1  CCOC(=O)c1cc(C(F)(F)F)ccc1C(F)(F)CF  FC(F)(F)COCCOc1c(F)cc(C(F)F)cc1N  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  Cc1ccc(CNC(=O)C(F)(F)C(F)F)cc1  Cc1c(OC(F)(F)F)cc(F)cc1CCl  Cc1cc(CC(=O)NCC(F)(F)F)ccc1F  OC(CC(F)(F)F)c1ccc(F)c(Cl)c1  O=C(c1cccnc1)c1cc(F)c(F)c(F)c1F  COc1cc(C(F)(F)F)c(F)cc1CCl  FC(F)(F)c1cccc(Oc2ccccc2)c1F  OCc1cnc(C(F)F)c(Cl)c1C(F)(F)F  CCNC(=O)Nc1ccc(F)c(C(F)(F)F)c1  Nc1cc(OCC(F)(F)C(F)F)ccc1C#N  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  OCCC(=O)Nc1c(F)cccc1C(F)(F)F  OCc1cc(OCCC(F)(F)F)cc(F)c1C  O=C(Cc1ccc(OC(F)(F)F)cc1)C1CC1  OCc1c(C(F)F)ncc(OC(F)F)c1CC  CCOc1c(OC(F)(F)F)cc(F)cc1C#N  COc1nc(OC(F)(F)F)c(F)cc1CC#N  CCOC1(C(F)(F)F)Oc2ccc(F)cc2C1  Cc1ccc(C(F)(F)C(F)(F)C(=O)O)cc1C  CC(C)CC(=O)NCC(O)CC(F)(F)C(F)F  Cc1nc(C(F)(F)F)c(CC(=O)O)cc1CF  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  O=C(NCC(F)(F)C(F)CF)CC(F)(F)F  OC(c1cc(F)c(F)c(F)c1)CC(F)(F)F  Cc1cnc(OC(F)(F)F)c(C(F)(F)F)c1  FCOc1cc(C(F)(F)F)ccc1C(F)(F)F  O=C(Nc1cc(F)cc(F)c1F)C(F)(F)F  Cc1ncc(C(F)(F)F)c(OC(F)(F)F)n1  NCC(O)CCC(C(F)(F)F)C(F)(F)F  OC(c1c(F)c(F)c(F)c(F)c1F)C(F)F  Fc1cc(OCC(F)(F)F)ccc1C(F)F  OCCc1c(F)c(F)c(C(F)(F)F)c(F)c1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  O=C(O)CCCCC(F)(F)C(F)(F)C(F)F  FC(F)(F)C1(C(F)(F)F)OCCCCOC1  CCOC(=O)CC(C(F)(F)F)C(F)(F)CF  COC(=O)CCC(C(F)(F)F)C(F)(F)CF  Fc1cccc(OC(F)(F)OC(F)(F)F)c1  Cc1c(O)cc(C(F)(F)F)cc1OC(F)(F)F  Oc1cc(OC(F)(F)F)cc(C(F)(F)F)c1  O=C(OCCCCC(F)(F)F)CC(F)(F)F  CCC(=O)OCC(C(F)(F)F)C(F)(F)CF  CC(O)CCC(O)(C(F)(F)F)C(F)(F)F  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  O=C(NCC(F)(F)C(F)F)c1ccc(Cl)cc1Cl  CN(C)c1cc(C(F)(F)F)nc(Oc2ccc(F)cc2)n1  CCc1ncc(OC(F)(F)F)c(F)c1CBr  OC(c1cccc(C(F)(F)F)c1)c1c(F)cccc1Cl  FC(F)(F)c1ccc(Oc2ncccc2Cl)c(F)c1  Cc1cnc(C(F)(F)F)c(Oc2ccc(F)c(Cl)c2)n1  Nc1ncc(F)cc1C(=O)Nc1ccc(C(F)(F)F)cc1  N#Cc1ccc(COc2ccccc2C(F)(F)F)c(F)c1  CCCc1nc(OC(F)(F)F)nc(F)c1Br  CNc1ccc(Oc2ccc(C(F)(F)F)nc2)c(F)c1C  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  CC(Oc1cccc(C(F)(F)F)c1)C(=O)c1ccccc1  CS(=O)(=O)N1CCN(c2c(F)c(F)cc(F)c2F)C1  COCc1nc(OC(F)(F)F)c(F)cc1Br  Oc1cc(OC(F)(F)F)ccc1CBr  O=C(NCC(F)(F)CO)c1c(F)cc(F)cc1CCl  CS(=O)(=O)Nc1ccc(SC(F)(F)C(F)F)cc1  FC(F)(F)Oc1cc(F)c(OCc2cccnc2)c(C)c1  O=S(=O)(c1cccc(C(F)(F)F)c1)c1ccc(F)cc1  CS(=O)(=O)Nc1ccc(C(F)(F)C(F)F)c(Cl)c1  CC(Nc1cc(C(F)(F)F)cc(F)c1)C(=O)OC(C)(C)C  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  Cc1c(C(F)(F)F)cc(OC(F)(F)F)nc1CCl  Oc1c(F)cccc1-c1cc(C(F)(F)F)cc(F)c1F  Nc1cc(OC(F)(F)F)cc(C(F)(F)F)c1CCl  OC(c1cccc(C(F)(F)F)c1)c1cccc(F)c1F  FC(F)(F)Oc1ccc(-c2ccc(C(F)(F)F)cc2)cc1  CC(=O)Nc1c(C(F)(F)F)cnc(C(F)(F)F)c1CN  O=Cc1ccc(C(F)(F)F)c(C(F)(F)F)c1CCl  OCc1cc(C(F)(F)F)cc(C(F)(F)F)c1CCl  --invalid--  OC(c1ccc(C(F)(F)F)nc1)c1c(F)cc(F)cc1F  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  OCC(Oc1cccc(C(F)(F)F)c1)CC(F)(F)CF  C[C@@H](NC(=O)O)c1cc(C(F)(F)F)cc(C(F)(F)F)c1  O=Cc1cc(OCC(F)(F)C(F)(F)C(F)F)ccc1N  CCOC(=O)Cc1c(F)cc(C(F)(F)F)cc1C(F)F  OCc1c(OC(F)(F)F)ncc(C(F)(F)F)c1Cl  NC(=O)c1c(OC(F)(F)F)cnc(C(F)(F)F)c1CN  NC(COCC(F)(F)F)c1cccc(OC(F)(F)F)c1  O=C(NCC(F)(F)F)N1CCC(O)(C(F)(F)F)CC1  OCc1ccccc1OCCC(F)(F)C(F)(F)C(F)F  FC(F)(F)Oc1ccc(OC(F)(F)C(F)Cl)cc1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  CNCC(=O)Nc1cc(F)c(C(F)(F)F)cc1  OC(c1cc(F)cc(C(F)(F)F)c1)C1CCC1  OC(CC(F)(F)F)c1ccc(F)c(Cl)c1  OCCc1cc(C(F)(F)F)c(Cl)cc1F  Fc1ccc(COc2ccccc2F)c(F)c1F  OCCc1nc(C(F)(F)F)c(F)cc1Cl  OCc1cc(C(F)(F)F)c(F)cc1CCl  Nc1cnc(OCCCC(F)(F)F)c(F)c1F  COc1c(C(F)(F)F)ccc(F)c1CCl  Nc1ccc(OCCC(F)(F)C(F)F)c(C)c1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  CN(C(=O)O)c1cc(C(F)(F)F)cc(F)c1C  CCCC(=O)OCCCCC(F)(F)C(F)(F)F  CS(=O)(=O)CCSCC(F)(F)C(F)F  O=Cc1cc(OCC(F)(F)C(F)F)cs1  CCC(=O)NCC(=O)NCC(F)(F)C(F)F  OC(COCC(F)(F)F)c1ccc(F)c(C)c1  CNC1CC(C(F)(F)C(F)(F)C(=O)O)CC1  CCCOC(=O)Nc1c(F)c(F)cc(F)c1F  COC(=O)Nc1cccc(C(F)(F)C(F)F)c1  CCOC(=O)Nc1nc(C(F)(F)F)ccc1F  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  C[C@H](O)c1cc(C(F)(F)F)cc(C(F)(F)F)c1  Cc1c(OC(F)(F)F)cccc1C(F)(F)F  OCC(F)(F)C(F)(F)c1cc(F)cc(F)c1  Nc1ncc(F)c(OC(F)(F)F)c1C(F)F  C[C@H](N)CC(=O)NC(C(F)(F)F)C(F)(F)F  CNCC(=O)NCC(F)(F)C(F)(F)C(F)F  Cc1cc(OC(F)(F)F)nc(C(F)(F)F)c1  Fc1cc(F)c(OCCC(F)(F)F)c(F)c1  --invalid--  FC(F)(F)CCOc1cc(F)c(F)c(F)c1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 250, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  OCc1c(F)c(F)c(OC(F)(F)F)c(F)c1  COC(=O)CCC(C(F)(F)F)C(F)(F)CF  C=CCOC(=O)CC(F)(F)C(F)(F)C(F)F  CC(CC(F)(F)C(F)(F)C(F)F)CC(=O)O  OCc1cc(C(F)(F)F)cc(C(F)(F)F)c1O  CC(C)(CC(F)(F)C(F)(F)C(F)F)C(=O)O  Cc1c(OC(F)(F)F)[nH]c(C(F)(F)F)c1O  Cc1ccc(OC(F)(F)F)c(OC(F)(F)F)c1  C=CCOC(=O)C(C(F)(F)F)C(F)(F)CF  FCOc1c(C(F)(F)F)[nH]c(C(F)F)c1O  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  OC(c1c(F)c(F)c(F)c(F)c1Br)C1CC1  OC(c1cccc(C(F)(F)F)c1)c1ccc(F)cc1Cl  Oc1nc(F)c(C(F)(F)F)cc1I  CC1CC(c2ccc(C(F)(F)F)cc2)NC(=O)NC1F  OC(Cc1ccc(F)c(Br)c1)CC(F)(F)F  CC(NC(=O)CC(F)(F)C(F)F)c1ccc(Cl)cc1  COc1nc(C(F)(F)F)ccc1CBr  COc1cc(Br)cc(CC(F)(F)C(F)F)c1  O=C(Cc1nc(C(F)(F)F)ns1)c1ccc(F)cc1C  Cn1nc(C(F)(F)F)cc1C(=O)Nc1ccc(F)cc1C  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  CC(=O)Nc1nc(-c2ccc(C(F)(F)F)c(F)c2)c(C)o1  CC(Oc1cccc(C(F)(F)F)c1)c1cccc(F)c1O  Oc1cccc(Oc2c(F)c(F)c(F)c(F)c2Cl)c1C  COc1nc(C(F)(F)F)ccc1OCc1ccc(F)cc1  O=S(=O)(Cc1ccc(F)cc1)c1c(F)cc(F)cc1F  OC(COCC(F)(F)C(F)F)Cc1ncccc1Cl  OC(O)(c1c(F)cccc1F)c1cc(F)c(Cl)cc1F  FC(F)C(F)(F)Oc1ccccc1COc1ccccc1  --invalid--  COC(=O)c1ncc(C(F)(F)F)cc1-c1ccc(F)cc1  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  OC(C(F)(F)C(F)(F)C(F)(F)F)C(Cl)(Cl)Cl  OCC(c1ccc(C(F)(F)F)c(C(F)(F)F)c1)C1CC1  OCC(c1c(F)cc(F)cc1Cl)C(F)(F)C(F)(F)F  FC(F)(F)Oc1cc(C(F)(F)F)c(Cl)cc1Cl  FC(F)(F)Oc1ccnc(-c2ccc(C(F)(F)F)cc2)c1  Cc1ccc(OCC(F)(F)C(F)(F)C(F)(F)Cl)cc1  CS(=O)c1cc(C(F)(F)F)cc(C(F)(F)F)c1C#N  Fc1cc(OC(F)(F)F)ccc1-c1cc(F)cc(F)c1  OC(F)(C(F)(F)F)C(F)(F)I  --invalid--  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content="0]  ['EA', 'IE', 'LogVis', 'MolWt', 'n_F', 'n_O'] :  [0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='5, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1, 300, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='0]  FC(F)(F)c1cc2c(cc1C(F)(F)F)OCCCCO2  OC(Cc1ccc(OC(F)(F)F)cc1)CC(F)(F)CF  CCCC(=O)OCCCCC(F)(F)C(F)(F)C(F)(F)F  OCc1ccc(COCC(F)(F)C(F)(F)C(F)F)cc1  COC(=O)Cc1cc(C(F)(F)F)cc(C(F)(F)F)c1C  Oc1cc(OC(F)(F)F)ccc1SCC(F)(F)F  O=C(Cc1cc(C(F)(F)F)cc(C(F)(F)F)c1)C(N)=O  NC(=O)Cc1cc(C(F)(F)F)nc(OC(F)(F)F)c1C  CCc1cc(C(F)(F)F)cc(C(F)(F)F)c1CC(=O)O  OC(c1c(F)c(F)c(F)c(F)c1F)c1ccc(F)cc1O  Conclusion  In summary,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' we demonstrate a novel conditional molecule generation algorithm ConGen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  which is based on semi-supervised variational auto-encoder (SSVAE) technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' However, unlike the  SSVAE model, the ConGen model is explicitly designed such that it can work with dirty training data  with incomplete labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' This is important because in practice, the molecules we can find from publicly  available databases or characterized by in-house simulations and experiments will have incomplete  sets of properties available, due to various factors (intellectual property, commercial secret, etc) as  well as experimental or computational cost considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A user of the baseline SSVAE model will  need to remove molecules with incomplete labels or assign dummy labels on the molecules at the  cost of lower model accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' On the other hand, the ConGen model can easily mix dirty training  datasets from multiple sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ConGen is also designed with flexibility for substituting its sub-models  with other types of models, enabling the user to include pre-trained models which can be helpful,  especially in cases where there is limited training data availability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Finally, we demonstrate the  practical use of our model for generating the virtual screening chemical space for Li-ion battery LHCE  diluent candidates with multiple co-constraint requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Experimental methods  Ab-initio EA and IA validation  These molecule EA and IE calculations are conducted with PySCF’s implementation23,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='24 of the  DFT Kohn-Sham method at the PBE6-31+G* level25 with Grimme’s dispersion correction26 for  geometry optimizations on the gas-phase and B3LYP/6-31+G* level of theory with the solvation  energy corrections of tetrahydrofuran (THF) using the integral equation formalism polarizable  continuum model (IEF-PCM)27 implicit solvation model for single point energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The vibrational  frequencies were computed at the same level of theory at 298.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='15K as for the geometry optimizations  to confirm whether each optimized stationary point is an energy minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Here, we optimize the  geometry at different charge states (cation, anion, neutral) to calculate the adiabatic IE/EA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Data availability  All the training data sources, as well as all the structural and computational validation of the  unconditionally and conditionally generated molecules are available in the ESI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Author contributions  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' conceptualized this project, developed the ConGen model, and performed and analysed  the model training and molecule generation experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' supervised the project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' performed  ab-initio computational validation for the generated molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' supported model training  optimization efforts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The manuscript was drafted by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', and reviewed by all the authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Conflicts of interest  There are no conflicts to declare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Acknowledgements  The computation efforts in this work were performed in Tencent Cloud platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  References  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Skinnider, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A deep generative model enables automated structure elucidation of  novel psychoactive substances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 3, 973–984 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Pei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Lai, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Structure-based de novo drug design using 3D deep generative models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 12, 13664–13675 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Peng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Yan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Ren, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A de novo substructure generation algorithm for  identifying the privileged chemical fragments of liver X receptorβ agonists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 7, 11121  (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Prykhodko, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A de novo molecular generation method using latent vector based  generative adversarial network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Cheminform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 11, 74 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Walters, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Barzilay, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Applications of deep learning in molecule generation and  molecular property prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Acc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 54, 263–270 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Gebauer, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Gastegger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Hessmann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Müller, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Schütt, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Inverse  design of 3d molecular structures with conditional generative neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 13, 973 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Tan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Dai, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Zheng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Chen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' DRlinker: Deep reinforcement learning for  optimization in fragment linking design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' (2022)  doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='1021/acs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='jcim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='2c00982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Kang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Cho, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Conditional molecular design with deep generative models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 59, 43–52 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Elton, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Boukouvalas, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Fuge, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Chung, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Deep learning for molecular design -  A review of the state of the art.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Des.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 4, 828–849 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' PubChem in 2021: New data content and improved web interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Nucleic Acids  Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 49, D1388–D1395 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Irwin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Shoichet, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ZINC - A free database of commercially available compounds for  virtual screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 45, 177–182 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Qu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The Electrolyte Genome project: A big data approach in battery materials  discovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Mater.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 103, 56–67 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Lorenzo-Seva, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Ferrando, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Not positive definite correlation matrices in exploratory  item factor analysis: Causes, consequences and a proposed solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Struct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Equ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 28,  138–147 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Chithrananda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Grand, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Ramsundar, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' ChemBERTa: Large-scale self-supervised  pretraining for molecular property prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 34th Neural Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  RDKit: Open-Source cheminformatics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='rdkit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='org/ (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Cao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Jia, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Xu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Review—Localized high-concentration electrolytes for  lithium batteries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Electrochem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 168, 010522 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Ren, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Enabling high-voltage Lithium-metal batteries under practical conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Joule  3, 1662–1676 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Chen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' High-efficiency Lithium metal batteries with fire-retardant electrolytes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Joule 2,  1548–1558 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Yamada, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Yamada, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Review—Superconcentrated electrolytes for Lithium batteries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Electrochem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 162, A2406–A2423 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Giffin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The role of concentration in electrolyte solutions for non-aqueous lithium-based  batteries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 13, 5250 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Austin Apple Github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='com/AustinApple/SSVAE-for-electrolyte-molecule-design  (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Goussard, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A new machine-learning tool for fast estimation of liquid viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Application to cosmetic oils.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 60, 2012–2023 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Sun, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Recent developments in the PySCF program package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 153,  024109 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Sun, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Libcint: An efficient general integral library for Gaussian basis functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 36, 1664–1671 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Perdew, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Burke, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Ernzerhof, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Generalized Gradient Approximation Made Simple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 77, 3865–3868 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Grimme, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Antony, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Ehrlich, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Krieg, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' A consistent and accurate ab initio  parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' 132, 154104 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Tomasi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=', Mennucci, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' & Cancès, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' The IEF version of the PCM solvation method: An  overview of a new method addressed to study molecular solutes at the QM ab initio level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content='  Mol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' Struct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
+page_content=' THEOCHEM 464, 211–226 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/sdE3T4oBgHgl3EQf9Qs1/content/2301.04814v1.pdf'}
diff --git a/wNE3T4oBgHgl3EQf-wup/content/tmp_files/2301.04829v1.pdf.txt b/wNE3T4oBgHgl3EQf-wup/content/tmp_files/2301.04829v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..75874480a9208ccb43b2df675e57c81103e37e12
--- /dev/null
+++ b/wNE3T4oBgHgl3EQf-wup/content/tmp_files/2301.04829v1.pdf.txt
@@ -0,0 +1,1350 @@
+IEEE INTERNET OF THINGS JOURNAL
+1
+Federated Transfer-Ordered-Personalized Learning
+for Driver Monitoring Application
+Liangqi Yuan, Student Member, IEEE, Lu Su, Member, IEEE, Ziran Wang, Member, IEEE
+Abstract—Federated learning (FL) shines through in the in-
+ternet of things (IoT) with its ability to realize collaborative
+learning and improve learning efficiency by sharing client model
+parameters trained on local data. Although FL has been suc-
+cessfully applied to various domains, including driver monitoring
+application (DMA) on the internet of vehicles (IoV), its usages
+still face some open issues, such as data and system heterogene-
+ity, large-scale parallelism communication resources, malicious
+attacks, and data poisoning. This paper proposes a federated
+transfer-ordered-personalized learning (FedTOP) framework to
+address the above problems and test on two real-world datasets
+with and without system heterogeneity. The performance of the
+three extensions, transfer, ordered, and personalized, is compared
+by an ablation study and achieves 92.32% and 95.96% accuracy
+on the test clients of two datasets, respectively. Compared to
+the baseline, there is a 462% improvement in accuracy and a
+37.46% reduction in communication resource consumption. The
+results demonstrate that the proposed FedTOP can be used as a
+highly accurate, streamlined, privacy-preserving, cybersecurity-
+oriented, personalized framework for DMA.
+Index Terms—Federated learning, internet of things (IoT),
+driver monitoring, privacy protection, personalization.
+I. INTRODUCTION
+W
+ITH the rapid development of sensing, computing,
+and communication technologies, the internet of things
+(IoT) is a popular solution to solve the problems in industry,
+agriculture, energy, transportation, etc. However, privacy is-
+sues in IoT are often a significant concern have been raised
+due to the intrusive behavior of sensors [1]. Specifically for the
+internet of vehicles (IoV), it massively parallels each vehicle
+and various sensors it carries, including global positioning
+system (GPS), radar, camera, light detection and ranging
+(LiDAR), etc., enabling pedestrian detection [2], automated
+driving [3], mobility digital twins [4], and other transportation
+applications. Federated learning (FL) has received extensive
+attention for protecting user privacy by sharing only model
+weights and not including users’ raw data. FL is widely known
+for its successful business case in Google mobile keyboard
+prediction [5]. Nowadays, It has also become one of the
+mainstream and thriving solutions for privacy protection and
+efficient learning.
+A. Federated Learning and Related Work
+FL is a potentially feasible solution to the privacy problem
+in IoT, which is able to avoid the proliferation, distribution,
+Manuscript received January 11, 2023.
+L. Yuan, L. Su, and Z. Wang are with the College of Engineering, Purdue
+University, West Lafayette, IN 47907, USA (e-mail: yuan383@purdue.edu;
+lusu@purdue.edu; ryanwang11@hotmail.com).
+and exchange of local client data by sharing model parameters
+after training the model on local client data. FL frameworks are
+widely used in healthcare [6], [7], industrial [8], [9], IoV [10],
+[11], etc., due to their usages of large scale and personalized
+data in an efficient and privacy-preserving way. Although FL
+has significant contributions to massively parallel devices and
+computations, it still has a notable drawback in that it cannot
+efficiently handle non-independent and identically distributed
+(non-i.i.d.) data. It is required to customize the applicable FL
+framework according to the features, resources, and constraints
+possessed by users, data, clients, and servers.
+Non-i.i.d. data and heterogeneity have always been a chal-
+lenge and a key to research in FL [12]–[14]. Non-i.i.d. data is a
+common phenomenon for real-world clients that are scattered
+and not interoperable: Taking IoV as an example, each driver
+is heterogeneous as a client. FedAvg [15], as one of the first
+proposed feasibility methods, has been the subject and center
+of research. FedAvg averages all local models to get the global
+model so that the local model may deviate far from the global
+optimum in the parameter space leading to some limitations
+in FedAvg. It is necessary to ensure that the local model does
+not deviate from the global model (prevent overfitting) and,
+simultaneously, that the local model can effectively learn the
+local client dataset (prevent underfitting). Based on FedAvg,
+FedProx [16] is proposed to limit the deviation of the local
+model from the global model by adding a proximal term.
+Besides considering accuracy, the FL framework in IoT
+should not underestimate communication and training resource
+constraints, cybersecurity, and ubiquity. Some of the recent
+surveys summarized challenges, threats, and solutions of the
+FL decentralization paradigm for IoT, including limited com-
+puting power, unreliable and limited availability, local training,
+accuracy, communication overhead, etc. [17]–[22].
+Transfer and edge learning are popular solutions to re-
+duce communication resource consumption in FL frameworks.
+Zhang et al. [23] performed a federated transfer learning
+framework to detect driver drowsiness, where transfer learning
+was employed to save the communication cost in the FL frame-
+work. Su et al. [24] introduced edge servers as a collaborative
+mechanism, where aggregation of local models was aggregated
+in the edge server and then sent to the global server to
+aggregate the global model. The benefit of the additional edge
+server was that the communication between massively parallel
+clients and the edge server was consumed because the edge
+server was geographically close to the clients. High latency
+and intermittent connections could be mitigated. In addition,
+the edge server could also provide personalized aggregated
+local models due to the similarity of geographically adjacent
+arXiv:2301.04829v1  [cs.LG]  12 Jan 2023
+
+IEEE INTERNET OF THINGS JOURNAL
+2
+clients.
+Cyber attack is a problem that cannot be ignored for FL
+frameworks. Sun et al. [25] developed an attack method for
+FL framework in IoT, in which a bi-level optimization frame-
+work was proposed to compute optimal poisoning attacked
+FL framework, including direct, indirect, and hybrid attacks.
+Meanwhile, Zhang et al. [26] utilized a generative adversarial
+network (GAN)-based approach to attack the FL framework,
+especially since the attacker did not need any prior knowledge
+to carry out the attack.
+Personalization is a common approach for FL frameworks
+to improve applicability for diverse users [27]. Fallah et al.
+[28] proposed a personalized variant of the FL, which allowed
+clients to perform several gradient descent iterations on an
+initial global model using local data to obtain a personalized
+local model. Wu et al. [29] explored a cloud edge-based per-
+sonalized FL framework for in-home health monitoring, which
+addressed the problem that a single global model performed
+poorly on a specific client. Since the global model could only
+capture the common features of all clients, it lacked the ability
+to analyze fine-grained information of specific clients.
+B. Federated Learning in Driver Monitoring Applications
+Driver monitoring application (DMA) in IoV is adopted as
+the research direction in this paper due to its real and visual
+image data, valuable application scenarios, and relatively blank
+research area. DMA also has challenges in terms of driver
+privacy issues, communication, and diversity and personalized
+driver behavior. Related DMA literature covers a wide variety
+of devices with algorithms to achieve different purposes, such
+as dangerous state detection [30], driver emotion recognition
+[31], driver lane change inference [32], etc. Compared to other
+methods [33]–[35], FL not only highlights efficient learning
+but also effectively protects the privacy of driver, passenger,
+and pedestrian biometric information, driving routes, and
+confidential driving areas such as military installations.
+In this paper, we introduce and adapt FL to DMA. Although
+some FL frameworks exist for DMA, they all suffer from
+some critical problems. Doshi et al. [36] proposed a FL edge-
+device framework to obtain a global model by aggregation
+feature representations and obtained considerable accuracy in
+recognizing driver activities. For the i.i.d. setting, the dataset
+was partitioned for each edge node in a random way, while for
+the non-i.i.d. setting, the dataset was assigned selectively. Zhao
+et al. [37] proposed a FL framework to monitor fatigue driving,
+where the non-i.i.d. setting was simulated by controlling the
+number of images per client. The above FL frameworks for
+DMA did not really take into account the actual situation
+of the application but artificially created a simulation sce-
+nario. Therefore, there is an urgent need for realistic analysis
+and research for real-world DMA, considering that the user
+(driver) should exist independently and be non-interoperable
+with different clients (vehicles). Moreover, in addition to the
+necessity of test datasets, the test client is also a critical
+evaluation criterion, which can reflect the universality of
+the FL framework. We summarize the existing neglects and
+challenges in the current FL for DMA framework as follows.
+Fig. 1. Structure illustration of a FL framework for IoV. The server interacts
+with the local client and saves different scenarios as different models. Trans-
+parent neurons are non-trainable parameters, and non-transparent neurons are
+trainable parameters.
+• Clients in FL for DMA frameworks are often defined
+in unreasonable and incomprehensible forms. A real and
+natural definition of a client should be a driver or a
+vehicle.
+• There is no paper proposing to test on a testing client
+(not involved in training process), which lacks universal
+testing for the FL framework.
+• For DMA scenario, there is a great diversity and individu-
+ality of driver behaviors, postures, and facial expressions,
+which call for more presonalized studies than other
+general IoV scenarios.
+• Similarly, DMA also has diverse scenarios, including
+diverse vehicle models, interior colors, seat positions,
+etc., which will greatly increase the learning difficulty.
+C. Proposed Solution and Contribution
+In this paper, we aim to propose a FL framework applicable
+and specific to practical applications in IoV, especially DMA,
+where an imaginary FL framework for IoV is illustrated in Fig.
+1. Each local client, i.e., vehicle, includes a training module
+and a perception module. The training module uploads the
+model parameters to the server after learning and training the
+local data. After aggregation and optimizing the parameters
+of the local client models, the server downloads the global
+model parameters to the perception module in the local client.
+Moreover, transfer learning can be used to reduce the number
+of trainable parameters, resulting in reduced communication
+consumption. The server can save different global models for
+different scenarios, such as road types, weather types, and
+vehicle types, so that the model can have better applicability.
+Therefore, a federated transfer-ordered-personalized learn-
+ing (FedTOP) framework is proposed to address the problems
+of accuracy, cybersecurity, communication resources, and di-
+versified scenarios. In addition to the transfer-extension shown
+in Fig. 1, the FedTOP framework also enhances robustness and
+cybersecurity by orderly dropout clients due to their possible
+overfitting and poisoning of the data. Furthermore, the FedTOP
+framework is able to remarkably improve accuracy by adapting
+all clients through personalized-extension. The contributions
+of this paper are:
+
+Road Model
+Training
+Upload
+Perception
+Download
+Server
+Weather Model
+Local Clients
+Vehicle ModelIEEE INTERNET OF THINGS JOURNAL
+3
+• For realistic problems and usage scenarios in DMA,
+we propose a feasible FL framework FedTOP, realizing
+privacy protection, high accuracy, low communication
+requirements, cybersecurity, and pervasiveness. To the
+best of our knowledge, this is one of the first papers to
+establish a feasible FL framework for DMA.
+• The proposed FedTOP framework is tested on two real-
+world driver monitoring datasets with and without system
+heterogeneity, systematically characterizing system het-
+erogeneity in real-world datasets and achieving consider-
+able accuracies with 92.32% and 95.96%, respectively.
+• The experiments highlight a realistic and natural client
+setup, i.e., drivers and vehicles are naturally formed as
+clients. Moreover, we innovatively propose evaluation
+criteria for training and testing clients to test the gen-
+eralization ability of the proposed FedTOP on different
+clients.
+• Through an ablation study, we demonstrate the perfor-
+mance and utility of the transfer, ordered, and person-
+alized extensions. These detachable extensions can be
+selectively installed according to the task description, and
+the FL framework combined with different extensions can
+effectively adapt to different IoT application scenarios.
+The presentation of this paper is as follows. The problem
+statement and proposed solution are described in Section
+II. The experimental setup, heterogeneity, and results have
+been demonstrated in Section III. Section IV discusses the
+performances of three extensions of the proposed framework,
+followed by Section V summarizing the paper and expounding
+on future work.
+II. METHODOLOGIES
+A. Problem Statement
+FL framework protects privacy, increases training efficiency,
+and saves communication resources by sharing only model
+parameters in IoT. In this paper, the FL framework is used
+to solve a driver activity classification task in DMA. Clients
+in real-world IoT are independent and heterogeneous due
+to the presence of only a minimal number of users per
+client. Considering the more general application scenarios, the
+global model ω for training clients C aggregation needs to
+be compatible with non-training clients C′ in addition to C.
+The data of each client Dc is non-i.i.d. when the data is not
+interoperable. We can consider a nested model
+Lc = ωc(Dc),
+(1)
+where ωc is the classifier model corresponding to client c ∈ C.
+Dc ∈ Rnc×i×j×d is the image set with nc samples, i rows,
+j columns, and d channels. Lc ∈ Znc is the corresponding
+label set. The global model ω are obtained by aggregating,
+e.g., averaging the weights of the local models,
+ω =
+�
+c∈C
+pcωc = E[ωc|c ∈ C],
+(2)
+where pc ∈ [0, 1] is a weight density function of clients, for
+which � pc = 1, pc will be assigned according to the number
+of samples. Therefore, the optimization problem of the FL
+Fig. 2. Illustration of the FL algorithm finds the optimal global model solution
+in the parameter space. The shaded areas are accuracy contour areas. The
+farther the optimal local model dissociates from the global model, the lower
+the client accuracy. Local models enclosed by shaded areas have similar
+accuracies.
+algorithm can be formulated as minimizing the global loss,
+which is equivalent to minimizing the sum of the local losses,
+min
+ω L(ω) =
+�
+c∈C
+pcL(ωc) = E[L(ωc)|c ∈ C],
+(3)
+where L is the loss function that will be assigned.
+For real-world classification tasks, we assume that the
+distribution of the local model in the parameter space presents
+a multivariate Normal distribution ωc ∼ N
+�
+µω, σ2
+ω
+�
+, where
+µω is mean of all local models, and σ2
+ω is the variance
+of all local models. Fig. 2 shows the process of the FL
+algorithm finding the optimal solution of the global model in
+the parameter space. After the initial model is trained locally,
+communicated, and aggregated globally, the final global model
+will be obtained by averaging and can be estimated as ˆω = µω.
+Especially in the large-scale parallel application scenarios of
+IoT, according to the law of large numbers, ˆω = µω = ω∗ is
+an unbiased estimation.
+However, there are still some defects in the method of ob-
+taining the global model through average aggregation. Firstly,
+we can confirm that there is enormous system heterogeneity
+in IoT, and the global model cannot ensure high accuracy for
+all clients. Secondly, we inevitably need a measure to prevent
+system heterogeneity and potential attacks and poisoning. As
+shown in Fig. 2, the farther the optimal local model is from
+the global model, the lower the accuracy, and vice versa.
+Therefore, it is conceivable that in the FL problem with
+heterogeneity, the clients’ accuracy will also obey a Normal
+distribution.
+B. Proposed Solution
+According to the problem statement, we propose a FedTOP
+algorithm to address all of the following issues. First, the
+aggregation of global models needs to be more stable, which
+can be achieved by preventing the overfitting of local models.
+Second, considering the actual communication situation in IoT,
+we propose transfer learning to reduce the trainable parameters
+and hence reduce communication requirements. Third, the
+global model should have the ability to resist interference,
+attacks, and data poisoning, which can be achieved by orderly
+dropping out local models with large loss. Fourth, a global
+model cannot take into account the situation of all clients,
+especially in the presence of data and system heterogeneity.
+Therefore, we recommend personalizing the global model to
+suit all the training and testing clients.
+
+Aggregation
+Aggregation
+Communication
+Communication
+70%
+50%
+t=
+t= T
+Optimal local model
+Estimated local model
+Initial model
+Aggregated global modelIEEE INTERNET OF THINGS JOURNAL
+4
+Fig. 3.
+The global model is shared with training and testing clients after
+iterative training and optimization on massively parallel training clients. Both
+training and testing clients are personalized locally and then get results on
+the testing set, respectively. Among them, some attack or poison clients will
+be discarded, such as Client 2 has a large loss.
+We refer to FedProx [16] using a proximal term to prevent
+local models ωc from deviating from the global model ω.
+In which, the proximal item Lp that computes the distance
+between the local and global model is added to the loss
+function,
+Lp = µ
+2 ∥ωc − ω∥2,
+(4)
+where µ is deviation coefficient, ωc is local client model
+parameters, and ω is global model parameters. The overall
+loss function can be updated as
+L = Ll + Lp,
+(5)
+where Ll is the loss between the true labels and the predicted
+labels, such as the negative log-likelihood loss used in our
+experiments.
+Transfer-extension is a common and popular solution in
+many learning frameworks. In particular, FL framework is
+favored because it can effectively reduce local client training
+resources and communication resources. In our experiments,
+the base model is ResNet34 [38] pre-trained on ImageNet,
+where only the last residual block and fully connected layer
+are trainable parameters. Although ImageNet is a large object
+classification dataset far from DMA images, the lower layers
+are similar for convolutional neural networks (CNN) and are
+used to extract image features. Therefore, the upper layers
+that are used to obtain high-level features and representations
+are given more attention. The ratio of reduced communication
+resource requirement in the network is approximately equal to
+the ratio of non-trainable parameters to total parameters,
+Commun↓ ≈ |ωnon-trainable|
+|ω|
+= 37.46%,
+(6)
+where Commun↓ is the reduced communication resource re-
+quirement, |ωnon-trainable| is the number of non-trainable model
+parameters, and |ω| is the total number of the model param-
+eters. Therefore, the transfer-extension reduces the commu-
+nication requirement by 37.46% by decreasing the trainable
+parameters.
+Ordered-extension is for orderly dropout clients with enor-
+mous variance, which may be subject to malicious attacks and
+poisoning, extensive data and system heterogeneity, and model
+underfitting. These local clients with large losses should be
+discarded to enhance the applicability of the global model.
+Ordered-extension not only enhances accuracy and robustness
+Algorithm 1 FedTOP
+Input: Communication rounds (T), training client set (C), training
+epoch (E), initial global model (ω1), loss function (Ll), deviation
+coefficient (µ), number of ordered clients (q)
+Output: Trained global model (ωT )
+for t = 1 to T − 1 do
+for c ∈ C in parallel do
+for e = 1 to E − 1 do
+Backpropagate the loss function and update the local
+model ωte+1
+c
+← arg minωte
+c Ll(ωte
+c ) + µ
+2 ∥ωte
+c − ωt∥2.
+end for
+Update the local model ωt
+c ← ωtE
+c .
+Client sends ωt
+c to the server.
+end for
+Find a set Ct
+q of top-q clients in Ct in term of loss values:
+Ct ∈ q − arg minc∈Ct L(ωt
+c).
+Server aggregates the ω as ωt+1 ← 1
+q
+�
+q∈Ctq ωt
+q.
+end for
+Send ωT to clients c ∈ {C, C′} do personalization.
+Algorithm 2 Personalized-extension
+Input: Training client set (C), testing client set (C′), personal-
+ization epoch (E), Trained global model (ωT ), loss function (Ll)
+Output: Personalized local model (ωc)
+for c ∈ {C, C′} do
+for e = 1 to E − 1 do
+Backpropagate the loss function and update the local model
+ωT e+1
+c
+← arg minωT e
+c
+Ll(ωT e
+c ).
+end for
+Update the personalized local model ωc ← ωT E
+c
+.
+end for
+but also secures the global model. After all of the clients
+upload the local model parameters and the final training loss
+to the server, the server only aggregates the q ∈ N ≤ |C| local
+models with the lowest loss as the global model. The set of q
+local models can be expressed as
+Cq ∈ q − arg min
+c∈C L(ωc).
+(7)
+Personalized-extension is to promote, popularize, and adapt
+the global model to the heterogeneity of all clients. As shown
+in Fig. 2, the global model cannot be applied to all clients due
+to the ubiquitous heterogeneity. The region of interest (ROI)
+of the model may vary depending on system heterogeneity,
+such as different camera angles, seat positions, and vehicle
+structures, resulting in differences in the relative position
+of the driver in the image. However, personalized-extension
+proposes to train the global model several times in each
+client to obtain a more personalized local model to improve
+accuracy. On the one hand, compared with the traditional
+FL algorithm, the personalized-extension can significantly and
+effectively improve accuracy and confidence. On the other
+hand, compared to the method that only trains locally, the
+personalized FL algorithm improves the training efficiency and
+avoids the overfitting of the local model. In particular, the
+personalized FL algorithm can help and generalize to other
+non-training clients C′, which may have minimal training
+resources. After receiving the global model, the non-training
+clients C′ can obtain a highly accurate and reliable local model
+
+Client 1
+Test Client 1
+Upload
+Download
+Download
+Client 2
+Initial Global Model
+Global Model
+Test Client 2
+Aggregate
+··
+Client IC
+Test ClientIC
+PersonalizationIEEE INTERNET OF THINGS JOURNAL
+5
+(a) SFDDD texting - right 1
+(b) SFDDD texting - right 2
+(c) SFDDD texting - right 3
+(d) SFDDD texting - right 4
+(e) DriveAct magazine 1
+(f) DriveAct magazine 2
+(g) DriveAct magazine 3
+(h) DriveAct magazine 4
+Fig. 4. Exampled activities of four drivers in each of SFDDD and DriveAct datasets.
+(a) SFDDD
+(b) DriveAct
+Fig. 5. Sampled client image histograms of SFDDD and DriveAct datasets.
+with minimal training. The system diagram of the proposed
+FedTOP is shown in Fig. 3
+For the proposed FedTOP framework, the client communi-
+cates with the server T rounds, and all clients C train E epochs
+in parallel between each communication. For our preliminary
+experiments, we set T = 10 and E = 5. For transfer-extension,
+the local model is the transfer learning model of ResNet34
+pre-trained on ImageNet. Only the last residual block and fully
+connected layer are set as trainable parameters. In addition, we
+add an additional fully connected layer to match the number of
+our classification categories. Based on FedProx, the activation
+function of the last layer is LogSoftmax, and the setting of
+the loss function Ll is a negative log-likelihood loss. ω1 is the
+initial model parameter. The proposed FedTOP is described in
+Algorithm 1, and the personalization process is described in
+Algorithm 2.
+III. EXPERIMENT AND RESULTS
+Considering the data and system heterogeneity, experiments
+are conducted on two open real-world driver monitoring
+datasets, including State Farm Distracted Driver Detection
+(SFDDD) [39] and DriveAct [40]. In addition to comparing
+with FedProx as a baseline, this paper also compares the per-
+formance of the transfer, ordered, and personalized extensions
+through an ablation study.
+A. Experiment Setup
+To compare the impact of system heterogeneity on FL
+frameworks, the proposed FedTOP is tested on driver monitor-
+ing datasets with and without system heterogeneity. SFDDD
+dataset includes 26 drivers and 10 activities, and DriveAct
+dataset includes 15 drivers and 12 activities. SFDDD dataset
+considers system heterogeneity, that is, different drivers have
+different vehicles, different seat positions, different camera
+angles, etc., as shown in Fig. 4a, 4b, 4c, and 4d. DriveAct
+dataset does not take into account system heterogeneity, i.e., all
+subjects had their data collected in the same system. Recorded
+from the same camera angle, different drivers read the same
+magazine in the same vehicle, as shown in Fig. 4e, 4f, 4g, and
+4h.
+To show more clearly and visually the heterogeneity be-
+tween different clients in the two datasets, Fig. 5 shows
+histograms of the sample images of the two datasets. It can be
+seen that the SFDDD dataset with system heterogeneity has a
+more considerable difference in the distribution of histograms
+than the DriveAct dataset without system heterogeneity, and
+the mean value of the SFDDD images is larger. The possible
+reason is that the vehicle interiors of the DriveAct dataset view
+are darker, resulting in most of the pixel values being lower.
+Therefore, the FL framework may be more challenged by the
+scene information when training on the SFDDD dataset, such
+as different vehicle interiors.
+Clients are naturally divided based on the drivers. In order
+to better demonstrate the role of personalized-extension, the
+datasets are first divided into training clients and testing clients
+at a ratio of about 0.8, 0.2, with |CSFDDD| = 20, |C′
+SFDDD| = 6,
+|CDriveAct| = 12, and |C′
+DriveAct| = 3. And then, the datasets
+for each client are divided into a training set, verification set,
+and testing set at a ratio of 0.7, 0.15, and 0.15, respectively.
+
+Sampled Histogram of SFDDD
+Client 1
+Client 2
+1000
+Client 3
+Client 4
+800
+Fregquency
+600
+400
+200
+0
+50
+100
+150
+200
+250
+0
+pixel valueSampled Histogram of DriveAct
+Client 1
+Client 2
+1000
+Client 3
+Client 4
+800
+Fregquency
+600
+400
+200
+0
+50
+100
+150
+200
+250
+0
+pixel valueIEEE INTERNET OF THINGS JOURNAL
+6
+TABLE I
+PERFORMANCE OF FEDTOP AND ABLATION STUDY ON SFDDD AND DRIVEACT DATASETS.
+Dataset
+Method 1
+|C|
+q
+µ
+Transfer
+Accuracy (%) 2
+Time↓ (%) 3
+Commun↓ (%) 4
+Cybersecurity
+Training
+Testing
+SFDDD
+FedProx (baseline)
+20
+20
+1
+No
+54.63
+16.44
+∼
+∼
+∼
+FedOP
+20
+15
+1
+No
+97.69
+96.37
+1.45 ↓
+∼
+↑
+FedTP
+20
+20
+1
+Yes
+94.76
+92.8
+17.3 ↓
+37.46 ↓
+∼
+FedTO
+20
+15
+1
+Yes
+46.16
+16.43
+18.91 ↓
+37.46 ↓
+↑
+FedTOP
+20
+15
+1
+Yes
+94.65
+92.32
+18.91 ↓
+37.46 ↓
+↑
+DriveAct
+FedProx (baseline)
+12
+12
+1
+No
+73.18
+23.96
+∼
+∼
+∼
+FedOP
+12
+10
+1
+No
+98.07
+97.97
+0.44 ↓
+∼
+↑
+FedTP
+12
+12
+1
+Yes
+97.00
+95.71
+16.83 ↓
+37.46 ↓
+∼
+FedTO
+12
+10
+1
+Yes
+62.30
+22.89
+19.18 ↓
+37.46 ↓
+↑
+FedTOP
+12
+10
+1
+Yes
+97.04
+95.96
+19.18 ↓
+37.46 ↓
+↑
+1 FedOP, FedTP, and FedTO refer to ablating the transfer, ordered, and personalized extensions of the FL framework, respectively. 2 Accuracy refers to the
+testing sets of training clients and testing clients, which is described in Section III-A. 3 Time↓ refers to the ratio of reduced training time per client to the
+baseline. 4 Commun↓ refers to ratio of reduced communication consumption to the baseline, which is described in (6).
+(a) FedProx
+(b) FedT
+(c) FedO
+(d) FedTO
+(e) FedProx
+(f) FedT
+(g) FedO
+(h) FedTO
+Fig. 6. Accuracy and loss curves of the FL framework and its extensions on the SFDDD and DriveAct datasets, which is the training process of Algorithm
+1. Personalization does not affect the convergence of the global model in the FL framework.
+After the global model is trained by the training dataset of
+training clients, the final trained global model is shared with
+all clients for personalization. The personalization of the global
+model will only be processed on the training sets, while the
+personalized local model will be tested on the unseen testing
+sets. The FL architectures are established on Pytorch and
+trained on an Intel(R) Core(TM) i9-10850K CPU @ 3.60GHz,
+and a Nvidia GeForce RTX(TM) 3080 GPU.
+B. Ablation Study and Results
+We explore the role of each FedTOP extension on two real-
+world datasets through an ablation study. FedProx is used as a
+baseline for comparison. According to the experimental setup
+described in the previous subsection, the experimental results
+are shown in Table I.
+The results and comparisons for two datasets and three
+extensions are shown in Fig. 6, which is equivalent to demon-
+strating Algorithm 1. By observing the accuracy and loss
+curves on the two datasets, it can be concluded that the
+(a) SFDDD TOP
+(b) DriveAct TOP
+Fig. 7. Testing accuracy of the training and testing clients on both SFDDD
+and DriveAct datasets varies with personalized epoch, which is the testing
+results of Algorithm 2.
+SFDDD dataset with system heterogeneity is fundamentally
+different from the DriveAct dataset without system hetero-
+geneity. It can be clearly seen that the SFDDD dataset
+with system heterogeneity requires more communication to
+
+SFDDD, Client Num: 20, q: 20, μ: 1
+100
+3.0
+2.5
+80
+2.0
+Accuracy
+60
+LOSS
+1.5
+40
+1.0
+0.5
+20
+0.0
+0
+200
+400
+600
+800
+1000
+Communications x Clients × EpochSFDDD, Client Num: 20, q: 20, μu: 1
+3.5
+100
+3.0
+80
+2.5
+Accuracy
+60
+2.0
+LOSS
+1.5
+40
+1.0
+20
+0.5
+0.0
+0
+200
+400
+600
+800
+1000
+Communications × Clients × EpochSFDDD,Client Num: 20,q: 15, μu: 1
+100
+3.0
+80
+2.5
+Accuracy
+2.0
+60
+LOSS
+1.5
+40
+1.0
+0.5
+20
+0.0
+200
+400
+600
+800
+1000
+0
+Communications × Clients × EpochSFDDD,Client Num: 20,q: 15, μu: 1
+100
+3.0
+80
+2.5
+Accuracy
+2.0
+60
+LOSS
+1.5
+40
+1.0
+20
+0.5
+0.0
+0
+200
+600
+400
+800
+1000
+Communications × Clients × EpochDriveAct, Client Num: 12, q: 12, u: 1
+100
+4
+80
+3 
+Accuracy
+60
+LOsS
+2
+40
+1
+20
+0
+0
+100
+200
+300
+400
+500
+600
+Communications × Clients × EpochDriveAct, Client Num: 12, q: 12, u: 1
+100
+3.5
+3.0
+80
+2.5
+Accuracy
+60
+LosS
+2.0
+1.5
+40
+1.0
+20
+0.5
+0.0
+0
+100
+200
+300
+400
+500
+600
+Communications x Clients × EpochDriveAct, Client Num: 12, q: 10, u: 1
+100
+80
+3
+Accuracy
+60
+LOSS
+2
+40
+1
+20
+0
+100
+200
+0
+300
+400
+500
+600
+Communications × Clients × EpochDriveAct, Client Num: 12, q: 10, u: 1
+100
+3.5
+3.0
+80
+2.5
+Accuracy
+60
+Loss
+2.0
+1.5
+40
+1.0
+20
+0.5
+0.0
+200
+100
+300
+400
+500
+600
+0
+Communications x Clients × EpochSFDDD, FedTOP
+100
+95
+90
+Accuracy
+85
+80
+75
+Train
+Test
+70 
+Train
+Test
+65
+4
+5
+1
+2
+3
+Personalization EpochDriveAct, FedTOP
+100
+95
+90
+Accuracy
+85 
+80
+75
+Train
+Test
+70
+Train
+Test
+65
+2
+3
+4
+1
+5
+Personalization EpochIEEE INTERNET OF THINGS JOURNAL
+7
+(a) Trained global model ωT
+(b) Personalization Epoch 1 ωT 1
+(c) Personalization Epoch 3 ωT 3
+(d) Personalization Epoch 5 ωT 5
+(e) Trained global model ωT
+(f) Personalization Epoch 1 ωT 1
+(g) Personalization Epoch 3 ωT 3
+(h) Personalization Epoch 5 ωT 5
+Fig. 8. CAMs of the test clients in SFDDD and DriveAct datasets during the personalization process. (a), (b), (c), and (d) are a test client in the SFDDD
+dataset, which is the same as Fig. 4a. (e), (f), (g), and (h) are a test client in the DriveAct dataset, which is the same as Fig. 4e.
+converge, while the DriveAct dataset without system het-
+erogeneity has a fast convergence speed, especially at the
+first communication. Therefore, for real-world datasets, system
+heterogeneity can be mitigated by more communication times.
+By observing Fig. 6c, 6d, 6g, and 6h, it can be found
+that the ordered-extension diminishes the stability of the
+system. Although the anomalous large-loss local model is
+discarded to reduce the bias of the global model, it also
+increases the variance of the global model resulting in reduced
+generalizability. By observing Fig. 6b, 6d, 6f, and 6h, we
+can see that the effect of transfer-extension is different for
+datasets with and without system heterogeneity. On the one
+hand, transfer-extension increases the variance of the model
+on the SFDDD dataset and leads to a reduced and unstable
+model convergence. On the other hand, transfer-extension
+improves the speed of model convergence on DriveAct, and
+the convergence effect is more stable. The possible reason
+is that the transfer-extension retains only a small number of
+trainable parameters, resulting in the neural network model
+not being able to learn human behavioral features effectively
+in the SFDDD dataset with system heterogeneity. However, for
+the DriveAct dataset without system heterogeneity, the factors
+are constant except for the driver, and the local model does
+not need to focus on these exact same pixels, but only on the
+changing pixels, including objects such as drivers, computers,
+and magazines. Therefore, for the DriveAct dataset, transfer-
+extension can effectively increase convergence and stability.
+The proposed FedTOP framework is able to obtain 92.32%
+and 95.96% accuracy on the SFDDD and DriveAct datasets,
+respectively, when considering five times of personalization
+training. Compared to FedProx as a baseline, FedTOP can
+effectively improve the accuracy by 462% in addition to
+considering a 37.46% reduction in communication resources.
+The results demonstrate the feasibility of the proposed Fed-
+TOP in terms of communication resource saving, accuracy
+improvement, robustness, and cybersecurity.
+C. Performance of Personalized-Extension
+Personalized-extension needs to be further discussed and
+analyzed as the most effective approach to improve accu-
+racy. Based on the division of training and testing clients
+in Section III-A, in this subsection, we further discuss how
+the trained and aggregated global model is adapted to both
+training and testing clients. The results of the personalized-
+extension on the two datasets are shown in Fig. 7 with different
+personalization epochs, which is equivalent to demonstrating
+Algorithm 2. It can be seen that the personalization process
+differs significantly on the datasets with and without system
+heterogeneity, which is similar to the results in Fig. 6. The
+clients in the DriveAct dataset have faster convergence, minor
+accuracy variance, and higher final accuracy. On the contrary,
+the clients in the SFDDD dataset not only converge slower but
+also have an anomalous client with relatively low accuracy.
+The possible reason is that the anomalous client has a huge
+data and system heterogeneity, causing the optimal model to
+deviate significantly far from the aggregated global model.
+Fig. 8 further demonstrates that the trained global model
+repositions the ROI during the personalized training process
+via class activation map (CAM) [41]. The test client of the
+SFDDD dataset can be seen struggling with the personalization
+process. The trained global model focus the ROI on the
+seat backrest, driver’s chest, hand, and knee, and vehicle
+door. Due to the system heterogeneity present in the SFDDD
+dataset, the positions of the driver, seat, and steering wheel,
+as shown in Fig. 8a is different from other clients, as shown
+in Fig. 4b, 4c, and 4d. Therefore, the initial ROI is likely
+to be a driver’s position among other clients. During the five
+personalization training processes, the local model is able to
+effectively reposition the ROI to the driver, which is what
+the personalized-extension is intended to show. Moreover, the
+
+IEEE INTERNET OF THINGS JOURNAL
+8
+personalization process also reduces the number of ROIs while
+targeting more attention to a specific area.
+On the contrary, for the test clients in the DriveAct dataset,
+the adjustment of the ROI is negligible. Note that the ROI does
+not necessarily have to cover the driver’s body or an object
+such as the magazine. The ROI should cover those pixels
+that can distinguish between different activities, such as static
+activities like reading the magazine, and dynamic activities
+like wearing a seatbelt in the DriveAct dataset activity setting.
+These ROIs focus on areas where large differences are likely
+to occur. The fact that the ROIs in the DriveAct dataset cover
+almost the same pixels during the personalization process can
+also prove the negative impact of system heterogeneity on the
+FL framework.
+IV. DISCUSSION
+The two datasets used, SFDDD and DriveAct, still have
+some flaws. First, although the SFDDD dataset takes system
+heterogeneity into account, quite a few drivers collect data
+in the same vehicle, that is, the number of clients is greater
+than the number of users. Therefore, there are still some
+differences between the dataset and the real-world data, which
+leads to the fact that the proposed FedTOP may need more
+communication rounds to achieve similar accuracy on a real-
+world dataset. Second, there is currently no driver monitoring
+dataset with real poisoning data currently existing, resulting
+in the effect of ordered-extension not being reflected. The
+different modalities, positions, and angles of the camera or
+the method of generating fake data may be a hypothesis for
+poisoned data, but it cannot be highlighted as real. Moreover,
+due to road safety guidelines, the current dataset is only driving
+on safe roads or simulated driving. Therefore, the driver’s
+posture, demeanor, facial concentration, etc., are far from the
+real driving behavior. Therefore, there is an urgent need for
+a more realistic dataset that can include camera images of
+different positions and angles, different vehicle scenes, and
+more drivers driving on real roads.
+For a FL framework in IoT, in addition to accuracy being
+the evaluation criterion, factors like communication require-
+ments, robustness, fairness, cybersecurity, etc., also need to
+be considered. Although it seems that transfer and ordered
+extensions may not improve accuracy but rather reduce it in
+the current experimental results, it can potentially improve
+the performance of the FL framework. Therefore, we keep
+two extensions as one of our future directions. Personalized-
+extension is an approach similar to transfer learning and
+incremental learning. On the one hand, the local client is
+incrementally learned based on the trained global model, but it
+does not intentionally retain the previously learned knowledge.
+On the other hand, the global model is transferred to the
+client dataset as in transfer-extension, but the low-level non-
+trainable weights are still pre-trained on ImageNet. Therefore,
+the proposed personalized-extension actually uses the trained
+global model weights to fit different client data, such as
+the reposition of ROIs. Although the personalized-extension
+requires additional training locally for each client, there are
+many benefits, including high accuracy, applicability to non-
+training clients, customization, etc. Conceivably, personalized-
+extension can effectively address the problem of system het-
+erogeneity, e.g., it can be applied to different cameras, camera
+angles, vehicle interiors, etc.
+V. CONCLUSION
+In this paper, we propose a FL framework FedTOP for
+DMA to address the issues of privacy preservation, efficient
+training, communication resource-saving, poisoned data, and
+diversified scenarios. Through the ablation study, the impact,
+role, and performance of three extensions, including trans-
+fer, ordered, and personalized on the model are disclosed.
+Moreover, the experiments demonstrate dramatic differences
+between datasets with and without system heterogeneity. In
+addition to the proposed FedTOP being able to exhibit 92.32%
+and 95.96% accuracy in two datasets for testing clients, it
+is also appreciated that FedTOP reduces communication con-
+sumption by 37.46% and potentially improves cybersecurity.
+The experimental results show that the proposed FedTOP
+is a highly accurate, lightweight, privacy-preserving, robust,
+cybersecure, and universally applicable FL framework for
+potential DMA.
+Future work lies in the continued research of extensions. For
+the ordered-extension, a possible plan is to introduce some ma-
+licious local clients to attack and poison with the global model.
+For example, subjects may not place the camera on the side
+as instructed but place it on the front or behind instead. Such
+outliers may cause the global model to deviate significantly
+from the optimal solution, so in the case, ordered-expansion
+can prevent the deviation of the global model by discarding
+the larger value of the losses. For the transfer-extension, there
+is currently a lack of a general driver monitoring model, so
+we used a model pre-trained on ImageNet. Future work can
+pre-train a driver model ourselves as a base model, which
+will get better performance in DMA. Fig. 1 shows the FL
+framework for foresight in IoV, but the dataset used does not
+contain scenario information such as road, weather, vehicle
+models, etc. Therefore, we expect a well-developed real-world
+dataset to include such scenario information, data and system
+heterogeneity, etc.
+REFERENCES
+[1] Y. Yang, L. Wu, G. Yin, L. Li, and H. Zhao, “A survey on security and
+privacy issues in internet-of-things,” IEEE Internet Things J., vol. 4,
+no. 5, pp. 1250–1258, Apr. 2017.
+[2] J. Cao, Y. Pang, J. Xie, F. S. Khan, and L. Shao, “From handcrafted to
+deep features for pedestrian detection: a survey,” IEEE Trans. Pattern
+Anal. Mach. Intell., Apr. 2021.
+[3] S. Kuutti, S. Fallah, K. Katsaros, M. Dianati, F. Mccullough, and
+A. Mouzakitis, “A survey of the state-of-the-art localization techniques
+and their potentials for autonomous vehicle applications,” IEEE Internet
+Things J., vol. 5, no. 2, pp. 829–846, Mar. 2018.
+[4] Z. Wang, R. Gupta, K. Han, H. Wang, A. Ganlath, N. Ammar, and
+P. Tiwari, “Mobility digital twin: Concept, architecture, case study, and
+future challenges,” IEEE Internet Things J., Mar. 2022.
+[5] A. Hard, K. Rao, R. Mathews, S. Ramaswamy, F. Beaufays, S. Augen-
+stein, H. Eichner, C. Kiddon, and D. Ramage, “Federated learning for
+mobile keyboard prediction,” arXiv preprint arXiv:1811.03604, 2018.
+[6] I. Dayan, H. R. Roth, A. Zhong, A. Harouni, A. Gentili, A. Z. Abidin,
+A. Liu, A. B. Costa, B. J. Wood, C.-S. Tsai et al., “Federated learning
+for predicting clinical outcomes in patients with covid-19,” Nat. Med.,
+vol. 27, no. 10, pp. 1735–1743, Oct. 2021.
+
+IEEE INTERNET OF THINGS JOURNAL
+9
+[7] N. Rieke, J. Hancox, W. Li, F. Milletari, H. R. Roth, S. Albarqouni,
+S. Bakas, M. N. Galtier, B. A. Landman, K. Maier-Hein et al., “The
+future of digital health with federated learning,” NPJ Digit. Med., vol. 3,
+no. 1, pp. 1–7, Sep. 2020.
+[8] M. Hao, H. Li, X. Luo, G. Xu, H. Yang, and S. Liu, “Efficient and
+privacy-enhanced federated learning for industrial artificial intelligence,”
+IEEE Trans. Industr. Inform., vol. 16, no. 10, pp. 6532–6542, Oct. 2019.
+[9] Y. Lu, X. Huang, Y. Dai, S. Maharjan, and Y. Zhang, “Blockchain and
+federated learning for privacy-preserved data sharing in industrial iot,”
+IEEE Trans. Industr. Inform., vol. 16, no. 6, pp. 4177–4186, Sep. 2019.
+[10] Z. Du, C. Wu, T. Yoshinaga, K.-L. A. Yau, Y. Ji, and J. Li, “Federated
+learning for vehicular internet of things: Recent advances and open
+issues,” IEEE open j. Comput. Soc., vol. 1, pp. 45–61, May 2020.
+[11] X. Kong, K. Wang, M. Hou, X. Hao, G. Shen, X. Chen, and F. Xia, “A
+federated learning-based license plate recognition scheme for 5g-enabled
+internet of vehicles,” IEEE Trans. Industr. Inform., vol. 17, no. 12, pp.
+8523–8530, Mar. 2021.
+[12] F. Sattler, S. Wiedemann, K.-R. M¨uller, and W. Samek, “Robust and
+communication-efficient federated learning from non-iid data,” IEEE
+Trans. Neural Netw. Learn. Syst., vol. 31, no. 9, pp. 3400–3413, Nov.
+2019.
+[13] S. P. Karimireddy, S. Kale, M. Mohri, S. Reddi, S. Stich, and A. T.
+Suresh, “Scaffold: Stochastic controlled averaging for federated learn-
+ing,” in International Conference on Machine Learning.
+PMLR, 2020,
+pp. 5132–5143.
+[14] S. Horvath, S. Laskaridis, M. Almeida, I. Leontiadis, S. Venieris, and
+N. Lane, “Fjord: Fair and accurate federated learning under heteroge-
+neous targets with ordered dropout,” Adv. Neural Inf. Process. Syst.,
+vol. 34, pp. 12 876–12 889, 2021.
+[15] B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas,
+“Communication-efficient learning of deep networks from decentralized
+data,” in Artificial intelligence and statistics.
+PMLR, 2017, pp. 1273–
+1282.
+[16] T. Li, A. K. Sahu, M. Zaheer, M. Sanjabi, A. Talwalkar, and V. Smith,
+“Federated optimization in heterogeneous networks,” Proceedings of
+Machine Learning and Systems, vol. 2, pp. 429–450, 2020.
+[17] B. Ghimire and D. B. Rawat, “Recent advances on federated learning
+for cybersecurity and cybersecurity for federated learning for internet of
+things,” IEEE Internet Things J., Feb. 2022.
+[18] T. Li, A. K. Sahu, A. Talwalkar, and V. Smith, “Federated learning:
+Challenges, methods, and future directions,” IEEE Signal Process. Mag.,
+vol. 37, no. 3, pp. 50–60, May 2020.
+[19] S. Niknam, H. S. Dhillon, and J. H. Reed, “Federated learning for
+wireless communications: Motivation, opportunities, and challenges,”
+IEEE Commun. Mag., vol. 58, no. 6, pp. 46–51, Jul. 2020.
+[20] L. Lyu, H. Yu, and Q. Yang, “Threats to federated learning: A survey,”
+arXiv preprint arXiv:2003.02133, Mar. 2020.
+[21] P. Kairouz, H. B. McMahan, B. Avent, A. Bellet, M. Bennis, A. N.
+Bhagoji, K. Bonawitz, Z. Charles, G. Cormode, R. Cummings et al.,
+“Advances and open problems in federated learning,” Found. Trends
+Mach. Learn., vol. 14, no. 1–2, pp. 1–210, Jun. 2021.
+[22] Q. Li, Z. Wen, Z. Wu, S. Hu, N. Wang, Y. Li, X. Liu, and B. He, “A
+survey on federated learning systems: vision, hype and reality for data
+privacy and protection,” IEEE Trans. Knowl. Data Eng., Nov. 2021.
+[23] L. Zhang, H. Saito, L. Yang, and J. Wu, “Privacy-preserving federated
+transfer learning for driver drowsiness detection,” IEEE Access, vol. 10,
+pp. 80 565–80 574, Jul. 2022.
+[24] Z. Su, Y. Wang, T. H. Luan, N. Zhang, F. Li, T. Chen, and H. Cao,
+“Secure and efficient federated learning for smart grid with edge-cloud
+collaboration,” IEEE Trans. Industr. Inform., vol. 18, no. 2, pp. 1333–
+1344, Jul. 2021.
+[25] G. Sun, Y. Cong, J. Dong, Q. Wang, L. Lyu, and J. Liu, “Data poisoning
+attacks on federated machine learning,” IEEE Internet Things J., Nov.
+2021.
+[26] J. Zhang, B. Chen, X. Cheng, H. T. T. Binh, and S. Yu, “Poisongan:
+Generative poisoning attacks against federated learning in edge com-
+puting systems,” IEEE Internet Things J., vol. 8, no. 5, pp. 3310–3322,
+Sep. 2020.
+[27] A. Z. Tan, H. Yu, L. Cui, and Q. Yang, “Towards personalized federated
+learning,” IEEE Trans. Neural Netw. Learn. Syst., Mar. 2022.
+[28] A. Fallah, A. Mokhtari, and A. Ozdaglar, “Personalized federated
+learning: A meta-learning approach,” arXiv preprint arXiv:2002.07948,
+Feb. 2020.
+[29] Q. Wu, X. Chen, Z. Zhou, and J. Zhang, “Fedhome: Cloud-edge based
+personalized federated learning for in-home health monitoring,” IEEE
+Trans. Mob. Comput., Dec. 2020.
+[30] A. Kashevnik, I. Lashkov, and A. Gurtov, “Methodology and mobile
+application for driver behavior analysis and accident prevention,” IEEE
+Trans. Intell. Transp. Syst., vol. 21, no. 6, pp. 2427–2436, Jun. 2019.
+[31] S. Zepf, J. Hernandez, A. Schmitt, W. Minker, and R. W. Picard, “Driver
+emotion recognition for intelligent vehicles: A survey,” ACM Comput.
+Surv., vol. 53, no. 3, pp. 1–30, Jun. 2020.
+[32] Y. Xing, C. Lv, H. Wang, H. Wang, Y. Ai, D. Cao, E. Velenis, and F.-Y.
+Wang, “Driver lane change intention inference for intelligent vehicles:
+framework, survey, and challenges,” IEEE Trans. Veh. Technol., vol. 68,
+no. 5, pp. 4377–4390, Mar. 2019.
+[33] A. Masood, D. S. Lakew, and S. Cho, “Security and privacy challenges
+in connected vehicular cloud computing,” IEEE Commun. Surv., vol. 22,
+no. 4, pp. 2725–2764, Jul. 2020.
+[34] S. Kuutti, R. Bowden, Y. Jin, P. Barber, and S. Fallah, “A survey of
+deep learning applications to autonomous vehicle control,” IEEE Trans.
+Intell. Transp. Syst., vol. 22, no. 2, pp. 712–733, Jan. 2020.
+[35] M. Ramzan, H. U. Khan, S. M. Awan, A. Ismail, M. Ilyas, and A. Mah-
+mood, “A survey on state-of-the-art drowsiness detection techniques,”
+IEEE Access, vol. 7, pp. 61 904–61 919, May 2019.
+[36] K. Doshi and Y. Yilmaz, “Federated learning-based driver activity recog-
+nition for edge devices,” in Proceedings of the IEEE/CVF Conference
+on Computer Vision and Pattern Recognition, 2022, pp. 3338–3346.
+[37] C. Zhao, Z. Gao, Q. Wang, K. Xiao, Z. Mo, and M. J. Deen, “Fedsup:
+A communication-efficient federated learning fatigue driving behaviors
+supervision approach,” Future Gener. Comput. Syst., vol. 138, pp. 52–60,
+Jan. 2023.
+[38] K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image
+recognition,” in Proceedings of the IEEE conference on computer vision
+and pattern recognition, 2016, pp. 770–778.
+[39] State
+Farm,
+“State
+farm
+distracted
+driver
+detection,”
+Apr
+2016.
+[Online].
+Available:
+https://www.kaggle.com/competitions/
+state-farm-distracted-driver-detection/overview/description
+[40] M. Martin, A. Roitberg, M. Haurilet, M. Horne, S. Reiß, M. Voit, and
+R. Stiefelhagen, “Drive&act: A multi-modal dataset for fine-grained
+driver behavior recognition in autonomous vehicles,” in Proceedings of
+the IEEE/CVF International Conference on Computer Vision, 2019, pp.
+2801–2810.
+[41] D. Omeiza, S. Speakman, C. Cintas, and K. Weldermariam, “Smooth
+grad-cam++: An enhanced inference level visualization technique
+for
+deep
+convolutional
+neural
+network
+models,”
+arXiv
+preprint
+arXiv:1908.01224, 2019.
+Liangqi Yuan (S’22) received the B.E. degree from
+the Beijing Information Science and Technology
+University, Beijing, China, in 2020, and the M.Sc.
+degree from the Oakland University, Rochester, MI,
+USA, in 2022. He is currently pursuing the Ph.D.
+degree with the School of Electrical and Computer
+Engineering, Purdue University, West Lafayette, IN,
+USA. His research interests are in the areas of
+sensors, the internet of things, human–computer
+interaction, signal processing, and machine learning.
+Lu Su (M’15) is an associate professor in the School
+of Electrical and Computer Engineering at Purdue
+University. His research interests are in the gen-
+eral areas of Internet of Things and Cyber-Physical
+Systems, with a current focus on wireless, mobile,
+and crowd sensing systems. He received Ph.D. in
+Computer Science, and M.S. in Statistics, both from
+the University of Illinois at Urbana-Champaign, in
+2013 and 2012, respectively. He has also worked
+at IBM T. J. Watson Research Center and National
+Center for Supercomputing Applications. He has
+published more than 100 papers in referred journals and conferences, and
+serves as an associate editor of ACM Transactions on Sensor Networks.
+He is the recipient of NSF CAREER Award, University at Buffalo Young
+Investigator Award, ICCPS’17 best paper award, and the ICDCS’17 best
+student paper award. He is a member of ACM and IEEE.
+
+IEEE INTERNET OF THINGS JOURNAL
+10
+Ziran Wang (S’16-M’19) received the Ph.D. de-
+gree from the University of California, Riverside in
+2019. He is an Assistant Professor in the College
+of Engineering at Purdue University, and was a
+Principal Researcher at Toyota Motor North Amer-
+ica. He serves as Founding Chair of IEEE Techni-
+cal Committee on Internet of Things in Intelligent
+Transportation Systems, and Associate Editor of
+four academic journals, including IEEE Internet of
+Things Journal and IEEE Transactions on Intelligent
+Vehicles. His research focuses on automated driving,
+human-autonomy teaming, and digital twin.
+
diff --git a/wNE3T4oBgHgl3EQf-wup/content/tmp_files/load_file.txt b/wNE3T4oBgHgl3EQf-wup/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8cac8b49cc769d24dded34a592770577e382158c
--- /dev/null
+++ b/wNE3T4oBgHgl3EQf-wup/content/tmp_files/load_file.txt
@@ -0,0 +1,984 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf,len=983
+page_content='IEEE INTERNET OF THINGS JOURNAL  1  Federated Transfer-Ordered-Personalized Learning  for Driver Monitoring Application  Liangqi Yuan, Student Member, IEEE, Lu Su, Member, IEEE, Ziran Wang, Member, IEEE  Abstract—Federated learning (FL) shines through in the in-  ternet of things (IoT) with its ability to realize collaborative  learning and improve learning efficiency by sharing client model  parameters trained on local data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Although FL has been suc-  cessfully applied to various domains, including driver monitoring  application (DMA) on the internet of vehicles (IoV), its usages  still face some open issues, such as data and system heterogene-  ity, large-scale parallelism communication resources, malicious  attacks, and data poisoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' This paper proposes a federated  transfer-ordered-personalized learning (FedTOP) framework to  address the above problems and test on two real-world datasets  with and without system heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The performance of the  three extensions, transfer, ordered, and personalized, is compared  by an ablation study and achieves 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='32% and 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='96% accuracy  on the test clients of two datasets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Compared to  the baseline, there is a 462% improvement in accuracy and a  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46% reduction in communication resource consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The  results demonstrate that the proposed FedTOP can be used as a  highly accurate, streamlined, privacy-preserving, cybersecurity-  oriented, personalized framework for DMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Index Terms—Federated learning, internet of things (IoT),  driver monitoring, privacy protection, personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' INTRODUCTION  W  ITH the rapid development of sensing, computing,  and communication technologies, the internet of things  (IoT) is a popular solution to solve the problems in industry,  agriculture, energy, transportation, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' However, privacy is-  sues in IoT are often a significant concern have been raised  due to the intrusive behavior of sensors [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Specifically for the  internet of vehicles (IoV), it massively parallels each vehicle  and various sensors it carries, including global positioning  system (GPS), radar, camera, light detection and ranging  (LiDAR), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', enabling pedestrian detection [2], automated  driving [3], mobility digital twins [4], and other transportation  applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Federated learning (FL) has received extensive  attention for protecting user privacy by sharing only model  weights and not including users’ raw data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' FL is widely known  for its successful business case in Google mobile keyboard  prediction [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Nowadays, It has also become one of the  mainstream and thriving solutions for privacy protection and  efficient learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Federated Learning and Related Work  FL is a potentially feasible solution to the privacy problem  in IoT, which is able to avoid the proliferation, distribution,  Manuscript received January 11, 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yuan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Su, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang are with the College of Engineering, Purdue  University, West Lafayette, IN 47907, USA (e-mail: yuan383@purdue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='edu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  lusu@purdue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='edu;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' ryanwang11@hotmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='com).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  and exchange of local client data by sharing model parameters  after training the model on local client data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' FL frameworks are  widely used in healthcare [6], [7], industrial [8], [9], IoV [10],  [11], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', due to their usages of large scale and personalized  data in an efficient and privacy-preserving way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Although FL  has significant contributions to massively parallel devices and  computations, it still has a notable drawback in that it cannot  efficiently handle non-independent and identically distributed  (non-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=') data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' It is required to customize the applicable FL  framework according to the features, resources, and constraints  possessed by users, data, clients, and servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Non-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' data and heterogeneity have always been a chal-  lenge and a key to research in FL [12]–[14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Non-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' data is a  common phenomenon for real-world clients that are scattered  and not interoperable: Taking IoV as an example, each driver  is heterogeneous as a client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' FedAvg [15], as one of the first  proposed feasibility methods, has been the subject and center  of research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' FedAvg averages all local models to get the global  model so that the local model may deviate far from the global  optimum in the parameter space leading to some limitations  in FedAvg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' It is necessary to ensure that the local model does  not deviate from the global model (prevent overfitting) and,  simultaneously, that the local model can effectively learn the  local client dataset (prevent underfitting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Based on FedAvg,  FedProx [16] is proposed to limit the deviation of the local  model from the global model by adding a proximal term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Besides considering accuracy, the FL framework in IoT  should not underestimate communication and training resource  constraints, cybersecurity, and ubiquity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Some of the recent  surveys summarized challenges, threats, and solutions of the  FL decentralization paradigm for IoT, including limited com-  puting power, unreliable and limited availability, local training,  accuracy, communication overhead, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' [17]–[22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Transfer and edge learning are popular solutions to re-  duce communication resource consumption in FL frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' [23] performed a federated transfer learning  framework to detect driver drowsiness, where transfer learning  was employed to save the communication cost in the FL frame-  work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Su et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' [24] introduced edge servers as a collaborative  mechanism, where aggregation of local models was aggregated  in the edge server and then sent to the global server to  aggregate the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The benefit of the additional edge  server was that the communication between massively parallel  clients and the edge server was consumed because the edge  server was geographically close to the clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' High latency  and intermittent connections could be mitigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In addition,  the edge server could also provide personalized aggregated  local models due to the similarity of geographically adjacent  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='04829v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='LG]  12 Jan 2023  IEEE INTERNET OF THINGS JOURNAL  2  clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Cyber attack is a problem that cannot be ignored for FL  frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' [25] developed an attack method for  FL framework in IoT, in which a bi-level optimization frame-  work was proposed to compute optimal poisoning attacked  FL framework, including direct, indirect, and hybrid attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Meanwhile, Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' [26] utilized a generative adversarial  network (GAN)-based approach to attack the FL framework,  especially since the attacker did not need any prior knowledge  to carry out the attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Personalization is a common approach for FL frameworks  to improve applicability for diverse users [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Fallah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [28] proposed a personalized variant of the FL, which allowed  clients to perform several gradient descent iterations on an  initial global model using local data to obtain a personalized  local model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' [29] explored a cloud edge-based per-  sonalized FL framework for in-home health monitoring, which  addressed the problem that a single global model performed  poorly on a specific client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Since the global model could only  capture the common features of all clients, it lacked the ability  to analyze fine-grained information of specific clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Federated Learning in Driver Monitoring Applications  Driver monitoring application (DMA) in IoV is adopted as  the research direction in this paper due to its real and visual  image data, valuable application scenarios, and relatively blank  research area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' DMA also has challenges in terms of driver  privacy issues, communication, and diversity and personalized  driver behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Related DMA literature covers a wide variety  of devices with algorithms to achieve different purposes, such  as dangerous state detection [30], driver emotion recognition  [31], driver lane change inference [32], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Compared to other  methods [33]–[35], FL not only highlights efficient learning  but also effectively protects the privacy of driver, passenger,  and pedestrian biometric information, driving routes, and  confidential driving areas such as military installations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  In this paper, we introduce and adapt FL to DMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Although  some FL frameworks exist for DMA, they all suffer from  some critical problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Doshi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' [36] proposed a FL edge-  device framework to obtain a global model by aggregation  feature representations and obtained considerable accuracy in  recognizing driver activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' For the i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' setting, the dataset  was partitioned for each edge node in a random way, while for  the non-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' setting, the dataset was assigned selectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhao  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' [37] proposed a FL framework to monitor fatigue driving,  where the non-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' setting was simulated by controlling the  number of images per client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The above FL frameworks for  DMA did not really take into account the actual situation  of the application but artificially created a simulation sce-  nario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, there is an urgent need for realistic analysis  and research for real-world DMA, considering that the user  (driver) should exist independently and be non-interoperable  with different clients (vehicles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Moreover, in addition to the  necessity of test datasets, the test client is also a critical  evaluation criterion, which can reflect the universality of  the FL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' We summarize the existing neglects and  challenges in the current FL for DMA framework as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Structure illustration of a FL framework for IoV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The server interacts  with the local client and saves different scenarios as different models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Trans-  parent neurons are non-trainable parameters, and non-transparent neurons are  trainable parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Clients in FL for DMA frameworks are often defined  in unreasonable and incomprehensible forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' A real and  natural definition of a client should be a driver or a  vehicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  There is no paper proposing to test on a testing client  (not involved in training process), which lacks universal  testing for the FL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  For DMA scenario, there is a great diversity and individu-  ality of driver behaviors, postures, and facial expressions,  which call for more presonalized studies than other  general IoV scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Similarly, DMA also has diverse scenarios, including  diverse vehicle models, interior colors, seat positions,  etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', which will greatly increase the learning difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Proposed Solution and Contribution  In this paper, we aim to propose a FL framework applicable  and specific to practical applications in IoV, especially DMA,  where an imaginary FL framework for IoV is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Each local client, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vehicle, includes a training module  and a perception module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The training module uploads the  model parameters to the server after learning and training the  local data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' After aggregation and optimizing the parameters  of the local client models, the server downloads the global  model parameters to the perception module in the local client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Moreover, transfer learning can be used to reduce the number  of trainable parameters, resulting in reduced communication  consumption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The server can save different global models for  different scenarios, such as road types, weather types, and  vehicle types, so that the model can have better applicability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Therefore, a federated transfer-ordered-personalized learn-  ing (FedTOP) framework is proposed to address the problems  of accuracy, cybersecurity, communication resources, and di-  versified scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In addition to the transfer-extension shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1, the FedTOP framework also enhances robustness and  cybersecurity by orderly dropout clients due to their possible  overfitting and poisoning of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Furthermore, the FedTOP  framework is able to remarkably improve accuracy by adapting  all clients through personalized-extension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The contributions  of this paper are:  Road Model  Training  Upload  Perception  Download  Server  Weather Model  Local Clients  Vehicle ModelIEEE INTERNET OF THINGS JOURNAL  3  For realistic problems and usage scenarios in DMA,  we propose a feasible FL framework FedTOP, realizing  privacy protection, high accuracy, low communication  requirements, cybersecurity, and pervasiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' To the  best of our knowledge, this is one of the first papers to  establish a feasible FL framework for DMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The proposed FedTOP framework is tested on two real-  world driver monitoring datasets with and without system  heterogeneity, systematically characterizing system het-  erogeneity in real-world datasets and achieving consider-  able accuracies with 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='32% and 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='96%, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The experiments highlight a realistic and natural client  setup, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', drivers and vehicles are naturally formed as  clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Moreover, we innovatively propose evaluation  criteria for training and testing clients to test the gen-  eralization ability of the proposed FedTOP on different  clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Through an ablation study, we demonstrate the perfor-  mance and utility of the transfer, ordered, and person-  alized extensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' These detachable extensions can be  selectively installed according to the task description, and  the FL framework combined with different extensions can  effectively adapt to different IoT application scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The presentation of this paper is as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The problem  statement and proposed solution are described in Section  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The experimental setup, heterogeneity, and results have  been demonstrated in Section III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Section IV discusses the  performances of three extensions of the proposed framework,  followed by Section V summarizing the paper and expounding  on future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' METHODOLOGIES  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Problem Statement  FL framework protects privacy, increases training efficiency,  and saves communication resources by sharing only model  parameters in IoT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In this paper, the FL framework is used  to solve a driver activity classification task in DMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Clients  in real-world IoT are independent and heterogeneous due  to the presence of only a minimal number of users per  client.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Considering the more general application scenarios, the  global model ω for training clients C aggregation needs to  be compatible with non-training clients C′ in addition to C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The data of each client Dc is non-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' when the data is not  interoperable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' We can consider a nested model  Lc = ωc(Dc),  (1)  where ωc is the classifier model corresponding to client c ∈ C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Dc ∈ Rnc×i×j×d is the image set with nc samples, i rows,  j columns, and d channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Lc ∈ Znc is the corresponding  label set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The global model ω are obtained by aggregating,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', averaging the weights of the local models,  ω =  �  c∈C  pcωc = E[ωc|c ∈ C],  (2)  where pc ∈ [0, 1] is a weight density function of clients, for  which � pc = 1, pc will be assigned according to the number  of samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, the optimization problem of the FL  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Illustration of the FL algorithm finds the optimal global model solution  in the parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The shaded areas are accuracy contour areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The  farther the optimal local model dissociates from the global model, the lower  the client accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Local models enclosed by shaded areas have similar  accuracies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  algorithm can be formulated as minimizing the global loss,  which is equivalent to minimizing the sum of the local losses,  min  ω L(ω) =  �  c∈C  pcL(ωc) = E[L(ωc)|c ∈ C],  (3)  where L is the loss function that will be assigned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  For real-world classification tasks, we assume that the  distribution of the local model in the parameter space presents  a multivariate Normal distribution ωc ∼ N  �  µω, σ2  ω  �  , where  µω is mean of all local models, and σ2  ω is the variance  of all local models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2 shows the process of the FL  algorithm finding the optimal solution of the global model in  the parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' After the initial model is trained locally,  communicated, and aggregated globally, the final global model  will be obtained by averaging and can be estimated as ˆω = µω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Especially in the large-scale parallel application scenarios of  IoT, according to the law of large numbers, ˆω = µω = ω∗ is  an unbiased estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  However, there are still some defects in the method of ob-  taining the global model through average aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Firstly,  we can confirm that there is enormous system heterogeneity  in IoT, and the global model cannot ensure high accuracy for  all clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Secondly, we inevitably need a measure to prevent  system heterogeneity and potential attacks and poisoning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' As  shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2, the farther the optimal local model is from  the global model, the lower the accuracy, and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Therefore, it is conceivable that in the FL problem with  heterogeneity, the clients’ accuracy will also obey a Normal  distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Proposed Solution  According to the problem statement, we propose a FedTOP  algorithm to address all of the following issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' First, the  aggregation of global models needs to be more stable, which  can be achieved by preventing the overfitting of local models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Second, considering the actual communication situation in IoT,  we propose transfer learning to reduce the trainable parameters  and hence reduce communication requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Third, the  global model should have the ability to resist interference,  attacks, and data poisoning, which can be achieved by orderly  dropping out local models with large loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Fourth, a global  model cannot take into account the situation of all clients,  especially in the presence of data and system heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Therefore, we recommend personalizing the global model to  suit all the training and testing clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Aggregation  Aggregation  Communication  Communication  70%  50%  t=  t= T  Optimal local model  Estimated local model  Initial model  Aggregated global modelIEEE INTERNET OF THINGS JOURNAL  4  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The global model is shared with training and testing clients after  iterative training and optimization on massively parallel training clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Both  training and testing clients are personalized locally and then get results on  the testing set, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Among them, some attack or poison clients will  be discarded, such as Client 2 has a large loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  We refer to FedProx [16] using a proximal term to prevent  local models ωc from deviating from the global model ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  In which, the proximal item Lp that computes the distance  between the local and global model is added to the loss  function,  Lp = µ  2 ∥ωc − ω∥2,  (4)  where µ is deviation coefficient, ωc is local client model  parameters, and ω is global model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The overall  loss function can be updated as  L = Ll + Lp,  (5)  where Ll is the loss between the true labels and the predicted  labels, such as the negative log-likelihood loss used in our  experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Transfer-extension is a common and popular solution in  many learning frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In particular, FL framework is  favored because it can effectively reduce local client training  resources and communication resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In our experiments,  the base model is ResNet34 [38] pre-trained on ImageNet,  where only the last residual block and fully connected layer  are trainable parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Although ImageNet is a large object  classification dataset far from DMA images, the lower layers  are similar for convolutional neural networks (CNN) and are  used to extract image features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, the upper layers  that are used to obtain high-level features and representations  are given more attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The ratio of reduced communication  resource requirement in the network is approximately equal to  the ratio of non-trainable parameters to total parameters,  Commun↓ ≈ |ωnon-trainable|  |ω|  = 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46%,  (6)  where Commun↓ is the reduced communication resource re-  quirement, |ωnon-trainable| is the number of non-trainable model  parameters, and |ω| is the total number of the model param-  eters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, the transfer-extension reduces the commu-  nication requirement by 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46% by decreasing the trainable  parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Ordered-extension is for orderly dropout clients with enor-  mous variance, which may be subject to malicious attacks and  poisoning, extensive data and system heterogeneity, and model  underfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' These local clients with large losses should be  discarded to enhance the applicability of the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Ordered-extension not only enhances accuracy and robustness  Algorithm 1 FedTOP  Input: Communication rounds (T), training client set (C), training  epoch (E), initial global model (ω1), loss function (Ll), deviation  coefficient (µ), number of ordered clients (q)  Output: Trained global model (ωT )  for t = 1 to T − 1 do  for c ∈ C in parallel do  for e = 1 to E − 1 do  Backpropagate the loss function and update the local  model ωte+1  c  ← arg minωte  c Ll(ωte  c ) + µ  2 ∥ωte  c − ωt∥2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  end for  Update the local model ωt  c ← ωtE  c .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Client sends ωt  c to the server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  end for  Find a set Ct  q of top-q clients in Ct in term of loss values:  Ct ∈ q − arg minc∈Ct L(ωt  c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Server aggregates the ω as ωt+1 ← 1  q  �  q∈Ctq ωt  q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  end for  Send ωT to clients c ∈ {C, C′} do personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Algorithm 2 Personalized-extension  Input: Training client set (C), testing client set (C′), personal-  ization epoch (E), Trained global model (ωT ), loss function (Ll)  Output: Personalized local model (ωc)  for c ∈ {C, C′} do  for e = 1 to E − 1 do  Backpropagate the loss function and update the local model  ωT e+1  c  ← arg minωT e  c  Ll(ωT e  c ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  end for  Update the personalized local model ωc ← ωT E  c  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  end for  but also secures the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' After all of the clients  upload the local model parameters and the final training loss  to the server, the server only aggregates the q ∈ N ≤ |C| local  models with the lowest loss as the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The set of q  local models can be expressed as  Cq ∈ q − arg min  c∈C L(ωc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  (7)  Personalized-extension is to promote, popularize, and adapt  the global model to the heterogeneity of all clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' As shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2, the global model cannot be applied to all clients due  to the ubiquitous heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The region of interest (ROI)  of the model may vary depending on system heterogeneity,  such as different camera angles, seat positions, and vehicle  structures, resulting in differences in the relative position  of the driver in the image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' However, personalized-extension  proposes to train the global model several times in each  client to obtain a more personalized local model to improve  accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' On the one hand, compared with the traditional  FL algorithm, the personalized-extension can significantly and  effectively improve accuracy and confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' On the other  hand, compared to the method that only trains locally, the  personalized FL algorithm improves the training efficiency and  avoids the overfitting of the local model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In particular, the  personalized FL algorithm can help and generalize to other  non-training clients C′, which may have minimal training  resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' After receiving the global model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' the non-training  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='clients C′ can obtain a highly accurate and reliable local model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Client 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Test Client 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Upload  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Download  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Download  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Client 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Initial Global Model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Global Model  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Test Client 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Aggregate  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='··  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Client IC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Test ClientIC  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='PersonalizationIEEE INTERNET OF THINGS JOURNAL  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='(a) SFDDD texting - right 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='(b) SFDDD texting - right 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='(c) SFDDD texting - right 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='(d) SFDDD texting - right 4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='(e) DriveAct magazine 1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='(f) DriveAct magazine 2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='(g) DriveAct magazine 3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='(h) DriveAct magazine 4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Exampled activities of four drivers in each of SFDDD and DriveAct datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  (a) SFDDD  (b) DriveAct  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Sampled client image histograms of SFDDD and DriveAct datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  with minimal training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The system diagram of the proposed  FedTOP is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 3  For the proposed FedTOP framework, the client communi-  cates with the server T rounds, and all clients C train E epochs  in parallel between each communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' For our preliminary  experiments, we set T = 10 and E = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' For transfer-extension,  the local model is the transfer learning model of ResNet34  pre-trained on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Only the last residual block and fully  connected layer are set as trainable parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In addition, we  add an additional fully connected layer to match the number of  our classification categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Based on FedProx, the activation  function of the last layer is LogSoftmax, and the setting of  the loss function Ll is a negative log-likelihood loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' ω1 is the  initial model parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The proposed FedTOP is described in  Algorithm 1, and the personalization process is described in  Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' EXPERIMENT AND RESULTS  Considering the data and system heterogeneity, experiments  are conducted on two open real-world driver monitoring  datasets, including State Farm Distracted Driver Detection  (SFDDD) [39] and DriveAct [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In addition to comparing  with FedProx as a baseline, this paper also compares the per-  formance of the transfer, ordered, and personalized extensions  through an ablation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Experiment Setup  To compare the impact of system heterogeneity on FL  frameworks, the proposed FedTOP is tested on driver monitor-  ing datasets with and without system heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' SFDDD  dataset includes 26 drivers and 10 activities, and DriveAct  dataset includes 15 drivers and 12 activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' SFDDD dataset  considers system heterogeneity, that is, different drivers have  different vehicles, different seat positions, different camera  angles, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4a, 4b, 4c, and 4d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' DriveAct  dataset does not take into account system heterogeneity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', all  subjects had their data collected in the same system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Recorded  from the same camera angle, different drivers read the same  magazine in the same vehicle, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4e, 4f, 4g, and  4h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  To show more clearly and visually the heterogeneity be-  tween different clients in the two datasets, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 5 shows  histograms of the sample images of the two datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' It can be  seen that the SFDDD dataset with system heterogeneity has a  more considerable difference in the distribution of histograms  than the DriveAct dataset without system heterogeneity, and  the mean value of the SFDDD images is larger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The possible  reason is that the vehicle interiors of the DriveAct dataset view  are darker, resulting in most of the pixel values being lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Therefore, the FL framework may be more challenged by the  scene information when training on the SFDDD dataset, such  as different vehicle interiors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Clients are naturally divided based on the drivers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In order  to better demonstrate the role of personalized-extension, the  datasets are first divided into training clients and testing clients  at a ratio of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='8, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='2, with |CSFDDD| = 20, |C′  SFDDD| = 6,  |CDriveAct| = 12, and |C′  DriveAct| = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' And then, the datasets  for each client are divided into a training set, verification set,  and testing set at a ratio of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='7, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='15, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='15, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Sampled Histogram of SFDDD  Client 1  Client 2  1000  Client 3  Client 4  800  Fregquency  600  400  200  0  50  100  150  200  250  0  pixel valueSampled Histogram of DriveAct  Client 1  Client 2  1000  Client 3  Client 4  800  Fregquency  600  400  200  0  50  100  150  200  250  0  pixel valueIEEE INTERNET OF THINGS JOURNAL  6  TABLE I  PERFORMANCE OF FEDTOP AND ABLATION STUDY ON SFDDD AND DRIVEACT DATASETS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Dataset  Method 1  |C|  q  µ  Transfer  Accuracy (%) 2  Time↓ (%) 3  Commun↓ (%) 4  Cybersecurity  Training  Testing  SFDDD  FedProx (baseline)  20  20  1  No  54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='63  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='44  ∼  ∼  ∼  FedOP  20  15  1  No  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='69  96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='37  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='45 ↓  ∼  ↑  FedTP  20  20  1  Yes  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='76  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='8  17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='3 ↓  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46 ↓  ∼  FedTO  20  15  1  Yes  46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='16  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='43  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='91 ↓  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46 ↓  ↑  FedTOP  20  15  1  Yes  94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='65  92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='32  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='91 ↓  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46 ↓  ↑  DriveAct  FedProx (baseline)  12  12  1  No  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='18  23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='96  ∼  ∼  ∼  FedOP  12  10  1  No  98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='07  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='97  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='44 ↓  ∼  ↑  FedTP  12  12  1  Yes  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='00  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='71  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='83 ↓  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46 ↓  ∼  FedTO  12  10  1  Yes  62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='30  22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='89  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='18 ↓  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46 ↓  ↑  FedTOP  12  10  1  Yes  97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='04  95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='96  19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='18 ↓  37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46 ↓  ↑  1 FedOP, FedTP, and FedTO refer to ablating the transfer, ordered, and personalized extensions of the FL framework, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2 Accuracy refers to the  testing sets of training clients and testing clients, which is described in Section III-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 3 Time↓ refers to the ratio of reduced training time per client to the  baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4 Commun↓ refers to ratio of reduced communication consumption to the baseline, which is described in (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  (a) FedProx  (b) FedT  (c) FedO  (d) FedTO  (e) FedProx  (f) FedT  (g) FedO  (h) FedTO  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Accuracy and loss curves of the FL framework and its extensions on the SFDDD and DriveAct datasets, which is the training process of Algorithm  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Personalization does not affect the convergence of the global model in the FL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  After the global model is trained by the training dataset of  training clients, the final trained global model is shared with  all clients for personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The personalization of the global  model will only be processed on the training sets, while the  personalized local model will be tested on the unseen testing  sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The FL architectures are established on Pytorch and  trained on an Intel(R) Core(TM) i9-10850K CPU @ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='60GHz,  and a Nvidia GeForce RTX(TM) 3080 GPU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ablation Study and Results  We explore the role of each FedTOP extension on two real-  world datasets through an ablation study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' FedProx is used as a  baseline for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' According to the experimental setup  described in the previous subsection, the experimental results  are shown in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The results and comparisons for two datasets and three  extensions are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 6, which is equivalent to demon-  strating Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' By observing the accuracy and loss  curves on the two datasets, it can be concluded that the  (a) SFDDD TOP  (b) DriveAct TOP  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Testing accuracy of the training and testing clients on both SFDDD  and DriveAct datasets varies with personalized epoch, which is the testing  results of Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  SFDDD dataset with system heterogeneity is fundamentally  different from the DriveAct dataset without system hetero-  geneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' It can be clearly seen that the SFDDD dataset  with system heterogeneity requires more communication to  SFDDD, Client Num: 20, q: 20, μ: 1  100  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  Accuracy  60  LOSS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  0  200  400  600  800  1000  Communications x Clients × EpochSFDDD, Client Num: 20, q: 20, μu: 1  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  100  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  Accuracy  60  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  LOSS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  0  200  400  600  800  1000  Communications × Clients × EpochSFDDD,Client Num: 20,q: 15, μu: 1  100  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  Accuracy  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  60  LOSS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  200  400  600  800  1000  0  Communications × Clients × EpochSFDDD,Client Num: 20,q: 15, μu: 1  100  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  Accuracy  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  60  LOSS  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  0  200  600  400  800  1000  Communications × Clients × EpochDriveAct, Client Num: 12, q: 12, u: 1  100  4  80  3  Accuracy  60  LOsS  2  40  1  20  0  0  100  200  300  400  500  600  Communications × Clients × EpochDriveAct, Client Num: 12, q: 12, u: 1  100  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  Accuracy  60  LosS  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  0  100  200  300  400  500  600  Communications x Clients × EpochDriveAct, Client Num: 12, q: 10, u: 1  100  80  3  Accuracy  60  LOSS  2  40  1  20  0  100  200  0  300  400  500  600  Communications × Clients × EpochDriveAct, Client Num: 12, q: 10, u: 1  100  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  80  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  Accuracy  60  Loss  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  40  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  20  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='0  200  100  300  400  500  600  0  Communications x Clients × EpochSFDDD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' FedTOP  100  95  90  Accuracy  85  80  75  Train  Test  70  Train  Test  65  4  5  1  2  3  Personalization EpochDriveAct,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' FedTOP  100  95  90  Accuracy  85  80  75  Train  Test  70  Train  Test  65  2  3  4  1  5  Personalization EpochIEEE INTERNET OF THINGS JOURNAL  7  (a) Trained global model ωT  (b) Personalization Epoch 1 ωT 1  (c) Personalization Epoch 3 ωT 3  (d) Personalization Epoch 5 ωT 5  (e) Trained global model ωT  (f) Personalization Epoch 1 ωT 1  (g) Personalization Epoch 3 ωT 3  (h) Personalization Epoch 5 ωT 5  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' CAMs of the test clients in SFDDD and DriveAct datasets during the personalization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' (a), (b), (c), and (d) are a test client in the SFDDD  dataset, which is the same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' (e), (f), (g), and (h) are a test client in the DriveAct dataset, which is the same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  converge, while the DriveAct dataset without system het-  erogeneity has a fast convergence speed, especially at the  first communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, for real-world datasets, system  heterogeneity can be mitigated by more communication times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  By observing Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 6c, 6d, 6g, and 6h, it can be found  that the ordered-extension diminishes the stability of the  system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Although the anomalous large-loss local model is  discarded to reduce the bias of the global model, it also  increases the variance of the global model resulting in reduced  generalizability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' By observing Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 6b, 6d, 6f, and 6h, we  can see that the effect of transfer-extension is different for  datasets with and without system heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' On the one  hand, transfer-extension increases the variance of the model  on the SFDDD dataset and leads to a reduced and unstable  model convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' On the other hand, transfer-extension  improves the speed of model convergence on DriveAct, and  the convergence effect is more stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The possible reason  is that the transfer-extension retains only a small number of  trainable parameters, resulting in the neural network model  not being able to learn human behavioral features effectively  in the SFDDD dataset with system heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' However, for  the DriveAct dataset without system heterogeneity, the factors  are constant except for the driver, and the local model does  not need to focus on these exact same pixels, but only on the  changing pixels, including objects such as drivers, computers,  and magazines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, for the DriveAct dataset, transfer-  extension can effectively increase convergence and stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The proposed FedTOP framework is able to obtain 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='32%  and 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='96% accuracy on the SFDDD and DriveAct datasets,  respectively, when considering five times of personalization  training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Compared to FedProx as a baseline, FedTOP can  effectively improve the accuracy by 462% in addition to  considering a 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46% reduction in communication resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The results demonstrate the feasibility of the proposed Fed-  TOP in terms of communication resource saving, accuracy  improvement, robustness, and cybersecurity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Performance of Personalized-Extension  Personalized-extension needs to be further discussed and  analyzed as the most effective approach to improve accu-  racy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Based on the division of training and testing clients  in Section III-A, in this subsection, we further discuss how  the trained and aggregated global model is adapted to both  training and testing clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The results of the personalized-  extension on the two datasets are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 7 with different  personalization epochs, which is equivalent to demonstrating  Algorithm 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' It can be seen that the personalization process  differs significantly on the datasets with and without system  heterogeneity, which is similar to the results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The  clients in the DriveAct dataset have faster convergence, minor  accuracy variance, and higher final accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' On the contrary,  the clients in the SFDDD dataset not only converge slower but  also have an anomalous client with relatively low accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The possible reason is that the anomalous client has a huge  data and system heterogeneity, causing the optimal model to  deviate significantly far from the aggregated global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 8 further demonstrates that the trained global model  repositions the ROI during the personalized training process  via class activation map (CAM) [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The test client of the  SFDDD dataset can be seen struggling with the personalization  process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The trained global model focus the ROI on the  seat backrest, driver’s chest, hand, and knee, and vehicle  door.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Due to the system heterogeneity present in the SFDDD  dataset, the positions of the driver, seat, and steering wheel,  as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 8a is different from other clients, as shown  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4b, 4c, and 4d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, the initial ROI is likely  to be a driver’s position among other clients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' During the five  personalization training processes, the local model is able to  effectively reposition the ROI to the driver, which is what  the personalized-extension is intended to show.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Moreover, the  IEEE INTERNET OF THINGS JOURNAL  8  personalization process also reduces the number of ROIs while  targeting more attention to a specific area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  On the contrary, for the test clients in the DriveAct dataset,  the adjustment of the ROI is negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Note that the ROI does  not necessarily have to cover the driver’s body or an object  such as the magazine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The ROI should cover those pixels  that can distinguish between different activities, such as static  activities like reading the magazine, and dynamic activities  like wearing a seatbelt in the DriveAct dataset activity setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  These ROIs focus on areas where large differences are likely  to occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The fact that the ROIs in the DriveAct dataset cover  almost the same pixels during the personalization process can  also prove the negative impact of system heterogeneity on the  FL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' DISCUSSION  The two datasets used, SFDDD and DriveAct, still have  some flaws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' First, although the SFDDD dataset takes system  heterogeneity into account, quite a few drivers collect data  in the same vehicle, that is, the number of clients is greater  than the number of users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, there are still some  differences between the dataset and the real-world data, which  leads to the fact that the proposed FedTOP may need more  communication rounds to achieve similar accuracy on a real-  world dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Second, there is currently no driver monitoring  dataset with real poisoning data currently existing, resulting  in the effect of ordered-extension not being reflected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' The  different modalities, positions, and angles of the camera or  the method of generating fake data may be a hypothesis for  poisoned data, but it cannot be highlighted as real.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Moreover,  due to road safety guidelines, the current dataset is only driving  on safe roads or simulated driving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, the driver’s  posture, demeanor, facial concentration, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', are far from the  real driving behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, there is an urgent need for  a more realistic dataset that can include camera images of  different positions and angles, different vehicle scenes, and  more drivers driving on real roads.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  For a FL framework in IoT, in addition to accuracy being  the evaluation criterion, factors like communication require-  ments, robustness, fairness, cybersecurity, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', also need to  be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Although it seems that transfer and ordered  extensions may not improve accuracy but rather reduce it in  the current experimental results, it can potentially improve  the performance of the FL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, we keep  two extensions as one of our future directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Personalized-  extension is an approach similar to transfer learning and  incremental learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' On the one hand, the local client is  incrementally learned based on the trained global model, but it  does not intentionally retain the previously learned knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  On the other hand, the global model is transferred to the  client dataset as in transfer-extension, but the low-level non-  trainable weights are still pre-trained on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore,  the proposed personalized-extension actually uses the trained  global model weights to fit different client data, such as  the reposition of ROIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Although the personalized-extension  requires additional training locally for each client, there are  many benefits, including high accuracy, applicability to non-  training clients, customization, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Conceivably, personalized-  extension can effectively address the problem of system het-  erogeneity, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', it can be applied to different cameras, camera  angles, vehicle interiors, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' CONCLUSION  In this paper, we propose a FL framework FedTOP for  DMA to address the issues of privacy preservation, efficient  training, communication resource-saving, poisoned data, and  diversified scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Through the ablation study, the impact,  role, and performance of three extensions, including trans-  fer, ordered, and personalized on the model are disclosed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Moreover, the experiments demonstrate dramatic differences  between datasets with and without system heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' In  addition to the proposed FedTOP being able to exhibit 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='32%  and 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='96% accuracy in two datasets for testing clients, it  is also appreciated that FedTOP reduces communication con-  sumption by 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='46% and potentially improves cybersecurity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  The experimental results show that the proposed FedTOP  is a highly accurate, lightweight, privacy-preserving, robust,  cybersecure, and universally applicable FL framework for  potential DMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Future work lies in the continued research of extensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' For  the ordered-extension, a possible plan is to introduce some ma-  licious local clients to attack and poison with the global model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  For example, subjects may not place the camera on the side  as instructed but place it on the front or behind instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Such  outliers may cause the global model to deviate significantly  from the optimal solution, so in the case, ordered-expansion  can prevent the deviation of the global model by discarding  the larger value of the losses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' For the transfer-extension, there  is currently a lack of a general driver monitoring model, so  we used a model pre-trained on ImageNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Future work can  pre-train a driver model ourselves as a base model, which  will get better performance in DMA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1 shows the FL  framework for foresight in IoV, but the dataset used does not  contain scenario information such as road, weather, vehicle  models, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Therefore, we expect a well-developed real-world  dataset to include such scenario information, data and system  heterogeneity, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  REFERENCES  [1] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Li, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhao, “A survey on security and  privacy issues in internet-of-things,” IEEE Internet Things J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1250–1258, Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Pang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Xie, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Khan, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Shao, “From handcrafted to  deep features for pedestrian detection: a survey,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Pattern  Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Kuutti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Fallah, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Katsaros, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Dianati, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mccullough, and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mouzakitis, “A survey of the state-of-the-art localization techniques  and their potentials for autonomous vehicle applications,” IEEE Internet  Things J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 829–846, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [4] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Gupta, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ganlath, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ammar, and  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Tiwari, “Mobility digital twin: Concept, architecture, case study, and  future challenges,” IEEE Internet Things J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Hard, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Rao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mathews, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ramaswamy, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Beaufays, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Augen-  stein, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Eichner, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Kiddon, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ramage, “Federated learning for  mobile keyboard prediction,” arXiv preprint arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='03604, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [6] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Dayan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Roth, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhong, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Harouni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Gentili, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Abidin,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Costa, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wood, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Tsai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', “Federated learning  for predicting clinical outcomes in patients with covid-19,” Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Med.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 27, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1735–1743, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  IEEE INTERNET OF THINGS JOURNAL  9  [7] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Rieke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Hancox, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Li, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Milletari, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Roth, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Albarqouni,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Bakas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Galtier, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Landman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Maier-Hein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', “The  future of digital health with federated learning,” NPJ Digit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Med.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 3,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1–7, Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Hao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Luo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yang, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Liu, “Efficient and  privacy-enhanced federated learning for industrial artificial intelligence,”  IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Industr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 6532–6542, Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [9] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Lu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Dai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Maharjan, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhang, “Blockchain and  federated learning for privacy-preserved data sharing in industrial iot,”  IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Industr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 16, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4177–4186, Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [10] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Du, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yoshinaga, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yau, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ji, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Li, “Federated  learning for vehicular internet of things: Recent advances and open  issues,” IEEE open j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 45–61, May 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [11] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Kong, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Hou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Hao, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Shen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Chen, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Xia, “A  federated learning-based license plate recognition scheme for 5g-enabled  internet of vehicles,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Industr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  8523–8530, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [12] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Sattler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wiedemann, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' M¨uller, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Samek, “Robust and  communication-efficient federated learning from non-iid data,” IEEE  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Neural Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 31, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 3400–3413, Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Karimireddy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Kale, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mohri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Reddi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Stich, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Suresh, “Scaffold: Stochastic controlled averaging for federated learn-  ing,” in International Conference on Machine Learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  PMLR, 2020,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 5132–5143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Horvath, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Laskaridis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Almeida, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Leontiadis, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Venieris, and  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Lane, “Fjord: Fair and accurate federated learning under heteroge-  neous targets with ordered dropout,” Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Neural Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 34, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 12 876–12 889, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [15] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' McMahan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Moore, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ramage, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Hampson, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' y Arcas,  “Communication-efficient learning of deep networks from decentralized  data,” in Artificial intelligence and statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  PMLR, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1273–  1282.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [16] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Sahu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zaheer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Sanjabi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Talwalkar, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Smith,  “Federated optimization in heterogeneous networks,” Proceedings of  Machine Learning and Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 429–450, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [17] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ghimire and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Rawat, “Recent advances on federated learning  for cybersecurity and cybersecurity for federated learning for internet of  things,” IEEE Internet Things J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [18] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Sahu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Talwalkar, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Smith, “Federated learning:  Challenges, methods, and future directions,” IEEE Signal Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=',  vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 37, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 50–60, May 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [19] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Niknam, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Dhillon, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Reed, “Federated learning for  wireless communications: Motivation, opportunities, and challenges,”  IEEE Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 58, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 46–51, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [20] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Lyu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yu, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yang, “Threats to federated learning: A survey,”  arXiv preprint arXiv:2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='02133, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [21] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Kairouz, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' McMahan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Avent, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Bellet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Bennis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Bhagoji, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Bonawitz, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Charles, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cormode, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cummings et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=',  “Advances and open problems in federated learning,” Found.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Trends  Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1–2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1–210, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [22] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Hu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Liu, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' He, “A  survey on federated learning systems: vision, hype and reality for data  privacy and protection,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Knowl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Data Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [23] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Saito, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wu, “Privacy-preserving federated  transfer learning for driver drowsiness detection,” IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 10,  pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 80 565–80 574, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [24] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Su, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Luan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Chen, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cao,  “Secure and efficient federated learning for smart grid with edge-cloud  collaboration,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Industr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Inform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1333–  1344, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [25] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Sun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Dong, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Lyu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Liu, “Data poisoning  attacks on federated machine learning,” IEEE Internet Things J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', Nov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cheng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Binh, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yu, “Poisongan:  Generative poisoning attacks against federated learning in edge com-  puting systems,” IEEE Internet Things J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 3310–3322,  Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Tan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cui, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yang, “Towards personalized federated  learning,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Neural Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [28] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Fallah, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mokhtari, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ozdaglar, “Personalized federated  learning: A meta-learning approach,” arXiv preprint arXiv:2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='07948,  Feb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [29] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhou, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhang, “Fedhome: Cloud-edge based  personalized federated learning for in-home health monitoring,” IEEE  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mob.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [30] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Kashevnik, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Lashkov, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Gurtov, “Methodology and mobile  application for driver behavior analysis and accident prevention,” IEEE  Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Transp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2427–2436, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [31] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zepf, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Hernandez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Schmitt, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Minker, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Picard, “Driver  emotion recognition for intelligent vehicles: A survey,” ACM Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 53, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 1–30, Jun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [32] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Xing, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Lv, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ai, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cao, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Velenis, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Wang, “Driver lane change intention inference for intelligent vehicles:  framework, survey, and challenges,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Veh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 68,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4377–4390, Mar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Masood, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Lakew, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cho, “Security and privacy challenges  in connected vehicular cloud computing,” IEEE Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 22,  no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2725–2764, Jul.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Kuutti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Bowden, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Jin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Barber, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Fallah, “A survey of  deep learning applications to autonomous vehicle control,” IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Intell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Transp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 712–733, Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [35] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ramzan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Khan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Awan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ismail, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ilyas, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mah-  mood, “A survey on state-of-the-art drowsiness detection techniques,”  IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 61 904–61 919, May 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [36] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Doshi and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Yilmaz, “Federated learning-based driver activity recog-  nition for edge devices,” in Proceedings of the IEEE/CVF Conference  on Computer Vision and Pattern Recognition, 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 3338–3346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [37] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Gao, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Xiao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Mo, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Deen, “Fedsup:  A communication-efficient federated learning fatigue driving behaviors  supervision approach,” Future Gener.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 138, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 52–60,  Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [38] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' He, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Ren, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Sun, “Deep residual learning for image  recognition,” in Proceedings of the IEEE conference on computer vision  and pattern recognition, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' 770–778.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [39] State  Farm,  “State  farm  distracted  driver  detection,”  Apr  2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Available:  https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='kaggle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='com/competitions/  state-farm-distracted-driver-detection/overview/description  [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Martin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Roitberg, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Haurilet, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Horne, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Reiß, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Voit, and  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Stiefelhagen, “Drive&act: A multi-modal dataset for fine-grained  driver behavior recognition in autonomous vehicles,” in Proceedings of  the IEEE/CVF International Conference on Computer Vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  2801–2810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  [41] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Omeiza, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Speakman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Cintas, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Weldermariam, “Smooth  grad-cam++: An enhanced inference level visualization technique  for  deep  convolutional  neural  network  models,”  arXiv  preprint  arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='01224, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Liangqi Yuan (S’22) received the B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' degree from  the Beijing Information Science and Technology  University, Beijing, China, in 2020, and the M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  degree from the Oakland University, Rochester, MI,  USA, in 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' He is currently pursuing the Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  degree with the School of Electrical and Computer  Engineering, Purdue University, West Lafayette, IN,  USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' His research interests are in the areas of  sensors, the internet of things, human–computer  interaction, signal processing, and machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  Lu Su (M’15) is an associate professor in the School  of Electrical and Computer Engineering at Purdue  University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' His research interests are in the gen-  eral areas of Internet of Things and Cyber-Physical  Systems, with a current focus on wireless, mobile,  and crowd sensing systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' He received Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' in  Computer Science, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' in Statistics, both from  the University of Illinois at Urbana-Champaign, in  2013 and 2012, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' He has also worked  at IBM T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' Watson Research Center and National  Center for Supercomputing Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' He has  published more than 100 papers in referred journals and conferences, and  serves as an associate editor of ACM Transactions on Sensor Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  He is the recipient of NSF CAREER Award, University at Buffalo Young  Investigator Award, ICCPS’17 best paper award, and the ICDCS’17 best  student paper award.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' He is a member of ACM and IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='  IEEE INTERNET OF THINGS JOURNAL  10  Ziran Wang (S’16-M’19) received the Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' de-  gree from the University of California, Riverside in  2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' He is an Assistant Professor in the College  of Engineering at Purdue University, and was a  Principal Researcher at Toyota Motor North Amer-  ica.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' He serves as Founding Chair of IEEE Techni-  cal Committee on Internet of Things in Intelligent  Transportation Systems, and Associate Editor of  four academic journals, including IEEE Internet of  Things Journal and IEEE Transactions on Intelligent  Vehicles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
+page_content=' His research focuses on automated driving,  human-autonomy teaming, and digital twin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/wNE3T4oBgHgl3EQf-wup/content/2301.04829v1.pdf'}
diff --git a/ydFKT4oBgHgl3EQf7S6i/content/tmp_files/2301.11944v1.pdf.txt b/ydFKT4oBgHgl3EQf7S6i/content/tmp_files/2301.11944v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9d193eeb145c6feeb0393a9edfd3d3a5e26e391f
--- /dev/null
+++ b/ydFKT4oBgHgl3EQf7S6i/content/tmp_files/2301.11944v1.pdf.txt
@@ -0,0 +1,1614 @@
+Phonon-induced localization of excitons in molecular crystals
+from first principles
+Antonios M. Alvertis,1, 2, ∗ Jonah B. Haber,2 Edgar A. Engel,3 Sahar Sharifzadeh,4, 5 and Jeffrey B. Neaton1, 2, 6, †
+1Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
+2Department of Physics, University of California Berkeley, Berkeley, United States
+3Cavendish Laboratory, University of Cambridge,
+J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
+4Division of Materials Science and Engineering, Boston University, United States
+5Department of Electrical and Computer Engineering, Boston University, United States
+6Kavli Energy NanoScience Institute at Berkeley, Berkeley, United States
+(Dated: January 31, 2023)
+The spatial extent of excitons in molecular systems underpins their photophysics and utility for
+optoelectronic applications. Phonons are reported to lead to both exciton localization and delo-
+calization. However, a microscopic understanding of phonon-induced (de)localization is lacking, in
+particular how localized states form, the role of specific vibrations, and the relative importance of
+quantum and thermal nuclear fluctuations. Here we present a first-principles study of these phenom-
+ena in solid pentacene, a prototypical molecular crystal, capturing the formation of bound excitons,
+exciton-phonon coupling to all orders, and phonon anharmonicity, using density functional theory,
+the ab initio GW-Bethe-Salpeter equation approach, finite difference, and path integral techniques.
+We find that for pentacene zero-point nuclear motion causes uniformly strong localization, with
+thermal motion providing additional localization only for Wannier-Mott-like excitons. Anharmonic
+effects drive temperature-dependent localization, and while such effects prevent the emergence of
+highly delocalized excitons, we explore the conditions under which these might be realized.
+Introduction.– Photoexcitation of organic molecular
+crystals leads to strongly bound electron-hole pairs, or
+excitons, due to the weak screening of the Coulomb in-
+teraction in these systems. Depending on factors such as
+the size of the molecular building blocks and the spin of
+the electron-hole pair, exciton radii can vary from those
+of localized Frenkel excitons [1, 2] to spatially extended
+excitons that approach the Wannier-Mott limit [3–7].
+The spatial extent of these excited states is important
+to applications of organic semiconductors such as photo-
+voltaics [8] and LEDs [9], since it affects properties in-
+cluding the nature of their interaction with phonons [10],
+their transport [11] and non-radiative recombination [12].
+Critical to affecting the spatial extent of excited states
+are lattice vibrations, which are generally thought to
+result in wavefunction localization [13].
+Phonons can
+strongly renormalize one- and two-particle excitation en-
+ergies of organic systems, influencing the optical gap and
+the charge carrier mobility [10, 14, 15]. Phonons in these
+systems have generally been thought to lead to local-
+ized excitons that diffuse via, e.g., a F¨orster or Dexter
+mechanism [16, 17]. However, it has recently been pro-
+posed that in certain well-ordered organic crystals atomic
+motion can give rise to configurations that favor strong
+transient exciton delocalization, having a beneficial ef-
+fect to transport [18–20]. This transient exciton delocal-
+ization is similar to transient charge delocalization [21–
+23], wherein phonons lead to configurations with large
+overlaps between neighboring molecular orbitals [24] and
+∗ amalvertis@lbl.gov
+† jbneaton@lbl.gov
+hence highly delocalized states [25].
+Despite these insights, a rigorous microscopic under-
+standing of phonon-induced modulations to exciton radii,
+one that accounts for electron-hole interactions, strong
+exciton-phonon coupling at finite temperatures [10, 26],
+and the anharmonicity of low-frequency motions in
+molecular crystals [27–30], is still lacking. Here we elu-
+cidate the microscopic mechanism of exciton localiza-
+tion in extended molecular solids.
+We employ a first-
+principles computational framework which captures all
+aforementioned effects, combining density functional the-
+ory (DFT), the Green’s function-based ab initio GW-
+Bethe Salpeter equation (BSE) approach for accurately
+describing exciton effects [31], finite-difference methods
+for strong exciton-phonon interactions [10, 32], and path
+integral techniques for describing phonon anharmonic-
+ity [33, 34].
+We apply this framework to the proto-
+typical molecular crystal pentacene and show that zero-
+point nuclear motion leads to strong localization of sin-
+glet and triplet excitons, reducing their average electron-
+hole separation by more than a factor of two.
+Tem-
+perature increases further reduce the size of delocalized
+Wannier-Mott-like excitons, an effect driven by anhar-
+monic phonons. The trends in exciton radii are reflected
+in the dispersion of their energies in reciprocal space.
+While highly delocalized excitons do appear at large
+phonon displacements, anharmonicity reduces the ampli-
+tude associated with these motions, suppressing transient
+delocalization for exciton transport.
+System and methods.– We focus on the widely stud-
+ied molecular crystal pentacene [35], which hosts a de-
+localized Wannier-Mott-like singlet exciton (Fig. 1a) and
+a more localized Frenkel-like triplet exciton (Fig. 1b) [7,
+arXiv:2301.11944v1  [cond-mat.mtrl-sci]  27 Jan 2023
+
+2
+10, 36], for which the effect of phonons is expected to be
+different. We compute excitons with principal quantum
+number S and center-of-mass momentum Q using ab ini-
+tio DFT and GW-BSE calculations with the Quantum
+Espresso [37] and BerkeleyGW [38] codes. This involves
+constructing the electron-hole kernel Ke−h and solving
+the BSE [31, 39] in reciprocal space in the electron-hole
+basis, namely
+(Eck+Q − Evk)AS
+cvkQ
+(1)
++
+�
+c′v′k′
+⟨ck + Q, vk| Ke−h |c′k′ + Q, v′k′⟩ AS
+c′v′k′Q
+= ΩS
+QAS
+cvkQ,
+with input from prior DFT and GW calculations.
+In
+Eq. 1 the indices c, v define conduction and valence states
+respectively, k is the crystal momentum, and AS
+cvkQ is
+the amplitude contributed by states c, v with momentum
+k to the exciton with momentum Q. The exciton wave-
+function can be written as
+ΨQ
+S (re, rh) =
+�
+cvk
+AS
+cvkQψck+Q(re)ψ∗
+vk(rh),
+(2)
+where ψnk are the Kohn-Sham wavefunctions. The kernel
+Ke−h consists only of an attractive ‘direct’ term between
+electrons and holes for triplets, while for singlets it also
+includes a repulsive ‘exchange’ term, giving singlets their
+greater spatial extent [7, 31]. The energies of the conduc-
+tion and valence bands in Eq. 1 are obtained within the
+so-called GW approximation [40] from self-energy correc-
+tions to DFT Kohn-Sham eigenvalues. This approach has
+been shown to give highly accurate descriptions of exci-
+tons in molecular crystals [7, 10, 36, 41, 42]. The compu-
+tational details for our DFT and GW-BSE calculations
+are given in Supplemental Material [43] Section S1.
+We treat the effect of phonons following Monser-
+rat [32, 44, 45], and in a manner similar in spirit to
+Zacharias and Giustino [46, 47].
+For an observable O
+at a temperature T, we compute the ensemble-average in
+the adiabatic approximation as
+⟨O(T)⟩H = 1
+Z
+�
+dXO(X)e−βH,
+(3)
+where the canonical partition function Z =
+�
+dXe−βH
+involves the configuration space integral
+�
+dX [48]. Non-
+adiabatic effects to the electron-phonon interactions of
+organic systems such as pentacene are negligible [49].
+The Hamiltonian H of the system includes electronic
+and nuclear degrees of freedom in general, and may be ap-
+proximated at different levels. One approach is to assume
+nuclear motion to be harmonic, reducing the phonon con-
+tribution to the Hamiltonian to the following form,
+Hhar ≡ 1
+2
+�
+n,q
+(∇2
+un,q + ω2
+n,qu2
+n,q),
+(4)
+in atomic units.
+Here, phonons of frequencies ω are
+labeled by their branch index n and wavevector q.
+We compute the ensemble-average
+�
+Ohar�
+in the Born-
+Oppenheimer approximation, tracing out all electronic
+degrees of freedom, using a finite-displacements ap-
+proach [50, 51] to calculate phonon frequencies {ωn,q}
+and eigendisplacements {un,q}, and then drawing N ran-
+dom samples {Xhar
+i
+} from the multivariate Gaussian
+phonon distribution and calculating the observables of
+interest {O(Xhar
+i
+)}.
+�
+Ohar�
+is then simply computed as
+the average of its value at the samples
+�
+Ohar�
+= lim
+N→∞
+1
+N
+N
+�
+i=1
+O(Xhar
+i
+).
+(5)
+Eqs. 4
+and 5
+are
+exact
+apart
+from
+the
+adiabatic
+and harmonic approximations, and the description of
+phonon effects on any observable O in Eq. 5 is non-
+perturbative [26].
+The use of the harmonic approximation in molecular
+crystals can lead to unphysical results, due to highly an-
+harmonic behavior of low-frequency phonons [27, 29]. In
+this work, we account for this anharmonicity by employ-
+ing path-integral molecular dynamics (PIMD) which are
+rendered computationally tractable using the surrogate
+machine-learning (ML) potential V ML from Refs. [27, 52],
+constructed to reproduce the potential energy surface
+(PES) from first-principles density functional theory
+(DFT) calculations. The modified phonon Hamiltonian
+Hanhar ≡
+Na
+�
+i=1
+ˆp2
+i
+2mi
++ V ML(ˆr1, . . . , ˆrNa)
+(6)
+is used to run PIMD simulations at reduced computa-
+tional cost, for a cell of Na atoms, with nucleus i having
+a mass mi, and ˆpi, ˆri its momentum and position opera-
+tors respectively. We then draw random samples from the
+PIMD trajectories, and use these to compute vibrational
+averages of observables, analogously to Eq. 5, namely
+�
+Oanhar�
+= lim
+N→∞
+1
+N
+N
+�
+i=1
+O(Xanhar
+i
+).
+(7)
+Our simulations use a 2 × 1 × 1 supercell of pentacene
+(Na = 144 atoms), capturing the effect of phonons at Γ
+and at the band-edge X on observables.
+Phonons be-
+yond Γ and X have a minor effect on pentacene opti-
+cal properties as discussed in Supplemental Material [43]
+Section S1.C.
+
+3
+a
+d
+b
+c
+E (eV)
+0
+0.2
+0.4
+1
+1.2
+1.4
+1.6
+1.8
+Γ
+X
+|Q| (A-1)
+o
+static
+100 K
+300 K
+FIG. 1. Isosurfaces of electron distributions of singlet (blue,
+panel a) and triplet (green, panel b) excitons for a hole fixed
+at the center of the plotted area, and corresponding dis-
+persions (panel c, same color scheme) in molecular crystals.
+A typical low-frequency (top) and high-frequency (bottom)
+phonon of pentacene is shown in panel d.
+To quantify exciton localization, we study two observ-
+ables O. The first are the exciton energies at finite center-
+of-mass momentum, ΩS
+Q, obtained through solving the
+BSE (Eq. 1).
+The second is the average electron-hole
+separation for each excitation S, which we refer to as the
+exciton radius rexc. This is obtained by post-processing
+the BSE solution ΨS, as discussed elsewhere [53] and in
+Supplemental Material [43] Section S1. To determine the
+exciton radius, we compute the electron-hole correlation
+function as defined in Ref. [53], namely
+FS(r) =
+�
+V
+drh|ΨQ=0
+S
+(re = rh + r, rh)|2,
+(8)
+where V the volume of the primitive cell. FS(r) describes
+the probability of finding the electron-hole pair at a dis-
+tance of r = re − rh, and is computed as a discrete sum
+over hole positions.
+The average exciton radius for a
+given atomic configuration is then
+rexc =
+�
+d|r|FS(|r|)|r|.
+(9)
+Having described the main quantities in our computa-
+tional framework, we may summarize it as follows. We
+generate displaced configurations Xhar
+i
+within the har-
+monic approximation using a finite differences approach,
+and Xanhar
+i
+within the anharmonic distribution through
+PIMD employing a previously-developed ML potential.
+The ab initio BSE, Eq. 1, is solved at these configura-
+tions, followed by a calculation of the exciton radius via
+Eq. 9. We then compute the vibrational averages using
+Eqs. 5 and 7. Details of the convergence of the vibrational
+averages, the ML potential, and PIMD simulations, are
+given in Supplemental Material [43] Section S1.
+Results.– We first discuss exciton properties obtained
+from solving the BSE without consideration of phonons.
+We refer to these clamped-ion solutions as the ‘static’
+case. Fig. 1 shows an isosurface of the electron density
+for the first singlet (S1, blue, panel a) and triplet (T1,
+green, panel b) exciton, for a hole fixed at the center of
+the visualized region. As shown previously [7, 10, 36], the
+singlet is significantly more delocalized than the triplet,
+which results in bands that are more dispersive in re-
+ciprocal space [7, 42], as shown in Fig. 1c. We plot the
+exciton energies along the path Γ → X in the Brillouin
+zone, corresponding to the dominant packing direction
+of the pentacene crystal. Table I summarizes the band-
+width W = Ω(X) − Ω(Γ) of the two excitons, as well
+as the width ∆ = Ω(Q = 0.4 ˚A
+−1) − Ω(Q = 0.1 ˚A
+−1),
+the values of the exciton momentum chosen to accom-
+modate comparison to recent experiments [54]. We see
+from our static calculations that the singlet bandwidth
+is more than twice that of the triplet.
+We now include the effect of phonons on the exciton
+band structures along Γ → X at 100 K and 300 K, within
+the harmonic and anharmonic distributions, and visu-
+alize the results in Fig. 1c when including anharmonic
+effects.
+There are two broad categories of phonons in
+molecular crystals, corresponding to low-frequency inter-
+molecular and high-frequency intramolecular motions, vi-
+sualized in Fig. 1d. While the former are predominantly
+activated when going from 100 K to 300 K, the latter have
+significant zero-point energies ℏω/2.
+Including 100 K
+phonon effects red-shifts both singlet and triplet exci-
+ton energies and flattens their dispersions, as shown in
+Fig. 1c and Table I. This effect is larger for the triplet,
+which is more localized and therefore more impacted
+by high-frequency intra-molecular modes. However, in-
+creasing the temperature to 300 K has no effect on the
+triplet, since there are negligible additional contributions
+from intramolecular modes at these temperatures and
+the modulations of intermolecular distances by lower-
+frequency phonons hardly affect this localized state. In
+contrast, the delocalized singlet red-shifts further, and
+its dispersion flattens by an additional 18 meV. Our re-
+sults for the singlet width ∆ at 100 K are in excellent
+agreement with recent experiments [54], as summarized
+in Table I. Our predicted decrease of the singlet width ∆
+by 13 meV when increasing the temperature from 100 K
+to 300 K underestimates the experimental decrease of
+
+4
+W anhar(S1) (meV)
+W har(S1) (meV)
+W anhar(T1) (meV)
+∆anhar(S1) (meV)
+∆exp(S1) (meV) [54]
+static
+110
+110
+52
+80
+− − −
+100 K
+59
+67
+18
+43
+44
+300 K
+41
+76
+19
+30
+23
+TABLE I. The effect of phonons on the dispersion width W = Ω(X) − Ω(Γ) for the first singlet ΩS and triplet ΩT excitons of
+pentacene, and on the width ∆ = Ω(Q = 0.4 ˚A
+−1) − Ω(Q = 0.1 ˚A
+−1) for the singlet.
+T (K)
+5
+10
+15
+x
+x
+x
+x
+0
+300
++
++
++
+x
+harmonic
+anharmonic
+a
+b
+c
++
++
+<rexc> (A)
+o
+static
+x
+x
+x
+x
+singlet
+triplet
+FIG. 2. Singlet (blue) and triplet (green) exciton radii within
+the different cases and temperatures (panel a). Representa-
+tive configuration showing electronic isosurfaces for fixed hole
+positions, indicating localization of the singlet (triplet) at 0 K
+towards the region in blue (green), shown in panel b (panel
+c).
+Red represents electronic wavefunction amplitude that
+disappears in the presence of phonons.
+21 meV, largely due to ignoring thermal expansion in our
+calculation, which reduces ∆ by a further 6 meV within
+this temperature range, see Supplemental Material [43]
+Section S2. Interestingly, we see in Table I that the har-
+monic approximation predicts an increase of the singlet
+bandwidth with increasing temperature, contrary to our
+calculations including anharmonic effects using PIMD
+and to experiment, a point that we return to below.
+The changes in the width of the exciton dispersions
+suggest phonon-induced modulations of real-space exci-
+ton properties, which are zero-point dominated for the
+triplet, and which have significant temperature depen-
+dence for the singlet. We highlight the connection be-
+tween the dispersion modulations and real-space exciton
+properties by computing vibrational averages of the exci-
+ton radii at a range of temperatures. The results are pre-
+sented in Fig. 2 for the singlet (blue) and triplet (green)
+within the harmonic approximation and including anhar-
+monic effects.
+Let us first comment on the harmonic
+case. Compared to the static limit (circles), the radii in
+the presence of phonons at 0 K are renormalized by more
+than a factor of two.
+For the singlet, the static value
+of 11.2 ˚A for its radius reduces to 4.9 ˚A, while the static
+triplet radius of 2.7 ˚A reduces to 1.2 ˚A. To visualize this
+we present in Fig. 2b and Fig. 2c differential plots for iso-
+surfaces of the electron density once a hole is placed at a
+high-probability position in the unit cell. Specifically, we
+plot the difference between the electronic density of the
+case without phonons and that of a typical atomic config-
+uration at 0 K. Red indicates amplitude vanishing due to
+phonons, while blue and green indicate areas where the
+singlet and triplet wavefunction respectively gain ampli-
+tude, demonstrating their tendency to localize.
+When increasing the temperature to 300 K within the
+harmonic approximation there is no change to the triplet
+exciton radius, in agreement with our expectation of the
+effect of phonons on the triplet exciton dispersion. The
+singlet however exhibits delocalization, with its radius
+increasing substantially to the average value of 6.96 ˚A,
+consistent with the increase of the singlet bandwidth with
+temperature in the harmonic case. Upon including an-
+harmonic effects, triplet radii agree with the harmonic
+case; however, for the singlet the results are qualitatively
+different, and we recover the expected behavior of de-
+creasing singlet radius with increasing temperature. All
+vibrational averages and errors for the exciton radii are
+given in Section S7 of the Supplemental Material [43].
+The discrepancy between the harmonic and anhar-
+monic cases is due to configurations with highly delocal-
+ized excitons within the harmonic approximation, with
+radii as large as 31 ˚A at 300 K. Such configurations are
+shown in Supplementary Material [43] Section S5, and
+their inclusion in the thermal averages of Eq. 5 for the
+radii leads to the observed temperature-induced increase
+of ⟨rexc⟩ in Fig. 2a.
+To understand why such configu-
+rations are not present within the anharmonic case, we
+plot in Fig. 3a the difference between the phonon root
+mean squared displacement
+�
+⟨u2⟩ of the two distribu-
+tions at 300 K. We find that a low-frequency acoustic
+mode, corresponding to a sliding along the z-axis of ad-
+jacent pentacene molecules, is significantly over-displaced
+
+O
+O5
+ b
+ a
+10
+15
+20
+25
+30
+u
+harmonic
+anharmonic
+<rexc> (A)
+o
+d-deq (A) 
+o
+0
+1
+2
+3
+4
+5
+6
+7
+15
+30
+45
+60
+75
+90
+ω (cm -1)
+deq = 16.3 A 
+o
+0
+5
+10
+15
+20
+25
+<uhar
+2>
+<uanhar
+2>
+-
+0
+500
+1000 1500
+2000 2500 3000
+FIG. 3.
+The difference between the RMS displacement of
+phonons in the harmonic and anharmonic distributions of
+pentacene (panel a).
+Singlet exciton radii (panel b) along
+the highly anharmonic phonon shown in panel a.
+Phonon
+displacements u are given in units of their zero-point width
+1/√2ωqν [32]. The dotted line in b is a guide to the eye.
+in the harmonic case at q = X. Anharmonic terms alter
+the PES associated with this phonon, limiting its aver-
+age amplitude at room temperature, as shown in Supple-
+mentary Material [43] Fig. S3, in agreement with known
+cases where the harmonic approximation breaks down in
+molecular crystals [27, 29, 30]. We confirm that the over-
+displacement of this phonon within the harmonic approx-
+imation leads to the temperature-induced singlet delocal-
+ization observed in Fig. 2a, by computing the singlet ra-
+dius as a function of amplitude of this mode, as visualized
+in Fig. 3b. The blue and red regions indicate the maxi-
+mum range of displacements which are accessible within
+the anharmonic and harmonic distributions respectively,
+due to thermal excitation of phonons at 300 K. The har-
+monic approximation leads to configurations with highly
+delocalized excitons of radii as large as 25 ˚A. The depen-
+dence of the exciton radius on the phonon displacement
+is non-monotonic due to the oscillating π orbital overlap
+between neighboring pentacene molecules [55].
+While highly delocalized excitons may appear at cer-
+tain nuclear configurations, anharmonicity prevents ac-
+cessing these, as seen in Fig. 3b. However, such configu-
+rations could appear out of equilibrium, e.g. due to pho-
+toexcitation, upon relaxation to the excited state PES
+minimum.
+For pentacene, the minimum of the singlet
+exciton PES along the anharmonic acoustic mode lies far
+from the ‘delocalized’ region of Fig. 3b (see Supplemental
+Material [43] Section S6), it is thus unlikely that for this
+and similar systems transiently delocalized excitons may
+be accessed, even outside equilibrium.
+Conclusions.– We have presented a first-principles
+study of the effect of phonons on the dispersion and
+radii of excitons in the prototypical molecular crystal
+pentacene. Zero-point nuclear motion uniformly causes
+substantial localization of excitons, manifesting as a
+flattening of the exciton dispersion in reciprocal space.
+Wannier-Mott-like singlet excitons also exhibit addi-
+tional temperature-activated localization due to their
+stronger coupling to low-frequency phonons, with anhar-
+monic effects being critical in capturing this effect and
+preventing transient exciton delocalization. Anharmonic
+low-frequency phonons are common in molecular materi-
+als [27] and can couple to singlets when these approach
+the Wannier-Mott limit, in a manner which is in turn de-
+termined by the size [10] and packing [56] of the molecular
+building blocks. Our work lays foundations for a deep un-
+derstanding and controlled enhancement of exciton trans-
+port in molecular crystals, for example by suppressing
+anharmonicity through chemical modifications [57].
+We thank Sivan Refaely-Abramson for useful discus-
+sions. This work was primarily supported by the Theory
+FWP, which provided GW and GW-BSE calculations
+and analysis of phonon effects, and the Center for Com-
+putational Study of Excited-State Phenomena in Energy
+Materials (C2SEPEM), which provided advanced codes,
+at the Lawrence Berkeley National Laboratory, funded
+by the U.S. Department of Energy, Office of Science,
+Basic Energy Sciences, Materials Sciences and Engineer-
+ing Division, under Contract No. DE-AC02-05CH11231.
+SS acknowledges funding from the U.S. National Science
+Foundation (NSF) under grant number DMR-1847774.
+Computational resources were provided by the National
+Energy Research Scientific Computing Center (NERSC).
+[1] J. Frenkel, On the transformation of light into heat in
+solids. i, Phys. Rev. 37, 17 (1931).
+[2] J. Frenkel, On the transformation of light into heat in
+solids. ii, Phys. Rev. 37, 1276 (1931).
+[3] G. H. Wannier, The structure of electronic excitation lev-
+els in insulating crystals, Phys. Rev. 52, 191 (1937).
+[4] N. F. Mott, Conduction in polar crystals. II. The con-
+duction band and ultra-violet absorption of alkali-halide
+crystals, Trans. Faraday Soc. 34, 500 (1938).
+[5] P. Cudazzo, M. Gatti, and A. Rubio, Excitons in molec-
+ular crystals from first-principles many-body perturba-
+tion theory: Picene versus pentacene, Phys. Rev. B 86,
+
+6
+1 (2012).
+[6] P. Cudazzo, M. Gatti, A. Rubio, and F. Sottile, Frenkel
+versus charge-transfer exciton dispersion in molecular
+crystals, Phys. Rev. B 88, 1 (2013).
+[7] P. Cudazzo, F. Sottile, A. Rubio, and M. Gatti, Exci-
+ton dispersion in molecular solids, Journal of Physics
+Condensed Matter 27, 10.1088/0953-8984/27/11/113204
+(2015).
+[8] A. Distler, C. J. Brabec, and H. J. Egelhaaf, Organic
+photovoltaic modules with new world record efficiencies,
+Progress in Photovoltaics: Research and Applications 29,
+24 (2021).
+[9] S.
+Reineke,
+F.
+Lindner,
+G.
+Schwartz,
+N.
+Seidler,
+K. Walzer, B. L¨ussem, and K. Leo, White organic light-
+emitting diodes with fluorescent tube efficiency., Nature
+459, 234 (2009).
+[10] A. M. Alvertis, R. Pandya, L. A. Muscarella, N. Sawhney,
+M. Nguyen, B. Ehrler, A. Rao, R. H. Friend, A. W. Chin,
+and B. Monserrat, Impact of exciton delocalization on
+exciton-vibration interactions in organic semiconductors,
+Phys. Rev. B 102, 081122 (2020).
+[11] J. Arag´o and A. Troisi, Dynamics of the excitonic cou-
+pling in organic crystals, Physical Review Letters 114, 1
+(2015).
+[12] G. Kupgan, X. K. Chen, and J. L. Br´edas, Molecular
+Packing in the Active Layers of Organic Solar Cells Based
+on Non-Fullerene Acceptors: Impact of Isomerization on
+Charge Transport, Exciton Dissociation, and Nonradia-
+tive Recombination, ACS Applied Energy Materials 4,
+4002 (2021).
+[13] P. W. Anderson, Absence of diffusion in certain random
+lattices, Phys. Rev. 109, 1492 (1958).
+[14] F. Brown-Altvater, G. Antonius, T. Rangel, M. Gi-
+antomassi, C. Draxl, X. Gonze, S. G. Louie, and J. B.
+Neaton, Band gap renormalization, carrier mobilities,
+and the electron-phonon self-energy in crystalline naph-
+thalene, Phys. Rev. B 101, 1 (2020).
+[15] G. Schweicher, G. D’Avino, M. T. Ruggiero, D. J.
+Harkin,
+K.
+Broch,
+D.
+Venkateshvaran,
+G.
+Liu,
+A. Richard, C. Ruzi´e, J. Armstrong, A. R. Kennedy,
+K. Shankland, K. Takimiya, Y. H. Geerts, J. A. Zeitler,
+S. Fratini, and H. Sirringhaus, Chasing the “Killer”
+Phonon Mode for the Rational Design of Low-Disorder,
+High-Mobility Molecular Semiconductors, Advanced Ma-
+terials 31, 10.1002/adma.201902407 (2019).
+[16] S. Athanasopoulos, E. V. Emelianova, A. B. Walker, and
+D. Beljonne, Exciton diffusion in energetically disordered
+organic materials, Phys. Rev. B 80, 1 (2009).
+[17] L. Sudha Devi, M. K. Al-Suti, C. Dosche, M. S. Khan,
+R. H. Friend, and A. K¨ohler, Triplet energy transfer in
+conjugated polymers. I. Experimental investigation of a
+weakly disordered compound, Phys. Rev. B 78, 1 (2008).
+[18] A. J. Sneyd, T. Fukui, D. Paleˇcek, S. Prodhan, I. Wag-
+ner, Y. Zhang, J. Sung, S. M. Collins, T. J. Slater,
+Z. Andaji-Garmaroudi, L. R. MacFarlane, J. D. Garcia-
+Hernandez, L. Wang, G. R. Whittell, J. M. Hodgkiss,
+K. Chen, D. Beljonne, I. Manners, R. H. Friend, and
+A. Rao, Efficient energy transport in an organic semi-
+conductor mediated by transient exciton delocalization,
+Science Advances 7, 10.1126/sciadv.abh4232 (2021).
+[19] S. Giannini,
+W.-T. Peng,
+L. Cupellini,
+D. Padula,
+A. Carof, and J. Blumberger, Exciton transport in
+molecular organic semiconductors boosted by transient
+quantum delocalization, Nature Communications 13, 1
+(2022).
+[20] A. J. Sneyd, D. Beljonne, and A. Rao, A New Frontier
+in Exciton Transport : Transient Delocalization, Journal
+of Physical Chemistry Letters 13, 6820 (2022).
+[21] S. Fratini, D. Mayou, and S. Ciuchi, The transient lo-
+calization scenario for charge transport in crystalline or-
+ganic materials, Advanced Functional Materials 26, 2292
+(2016), 1505.02686.
+[22] Y. Zhang, C. Liu, A. Balaeff, S. S. Skourtis, and D. N. Be-
+ratan, Biological charge transfer via flickering resonance,
+Proceedings of the National Academy of Sciences of the
+United States of America 111, 10049 (2014).
+[23] D. N. Beratan, Why Are DNA and Protein Electron
+Transfer So Different?, Annual Review of Physical Chem-
+istry 70, 71 (2019).
+[24] A. Troisi, G. Orlandi, and J. E. Anthony, Electronic in-
+teractions and thermal disorder in molecular crystals con-
+taining cofacial pentacene units, Chemistry of Materials
+17, 5024 (2005).
+[25] S. Giannini, A. Carof, M. Ellis, H. Yang, O. G. Ziogos,
+S. Ghosh, and J. Blumberger, Quantum localization and
+delocalization of charge carriers in organic semiconduct-
+ing crystals, Nature Communications 10, 1 (2019).
+[26] B. Monserrat, E. A. Engel, and R. J. Needs, Giant
+electron-phonon interactions in molecular crystals and
+the importance of nonquadratic coupling, Phys. Rev. B
+92, 1 (2015).
+[27] A. M. Alvertis and E. A. Engel, Importance of vibrational
+anharmonicity for electron-phonon coupling in molecular
+crystals, Phys. Rev. B 105, 1 (2022).
+[28] H. Seiler, M. Krynski, D. Zahn, S. Hammer, Y. W. Wind-
+sor, T. Vasileiadis, J. Pflaum, R. Ernstorfer, M. Rossi,
+and H. Schwoerer, Nuclear dynamics of singlet exciton
+fission: a direct observation in pentacene single crystals,
+Science Advances 7, eabg0869 (2021).
+[29] J. H. Fetherolf, P. Shih, and T. C. Berkelbach, Con-
+ductivity of an electron coupled to anharmonic phonons,
+arXiv (2022).
+[30] M. Rossi, P. Gasparotto, and M. Ceriotti, Anharmonic
+and Quantum Fluctuations in Molecular Crystals:
+A
+First-Principles Study of the Stability of Paracetamol,
+Phys. Rev. Lett. 117, 115702 (2016).
+[31] M. Rohlfing and S. G. Louie, Electron-hole excitations
+and optical spectra from first principles, Phys. Rev. B
+62, 4927 (2000), 0406203v3 [arXiv:cond-mat].
+[32] B. Monserrat, Electron – phonon coupling from finite dif-
+ferences, Journal of Physics Condensed Matter 30 (2018).
+[33] V. Kapil, J. Behler, and M. Ceriotti, High order path
+integrals made easy, The Journal of Chemical Physics
+145, 234103 (2016).
+[34] M. Ceriotti, M. Parrinello, T. E. Markland, and D. E.
+Manolopoulos, Efficient stochastic thermostatting of
+path integral molecular dynamics, J. Chem. Phys. 133,
+124104 (2010).
+[35] S. Haas, B. Batlogg, C. Besnard, M. Schiltz, C. Kloc, and
+T. Siegrist, Large uniaxial negative thermal expansion in
+pentacene due to steric hindrance, Phys. Rev. B 76, 1
+(2007).
+[36] S. Refaely-Abramson, F. H. Da Jornada, S. G. Louie,
+and J. B. Neaton, Origins of Singlet Fission in Solid
+Pentacene from an ab initio Green’s Function Approach,
+Physical Review Letters 119, 1 (2017), 1706.01564.
+[37] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car,
+C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococ-
+
+7
+cioni, I. Dabo, A. Dal Corso, S. Fabris, G. Fratesi, S. de
+Gironcoli, R. Gebauer, U. Gerstmann, C. Gougoussis,
+A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari,
+F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello,
+L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P.
+Seitsonen, A. Smogunov, P. Umari, and R. M. Wentz-
+covitch, QUANTUM ESPRESSO: a modular and open-
+source software project for quantum simulations of mate-
+rials, Journal of Physics: Condensed Matter 21, 395502
+(2009).
+[38] J. Deslippe, G. Samsonidze, D. A. Strubbe, M. Jain,
+M. L. Cohen, and S. G. Louie, BerkeleyGW: A mas-
+sively parallel computer package for the calculation of
+the quasiparticle and optical properties of materials and
+nanostructures, Computer Physics Communications 183,
+1269 (2012), 1111.4429.
+[39] D. Y. Qiu, G. Cohen, D. Novichkova, and S. Refaely-
+Abramson, Signatures of Dimensionality and Symmetry
+in Exciton Band Structure: Consequences for Exciton
+Dynamics and Transport, Nano Letters 21, 7644 (2021).
+[40] M. S. Hybertsen and S. G. Louie, Electron correlation in
+semiconductors and insulators: Band gaps and quasipar-
+ticle energies, Phys. Rev. B 34, 5390 (1986).
+[41] T. Rangel,
+K. Berland,
+S. Sharifzadeh,
+F. Brown-
+Altvater,
+K.
+Lee,
+P.
+Hyldgaard,
+L.
+Kronik,
+and
+J. B. Neaton, Structural and excited-state properties of
+oligoacene crystals from first principles, Phys. Rev. B 93,
+1 (2016).
+[42] T. Lettmann and M. Rohlfing, Finite-momentum exci-
+tons in rubrene single crystals, Phys. Rev. B 104, 1
+(2021).
+[43] See supplemental material at [url will be inserted by the
+production group] which includes references [10, 27, 34,
+36–38, 41, 44, 52, 53, 58–68] for computational details.
+[44] B. Monserrat, Vibrational averages along thermal lines,
+Phys. Rev. B 93, 1 (2016), 1512.06377.
+[45] B. Monserrat, Correlation effects on electron-phonon
+coupling in semiconductors:
+Many-body theory along
+thermal
+lines,
+Phys.
+Rev.
+B
+93,
+10.1103/Phys-
+RevB.93.100301 (2016), 0703642 [astro-ph].
+[46] M. Zacharias and F. Giustino, One-shot calculation
+of temperature-dependent optical spectra and phonon-
+induced band-gap renormalization, Phys. Rev. B 94,
+10.1103/PhysRevB.94.075125 (2016), 1604.02394.
+[47] M. Zacharias and F. Giustino, Theory of the special dis-
+placement method for electronic structure calculations at
+finite temperature, Physical Review Research 2, 7 (2020),
+1912.10929.
+[48] C. E. Patrick and F. Giustino, Unified theory of elec-
+tron–phonon renormalization and phonon-assisted opti-
+cal absorption, Journal of Physics: Condensed Matter
+26, 365503 (2014).
+[49] A. Miglio, V. Brousseau-Couture, E. Godbout, G. Anto-
+nius, Y. H. Chan, S. G. Louie, M. Cˆot´e, M. Giantomassi,
+and X. Gonze, Predominance of non-adiabatic effects
+in zero-point renormalization of the electronic band
+gap, npj Computational Materials 6, 10.1038/s41524-
+020-00434-z (2020), 2011.12765.
+[50] G. Kresse, J. Furthm¨uller, and J. Hafner, Ab initio Force
+Constant Approach to Phonon Dispersion Relations of
+Diamond and Graphite, Europhysics Letters 32, 729
+(1995).
+[51] K. Parlinski, Z. Q. Li, and Y. Kawazoe, First-Principles
+Determination of the Soft Mode in Cubic ZrO2, Physical
+Review Letters 78, 4063 (1997).
+[52] V. Kapil and E. A. Engel, A complete description of ther-
+modynamic stabilities of molecular crystals, Proc. Natl.
+Acad. Sci. U.S.A. 119, e2111769119 (2022).
+[53] S. Sharifzadeh, P. Darancet, L. Kronik, and J. B. Neaton,
+Low-Energy Charge-Transfer Excitons in Organic Solids
+from First-Principles: The Case of Pentacene, The Jour-
+nal of Physical Chemistry Letters 4, 2197 (2013).
+[54] L. Graf, A. Kusber, B. B¨uchner, and M. Knupfer, Strong
+exciton bandwidth reduction in pentacene as a function
+of temperature, Phys. Rev. B 106, 165429 (2022).
+[55] J. Arag´o and A. Troisi, Regimes of exciton transport in
+molecular crystals in the presence of dynamic disorder,
+Advanced Functional Materials 26, 2316 (2016).
+[56] S. Sharifzadeh, C. Y. Wong, H. Wu, B. L. Cotts, L. Kro-
+nik, N. S. Ginsberg, and J. B. Neaton, Relating the
+Physical Structure and Optoelectronic Function of Crys-
+talline TIPS-Pentacene, Advanced Functional Materials
+25, 2038 (2015).
+[57] M. Asher, R. Jouclas, M. Bardini, Y. Diskin-posner,
+N. Kahn, R. Korobko, A. R. Kennedy, L. S. D. Moraes,
+G. Schweicher, J. Liu, D. Beljonne, Y. Geerts, and O. Ya,
+Chemical Modifications Suppress Anharmonic Effects in
+the Lattice Dynamics of Organic Semiconductors, ACS
+Materials Au 10.1021/acsmaterialsau.2c00020 (2022).
+[58] S. Haas, B. Batlogg, C. Besnard, M. Schiltz, C. Kloc, and
+T. Siegrist, Large uniaxial negative thermal expansion in
+pentacene due to steric hindrance, Phys. Rev. B 76, 1
+(2007).
+[59] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized
+Gradient Approximation Made Simple, Physical Review
+Letters 77, 3865 (1996).
+[60] H. J. Monkhorst and J. D. Pack, Special points for
+Brillouin-zone integrations, Phys. Rev. B 13, 5188
+(1976).
+[61] A. Tkatchenko and M. Scheffler, Accurate molecular van
+der Waals interactions from ground-state electron density
+and free-atom reference data, Physical Review Letters
+102, 6 (2009).
+[62] Y. Eldar, M. Lindenbaum, M. Porat, and Y. Y. Zeevi,
+The Farthest Point Strategy for Progressive Image Sam-
+pling, IEEE Transactions on Image Processing 6, 1305
+(1997).
+[63] R. J. G. B. Campello, D. Moulavi, A. Zimek, and
+J. Sander, Hierarchical density estimates for data clus-
+tering, visualization, and outlier detection, ACM Trans.
+Knowl. Discov. Data 10, 5 (2015).
+[64] A. P. Bart´ok, R. Kondor, and G. Cs´anyi, On representing
+chemical environments, Phys. Rev. B 87, 184115 (2013).
+[65] M. J. Willatt, F. Musil, and M. Ceriotti, Feature opti-
+mization for atomistic machine learning yields a data-
+driven construction of the periodic table of the elements,
+Phys Chem Chem Phys 20, 29661 (2018).
+[66] A.
+Singraber,
+N2P2,
+https://github.com/
+CompPhysVienna/n2p2.
+[67] V. Kapil, M. Rossi, O. Marsalek, R. Petraglia, Y. Lit-
+man, T. Spura, B. Cheng, A. Cuzzocrea, R. H. Meißner,
+D. M.Wilkins, B. A. Helfrecht, P. Juda, S. P. Bienv-
+enue, W. Fang, J. Kessler, I. Poltavsky, S. Vandenbrande,
+J. Wieme, and M. Ceriotti, i-PI 2.0: A universal force
+engine for advanced molecular simulations, Computer
+Physics Communications 236, 214 (2018).
+[68] S. Plimpton, Fast parallel algorithms for short-range
+molecular dynamics, J. Compt. Phys. 117, 1 (1995).
+
+Supplemental Material: Phonon-induced localization
+of excitons in molecular crystals from first principles
+Antonios M. Alvertis,1, 2, ∗ Jonah B. Haber,2 Edgar A.
+Engel,3 Sahar Sharifzadeh,4, 5 and Jeffrey B. Neaton1, 2, 6, †
+1Materials Sciences Division, Lawrence Berkeley
+National Laboratory, Berkeley, California 94720, USA
+2Department of Physics, University of California Berkeley, Berkeley, United States
+3Cavendish Laboratory, University of Cambridge,
+J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
+4Division of Materials Science and Engineering, Boston University, United States
+5Department of Electrical and Computer Engineering, Boston University, United States
+6Kavli Energy NanoScience Institute at Berkeley, Berkeley, United States
+1
+arXiv:2301.11944v1  [cond-mat.mtrl-sci]  27 Jan 2023
+
+CONTENTS
+S1. Computational details
+3
+A. DFT calculations
+3
+B. GW-BSE calculations
+3
+C. Phonon calculations and Monte Carlo sampling of vibrational averages
+3
+D. Machine learning potential and path-integral molecular dynamics
+6
+E. Calculation of exciton radii
+7
+S2. Effect of thermal expansion
+8
+S3. Contributions of Γ and X phonons
+9
+A. Exciton radii
+9
+B. Exciton dispersion
+10
+S4. Anharmonic potential energy surfaces
+11
+S5. Highly delocalized excitons within the harmonic approximation
+12
+S6. Estimation of the minimum of the singlet exciton potential energy surface
+12
+S7. Tables of averages and standard deviations of exciton energies and radii
+15
+References
+17
+∗ amalvertis@lbl.gov
+† jbneaton@lbl.gov
+2
+
+S1.
+COMPUTATIONAL DETAILS
+A.
+DFT calculations
+First-principles energies, forces, band gaps and wavefunctions are computed using the
+Quantum Espresso [1] DFT code with the semi-local PBE exchange-correlation functional [2]
+and a plane-wave energy cut-off of 60 Rydberg for the wavefunction.
+For the unit cell
+of pentacene we start from the experimental structure PENCEN08 as in the Cambridge
+Crystallographic Database [3], and relax the internal coordinates while leaving the volume
+fixed and using the Tkatchenko-Scheffler (TS) dispersion correction [4]. For the geometry
+optimization we employ a 4 × 4 × 2 Monkhorst-Pack k-point grid [5].
+B.
+GW-BSE calculations
+We employ the one-shot GoWo approximation for the quasiparticle properties of pen-
+tacene, as implemented in the BerkeleyGW code [6]. We use a 4 × 4 × 2 k-grid, 400 bands
+and a 7 Ry plane wave cutoff to calculate the dielectric screening. For exciton calculations,
+we construct the electron-hole kernel on a 4 × 4 × 2 grid using 4 valence and 4 conduction
+states, and then interpolate on a 8 × 8 × 4 k-grid with the same number of bands. This set
+of parameters has been shown to give converged results in previous computational studies of
+pentacene [7, 8]. When studying 2 × 1 × 1 supercells of pentacene (see following subsection
+on the Monte Carlo sampling of vibrational averages), we use a half the number of k-points
+in the x direction in all cases (2 × 4 × 2 to calculate the dielectric screening and 4 × 8 × 4
+to interpolate the BSE kernel), and double the number of bands for the dielectric screening
+(800 bands) and exciton calculations (8 valence and 8 conduction bands).
+C.
+Phonon calculations and Monte Carlo sampling of vibrational averages
+We include the contribution from lattice dynamics at temperature T to an observable O
+by means of the quantum mechanical expectation value
+O(T) = 1
+Z
+�
+s
+⟨χs(u)|O(u)|χs(u)⟩e−Es/kBT,
+(1)
+3
+
+0
+20
+40
+60
+80
+100
+configuration
+0.3
+0.2
+0.1
+0.0
+Eg (eV)
+FIG. S1. Convergence of the DFT band gap renormalization ∆Eg as a function of the number of
+configurations used in the Monte Carlo sampling, for the example of using a 2 × 1 × 1 supercell
+at T = 100 K. The value of the gap renormalization for each configuration is denoted in black
+crosses, while the blue line is the running average of the band gap renormalization due to phonons.
+The dashed line is the final computed average value for the band gap renormalization, while the
+red crosses indicate the ten configurations for which we run GW-BSE calculations to obtain their
+exciton properties.
+where |χs⟩ is the harmonic vibrational wavefunction in state s with energy Es, Z =
+�
+s e−Es/kBT is the partition function, and u = {uqν} is a collective coordinate that in-
+cludes the amplitudes of all normal modes of vibration in the system labeled by the phonon
+wave vector q and the phonon branch ν.
+Substituting the harmonic vibrational wavefunction, the above expectation value can be
+rewritten
+O(T) =
+�
+du|Φ(u; T)|2O(u),
+(2)
+where:
+|Φ(u; T)|2 =
+�
+q,ν
+(2πσ2
+qν(T))−1/2 exp
+�
+−
+u2
+qν
+2σ2
+qν(T)
+�
+,
+(3)
+4
+
+the harmonic density at temperature T, which is a product of Gaussian functions of width:
+σ2
+qν(T) =
+1
+2ωqν
+· coth
+� ωqν
+2kBT
+�
+.
+(4)
+We evaluate Eq. (2) by generating stochastic samples distributed according to the har-
+monic vibrational ensemble, calculating the observable of interest at each configuration, and
+averaging over all configurations. To sample the single-particle DFT electronic band gap
+we generate 100 configurations, which are sufficient for convergence, as demonstrated in
+Fig. S1. We obtain the band gap correction for each of these configurations at temperatures
+of T = 0 K, T = 100 K, T = 200 K and T = 300 K. We then apply GW corrections to these
+DFT values. Due to the large computational cost of these calculations, we only perform
+GW calculations on the ten configurations whose single-particle DFT band gap value is
+closest to the calculated average band gap for each temperature, as also shown in Fig. S1.
+This correlated sampling strategy between DFT and GW has been shown to be accurate
+in pentacene [8] and other systems [9]. Having calculated the effects of electron-phonon
+coupling on the quasiparticle band gap, we solve the Bethe-Salpeter equation for the same
+ten configurations at the various temperatures, using the parameters of the previous section
+and computing exciton energies (at finite exciton momenta) and exciton radii.
+The sampling of the expectation value of equation 2 becomes increasingly accurate with
+the inclusion of more q-points in the Brillouin zone. Within the finite differences approach
+for phonon calculations and the expectation values of observables at finite temperatures,
+q-points are described using commensurate supercells. For pentacene a 2 × 1 × 1 (size 2)
+supercell (four pentacene molecules) is 98% converged with respect to a 2 × 2 × 2 (size 8)
+supercell (sixteen molecules) for the band gap zero-point renormalization (−139 meV and
+−142 meV respectively), as seen in Fig. S2 where we plot the convergence of the pentacene
+band gap renormalization at 100 K, as obtained from sampling within the anharmonic dis-
+tribution. Therefore a 2 × 1 × 1 supercell offers a good balance between computational cost
+for the GW-BSE calculations, and accuracy.
+5
+
+-100
+-110
+-120
+-130
+-140
+-ΔEg (meV)
+supercell size
+1
+2
+8
+FIG. S2. Convergence of the pentacene DFT band gap renormalization ∆Eg at T = 100 K, as a
+function of the supercell size. The dashed line is given as a guide to the eye.
+D.
+Machine learning potential and path-integral molecular dynamics
+The details of the construction of the machine learning potential for pentacene (and
+other acene crystals), as well as the procedure for obtaining trajectories within path-integral
+molecular dynamics, have been described elsewhere [10]. Here we include some key points
+and refer the reader interested in a more in-depth discussion to Ref. [10].
+A machine learning potential describing the dynamics of the acene series of molecular
+crystals was trained on a set of training data including the total energies of 4862 configu-
+rations of naphthalene, anthracene, tetracene and pentacene, obtained from the harmonic
+distributions at 0 K, 150 K, and 300 K. From this set, 400 validation and 400 test con-
+figurations were drawn randomly. For tuning the ML potential architecture and training
+procedure, the training data was sparsified by farthest-point-sampling (FPS) [11, 12], retain-
+ing the 1000 most structurally distinct training configurations. This FPS was performed on
+the basis of Euclidean distances between configurations described in terms of their smooth
+overlap of atomic positions (SOAP) powerspectra [13], using the radially-scaled implemen-
+tation [14] with a radial and angular basis of 12 and nine functions, respectively, a cut-off
+radius of 8 ˚A, a width of 0.275 ˚A for the Gaussian densities associated with the atomic posi-
+tions, and a scaling onset and exponent of 2.5 ˚A and 4.5, respectively. An ensemble of seven
+fully-connected, feed-forward neural networks with two hidden layers of 16 nodes each was
+constructed by using the N2P2 code [15].
+6
+
+For the independent testset, the ML potentials reproduce the reference energies and forces
+with root-mean-square errors of 2.4 meV/atom and 0.157 meV/ ˚A, respectively. Crucially,
+this suffices to run stable path integral simulations in the constant-volume ensemble over
+extended simulation times, and to accurately compute the quantum-mechanical expectation
+values of observables within the reference first-principles thermodynamic ensemble.
+Finite-temperature, quantum-mechanical thermodynamic averages of observables can be
+computed as averages of their values for (random) configurations drawn from PIMD sim-
+ulations. We exploit the affordability of the ML potential to perform PIMD in the NV T
+ensemble at temperatures of 100 K and 300 K, and subsequently compute observables for
+configurations extracted from the PIMD trajectory (after equilibration) at regular intervals
+of 50 fs, which ensures that these samples are decorrelated. The PIMD simulations of at least
+10 ps were performed using the i-PI [16] molecular dynamics engine to drive LAMMPS [17]
+energy and force evaluations of the ML potential, a 0.25 fs timestep, and a path integral
+Langevin equation thermostat [18] with τ = 100 fs.
+The number of replicas required for PIMD simulations is determined by the highest
+frequency phonon modes that are present in the system, which in our case is C–H stretching
+and is common among all acene crystals. For benzene it has been shown that 32 replicas
+are sufficient to convergence electronic band gaps within 15 meV[10, 19], and the same value
+has therefore been employed for pentacene.
+For obtaining the exciton properties (energies and radii) within the anharmonic distri-
+butions we follow a tactic similar to the correlated sampling described in the case of the
+harmonic Monte Carlo sampling. We first draw 100 configurations at which we compute the
+DFT band gap and then we rank the configurations based on their band gap proximity to the
+computed mean value. We then perform GW-BSE calculations on the top 10 configurations
+among these.
+E.
+Calculation of exciton radii
+As discussed in the main text, we compute the electron-hole correlation function as
+defined in Ref. [20], namely
+FS(r) =
+�
+V
+d3rh|ψQ=0
+S
+(re = rh + r, rh)|2,
+(5)
+7
+
+where V the volume of the primitive cell. FS(r) describes the probability of finding the
+electron-hole pair at a vector r = re − rh, and is computed as a discrete sum over hole
+positions. We note here that even if we only integrate over the volume of the primitive cell,
+the exciton wavefunction can delocalize over the whole supercell used in the Bethe-Salpeter
+calculation, i.e., 8×8×4 or 4×8×4 for pentacene, as discussed below. Even if the hole was
+moved outside the primitive cell, we would simply obtain a shifted exciton wavefunction.
+For pentacene, it was found in Ref. [20] that the average electron-hole distance of the
+correlation function is converged, and that its envelope produces a smooth function for
+88 high-probability hole positions in the unit cell, corresponding to two hole positions per
+carbon atom, at ±0.5˚A above and below the plane of the molecule for each atom (effectively
+sampling the C pz orbitals). For each sampled hole, the correlation function is computed
+on an 8 × 8 × 4 supercell of pentacene, which is necessary for convergence of the exciton
+wavefunctions. For the 2×1×1 cell of pentacene, which includes the effects of phonons (see
+section S1 C), the real-space supercell used for FS(r) is reduced to 4 × 8 × 4, since every cell
+along the x direction already contains two unit cells. Moreover the number of carbon atoms
+per cell doubles, and so we sample at 88 · 2 = 176 hole positions in this case.
+Having computed the electron-hole correlation function for a given atomic configuration
+u, the exciton radius is computed as
+rexc(u) =
+�
+d|r|FS(|r|)|r|.
+(6)
+To compute the vibrationally renormalized exciton radii at a temperature T, we apply
+equations 5 and 7 of the main manuscript with O = rexc. In the example case where we
+make the harmonic approximation this results in
+⟨rexc(T)⟩ =
+�
+du|Φ(u; T)|2rexc(u),
+(7)
+where |Φ(u; T)|2 the harmonic density function, as discussed in section S1 C above.
+S2.
+EFFECT OF THERMAL EXPANSION
+To study the effect of thermal expansion on the exciton dispersion of pentacene, we
+perform GW-BSE calculations on two pentacene structures deposited in the Cambridge
+8
+
+Crystallographic Database, which have been obtained through X-ray diffraction measure-
+ments at temperatures within the range of interest of 100 − 300 K. These are the structures
+PENCEN06 and PENCEN07 [3], obtained at 120 K and 293 K respectively. We use the
+experimental crystal structures without any optimization of the internal coordinates. The
+absolute value of the singlet exciton energy and width are known to be very sensitive to
+coordinate optimization and the precise level of theory employed to perform this optimiza-
+tion [21]. Therefore here we will focus on differences between energies and dispersion widths
+of the two experimental structures, without attempting a direct comparison to values ob-
+tained for the optimized structure necessary to perform phonon calculations. In principle
+phonons and thermal expansion need to be accounted for concurrently, however the large
+number of degrees of freedom in molecular crystals constitute such an analysis extremely
+challenging.
+The dispersion width W = E(X) − E(Γ) is found to be 11 meV smaller in the high-
+temperature phase. Given the linear character of the static exciton dispersion of pentacene,
+we can estimate the bandwidth ∆ = Ω(Q = 0.4 ˚A
+−1) − Ω(Q = 0.1 ˚A
+−1), and find that
+∆ for the singlet exciton shrinks by 6 meV due to thermal expansion within this range of
+temperatures. There is therefore no competition between thermal expansion and exciton-
+phonon coupling in terms of their effect on the exciton dispersion. Moreover, this flattening
+of the exciton dispersion caused by thermal expansion will bring the predicted value of
+∆ = 30 meV for the width at 300 K and when including anharmonic effects, even closer to
+the experimental value of 23 meV at the same temperature (Table I, main manuscript).
+S3.
+CONTRIBUTIONS OF Γ AND X PHONONS
+A.
+Exciton radii
+The values for the vibrationally renormalized exciton radii given in the main manuscript,
+in both the harmonic and anharmonic cases, include the effects of Γ and X phonons, i.e.
+include phonons within a 2 × 1 × 1 supercell of pentacene. As shown in Fig. 2 of the main
+manuscript, the harmonic approximation predicts an increase of the average exciton radius
+with increasing the temperature from 0 K to 300 K. Qualitatively, this is in agreement with
+the case of only including the effect of Γ phonons within the harmonic approximation, i.e.
+9
+
+rexc(T) (˚A)
+1 × 1 × 1 (Γ)
+2 × 1 × 1 (Γ, X)
+0 K
+4.73 ± 0.35
+4.85 ± 0.30
+300 K
+5.09 ± 0.40
+6.96 ± 1.25
+TABLE S1. The effect of Γ and X phonons on the vibrationally-averaged exciton radius, within
+the harmonic approximation.
+W(S1) (meV)
+W(T1) (meV)
+static
+110
+52
+100 K
+67
+18
+300 K
+59
+19
+TABLE S2. The effect of Γ phonons on the dispersion width W for the first singlet and triplet
+excitons of pentacene, including anharmonic effects.
+focusing on a single unit cell of pentacene, as seen in Table S1. Quantitatively, this increase
+of the radius becomes more prevalent when including X phonons (in the 2×1×1 supercell),
+which is to be expected given that anharmonic effects are more relevant for finite phonon
+wavevectors q as discussed in the main manuscript and in Ref. [10].
+B.
+Exciton dispersion
+Tables S2 and S3 summarize the effect of Γ phonons only on the width W = E(X)−E(Γ)
+of the exciton dispersion within the anharmonic and harmonic distributions respectively.
+The results given in Table I of the main manuscript also contain the effect of phonons at the
+band-edge X.
+For both the harmonic and anharmonic cases, the result for the triplet is the same: the
+width of the exciton band narrows entirely due to zero-point motion, and increasing the
+temperature to 300 K has no effect on it. For the singlet, while we find that including an-
+harmonic effects at 100 K leads to a greater band-narrowing compared to the harmonic case
+(at 0 K), increasing the temperature to 300 K leads to a further reduction of the bandwidth
+by 8 meV, compared to the 12 meV of the harmonic case. For the exact values of the exciton
+energies please refer to the tables of section S7. It is also worth noting that in this case of
+including Γ phonons only, the harmonic approximation does not show the unphysical in-
+crease of the dispersion width with increasing temperature, due to not including the highly
+anharmonic acoustic phonon at q = X, see also section S4.
+10
+
+W(S1) (meV)
+W(T1) (meV)
+static
+110
+52
+0 K
+82
+20
+300 K
+70
+19
+TABLE S3. The effect of Γ phonons on the dispersion width W for the first singlet and triplet
+excitons of pentacene, within the harmonic approximation.
+FIG. S3. Comparison between the harmonic (red) and anharmonic (black) potential energy surfaces
+of the acoustic mode with frequency ω = 40 cm−1 at q = X. The phonon displacement u is given
+in units of the zero-point width
+1
+√
+2ω.
+S4.
+ANHARMONIC POTENTIAL ENERGY SURFACES
+Fig. S3 visualizes the potential energy surface of the anharmonic acoustic mode of pen-
+tacene discussed in the main manuscript, at q = X, where it has a frequency of ω = 40 cm−1.
+In red we show the harmonic potential energy surface as predicted by the relationship
+E = 1
+2ω2u2, while the black crosses indicate the total energy of the system (with respect
+to that of the optimized geometry) upon explicitly displacing along this phonon and per-
+forming DFT calculations at different displacements u. While for small values of u the two
+results coincide, they quickly start to diverge, and anharmonicity provides an energetic bar-
+rier which prevents the over-displacement of pentacene along this mode, as permitted within
+the harmonic approximation.
+11
+
+S5.
+HIGHLY DELOCALIZED EXCITONS WITHIN THE HARMONIC APPROX-
+IMATION
+As discussed in the main manuscript, the thermal excitation of phonons within the har-
+monic approximation leads to configurations with highly delocalized excitons. The most
+prominent examples appear when the anharmonic acoustic phonon of pentacene, corre-
+sponding to a sliding of adjacent molecules along the z-axis, is displaced significantly. Let us
+consider the case of thermal excitation at 300 K for a 2×1×1 supercell, which describes this
+phonon at q = X. In this case, several high-probability hole positions used to sample the
+electron-hole correlation function of Eq. 5 lead to very large radii in the range of 25−30 ˚A, for
+several nuclear geometries. It is worth noting that for some nuclear configurations, it is the
+hole position with the highest probability entering Eq. 5 which already leads to large exciton
+radii. As an example, we plot in Fig. S4 the delocalized exciton that arises for a configura-
+tion used in the sampling of exciton properties. Here the hole is placed in the most likely
+position out of the 176 ones used for the sampling of the electron-hole correlation function
+of the specific nuclear configuration, resulting in an exciton radius of 31 ˚A. Other exam-
+ples include two sampled nuclear configurations where the highest probability hole positions
+lead to excitons with radii of 23 ˚A and 25 ˚A. It is also emphasized that for every nuclear
+configuration resulting from thermal phonon excitation at 300 K within the harmonic ap-
+proximation we find highly probable hole positions that lead to similarly highly delocalized
+excitons, although in the above three examples these are not only high-probability holes,
+but the ones with the highest probability.
+S6.
+ESTIMATION OF THE MINIMUM OF THE SINGLET EXCITON POTEN-
+TIAL ENERGY SURFACE
+We would like to estimate the position of the minimum of the singlet exciton potential
+energy surface along the acoustic phonon of pentacene, which is responsible for exciton
+delocalization at large displacements u. To do so, we have to assume the ground and excited
+state potential energy surfaces to be harmonic. The ground state energy along this phonon
+will be
+EGS(u) = 1
+2ω2
+GSu2,
+(8)
+12
+
+FIG. S4. Isosurface of the electron distribution (blue) for a highly delocalized pentacene singlet
+exciton, for a hole placed at the position in red. This exciton with a radius of 31 ˚A appears within
+the harmonic approximation for a 2 × 1 × 1, as a result of thermal phonon excitation at 300 K.
+where ωGS the phonon frequency in the ground state. Reexpressing the phonon displacement
+u in units of the zero-point width 1/
+√
+2ω of the harmonic distribution, this may be rewritten
+as
+EGS(u) = 1
+4ωGSu2.
+(9)
+The excited state surface within these units is written as
+EES(u) = 1
+4ωES(u − uES)2 + ∆,
+(10)
+where we have the following unknown quantities: uES, which is the position at which the
+excited state obtains its minimum energy, ∆, which is the total energy of the system when in
+the excited state and at that geometry and ωES, which is the excited state mode frequency.
+We would now like to estimate uES, for this purpose we perform DFT and GW-BSE
+calculations at u = 5, 15 for this phonon mode. At each of these atomic configurations, we
+obtain the excited state surface energy as the vertical excitation energy (from GW-BSE)
+plus the ground state energy (from DFT), in order to obtain the total energy of the system
+in the excited state. Solving the resulting system and after a few algebraic manipulations
+13
+
+we find uES ≈ 1. While this is a rough estimate, it is clear that the potential energy surface
+minimum is far from the very large values of u which are required in order to find the highly
+delocalized excitons that appear for values of u that are equal to 30 or greater (see main
+manuscript Fig. 3b).
+14
+
+S7.
+TABLES OF AVERAGES AND STANDARD DEVIATIONS OF EXCITON
+ENERGIES AND RADII
+rexc(T) (˚A)
+singlet
+triplet
+0 K
+4.85 ± 0.30
+1.23 ± 0.13
+100 K
+5.04 ± 0.17
+1.23 ± 0.10
+200 K
+4.98 ± 0.21
+1.32 ± 0.07
+300 K
+6.96 ± 1.25
+1.26 ± 0.13
+TABLE S4. Vibrational averages of exciton radii within the harmonic approximation - 2 × 1 × 1
+supercell.
+rexc(T) (˚A)
+singlet
+triplet
+100 K
+5.90 ± 0.65
+1.48 ± 0.15
+300 K
+5.25 ± 0.35
+1.57 ± 0.08
+TABLE S5. Vibrational averages of exciton radii within the anharmonic distribution - 2 × 1 × 1
+supercell.
+E(S1)(T) (eV)
+−X
+−X/2
+Γ
+X/2
+X
+0 K
+1.771 ± 0.047
+1.735 ± 0.056
+1.688 ± 0.064
+1.737 ± 0.056
+1.771 ± 0.047
+300 K
+1.730 ± 0.030
+1.704 ± 0.043
+1.663 ± 0.053
+1.706 ± 0.045
+1.733 ± 0.033
+TABLE S6. Singlet exciton energies at various points in reciprocal space, including the effect of Γ
+phonons at 0 K and 300 K within the harmonic approximation.
+E(T1)(T) (eV)
+−X
+−X/2
+Γ
+X/2
+X
+0 K
+0.918 ± 0.030
+0.909 ± 0.027
+0.898 ± 0.027
+0.910 ± 0.028
+0.918 ± 0.030
+300 K
+0.918 ± 0.051
+0.910 ± 0.048
+0.899 ± 0.045
+0.910 ± 0.048
+0.918 ± 0.052
+TABLE S7. Triplet exciton energies at various points in reciprocal space, including the effect of Γ
+phonons at 0 K and 300 K within the harmonic approximation.
+E(S1)(T) (eV)
+Γ
+X
+0 K
+1.593 ± 0.064
+1.654 ± 0.041
+300 K
+1.636 ± 0.064
+1.712 ± 0.061
+TABLE S8. Singlet exciton energies at various points in reciprocal space, including the effects of
+Γ,X phonons at 0 K and 300 K within the harmonic approximation.
+15
+
+E(S1)(T) (eV)
+Γ
+X/2
+X
+100 K
+1.713 ± 0.037
+1.739 ± 0.038
+1.780 ± 0.043
+300 K
+1.695 ± 0.041
+1.719 ± 0.039
+1.754 ± 0.038
+TABLE S9. Singlet exciton energies at various points in reciprocal space, including anharmonic
+effects and Γ phonons at 100 K and 300 K.
+E(T1)(T) (eV)
+Γ
+X/2
+X
+100 K
+0.885 ± 0.078
+0.896 ± 0.081
+0.904 ± 0.083
+300 K
+0.872 ± 0.063
+0.878 ± 0.068
+0.891 ± 0.068
+TABLE S10. Triplet exciton energies at various points in reciprocal space, including anharmonic
+effects and Γ phonons at 100 K and 300 K.
+E(S1)(T) (eV)
+Γ
+X/2
+X
+100 K
+1.659 ± 0.036
+1.692 ± 0.033
+1.718 ± 0.026
+300 K
+1.656 ± 0.046
+1.675 ± 0.044
+1.698 ± 0.040
+TABLE S11. Singlet exciton energies at various points in reciprocal space, including anharmonic
+effects and Γ,X phonons at 100 K and 300 K.
+E(T1)(T) (eV)
+Γ
+X/2
+X
+100 K
+0.859 ± 0.048
+0.870 ± 0.037
+0.877 ± 0.030
+300 K
+0.859 ± 0.037
+0.865 ± 0.044
+0.878 ± 0.070
+TABLE S12. Triplet exciton energies at various points in reciprocal space, including anharmonic
+effects and Γ,X phonons at 100 K and 300 K.
+16
+
+[1] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli,
+G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. Fabris, G. Fratesi, S. de Giron-
+coli, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos,
+N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia,
+S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch,
+QUANTUM ESPRESSO: a modular and open-source software project for quantum simula-
+tions of materials, Journal of Physics: Condensed Matter 21, 395502 (2009).
+[2] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple,
+Physical Review Letters 77, 3865 (1996).
+[3] S. Haas, B. Batlogg, C. Besnard, M. Schiltz, C. Kloc, and T. Siegrist, Large uniaxial negative
+thermal expansion in pentacene due to steric hindrance, Phys. Rev. B 76, 1 (2007).
+[4] A. Tkatchenko and M. Scheffler, Accurate molecular van der Waals interactions from ground-
+state electron density and free-atom reference data, Physical Review Letters 102, 6 (2009).
+[5] H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B
+13, 5188 (1976).
+[6] J. Deslippe, G. Samsonidze, D. A. Strubbe, M. Jain, M. L. Cohen, and S. G. Louie, Berke-
+leyGW: A massively parallel computer package for the calculation of the quasiparticle and
+optical properties of materials and nanostructures, Computer Physics Communications 183,
+1269 (2012), 1111.4429.
+[7] S. Refaely-Abramson, F. H. Da Jornada, S. G. Louie, and J. B. Neaton, Origins of Singlet
+Fission in Solid Pentacene from an ab initio Green’s Function Approach, Physical Review
+Letters 119, 1 (2017), 1706.01564.
+[8] A. M. Alvertis, R. Pandya, L. A. Muscarella, N. Sawhney, M. Nguyen, B. Ehrler, A. Rao, R. H.
+Friend, A. W. Chin, and B. Monserrat, Impact of exciton delocalization on exciton-vibration
+interactions in organic semiconductors, Phys. Rev. B 102, 081122 (2020).
+[9] B. Monserrat, Vibrational averages along thermal lines, Phys. Rev. B 93, 1 (2016), 1512.06377.
+[10] A. M. Alvertis and E. A. Engel, Importance of vibrational anharmonicity for electron-phonon
+coupling in molecular crystals, Phys. Rev. B 105, 1 (2022).
+17
+
+[11] Y. Eldar, M. Lindenbaum, M. Porat, and Y. Y. Zeevi, The Farthest Point Strategy for Pro-
+gressive Image Sampling, IEEE Transactions on Image Processing 6, 1305 (1997).
+[12] R. J. G. B. Campello, D. Moulavi, A. Zimek, and J. Sander, Hierarchical density estimates
+for data clustering, visualization, and outlier detection, ACM Trans. Knowl. Discov. Data 10,
+5 (2015).
+[13] A. P. Bart´ok, R. Kondor, and G. Cs´anyi, On representing chemical environments, Phys. Rev.
+B 87, 184115 (2013).
+[14] M. J. Willatt, F. Musil, and M. Ceriotti, Feature optimization for atomistic machine learning
+yields a data-driven construction of the periodic table of the elements, Phys Chem Chem Phys
+20, 29661 (2018).
+[15] A. Singraber, N2P2, https://github.com/CompPhysVienna/n2p2.
+[16] V. Kapil, M. Rossi, O. Marsalek, R. Petraglia, Y. Litman, T. Spura, B. Cheng, A. Cuzzocrea,
+R. H. Meißner, D. M.Wilkins, B. A. Helfrecht, P. Juda, S. P. Bienvenue, W. Fang, J. Kessler,
+I. Poltavsky, S. Vandenbrande, J. Wieme, and M. Ceriotti, i-PI 2.0: A universal force engine
+for advanced molecular simulations, Computer Physics Communications 236, 214 (2018).
+[17] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Compt. Phys.
+117, 1 (1995).
+[18] M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, Efficient stochastic
+thermostatting of path integral molecular dynamics, J. Chem. Phys. 133, 124104 (2010).
+[19] V. Kapil and E. A. Engel, A complete description of thermodynamic stabilities of molecular
+crystals, Proc. Natl. Acad. Sci. U.S.A. 119, e2111769119 (2022).
+[20] S. Sharifzadeh, P. Darancet, L. Kronik, and J. B. Neaton, Low-Energy Charge-Transfer Exci-
+tons in Organic Solids from First-Principles: The Case of Pentacene, The Journal of Physical
+Chemistry Letters 4, 2197 (2013).
+[21] T. Rangel, K. Berland, S. Sharifzadeh, F. Brown-Altvater, K. Lee, P. Hyldgaard, L. Kronik,
+and J. B. Neaton, Structural and excited-state properties of oligoacene crystals from first
+principles, Phys. Rev. B 93, 1 (2016).
+18
+
diff --git a/ydFKT4oBgHgl3EQf7S6i/content/tmp_files/load_file.txt b/ydFKT4oBgHgl3EQf7S6i/content/tmp_files/load_file.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f549781b0f26836ba3f7b04e2de68570c0ac1600
--- /dev/null
+++ b/ydFKT4oBgHgl3EQf7S6i/content/tmp_files/load_file.txt
@@ -0,0 +1,1323 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf,len=1322
+page_content='Phonon-induced localization of excitons in molecular crystals  from first principles  Antonios M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Alvertis,1, 2, ∗ Jonah B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Haber,2 Edgar A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Engel,3 Sahar Sharifzadeh,4, 5 and Jeffrey B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Neaton1, 2, 6, †  1Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA  2Department of Physics, University of California Berkeley, Berkeley, United States  3Cavendish Laboratory, University of Cambridge,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Thomson Avenue, Cambridge CB3 0HE, United Kingdom  4Division of Materials Science and Engineering, Boston University, United States  5Department of Electrical and Computer Engineering, Boston University, United States  6Kavli Energy NanoScience Institute at Berkeley, Berkeley, United States  (Dated: January 31, 2023)  The spatial extent of excitons in molecular systems underpins their photophysics and utility for  optoelectronic applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Phonons are reported to lead to both exciton localization and delo-  calization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' However, a microscopic understanding of phonon-induced (de)localization is lacking, in  particular how localized states form, the role of specific vibrations, and the relative importance of  quantum and thermal nuclear fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Here we present a first-principles study of these phenom-  ena in solid pentacene, a prototypical molecular crystal, capturing the formation of bound excitons,  exciton-phonon coupling to all orders, and phonon anharmonicity, using density functional theory,  the ab initio GW-Bethe-Salpeter equation approach, finite difference, and path integral techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  We find that for pentacene zero-point nuclear motion causes uniformly strong localization, with  thermal motion providing additional localization only for Wannier-Mott-like excitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Anharmonic  effects drive temperature-dependent localization, and while such effects prevent the emergence of  highly delocalized excitons, we explore the conditions under which these might be realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='– Photoexcitation of organic molecular  crystals leads to strongly bound electron-hole pairs, or  excitons, due to the weak screening of the Coulomb in-  teraction in these systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Depending on factors such as  the size of the molecular building blocks and the spin of  the electron-hole pair, exciton radii can vary from those  of localized Frenkel excitons [1, 2] to spatially extended  excitons that approach the Wannier-Mott limit [3–7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The spatial extent of these excited states is important  to applications of organic semiconductors such as photo-  voltaics [8] and LEDs [9], since it affects properties in-  cluding the nature of their interaction with phonons [10],  their transport [11] and non-radiative recombination [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Critical to affecting the spatial extent of excited states  are lattice vibrations, which are generally thought to  result in wavefunction localization [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Phonons can  strongly renormalize one- and two-particle excitation en-  ergies of organic systems, influencing the optical gap and  the charge carrier mobility [10, 14, 15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Phonons in these  systems have generally been thought to lead to local-  ized excitons that diffuse via, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=', a F¨orster or Dexter  mechanism [16, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' However, it has recently been pro-  posed that in certain well-ordered organic crystals atomic  motion can give rise to configurations that favor strong  transient exciton delocalization, having a beneficial ef-  fect to transport [18–20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' This transient exciton delocal-  ization is similar to transient charge delocalization [21–  23], wherein phonons lead to configurations with large  overlaps between neighboring molecular orbitals [24] and  ∗ amalvertis@lbl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='gov  † jbneaton@lbl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='gov  hence highly delocalized states [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Despite these insights, a rigorous microscopic under-  standing of phonon-induced modulations to exciton radii,  one that accounts for electron-hole interactions, strong  exciton-phonon coupling at finite temperatures [10, 26],  and the anharmonicity of low-frequency motions in  molecular crystals [27–30], is still lacking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Here we elu-  cidate the microscopic mechanism of exciton localiza-  tion in extended molecular solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  We employ a first-  principles computational framework which captures all  aforementioned effects, combining density functional the-  ory (DFT), the Green’s function-based ab initio GW-  Bethe Salpeter equation (BSE) approach for accurately  describing exciton effects [31], finite-difference methods  for strong exciton-phonon interactions [10, 32], and path  integral techniques for describing phonon anharmonic-  ity [33, 34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  We apply this framework to the proto-  typical molecular crystal pentacene and show that zero-  point nuclear motion leads to strong localization of sin-  glet and triplet excitons, reducing their average electron-  hole separation by more than a factor of two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Tem-  perature increases further reduce the size of delocalized  Wannier-Mott-like excitons, an effect driven by anhar-  monic phonons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The trends in exciton radii are reflected  in the dispersion of their energies in reciprocal space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  While highly delocalized excitons do appear at large  phonon displacements, anharmonicity reduces the ampli-  tude associated with these motions, suppressing transient  delocalization for exciton transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  System and methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='– We focus on the widely stud-  ied molecular crystal pentacene [35], which hosts a de-  localized Wannier-Mott-like singlet exciton (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1a) and  a more localized Frenkel-like triplet exciton (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1b) [7,  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='11944v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='mtrl-sci]  27 Jan 2023  2  10, 36], for which the effect of phonons is expected to be  different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We compute excitons with principal quantum  number S and center-of-mass momentum Q using ab ini-  tio DFT and GW-BSE calculations with the Quantum  Espresso [37] and BerkeleyGW [38] codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' This involves  constructing the electron-hole kernel Ke−h and solving  the BSE [31, 39] in reciprocal space in the electron-hole  basis, namely  (Eck+Q − Evk)AS  cvkQ  (1)  +  �  c′v′k′  ⟨ck + Q, vk| Ke−h |c′k′ + Q, v′k′⟩ AS  c′v′k′Q  = ΩS  QAS  cvkQ,  with input from prior DFT and GW calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  In  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1 the indices c, v define conduction and valence states  respectively, k is the crystal momentum, and AS  cvkQ is  the amplitude contributed by states c, v with momentum  k to the exciton with momentum Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The exciton wave-  function can be written as  ΨQ  S (re, rh) =  �  cvk  AS  cvkQψck+Q(re)ψ∗  vk(rh),  (2)  where ψnk are the Kohn-Sham wavefunctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The kernel  Ke−h consists only of an attractive ‘direct’ term between  electrons and holes for triplets, while for singlets it also  includes a repulsive ‘exchange’ term, giving singlets their  greater spatial extent [7, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The energies of the conduc-  tion and valence bands in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1 are obtained within the  so-called GW approximation [40] from self-energy correc-  tions to DFT Kohn-Sham eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' This approach has  been shown to give highly accurate descriptions of exci-  tons in molecular crystals [7, 10, 36, 41, 42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The compu-  tational details for our DFT and GW-BSE calculations  are given in Supplemental Material [43] Section S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  We treat the effect of phonons following Monser-  rat [32, 44, 45], and in a manner similar in spirit to  Zacharias and Giustino [46, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  For an observable O  at a temperature T, we compute the ensemble-average in  the adiabatic approximation as  ⟨O(T)⟩H = 1  Z  �  dXO(X)e−βH,  (3)  where the canonical partition function Z =  �  dXe−βH  involves the configuration space integral  �  dX [48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Non-  adiabatic effects to the electron-phonon interactions of  organic systems such as pentacene are negligible [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The Hamiltonian H of the system includes electronic  and nuclear degrees of freedom in general, and may be ap-  proximated at different levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' One approach is to assume  nuclear motion to be harmonic, reducing the phonon con-  tribution to the Hamiltonian to the following form,  Hhar ≡ 1  2  �  n,q  (∇2  un,q + ω2  n,qu2  n,q),  (4)  in atomic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Here, phonons of frequencies ω are  labeled by their branch index n and wavevector q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  We compute the ensemble-average  �  Ohar�  in the Born-  Oppenheimer approximation, tracing out all electronic  degrees of freedom, using a finite-displacements ap-  proach [50, 51] to calculate phonon frequencies {ωn,q}  and eigendisplacements {un,q}, and then drawing N ran-  dom samples {Xhar  i  } from the multivariate Gaussian  phonon distribution and calculating the observables of  interest {O(Xhar  i  )}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  �  Ohar�  is then simply computed as  the average of its value at the samples  �  Ohar�  = lim  N→∞  1  N  N  �  i=1  O(Xhar  i  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  (5)  Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 4  and 5  are  exact  apart  from  the  adiabatic  and harmonic approximations, and the description of  phonon effects on any observable O in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 5 is non-  perturbative [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The use of the harmonic approximation in molecular  crystals can lead to unphysical results, due to highly an-  harmonic behavior of low-frequency phonons [27, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' In  this work, we account for this anharmonicity by employ-  ing path-integral molecular dynamics (PIMD) which are  rendered computationally tractable using the surrogate  machine-learning (ML) potential V ML from Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' [27, 52],  constructed to reproduce the potential energy surface  (PES) from first-principles density functional theory  (DFT) calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The modified phonon Hamiltonian  Hanhar ≡  Na  �  i=1  ˆp2  i  2mi  + V ML(ˆr1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' , ˆrNa)  (6)  is used to run PIMD simulations at reduced computa-  tional cost, for a cell of Na atoms, with nucleus i having  a mass mi, and ˆpi, ˆri its momentum and position opera-  tors respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We then draw random samples from the  PIMD trajectories, and use these to compute vibrational  averages of observables, analogously to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 5, namely  �  Oanhar�  = lim  N→∞  1  N  N  �  i=1  O(Xanhar  i  ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  (7)  Our simulations use a 2 × 1 × 1 supercell of pentacene  (Na = 144 atoms), capturing the effect of phonons at Γ  and at the band-edge X on observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Phonons be-  yond Γ and X have a minor effect on pentacene opti-  cal properties as discussed in Supplemental Material [43]  Section S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  3  a  d  b  c  E (eV)  0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='4  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='8  Γ  X  |Q| (A-1)  o  static  100 K  300 K  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Isosurfaces of electron distributions of singlet (blue,  panel a) and triplet (green, panel b) excitons for a hole fixed  at the center of the plotted area, and corresponding dis-  persions (panel c, same color scheme) in molecular crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  A typical low-frequency (top) and high-frequency (bottom)  phonon of pentacene is shown in panel d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  To quantify exciton localization, we study two observ-  ables O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The first are the exciton energies at finite center-  of-mass momentum, ΩS  Q, obtained through solving the  BSE (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The second is the average electron-hole  separation for each excitation S, which we refer to as the  exciton radius rexc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' This is obtained by post-processing  the BSE solution ΨS, as discussed elsewhere [53] and in  Supplemental Material [43] Section S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' To determine the  exciton radius, we compute the electron-hole correlation  function as defined in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' [53], namely  FS(r) =  �  V  drh|ΨQ=0  S  (re = rh + r, rh)|2,  (8)  where V the volume of the primitive cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' FS(r) describes  the probability of finding the electron-hole pair at a dis-  tance of r = re − rh, and is computed as a discrete sum  over hole positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The average exciton radius for a  given atomic configuration is then  rexc =  �  d|r|FS(|r|)|r|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  (9)  Having described the main quantities in our computa-  tional framework, we may summarize it as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We  generate displaced configurations Xhar  i  within the har-  monic approximation using a finite differences approach,  and Xanhar  i  within the anharmonic distribution through  PIMD employing a previously-developed ML potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The ab initio BSE, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1, is solved at these configura-  tions, followed by a calculation of the exciton radius via  Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We then compute the vibrational averages using  Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 5 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Details of the convergence of the vibrational  averages, the ML potential, and PIMD simulations, are  given in Supplemental Material [43] Section S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='– We first discuss exciton properties obtained  from solving the BSE without consideration of phonons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  We refer to these clamped-ion solutions as the ‘static’  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1 shows an isosurface of the electron density  for the first singlet (S1, blue, panel a) and triplet (T1,  green, panel b) exciton, for a hole fixed at the center of  the visualized region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' As shown previously [7, 10, 36], the  singlet is significantly more delocalized than the triplet,  which results in bands that are more dispersive in re-  ciprocal space [7, 42], as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We plot the  exciton energies along the path Γ → X in the Brillouin  zone, corresponding to the dominant packing direction  of the pentacene crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Table I summarizes the band-  width W = Ω(X) − Ω(Γ) of the two excitons, as well  as the width ∆ = Ω(Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='4 ˚A  −1) − Ω(Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1 ˚A  −1),  the values of the exciton momentum chosen to accom-  modate comparison to recent experiments [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We see  from our static calculations that the singlet bandwidth  is more than twice that of the triplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  We now include the effect of phonons on the exciton  band structures along Γ → X at 100 K and 300 K, within  the harmonic and anharmonic distributions, and visu-  alize the results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1c when including anharmonic  effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  There are two broad categories of phonons in  molecular crystals, corresponding to low-frequency inter-  molecular and high-frequency intramolecular motions, vi-  sualized in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' While the former are predominantly  activated when going from 100 K to 300 K, the latter have  significant zero-point energies ℏω/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Including 100 K  phonon effects red-shifts both singlet and triplet exci-  ton energies and flattens their dispersions, as shown in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 1c and Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' This effect is larger for the triplet,  which is more localized and therefore more impacted  by high-frequency intra-molecular modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' However, in-  creasing the temperature to 300 K has no effect on the  triplet, since there are negligible additional contributions  from intramolecular modes at these temperatures and  the modulations of intermolecular distances by lower-  frequency phonons hardly affect this localized state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' In  contrast, the delocalized singlet red-shifts further, and  its dispersion flattens by an additional 18 meV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Our re-  sults for the singlet width ∆ at 100 K are in excellent  agreement with recent experiments [54], as summarized  in Table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Our predicted decrease of the singlet width ∆  by 13 meV when increasing the temperature from 100 K  to 300 K underestimates the experimental decrease of  4  W anhar(S1) (meV)  W har(S1) (meV)  W anhar(T1) (meV)  ∆anhar(S1) (meV)  ∆exp(S1) (meV) [54]  static  110  110  52  80  − − −  100 K  59  67  18  43  44  300 K  41  76  19  30  23  TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The effect of phonons on the dispersion width W = Ω(X) − Ω(Γ) for the first singlet ΩS and triplet ΩT excitons of  pentacene, and on the width ∆ = Ω(Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='4 ˚A  −1) − Ω(Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1 ˚A  −1) for the singlet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  T (K)  5  10  15  x  x  x  x  0  300  +  +  +  x  harmonic  anharmonic  a  b  c  +  +  <rexc> (A)  o  static  x  x  x  x  singlet  triplet  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Singlet (blue) and triplet (green) exciton radii within  the different cases and temperatures (panel a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Representa-  tive configuration showing electronic isosurfaces for fixed hole  positions, indicating localization of the singlet (triplet) at 0 K  towards the region in blue (green), shown in panel b (panel  c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Red represents electronic wavefunction amplitude that  disappears in the presence of phonons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  21 meV, largely due to ignoring thermal expansion in our  calculation, which reduces ∆ by a further 6 meV within  this temperature range, see Supplemental Material [43]  Section S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Interestingly, we see in Table I that the har-  monic approximation predicts an increase of the singlet  bandwidth with increasing temperature, contrary to our  calculations including anharmonic effects using PIMD  and to experiment, a point that we return to below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The changes in the width of the exciton dispersions  suggest phonon-induced modulations of real-space exci-  ton properties, which are zero-point dominated for the  triplet, and which have significant temperature depen-  dence for the singlet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We highlight the connection be-  tween the dispersion modulations and real-space exciton  properties by computing vibrational averages of the exci-  ton radii at a range of temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The results are pre-  sented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 2 for the singlet (blue) and triplet (green)  within the harmonic approximation and including anhar-  monic effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Let us first comment on the harmonic  case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Compared to the static limit (circles), the radii in  the presence of phonons at 0 K are renormalized by more  than a factor of two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  For the singlet, the static value  of 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='2 ˚A for its radius reduces to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='9 ˚A, while the static  triplet radius of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='7 ˚A reduces to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='2 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' To visualize this  we present in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 2b and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 2c differential plots for iso-  surfaces of the electron density once a hole is placed at a  high-probability position in the unit cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Specifically, we  plot the difference between the electronic density of the  case without phonons and that of a typical atomic config-  uration at 0 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Red indicates amplitude vanishing due to  phonons, while blue and green indicate areas where the  singlet and triplet wavefunction respectively gain ampli-  tude, demonstrating their tendency to localize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  When increasing the temperature to 300 K within the  harmonic approximation there is no change to the triplet  exciton radius, in agreement with our expectation of the  effect of phonons on the triplet exciton dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The  singlet however exhibits delocalization, with its radius  increasing substantially to the average value of 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='96 ˚A,  consistent with the increase of the singlet bandwidth with  temperature in the harmonic case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Upon including an-  harmonic effects, triplet radii agree with the harmonic  case;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' however, for the singlet the results are qualitatively  different, and we recover the expected behavior of de-  creasing singlet radius with increasing temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' All  vibrational averages and errors for the exciton radii are  given in Section S7 of the Supplemental Material [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The discrepancy between the harmonic and anhar-  monic cases is due to configurations with highly delocal-  ized excitons within the harmonic approximation, with  radii as large as 31 ˚A at 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Such configurations are  shown in Supplementary Material [43] Section S5, and  their inclusion in the thermal averages of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 5 for the  radii leads to the observed temperature-induced increase  of ⟨rexc⟩ in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  To understand why such configu-  rations are not present within the anharmonic case, we  plot in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 3a the difference between the phonon root  mean squared displacement  �  ⟨u2⟩ of the two distribu-  tions at 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We find that a low-frequency acoustic  mode, corresponding to a sliding along the z-axis of ad-  jacent pentacene molecules, is significantly over-displaced  O  O5  b  a  10  15  20  25  30  u  harmonic  anharmonic  <rexc> (A)  o  d-deq (A)  o  0  1  2  3  4  5  6  7  15  30  45  60  75  90  ω (cm -1)  deq = 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='3 A  o  0  5  10  15  20  25  <uhar  2>  <uanhar  2> 0  500  1000 1500  2000 2500 3000  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The difference between the RMS displacement of  phonons in the harmonic and anharmonic distributions of  pentacene (panel a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Singlet exciton radii (panel b) along  the highly anharmonic phonon shown in panel a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Phonon  displacements u are given in units of their zero-point width  1/√2ωqν [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The dotted line in b is a guide to the eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  in the harmonic case at q = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Anharmonic terms alter  the PES associated with this phonon, limiting its aver-  age amplitude at room temperature, as shown in Supple-  mentary Material [43] Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S3, in agreement with known  cases where the harmonic approximation breaks down in  molecular crystals [27, 29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We confirm that the over-  displacement of this phonon within the harmonic approx-  imation leads to the temperature-induced singlet delocal-  ization observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 2a, by computing the singlet ra-  dius as a function of amplitude of this mode, as visualized  in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 3b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The blue and red regions indicate the maxi-  mum range of displacements which are accessible within  the anharmonic and harmonic distributions respectively,  due to thermal excitation of phonons at 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The har-  monic approximation leads to configurations with highly  delocalized excitons of radii as large as 25 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The depen-  dence of the exciton radius on the phonon displacement  is non-monotonic due to the oscillating π orbital overlap  between neighboring pentacene molecules [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  While highly delocalized excitons may appear at cer-  tain nuclear configurations, anharmonicity prevents ac-  cessing these, as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 3b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' However, such configu-  rations could appear out of equilibrium, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' due to pho-  toexcitation, upon relaxation to the excited state PES  minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  For pentacene, the minimum of the singlet  exciton PES along the anharmonic acoustic mode lies far  from the ‘delocalized’ region of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 3b (see Supplemental  Material [43] Section S6), it is thus unlikely that for this  and similar systems transiently delocalized excitons may  be accessed, even outside equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Conclusions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='– We have presented a first-principles  study of the effect of phonons on the dispersion and  radii of excitons in the prototypical molecular crystal  pentacene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zero-point nuclear motion uniformly causes  substantial localization of excitons, manifesting as a  flattening of the exciton dispersion in reciprocal space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Wannier-Mott-like singlet excitons also exhibit addi-  tional temperature-activated localization due to their  stronger coupling to low-frequency phonons, with anhar-  monic effects being critical in capturing this effect and  preventing transient exciton delocalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Anharmonic  low-frequency phonons are common in molecular materi-  als [27] and can couple to singlets when these approach  the Wannier-Mott limit, in a manner which is in turn de-  termined by the size [10] and packing [56] of the molecular  building blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Our work lays foundations for a deep un-  derstanding and controlled enhancement of exciton trans-  port in molecular crystals, for example by suppressing  anharmonicity through chemical modifications [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  We thank Sivan Refaely-Abramson for useful discus-  sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' This work was primarily supported by the Theory  FWP, which provided GW and GW-BSE calculations  and analysis of phonon effects, and the Center for Com-  putational Study of Excited-State Phenomena in Energy  Materials (C2SEPEM), which provided advanced codes,  at the Lawrence Berkeley National Laboratory, funded  by the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Department of Energy, Office of Science,  Basic Energy Sciences, Materials Sciences and Engineer-  ing Division, under Contract No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' DE-AC02-05CH11231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  SS acknowledges funding from the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' National Science  Foundation (NSF) under grant number DMR-1847774.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Computational resources were provided by the National  Energy Research Scientific Computing Center (NERSC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Frenkel, On the transformation of light into heat in  solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' i, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 37, 17 (1931).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Frenkel, On the transformation of light into heat in  solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' ii, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 37, 1276 (1931).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wannier, The structure of electronic excitation lev-  els in insulating crystals, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 52, 191 (1937).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [4] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Mott, Conduction in polar crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The con-  duction band and ultra-violet absorption of alkali-halide  crystals, Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Faraday Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 34, 500 (1938).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [5] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cudazzo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gatti, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rubio, Excitons in molec-  ular crystals from first-principles many-body perturba-  tion theory: Picene versus pentacene, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 86,  6  1 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [6] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cudazzo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gatti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rubio, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sottile, Frenkel  versus charge-transfer exciton dispersion in molecular  crystals, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 88, 1 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [7] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cudazzo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sottile, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rubio, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gatti, Exci-  ton dispersion in molecular solids, Journal of Physics  Condensed Matter 27, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1088/0953-8984/27/11/113204  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Distler, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Brabec, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Egelhaaf, Organic  photovoltaic modules with new world record efficiencies,  Progress in Photovoltaics: Research and Applications 29,  24 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Reineke,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Lindner,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Schwartz,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Seidler,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Walzer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' L¨ussem, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Leo, White organic light-  emitting diodes with fluorescent tube efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=', Nature  459, 234 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Alvertis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Pandya, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Muscarella, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sawhney,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Nguyen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ehrler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Friend, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Chin,  and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Monserrat, Impact of exciton delocalization on  exciton-vibration interactions in organic semiconductors,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 102, 081122 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [11] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Arag´o and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Troisi, Dynamics of the excitonic cou-  pling in organic crystals, Physical Review Letters 114, 1  (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [12] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kupgan, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Chen, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Br´edas, Molecular  Packing in the Active Layers of Organic Solar Cells Based  on Non-Fullerene Acceptors: Impact of Isomerization on  Charge Transport, Exciton Dissociation, and Nonradia-  tive Recombination, ACS Applied Energy Materials 4,  4002 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [13] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Anderson, Absence of diffusion in certain random  lattices, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 109, 1492 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [14] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Brown-Altvater, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Antonius, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rangel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gi-  antomassi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Draxl, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gonze, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Louie, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Neaton, Band gap renormalization, carrier mobilities,  and the electron-phonon self-energy in crystalline naph-  thalene, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 101, 1 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [15] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Schweicher, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' D’Avino, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ruggiero, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Harkin,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Broch,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Venkateshvaran,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Liu,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Richard, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ruzi´e, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Armstrong, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kennedy,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Shankland, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Takimiya, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Geerts, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zeitler,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fratini, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sirringhaus, Chasing the “Killer”  Phonon Mode for the Rational Design of Low-Disorder,  High-Mobility Molecular Semiconductors, Advanced Ma-  terials 31, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1002/adma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='201902407 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Athanasopoulos, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Emelianova, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Walker, and  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Beljonne, Exciton diffusion in energetically disordered  organic materials, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 80, 1 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [17] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sudha Devi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Al-Suti, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Dosche, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Khan,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Friend, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' K¨ohler, Triplet energy transfer in  conjugated polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Experimental investigation of a  weakly disordered compound, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 78, 1 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [18] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sneyd, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fukui, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Paleˇcek, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Prodhan, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wag-  ner, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sung, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Collins, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Slater,  Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Andaji-Garmaroudi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' MacFarlane, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Garcia-  Hernandez, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wang, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Whittell, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Hodgkiss,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Beljonne, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Manners, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Friend, and  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rao, Efficient energy transport in an organic semi-  conductor mediated by transient exciton delocalization,  Science Advances 7, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1126/sciadv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='abh4232 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [19] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Giannini,  W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Peng,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cupellini,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Padula,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Carof, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Blumberger, Exciton transport in  molecular organic semiconductors boosted by transient  quantum delocalization, Nature Communications 13, 1  (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sneyd, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Beljonne, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rao, A New Frontier  in Exciton Transport : Transient Delocalization, Journal  of Physical Chemistry Letters 13, 6820 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fratini, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Mayou, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ciuchi, The transient lo-  calization scenario for charge transport in crystalline or-  ganic materials, Advanced Functional Materials 26, 2292  (2016), 1505.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='02686.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [22] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Balaeff, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Skourtis, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Be-  ratan, Biological charge transfer via flickering resonance,  Proceedings of the National Academy of Sciences of the  United States of America 111, 10049 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [23] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Beratan, Why Are DNA and Protein Electron  Transfer So Different?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=', Annual Review of Physical Chem-  istry 70, 71 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [24] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Troisi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Orlandi, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Anthony, Electronic in-  teractions and thermal disorder in molecular crystals con-  taining cofacial pentacene units, Chemistry of Materials  17, 5024 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Giannini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Carof, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ellis, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Yang, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ziogos,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ghosh, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Blumberger, Quantum localization and  delocalization of charge carriers in organic semiconduct-  ing crystals, Nature Communications 10, 1 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [26] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Monserrat, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Engel, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Needs, Giant  electron-phonon interactions in molecular crystals and  the importance of nonquadratic coupling, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B  92, 1 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Alvertis and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Engel, Importance of vibrational  anharmonicity for electron-phonon coupling in molecular  crystals, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 105, 1 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [28] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Seiler, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Krynski, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zahn, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Hammer, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wind-  sor, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Vasileiadis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Pflaum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ernstorfer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rossi,  and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Schwoerer, Nuclear dynamics of singlet exciton  fission: a direct observation in pentacene single crystals,  Science Advances 7, eabg0869 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fetherolf, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Shih, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Berkelbach, Con-  ductivity of an electron coupled to anharmonic phonons,  arXiv (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rossi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gasparotto, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceriotti, Anharmonic  and Quantum Fluctuations in Molecular Crystals:  A  First-Principles Study of the Stability of Paracetamol,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 117, 115702 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [31] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rohlfing and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Louie, Electron-hole excitations  and optical spectra from first principles, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B  62, 4927 (2000), 0406203v3 [arXiv:cond-mat].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [32] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Monserrat, Electron – phonon coupling from finite dif-  ferences, Journal of Physics Condensed Matter 30 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [33] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kapil, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Behler, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceriotti, High order path  integrals made easy, The Journal of Chemical Physics  145, 234103 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [34] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceriotti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Parrinello, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Markland, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Manolopoulos, Efficient stochastic thermostatting of  path integral molecular dynamics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 133,  124104 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [35] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Haas, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Batlogg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Besnard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Schiltz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kloc, and  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Siegrist, Large uniaxial negative thermal expansion in  pentacene due to steric hindrance, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 76, 1  (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Refaely-Abramson, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Da Jornada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Louie,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Neaton, Origins of Singlet Fission in Solid  Pentacene from an ab initio Green’s Function Approach,  Physical Review Letters 119, 1 (2017), 1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='01564.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [37] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Giannozzi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Baroni, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Bonini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Calandra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Car,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cavazzoni, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceresoli, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Chiarotti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cococ-  7  cioni, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Dabo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Dal Corso, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fabris, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fratesi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' de  Gironcoli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gebauer, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gerstmann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gougoussis,  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kokalj, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Lazzeri, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Martin-Samos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Marzari,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Mauri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Mazzarello, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Paolini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Pasquarello,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Paulatto, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sbraccia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Scandolo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sclauzero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Seitsonen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Smogunov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Umari, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wentz-  covitch, QUANTUM ESPRESSO: a modular and open-  source software project for quantum simulations of mate-  rials, Journal of Physics: Condensed Matter 21, 395502  (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [38] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Deslippe, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Samsonidze, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Strubbe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Jain,  M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cohen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Louie, BerkeleyGW: A mas-  sively parallel computer package for the calculation of  the quasiparticle and optical properties of materials and  nanostructures, Computer Physics Communications 183,  1269 (2012), 1111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='4429.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [39] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Qiu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cohen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Novichkova, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Refaely-  Abramson, Signatures of Dimensionality and Symmetry  in Exciton Band Structure: Consequences for Exciton  Dynamics and Transport, Nano Letters 21, 7644 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Hybertsen and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Louie, Electron correlation in  semiconductors and insulators: Band gaps and quasipar-  ticle energies, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 34, 5390 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [41] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rangel,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Berland,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sharifzadeh,  F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Brown-  Altvater,  K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Lee,  P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Hyldgaard,  L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Kronik,  and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Neaton, Structural and excited-state properties of  oligoacene crystals from first principles, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 93,  1 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [42] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Lettmann and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rohlfing, Finite-momentum exci-  tons in rubrene single crystals, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 104, 1  (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [43] See supplemental material at [url will be inserted by the  production group] which includes references [10, 27, 34,  36–38, 41, 44, 52, 53, 58–68] for computational details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [44] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Monserrat, Vibrational averages along thermal lines,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 93, 1 (2016), 1512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='06377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [45] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Monserrat, Correlation effects on electron-phonon  coupling in semiconductors:  Many-body theory along  thermal  lines,  Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  B  93,  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1103/Phys-  RevB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='100301 (2016), 0703642 [astro-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [46] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zacharias and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Giustino, One-shot calculation  of temperature-dependent optical spectra and phonon-  induced band-gap renormalization, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 94,  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1103/PhysRevB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='075125 (2016), 1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='02394.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [47] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zacharias and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Giustino, Theory of the special dis-  placement method for electronic structure calculations at  finite temperature, Physical Review Research 2, 7 (2020),  1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='10929.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [48] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Patrick and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Giustino, Unified theory of elec-  tron–phonon renormalization and phonon-assisted opti-  cal absorption, Journal of Physics: Condensed Matter  26, 365503 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [49] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Miglio, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Brousseau-Couture, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Godbout, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Anto-  nius, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Chan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Louie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cˆot´e, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Giantomassi,  and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gonze, Predominance of non-adiabatic effects  in zero-point renormalization of the electronic band  gap, npj Computational Materials 6, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1038/s41524-  020-00434-z (2020), 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='12765.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [50] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kresse, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Furthm¨uller, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Hafner, Ab initio Force  Constant Approach to Phonon Dispersion Relations of  Diamond and Graphite, Europhysics Letters 32, 729  (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [51] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Parlinski, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Li, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kawazoe, First-Principles  Determination of the Soft Mode in Cubic ZrO2, Physical  Review Letters 78, 4063 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [52] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kapil and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Engel, A complete description of ther-  modynamic stabilities of molecular crystals, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 119, e2111769119 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [53] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sharifzadeh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Darancet, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kronik, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Neaton,  Low-Energy Charge-Transfer Excitons in Organic Solids  from First-Principles: The Case of Pentacene, The Jour-  nal of Physical Chemistry Letters 4, 2197 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [54] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Graf, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kusber, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B¨uchner, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Knupfer, Strong  exciton bandwidth reduction in pentacene as a function  of temperature, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 106, 165429 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [55] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Arag´o and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Troisi, Regimes of exciton transport in  molecular crystals in the presence of dynamic disorder,  Advanced Functional Materials 26, 2316 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [56] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sharifzadeh, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cotts, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kro-  nik, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ginsberg, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Neaton, Relating the  Physical Structure and Optoelectronic Function of Crys-  talline TIPS-Pentacene, Advanced Functional Materials  25, 2038 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [57] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Asher, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Jouclas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Bardini, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Diskin-posner,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kahn, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Korobko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kennedy, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Moraes,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Schweicher, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Beljonne, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Geerts, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ya,  Chemical Modifications Suppress Anharmonic Effects in  the Lattice Dynamics of Organic Semiconductors, ACS  Materials Au 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1021/acsmaterialsau.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='2c00020 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [58] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Haas, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Batlogg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Besnard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Schiltz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kloc, and  T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Siegrist, Large uniaxial negative thermal expansion in  pentacene due to steric hindrance, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 76, 1  (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [59] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Perdew, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Burke, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ernzerhof, Generalized  Gradient Approximation Made Simple, Physical Review  Letters 77, 3865 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [60] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Monkhorst and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Pack, Special points for  Brillouin-zone integrations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 13, 5188  (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [61] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Tkatchenko and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Scheffler, Accurate molecular van  der Waals interactions from ground-state electron density  and free-atom reference data, Physical Review Letters  102, 6 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [62] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Eldar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Lindenbaum, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Porat, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zeevi,  The Farthest Point Strategy for Progressive Image Sam-  pling, IEEE Transactions on Image Processing 6, 1305  (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [63] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Campello, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Moulavi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zimek, and  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sander, Hierarchical density estimates for data clus-  tering, visualization, and outlier detection, ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Knowl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Discov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Data 10, 5 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [64] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Bart´ok, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kondor, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cs´anyi, On representing  chemical environments, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 87, 184115 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [65] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Willatt, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Musil, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceriotti, Feature opti-  mization for atomistic machine learning yields a data-  driven construction of the periodic table of the elements,  Phys Chem Chem Phys 20, 29661 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [66] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Singraber,  N2P2,  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='com/  CompPhysVienna/n2p2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [67] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kapil, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rossi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Marsalek, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Petraglia, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Lit-  man, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Spura, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cheng, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cuzzocrea, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Meißner,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='Wilkins, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Helfrecht, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Juda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Bienv-  enue, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kessler, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Poltavsky, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Vandenbrande,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wieme, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceriotti, i-PI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='0: A universal force  engine for advanced molecular simulations, Computer  Physics Communications 236, 214 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [68] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Plimpton, Fast parallel algorithms for short-range  molecular dynamics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Compt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 117, 1 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Supplemental Material: Phonon-induced localization  of excitons in molecular crystals from first principles  Antonios M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Alvertis,1, 2, ∗ Jonah B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Haber,2 Edgar A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Engel,3 Sahar Sharifzadeh,4, 5 and Jeffrey B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Neaton1, 2, 6, †  1Materials Sciences Division, Lawrence Berkeley  National Laboratory, Berkeley, California 94720, USA  2Department of Physics, University of California Berkeley, Berkeley, United States  3Cavendish Laboratory, University of Cambridge,  J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Thomson Avenue, Cambridge CB3 0HE, United Kingdom  4Division of Materials Science and Engineering, Boston University, United States  5Department of Electrical and Computer Engineering, Boston University, United States  6Kavli Energy NanoScience Institute at Berkeley, Berkeley, United States  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='11944v1  [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='mtrl-sci]  27 Jan 2023  CONTENTS  S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Computational details  3  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' DFT calculations  3  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' GW-BSE calculations  3  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Phonon calculations and Monte Carlo sampling of vibrational averages  3  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Machine learning potential and path-integral molecular dynamics  6  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Calculation of exciton radii  7  S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Effect of thermal expansion  8  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Contributions of Γ and X phonons  9  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Exciton radii  9  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Exciton dispersion  10  S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Anharmonic potential energy surfaces  11  S5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Highly delocalized excitons within the harmonic approximation  12  S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Estimation of the minimum of the singlet exciton potential energy surface  12  S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Tables of averages and standard deviations of exciton energies and radii  15  References  17  ∗ amalvertis@lbl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='gov  † jbneaton@lbl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='gov  2  S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  COMPUTATIONAL DETAILS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  DFT calculations  First-principles energies, forces, band gaps and wavefunctions are computed using the  Quantum Espresso [1] DFT code with the semi-local PBE exchange-correlation functional [2]  and a plane-wave energy cut-off of 60 Rydberg for the wavefunction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  For the unit cell  of pentacene we start from the experimental structure PENCEN08 as in the Cambridge  Crystallographic Database [3], and relax the internal coordinates while leaving the volume  fixed and using the Tkatchenko-Scheffler (TS) dispersion correction [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' For the geometry  optimization we employ a 4 × 4 × 2 Monkhorst-Pack k-point grid [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  GW-BSE calculations  We employ the one-shot GoWo approximation for the quasiparticle properties of pen-  tacene, as implemented in the BerkeleyGW code [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We use a 4 × 4 × 2 k-grid, 400 bands  and a 7 Ry plane wave cutoff to calculate the dielectric screening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' For exciton calculations,  we construct the electron-hole kernel on a 4 × 4 × 2 grid using 4 valence and 4 conduction  states, and then interpolate on a 8 × 8 × 4 k-grid with the same number of bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' This set  of parameters has been shown to give converged results in previous computational studies of  pentacene [7, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' When studying 2 × 1 × 1 supercells of pentacene (see following subsection  on the Monte Carlo sampling of vibrational averages), we use a half the number of k-points  in the x direction in all cases (2 × 4 × 2 to calculate the dielectric screening and 4 × 8 × 4  to interpolate the BSE kernel), and double the number of bands for the dielectric screening  (800 bands) and exciton calculations (8 valence and 8 conduction bands).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Phonon calculations and Monte Carlo sampling of vibrational averages  We include the contribution from lattice dynamics at temperature T to an observable O  by means of the quantum mechanical expectation value  O(T) = 1  Z  �  s  ⟨χs(u)|O(u)|χs(u)⟩e−Es/kBT,  (1)  3  0  20  40  60  80  100  configuration  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='0  Eg (eV)  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Convergence of the DFT band gap renormalization ∆Eg as a function of the number of  configurations used in the Monte Carlo sampling, for the example of using a 2 × 1 × 1 supercell  at T = 100 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The value of the gap renormalization for each configuration is denoted in black  crosses, while the blue line is the running average of the band gap renormalization due to phonons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The dashed line is the final computed average value for the band gap renormalization, while the  red crosses indicate the ten configurations for which we run GW-BSE calculations to obtain their  exciton properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  where |χs⟩ is the harmonic vibrational wavefunction in state s with energy Es, Z =  �  s e−Es/kBT is the partition function, and u = {uqν} is a collective coordinate that in-  cludes the amplitudes of all normal modes of vibration in the system labeled by the phonon  wave vector q and the phonon branch ν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Substituting the harmonic vibrational wavefunction, the above expectation value can be  rewritten  O(T) =  �  du|Φ(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' T)|2O(u),  (2)  where:  |Φ(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' T)|2 =  �  q,ν  (2πσ2  qν(T))−1/2 exp  �  −  u2  qν  2σ2  qν(T)  �  ,  (3)  4  the harmonic density at temperature T, which is a product of Gaussian functions of width:  σ2  qν(T) =  1  2ωqν  coth  � ωqν  2kBT  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  (4)  We evaluate Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' (2) by generating stochastic samples distributed according to the har-  monic vibrational ensemble, calculating the observable of interest at each configuration, and  averaging over all configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' To sample the single-particle DFT electronic band gap  we generate 100 configurations, which are sufficient for convergence, as demonstrated in  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We obtain the band gap correction for each of these configurations at temperatures  of T = 0 K, T = 100 K, T = 200 K and T = 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We then apply GW corrections to these  DFT values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Due to the large computational cost of these calculations, we only perform  GW calculations on the ten configurations whose single-particle DFT band gap value is  closest to the calculated average band gap for each temperature, as also shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  This correlated sampling strategy between DFT and GW has been shown to be accurate  in pentacene [8] and other systems [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Having calculated the effects of electron-phonon  coupling on the quasiparticle band gap, we solve the Bethe-Salpeter equation for the same  ten configurations at the various temperatures, using the parameters of the previous section  and computing exciton energies (at finite exciton momenta) and exciton radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The sampling of the expectation value of equation 2 becomes increasingly accurate with  the inclusion of more q-points in the Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Within the finite differences approach  for phonon calculations and the expectation values of observables at finite temperatures,  q-points are described using commensurate supercells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' For pentacene a 2 × 1 × 1 (size 2)  supercell (four pentacene molecules) is 98% converged with respect to a 2 × 2 × 2 (size 8)  supercell (sixteen molecules) for the band gap zero-point renormalization (−139 meV and  −142 meV respectively), as seen in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S2 where we plot the convergence of the pentacene  band gap renormalization at 100 K, as obtained from sampling within the anharmonic dis-  tribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Therefore a 2 × 1 × 1 supercell offers a good balance between computational cost  for the GW-BSE calculations, and accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  5  100  110  120  130  140  ΔEg (meV)  supercell size  1  2  8  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Convergence of the pentacene DFT band gap renormalization ∆Eg at T = 100 K, as a  function of the supercell size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The dashed line is given as a guide to the eye.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Machine learning potential and path-integral molecular dynamics  The details of the construction of the machine learning potential for pentacene (and  other acene crystals), as well as the procedure for obtaining trajectories within path-integral  molecular dynamics, have been described elsewhere [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Here we include some key points  and refer the reader interested in a more in-depth discussion to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  A machine learning potential describing the dynamics of the acene series of molecular  crystals was trained on a set of training data including the total energies of 4862 configu-  rations of naphthalene, anthracene, tetracene and pentacene, obtained from the harmonic  distributions at 0 K, 150 K, and 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' From this set, 400 validation and 400 test con-  figurations were drawn randomly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' For tuning the ML potential architecture and training  procedure, the training data was sparsified by farthest-point-sampling (FPS) [11, 12], retain-  ing the 1000 most structurally distinct training configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' This FPS was performed on  the basis of Euclidean distances between configurations described in terms of their smooth  overlap of atomic positions (SOAP) powerspectra [13], using the radially-scaled implemen-  tation [14] with a radial and angular basis of 12 and nine functions, respectively, a cut-off  radius of 8 ˚A, a width of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='275 ˚A for the Gaussian densities associated with the atomic posi-  tions, and a scaling onset and exponent of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='5 ˚A and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='5, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' An ensemble of seven  fully-connected, feed-forward neural networks with two hidden layers of 16 nodes each was  constructed by using the N2P2 code [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  6  For the independent testset, the ML potentials reproduce the reference energies and forces  with root-mean-square errors of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='4 meV/atom and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='157 meV/ ˚A, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Crucially,  this suffices to run stable path integral simulations in the constant-volume ensemble over  extended simulation times, and to accurately compute the quantum-mechanical expectation  values of observables within the reference first-principles thermodynamic ensemble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Finite-temperature, quantum-mechanical thermodynamic averages of observables can be  computed as averages of their values for (random) configurations drawn from PIMD sim-  ulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We exploit the affordability of the ML potential to perform PIMD in the NV T  ensemble at temperatures of 100 K and 300 K, and subsequently compute observables for  configurations extracted from the PIMD trajectory (after equilibration) at regular intervals  of 50 fs, which ensures that these samples are decorrelated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The PIMD simulations of at least  10 ps were performed using the i-PI [16] molecular dynamics engine to drive LAMMPS [17]  energy and force evaluations of the ML potential, a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='25 fs timestep, and a path integral  Langevin equation thermostat [18] with τ = 100 fs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The number of replicas required for PIMD simulations is determined by the highest  frequency phonon modes that are present in the system, which in our case is C–H stretching  and is common among all acene crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' For benzene it has been shown that 32 replicas  are sufficient to convergence electronic band gaps within 15 meV[10, 19], and the same value  has therefore been employed for pentacene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  For obtaining the exciton properties (energies and radii) within the anharmonic distri-  butions we follow a tactic similar to the correlated sampling described in the case of the  harmonic Monte Carlo sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We first draw 100 configurations at which we compute the  DFT band gap and then we rank the configurations based on their band gap proximity to the  computed mean value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We then perform GW-BSE calculations on the top 10 configurations  among these.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Calculation of exciton radii  As discussed in the main text, we compute the electron-hole correlation function as  defined in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' [20], namely  FS(r) =  �  V  d3rh|ψQ=0  S  (re = rh + r, rh)|2,  (5)  7  where V the volume of the primitive cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' FS(r) describes the probability of finding the  electron-hole pair at a vector r = re − rh, and is computed as a discrete sum over hole  positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We note here that even if we only integrate over the volume of the primitive cell,  the exciton wavefunction can delocalize over the whole supercell used in the Bethe-Salpeter  calculation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=', 8×8×4 or 4×8×4 for pentacene, as discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Even if the hole was  moved outside the primitive cell, we would simply obtain a shifted exciton wavefunction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  For pentacene, it was found in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' [20] that the average electron-hole distance of the  correlation function is converged, and that its envelope produces a smooth function for  88 high-probability hole positions in the unit cell, corresponding to two hole positions per  carbon atom, at ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='5˚A above and below the plane of the molecule for each atom (effectively  sampling the C pz orbitals).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' For each sampled hole, the correlation function is computed  on an 8 × 8 × 4 supercell of pentacene, which is necessary for convergence of the exciton  wavefunctions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' For the 2×1×1 cell of pentacene, which includes the effects of phonons (see  section S1 C), the real-space supercell used for FS(r) is reduced to 4 × 8 × 4, since every cell  along the x direction already contains two unit cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Moreover the number of carbon atoms  per cell doubles, and so we sample at 88 · 2 = 176 hole positions in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Having computed the electron-hole correlation function for a given atomic configuration  u, the exciton radius is computed as  rexc(u) =  �  d|r|FS(|r|)|r|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  (6)  To compute the vibrationally renormalized exciton radii at a temperature T, we apply  equations 5 and 7 of the main manuscript with O = rexc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' In the example case where we  make the harmonic approximation this results in  ⟨rexc(T)⟩ =  �  du|Φ(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' T)|2rexc(u),  (7)  where |Φ(u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' T)|2 the harmonic density function, as discussed in section S1 C above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  EFFECT OF THERMAL EXPANSION  To study the effect of thermal expansion on the exciton dispersion of pentacene, we  perform GW-BSE calculations on two pentacene structures deposited in the Cambridge  8  Crystallographic Database, which have been obtained through X-ray diffraction measure-  ments at temperatures within the range of interest of 100 − 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' These are the structures  PENCEN06 and PENCEN07 [3], obtained at 120 K and 293 K respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' We use the  experimental crystal structures without any optimization of the internal coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The  absolute value of the singlet exciton energy and width are known to be very sensitive to  coordinate optimization and the precise level of theory employed to perform this optimiza-  tion [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Therefore here we will focus on differences between energies and dispersion widths  of the two experimental structures, without attempting a direct comparison to values ob-  tained for the optimized structure necessary to perform phonon calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' In principle  phonons and thermal expansion need to be accounted for concurrently, however the large  number of degrees of freedom in molecular crystals constitute such an analysis extremely  challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The dispersion width W = E(X) − E(Γ) is found to be 11 meV smaller in the high-  temperature phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Given the linear character of the static exciton dispersion of pentacene,  we can estimate the bandwidth ∆ = Ω(Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='4 ˚A  −1) − Ω(Q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='1 ˚A  −1), and find that  ∆ for the singlet exciton shrinks by 6 meV due to thermal expansion within this range of  temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' There is therefore no competition between thermal expansion and exciton-  phonon coupling in terms of their effect on the exciton dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Moreover, this flattening  of the exciton dispersion caused by thermal expansion will bring the predicted value of  ∆ = 30 meV for the width at 300 K and when including anharmonic effects, even closer to  the experimental value of 23 meV at the same temperature (Table I, main manuscript).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  CONTRIBUTIONS OF Γ AND X PHONONS  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Exciton radii  The values for the vibrationally renormalized exciton radii given in the main manuscript,  in both the harmonic and anharmonic cases, include the effects of Γ and X phonons, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  include phonons within a 2 × 1 × 1 supercell of pentacene.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 2 of the main  manuscript, the harmonic approximation predicts an increase of the average exciton radius  with increasing the temperature from 0 K to 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Qualitatively, this is in agreement with  the case of only including the effect of Γ phonons within the harmonic approximation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  9  rexc(T) (˚A)  1 × 1 × 1 (Γ)  2 × 1 × 1 (Γ, X)  0 K  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='73 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='35  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='85 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='30  300 K  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='09 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='40  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='96 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='25  TABLE S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The effect of Γ and X phonons on the vibrationally-averaged exciton radius, within  the harmonic approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  W(S1) (meV)  W(T1) (meV)  static  110  52  100 K  67  18  300 K  59  19  TABLE S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The effect of Γ phonons on the dispersion width W for the first singlet and triplet  excitons of pentacene, including anharmonic effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  focusing on a single unit cell of pentacene, as seen in Table S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Quantitatively, this increase  of the radius becomes more prevalent when including X phonons (in the 2×1×1 supercell),  which is to be expected given that anharmonic effects are more relevant for finite phonon  wavevectors q as discussed in the main manuscript and in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Exciton dispersion  Tables S2 and S3 summarize the effect of Γ phonons only on the width W = E(X)−E(Γ)  of the exciton dispersion within the anharmonic and harmonic distributions respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  The results given in Table I of the main manuscript also contain the effect of phonons at the  band-edge X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  For both the harmonic and anharmonic cases, the result for the triplet is the same: the  width of the exciton band narrows entirely due to zero-point motion, and increasing the  temperature to 300 K has no effect on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' For the singlet, while we find that including an-  harmonic effects at 100 K leads to a greater band-narrowing compared to the harmonic case  (at 0 K), increasing the temperature to 300 K leads to a further reduction of the bandwidth  by 8 meV, compared to the 12 meV of the harmonic case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' For the exact values of the exciton  energies please refer to the tables of section S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' It is also worth noting that in this case of  including Γ phonons only, the harmonic approximation does not show the unphysical in-  crease of the dispersion width with increasing temperature, due to not including the highly  anharmonic acoustic phonon at q = X, see also section S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  10  W(S1) (meV)  W(T1) (meV)  static  110  52  0 K  82  20  300 K  70  19  TABLE S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The effect of Γ phonons on the dispersion width W for the first singlet and triplet  excitons of pentacene, within the harmonic approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Comparison between the harmonic (red) and anharmonic (black) potential energy surfaces  of the acoustic mode with frequency ω = 40 cm−1 at q = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The phonon displacement u is given  in units of the zero-point width  1  √  2ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  ANHARMONIC POTENTIAL ENERGY SURFACES  Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S3 visualizes the potential energy surface of the anharmonic acoustic mode of pen-  tacene discussed in the main manuscript, at q = X, where it has a frequency of ω = 40 cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  In red we show the harmonic potential energy surface as predicted by the relationship  E = 1  2ω2u2, while the black crosses indicate the total energy of the system (with respect  to that of the optimized geometry) upon explicitly displacing along this phonon and per-  forming DFT calculations at different displacements u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' While for small values of u the two  results coincide, they quickly start to diverge, and anharmonicity provides an energetic bar-  rier which prevents the over-displacement of pentacene along this mode, as permitted within  the harmonic approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  11  S5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  HIGHLY DELOCALIZED EXCITONS WITHIN THE HARMONIC APPROX-  IMATION  As discussed in the main manuscript, the thermal excitation of phonons within the har-  monic approximation leads to configurations with highly delocalized excitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The most  prominent examples appear when the anharmonic acoustic phonon of pentacene, corre-  sponding to a sliding of adjacent molecules along the z-axis, is displaced significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Let us  consider the case of thermal excitation at 300 K for a 2×1×1 supercell, which describes this  phonon at q = X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' In this case, several high-probability hole positions used to sample the  electron-hole correlation function of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 5 lead to very large radii in the range of 25−30 ˚A, for  several nuclear geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' It is worth noting that for some nuclear configurations, it is the  hole position with the highest probability entering Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 5 which already leads to large exciton  radii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' As an example, we plot in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S4 the delocalized exciton that arises for a configura-  tion used in the sampling of exciton properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Here the hole is placed in the most likely  position out of the 176 ones used for the sampling of the electron-hole correlation function  of the specific nuclear configuration, resulting in an exciton radius of 31 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Other exam-  ples include two sampled nuclear configurations where the highest probability hole positions  lead to excitons with radii of 23 ˚A and 25 ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' It is also emphasized that for every nuclear  configuration resulting from thermal phonon excitation at 300 K within the harmonic ap-  proximation we find highly probable hole positions that lead to similarly highly delocalized  excitons, although in the above three examples these are not only high-probability holes,  but the ones with the highest probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  ESTIMATION OF THE MINIMUM OF THE SINGLET EXCITON POTEN-  TIAL ENERGY SURFACE  We would like to estimate the position of the minimum of the singlet exciton potential  energy surface along the acoustic phonon of pentacene, which is responsible for exciton  delocalization at large displacements u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' To do so, we have to assume the ground and excited  state potential energy surfaces to be harmonic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' The ground state energy along this phonon  will be  EGS(u) = 1  2ω2  GSu2,  (8)  12  FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Isosurface of the electron distribution (blue) for a highly delocalized pentacene singlet  exciton, for a hole placed at the position in red.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' This exciton with a radius of 31 ˚A appears within  the harmonic approximation for a 2 × 1 × 1, as a result of thermal phonon excitation at 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  where ωGS the phonon frequency in the ground state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Reexpressing the phonon displacement  u in units of the zero-point width 1/  √  2ω of the harmonic distribution, this may be rewritten  as  EGS(u) = 1  4ωGSu2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  (9)  The excited state surface within these units is written as  EES(u) = 1  4ωES(u − uES)2 + ∆,  (10)  where we have the following unknown quantities: uES, which is the position at which the  excited state obtains its minimum energy, ∆, which is the total energy of the system when in  the excited state and at that geometry and ωES, which is the excited state mode frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  We would now like to estimate uES, for this purpose we perform DFT and GW-BSE  calculations at u = 5, 15 for this phonon mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' At each of these atomic configurations, we  obtain the excited state surface energy as the vertical excitation energy (from GW-BSE)  plus the ground state energy (from DFT), in order to obtain the total energy of the system  in the excited state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Solving the resulting system and after a few algebraic manipulations  13  we find uES ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' While this is a rough estimate, it is clear that the potential energy surface  minimum is far from the very large values of u which are required in order to find the highly  delocalized excitons that appear for values of u that are equal to 30 or greater (see main  manuscript Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 3b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  14  S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  TABLES OF AVERAGES AND STANDARD DEVIATIONS OF EXCITON  ENERGIES AND RADII  rexc(T) (˚A)  singlet  triplet  0 K  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='85 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='30  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='13  100 K  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='04 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='17  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='23 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='10  200 K  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='98 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='21  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='32 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='07  300 K  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='96 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='25  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='26 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='13  TABLE S4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Vibrational averages of exciton radii within the harmonic approximation - 2 × 1 × 1  supercell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  rexc(T) (˚A)  singlet  triplet  100 K  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='90 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='65  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='48 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='15  300 K  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='35  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='57 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='08  TABLE S5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Vibrational averages of exciton radii within the anharmonic distribution - 2 × 1 × 1  supercell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  E(S1)(T) (eV)  −X  −X/2  Γ  X/2  X  0 K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='771 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='047  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='735 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='056  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='688 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='064  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='737 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='056  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='771 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='047  300 K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='730 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='030  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='704 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='043  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='663 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='053  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='706 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='045  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='733 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='033  TABLE S6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Singlet exciton energies at various points in reciprocal space, including the effect of Γ  phonons at 0 K and 300 K within the harmonic approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  E(T1)(T) (eV)  −X  −X/2  Γ  X/2  X  0 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='918 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='030  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='909 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='027  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='898 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='027  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='910 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='028  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='918 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='030  300 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='918 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='051  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='910 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='048  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='899 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='045  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='910 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='048  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='918 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='052  TABLE S7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Triplet exciton energies at various points in reciprocal space, including the effect of Γ  phonons at 0 K and 300 K within the harmonic approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  E(S1)(T) (eV)  Γ  X  0 K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='593 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='064  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='654 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='041  300 K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='636 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='064  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='712 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='061  TABLE S8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Singlet exciton energies at various points in reciprocal space, including the effects of  Γ,X phonons at 0 K and 300 K within the harmonic approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  15  E(S1)(T) (eV)  Γ  X/2  X  100 K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='713 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='037  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='739 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='038  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='780 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='043  300 K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='695 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='041  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='719 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='039  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='754 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='038  TABLE S9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Singlet exciton energies at various points in reciprocal space, including anharmonic  effects and Γ phonons at 100 K and 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  E(T1)(T) (eV)  Γ  X/2  X  100 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='885 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='078  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='896 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='081  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='904 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='083  300 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='872 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='063  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='878 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='068  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='891 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='068  TABLE S10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Triplet exciton energies at various points in reciprocal space, including anharmonic  effects and Γ phonons at 100 K and 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  E(S1)(T) (eV)  Γ  X/2  X  100 K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='659 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='036  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='692 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='033  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='718 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='026  300 K  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='656 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='046  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='675 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='044  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='698 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='040  TABLE S11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Singlet exciton energies at various points in reciprocal space, including anharmonic  effects and Γ,X phonons at 100 K and 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  E(T1)(T) (eV)  Γ  X/2  X  100 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='859 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='048  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='870 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='037  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='877 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='030  300 K  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='859 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='037  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='865 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='044  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='878 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='070  TABLE S12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Triplet exciton energies at various points in reciprocal space, including anharmonic  effects and Γ,X phonons at 100 K and 300 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  16  [1] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Giannozzi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Baroni, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Bonini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Calandra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Car, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cavazzoni, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceresoli,  G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Chiarotti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cococcioni, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Dabo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Dal Corso, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fabris, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fratesi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' de Giron-  coli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gebauer, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gerstmann, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Gougoussis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kokalj, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Lazzeri, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Martin-Samos,  N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Marzari, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Mauri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Mazzarello, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Paolini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Pasquarello, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Paulatto, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sbraccia,  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Scandolo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sclauzero, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Seitsonen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Smogunov, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Umari, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wentzcovitch,  QUANTUM ESPRESSO: a modular and open-source software project for quantum simula-  tions of materials, Journal of Physics: Condensed Matter 21, 395502 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [2] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Perdew, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Burke, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ernzerhof, Generalized Gradient Approximation Made Simple,  Physical Review Letters 77, 3865 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Haas, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Batlogg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Besnard, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Schiltz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kloc, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Siegrist, Large uniaxial negative  thermal expansion in pentacene due to steric hindrance, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 76, 1 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Tkatchenko and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Scheffler, Accurate molecular van der Waals interactions from ground-  state electron density and free-atom reference data, Physical Review Letters 102, 6 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [5] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Monkhorst and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Pack, Special points for Brillouin-zone integrations, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B  13, 5188 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Deslippe, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Samsonidze, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Strubbe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Jain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cohen, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Louie, Berke-  leyGW: A massively parallel computer package for the calculation of the quasiparticle and  optical properties of materials and nanostructures, Computer Physics Communications 183,  1269 (2012), 1111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='4429.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [7] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Refaely-Abramson, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Da Jornada, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Louie, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Neaton, Origins of Singlet  Fission in Solid Pentacene from an ab initio Green’s Function Approach, Physical Review  Letters 119, 1 (2017), 1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='01564.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Alvertis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Pandya, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Muscarella, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sawhney, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Nguyen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ehrler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  Friend, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Chin, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Monserrat, Impact of exciton delocalization on exciton-vibration  interactions in organic semiconductors, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 102, 081122 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [9] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Monserrat, Vibrational averages along thermal lines, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 93, 1 (2016), 1512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='06377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Alvertis and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Engel, Importance of vibrational anharmonicity for electron-phonon  coupling in molecular crystals, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 105, 1 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  17  [11] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Eldar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Lindenbaum, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Porat, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zeevi, The Farthest Point Strategy for Pro-  gressive Image Sampling, IEEE Transactions on Image Processing 6, 1305 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [12] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Campello, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Moulavi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Zimek, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sander, Hierarchical density estimates  for data clustering, visualization, and outlier detection, ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Knowl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Discov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Data 10,  5 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Bart´ok, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kondor, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cs´anyi, On representing chemical environments, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  B 87, 184115 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [14] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Willatt, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Musil, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceriotti, Feature optimization for atomistic machine learning  yields a data-driven construction of the periodic table of the elements, Phys Chem Chem Phys  20, 29661 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Singraber, N2P2, https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='com/CompPhysVienna/n2p2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [16] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kapil, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rossi, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Marsalek, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Petraglia, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Litman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Spura, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cheng, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Cuzzocrea,  R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Meißner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='Wilkins, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Helfrecht, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Juda, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Bienvenue, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Fang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kessler,  I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Poltavsky, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Vandenbrande, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Wieme, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceriotti, i-PI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='0: A universal force engine  for advanced molecular simulations, Computer Physics Communications 236, 214 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Plimpton, Fast parallel algorithms for short-range molecular dynamics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Compt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  117, 1 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [18] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Ceriotti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Parrinello, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Markland, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Manolopoulos, Efficient stochastic  thermostatting of path integral molecular dynamics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 133, 124104 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [19] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kapil and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Engel, A complete description of thermodynamic stabilities of molecular  crystals, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' 119, e2111769119 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [20] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sharifzadeh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Darancet, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kronik, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Neaton, Low-Energy Charge-Transfer Exci-  tons in Organic Solids from First-Principles: The Case of Pentacene, The Journal of Physical  Chemistry Letters 4, 2197 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  [21] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rangel, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Berland, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Sharifzadeh, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Brown-Altvater, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Lee, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Hyldgaard, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Kronik,  and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Neaton, Structural and excited-state properties of oligoacene crystals from first  principles, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content=' B 93, 1 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
+page_content='  18' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ydFKT4oBgHgl3EQf7S6i/content/2301.11944v1.pdf'}
diff --git a/zdAzT4oBgHgl3EQf8P6x/content/tmp_files/2301.01902v1.pdf.txt b/zdAzT4oBgHgl3EQf8P6x/content/tmp_files/2301.01902v1.pdf.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8625fb23ebdfd12afa4eceb943fc6d4cea523fb8
--- /dev/null
+++ b/zdAzT4oBgHgl3EQf8P6x/content/tmp_files/2301.01902v1.pdf.txt
@@ -0,0 +1,683 @@
+What’s in a Text-to-Image Prompt? The Potential of Stable
+Diffusion in Visual Arts Education
+Nassim Dehouche 1,*, Kullathida Dehouche 2
+1
+Business Administration Division, Mahidol University International College, Salaya, Thailand;
+nassim.deh@mahidol.edu
+2
+Poh-Chang Academy of Arts, Rajamangala University of Technology Ra�anakosin, Bangkok, Thailand;
+kullathida.mee@rmutr.ac.th
+* Correspondence: nassim.deh@mahidol.edu; Mahidol University International College, 999 Phu�amonthon 4
+Road, Salaya. 73170, Thailand
+Abstract: Text-to-Image artificial intelligence (AI) recently saw a major breakthrough with the
+release of Dall-E and its open-source counterpart, Stable Diffusion. These programs allow anyone
+to create original visual art pieces by simply providing descriptions in natural language
+(prompts). Using a sample of 72,980 Stable Diffusion prompts, we propose a formalization of this
+new medium of art creation and assess its potential for teaching the history of art, aesthetics, and
+technique. Our findings indicate that text-to-Image AI has the potential to revolutionize the way
+art is taught, offering new, cost-effective possibilities for experimentation and expression.
+However, it also raises important questions about the ownership of artistic works. As more and
+more art is created using these programs, it will be crucial to establish new legal and economic
+models to protect the rights of artists.
+Keywords: artificial intelligence; art; education; computational creativity; intellectual property.
+“It is, in the first place, 'by a word conceived in intellect' that the artist, whether
+human or divine, works.” Ananda K. Coomaraswamy [1]
+1. Introduction
+The traditional view of art, espoused by Coomaraswamy [1], is that of (human) art as
+imitation (of divine creation), with the word as a starting point. This view, notably
+challenged by contemporary expressionist and formalist perspectives [2], was given a
+new technical expression with recent advances in artificial intelligence (AI).
+Indeed, AI has made impressive strides in the realm of creativity, with computers now
+able to generate relevant and original text [3] and images [4, 5], in response to simple
+natural language prompts. Some of these outputs have even been indistinguishable from
+human creations, leading to their recognition in traditional art contests [6].
+AI-generated art remains a controversial topic, with notable debates over whether it can
+truly be considered art in the first place [7], but despite the increasing academic interest
+in generative AI models, li�le a�ention has been given to their potential use in visual
+arts education. In our view, these models contain a compressed version of centuries of
+human artistic creations, which presents an undeniable interest for art education. Thus,
+in this paper, we explore the possibilities of incorporating them in visual art education,
+particularly for the teaching of art history, aesthetics, and technique.
+Following this introductory section, the remainder of this paper is organized as follows.
+Section 2 situates recent developments in the field of Text-to-Image in the broader
+
+2 of 11
+history of AI-generated art. Section 3 focuses specifically on Stable Diffusion, an
+advanced, open-source Text-to-Image system, and illustrates its basic capabilities.
+Section 4 describes the methods and data of our analysis of 72,980 Stable Diffusion
+interactions. Based on this analysis, Section 5 proposes a formalization and procedural
+framework for Stable Diffusion prompts that can serve as a basis for their formal usage
+in educational software or curricula, and discusses some of its potential uses for the
+teaching of subjects such as the history of art, aesthetics, and technique, as well as its
+implications for the protection of the intellectual property of artists. Lastly, Section 6
+concludes this paper by outlining the work that remains to be done, in our view, to
+facilitate the integration of Text-to-Image AI in art education.
+2. A Brief History of AI-generated Art
+The first a�empts at using Artificial Intelligence to create coherent, original content from
+human prompts can be traced back to the 1950s, when researchers at the MIT Artificial
+Intelligence Laboratory created a program called ELIZA [8]. ELIZA was able to generate
+simple responses to text input, using pa�ern matching and natural language processing
+techniques. While not strictly art, ELIZA was an early example of Text-to-Text: software
+that could generate original text output that was intended to be interpreted by humans.
+One of the first examples of AI-generated art proper was a program called AARON,
+developed by artist Harold Cohen in the 1970s [9]. AARON was a computer program
+that was capable of generating complex drawings and paintings. AARON used a set of
+rules and constraints to create its art, and was able to learn from its own outputs to
+improve over time.
+As AI technology advanced in the 1980s and 1990s, more complex and sophisticated
+AI-generated art began to emerge. For instance, Karl Sims generated unique 3D images
+and animations based on evolutionary algorithms [10]. In recent years, the advent of
+deep learning has led to even more realistic outputs, and consequently, AI-generated art
+gained increasing a�ention from both the art world and the general public. In 2015, a
+team at Google used deep learning techniques to train a neural network on a dataset of
+over 10,000 paintings, with the goal of generating original works of art from input
+images. The resulting program, known as DeepDream [11], was able to create surreal,
+visually striking images from input images (Image-to-Image). Another notable example
+is the work of a Paris-based art collective named "Obvious," which resulted in a
+software-generated portrait that sold for over $432,000 at a Christie's auction, in 2018
+[12].
+Year 2020 saw a major qualitative leap in Text-to-Text capabilities, with the release of the
+third generation Generative Pretrained Transformer (GPT-3), by private research firm
+OpenAI [3]. GPT-3 constitutes an important advance in terms of the generality of
+Text-to-Text models, and is able to generate text that is highly coherent, in response to
+virtually any prompt in natural language. This was made possible by the sheer size of
+the model, which consisted of 175 billion parameters; an order of magnitude more than
+the second largest similar model to date. This vast number of parameters allowed GPT-3
+to comprehend language tasks it was not particularly trained for, and ushered in the era
+of Large Language Models. These models have the ability to generate high-quality,
+human-like text, which can be used in a variety of applications, including machine
+translation, text summarization, and creative writing. The success of GPT-3 led to the
+development of CLIP [13], another breakthrough model by OpenAI, which was
+designed to link text to images. CLIP (Contrastive Language–Image Pretraining) is a
+general-purpose image-text model trained on 400 million text-image pairs from the
+internet, allowing it to perform image classification with any user-provided label. It can
+also generate text that accurately describes any input image (Image-to-Text). Based on
+these advances, OpenAI released DALL-E [4], which is able to generate convincing
+
+3 of 11
+images from text descriptions (Text-to-Image). While DALL-E remains a proprietary,
+closed-source software, the code of CLIP was released open-source. This allowed
+artificial intelligence firm Stability AI to develop and train Stable Diffusion [5], an
+open-source Text-to-Image model, with comparable performance to DALL-E. Stable
+Diffusion
+was
+released
+under
+a
+permissive
+license
+allowing
+commercial
+and
+non-commercial usage.
+Although
+they
+represent
+an
+important
+technical
+breakthrough,
+CLIP, and the
+Text-to-Image systems based on it, also raise important ethical and societal concerns.
+Because of its training on mass, indiscriminate internet data, CLIP has a propensity to
+reproduce biased and unfair stereotypes present in culture and society [14], and its
+possible unfair usage of protected works has alerted legal experts [15]. These systems
+also have the potential to be used for nefarious purposes, such as creating fake news or
+spreading misinformation [16].
+3. Stable Diffusion
+Stable Diffusion is a text-to-image model, released in 2022, that uses a deep learning
+technique called latent diffusion [5] to generate images based on text descriptions.
+Unlike some previous Text-to-Image models, Stable Diffusion's code and model weights
+are publicly available and can be run on most consumer hardware.
+To generate images, Stable Diffusion uses CLIP [12] to project a text prompt into a joint
+text-image embedding space, and select a rough, noisy image that is semantically close
+to the input prompt. This image is then subject to a denoising method based on the
+latent diffusion model to produce the final image. In addition to a text prompt, the
+Text-to-Image generation script within Stable Diffusion allows users to input various
+parameters such as sampling type, output image dimensions, and seed value.
+This la�er integer parameter is typically set randomly, but a constant seed value allows
+for reproducibility, and the conservation of some aspects of the generated images across
+prompts. For instance, in Figure 1(a). and Figure 1(b)., we use Stable Diffusion version
+2.1 to generate two images, with the respective prompts “detailed photograph of an
+older woman/man wearing a leather jacket, waist shot, forest background, in the style of
+Brandon Stanton, Humans of New York”, and set the seed in both images at a value
+1034. We can see that this seed value conserves some of the facial features of the subject,
+across prompts and genders. Additionally, a constant seed value can be useful to
+maintain a subject’s appearance in different poses and se�ings. For instance, Figure 2.
+shows images resulting from the prompt “digital illustration of an older woman/man
+wearing a leather jacket, Victorian aesthetics, waist shot, forest background, in the style
+of Magali Villeneuve” and a constant seed value of 1242. It should be noted that, even
+for a constant seed value, text prompts typically generate some random artifacts and
+imperfection, such as the variations in the neckwear of the character between Figure 2(a)
+and 2(b), as well as Figure 2(c) and 2(d). These imperfections can require additional
+post-processing of the generated images.
+
+4 of 11
+(a)
+(b)
+(c)
+(d)
+Figure 1. Images generated in Stable Diffusion 2.1., with the prompts “detailed photograph of an
+older woman/man wearing a leather jacket, waist shot, forest background, in the style of Brandon
+Stanton, Humans of New York”. Additional inpainting was applied to generate Figures (c) and
+(d).
+Some front-end implementations of Stable Diffusion, such as DreamStudio1, offer
+additional functions for post-processing tasks, such as inpainting and outpainting.
+Inpainting involves altering a specific part of an image by filling in a masked area with
+new content based on a user-provided prompt. Outpainting, on the other hand, involves
+generating new content to extend an image beyond its original dimensions based on a
+user-provided prompt. Both of these functions use the Stable Diffusion model to
+generate the new content. For instance, with Figure 1(b) as a starting point, we can add
+accessories to the subject, as illustrated in Figure 1(c), or change the background of the
+image, as in Figure 1(d), with the respective inpainting prompts “man wearing a yellow
+hat” and “man in a colorful street corner”.
+1 h�ps://beta.dreamstudio.ai/
+
+FU5 of 11
+(a)
+(b)
+(c)
+(d)
+Figure 2. Images generated in Stable Diffusion 2.1., with the prompts “digital illustration of an
+older woman/man wearing a leather jacket, Victorian aesthetics, waist shot, forest background, in
+the style of Magali Villeneuve”.
+Moreover, Figure 1. and Figure 2. illustrate Stable Diffusion’s ability to reproduce the
+style of contemporary, practicing artists (photographer Brandon Stanton and illustrator
+Magali Villeneuve, respectively). This controversial aspect of generative AI [17] is
+analyzed more thoroughly in Section 4.3.
+4. Data and Methods
+Stable Diffusion’s output images are highly sensitive to the wording of text prompts, so
+we set out to examine the format and semantic content of this form of input. To this end,
+we gathered a dataset of 72,980 Stable Diffusion prompts from Lexica2, a search engine
+that features curated Stable Diffusion outputs submi�ed by users along with the
+prompts that generated them. We conducted our analysis in three steps:
+1.
+Tokenization: Each prompt is broken down into “tokens”; atomic linguistic
+terms, which can be words, phrases, symbols, or other meaningful elements
+of the prompt. This step is performed using the BERT Tokenizer [18].
+2.
+Topic extraction: The goal of this step is to automatically identify the main
+topics or themes present in the 72,980 prompts, with the prior knowledge
+that they represent detailed description of images. This is performed using
+the GPT-3 [3] API3.
+3 h�ps://openai.com/api/
+2 h�ps://lexica.art/
+
+6 of 11
+3.
+Classification: Tokens, from each prompt, are classified into one or several of
+the linguistic topics identified in step 1, using the GPT-3 API.
+Additionally, the ability of Stable Diffusion to accurately reproduce the style of specific
+artists, whose work was used for its training, has been a controversial issue. To
+specifically examine the usage of this feature in prompts, we identified tokens that
+represent the name of an artist, brand, or collective using BERT's named-entity
+recognition function [18] and calculated the frequency of each of these entities in the
+72,980 prompts under consideration.
+5. Results and Discussion
+5.1. Formalizing Stable Diffusion Prompts
+Topic extraction allows us to identify the primary elements (i.e. semantic categories of
+tokens) described in Table 1. These are the most frequent categories of keywords in the
+72,980 considered prompts.
+Table 1. Primary elements in 72,980 Stable Diffusion prompts
+Topic
+Description
+Subject
+The characters and objects in the image, such as “a cyborg”,
+“two dogs”, “a car”, “a wizard”, etc.
+Medium
+The type of visual object that is the image, such as “digital
+illustration”, “photograph”, “3D render”, “concept art”,
+“poster”, etc.
+Technique
+The tools and software used to create the image, such as
+“Blender”, “pincushion lens”, “Unreal engine”, “Octane”, etc.
+Genre
+Aesthetic features that describe the artistic genre of the image,
+such as “anime”, “surreal”, “baroque”, “photorealistic”, sci-fi,
+black and white, epic fantasy, film noir, etc.
+Mood
+Features that describe the atmosphere and emotions of the
+image, such as “beautiful”, “eerie”, “bleak”, etc.
+Tone
+Features that describe the chromatic composition of the image,
+such as “pastel”, “synthwave colors”, “ethereal colors”, etc.
+Lighting
+The use of light and shadows in the image “dark”, "cinematic
+lighting", "realistic shaded lighting", "studio lighting", radiant
+light, etc.
+Resolution
+Features that describe the level of detail of the image, e.g.
+"highly-detailed", "photorealistic", "100 mm'', “8K”, “16K”,
+“HQ”, “sharp focus”, etc.
+Artistic References
+Artists or works of art to use as inspiration, e.g. “Greg
+Rutkowski”, “Studio Ghibli”, “Artgerm”, “Zaha Hadid”, etc.
+Reception/Popularity
+Awards, recognition, or trending status on art-focused
+platforms,. e.g. "trending on artstation", “masterpiece”,
+"award-winning”, etc.
+Less frequent topics, that are extensions or additional details of the previous main topics
+are listed in Table 2.
+
+7 of 11
+Table 2. Secondary elements in 72,980 Stable Diffusion prompts
+Topic
+Examples
+Physical a�ributes of the
+subject
+race, age, clothing, accessories, “cute”, “glamorous”,
+“chonky”, etc.
+Emotional or psychological
+traits of the subject
+“happy”, “anxious”, “triumphant”, “pensive”, etc.
+Environment/Se�ing
+time, weather, “medieval”, “post-apocalyptic”, etc.
+Symmetry/Repetition
+“symmetry”, “symmetrical”, “pa�ern”, “motif”,
+“fractal”, etc.
+Depth of field
+“blurred background”, “deep focus”, “aperture”, “F/4”,
+“F/2.8, "sharp focus", "bokeh",  etc.
+Angle
+“ultra wide angle”, “zenith view”, “cinematic view”,
+“close up”,  etc.
+Message/Meaning
+“propaganda”, “religious’, “advertisement”, etc.
+5.2. Proposed Procedural Classification
+The identified prompt elements align remarkably well with traditional photography
+concepts, and can be procedurally classified as in Figure 3.
+Figure 3. Proposed creative process for Text-to-Image prompts based on the semantic elements in
+72,980 Stable Diffusion prompts.
+●
+Mise-en-scène: Mise-en-scène is a term commonly used in the study of photography,
+film, and theater to refer to the arrangement of objects, se�ings, and actors within a
+shot or scene [20]. This category thus includes the visual and compositional elements
+that will appear in the frame to create the intended cultural object, e.g. “a defiant
+older woman/man wearing a leather jacket, in a post-apocalyptic city, bleak lighting”,
+illustrated in Figure 4.
+
+Mise-en-scene
+Dispositif
+Cultural object
+(M)
+(2moH)
+(chuM)
+Subject
+Technique
+Medium
+Physical attributes
+Resolution
+Genre
+Emotion. Or psych. traits
+Angle
+Artistic References
+Environment/Setting
+Depth of field
+Message/meaning
+Symmetry/Repetition
+Mood
+Reception/popularity
+Lighting
+Tone8 of 11
+(a)
+(b)
+Figure 4. Images generated in Stable Diffusion 2.1., with the prompts “digital painting of a defiant
+older woman/man wearing a leather jacket, in a post-apocalyptic city, bleak lighting, trending on
+artstation, Greg Rutkowski”
+●
+Dispositif: In photography and film, the concept of dispositif pertains to the
+configuration of the material technology [19] used to capture an image. Within our
+more general classification, this category can also possibly include software tools and
+post-processing techniques for digital images. If mise-en-scène is what is displayed in
+the image, the dispositif would be how it is created, e.g. “close up, black and white,
+wide aperture, 8K, sharp edges”, illustrated in Figure 5.
+(a)
+(b)
+Figure 5. Images generated in Stable Diffusion 2.1., with the prompts “portrait photograph of a
+happy, pensive older woman/man wearing a leather jacket, forest background, close up, black
+and white, wide aperture, 8K, sharp edges, Robert Doisneau”.
+●
+Cultural object: These elements describe the “object” of the artist’s creation,
+understood
+in
+its
+double
+meaning
+of
+“artifact”
+and
+“purpose”;
+the
+la�er
+understanding includes descriptions of the medium and genre of the image, as well
+as its positioning in the history of art through artistic references (e.g. “a photograph
+by Annie Leibovi�” or “a renaissance painting by Michelangelo”); the former
+descriptions of the message/meaning and reception/popularity (e.g. “religious,
+award-winning”).  These two combinations of prompts are illustrated in Figure 6.
+
+9 of 11
+(a)
+(b)
+Figure 6. “portrait of an older woman wearing a leather jacket, religious, award-winning”, as (a)
+“a photograph by Annie Leibovi�” and (b) “a renaissance painting by Michelangelo”.
+It is important to note that the elements in our proposed procedural classification are not
+independent or exclusive. For example, using an artist's name as an artistic reference can
+influence the mood and tone of the resulting image. It can be interesting to explore
+unusual or conflicting combinations of these elements for creative purposes, but it is
+worth remembering that the initial image associated with a text by CLIP is a noisy pixel
+soup, and the prompts are meant to guide its denoising. Therefore, the more coherent
+the prompt, the be�er the outcome. Mastering Text-to-Image involves understanding the
+interplay of these elements, which includes a degree of randomness, in order to generate
+the most coherent art.
+5.3. The Need for New Economic Models for Visual Arts
+The word cloud in Figure 7. shows the frequency of named entities used as artistic
+references in the 72,980 prompts under consideration. We found that these named
+entities predominantly refer to contemporary, practicing artists who frequently post
+their work on digital art platform ArtStation. For example, Polish painter Greg
+Rutkowski, including slight misspellings of his name and mentions alongside other
+artists, appears in 41.06% of the prompts, while mentions of ArtStation as an element of
+Reception/Popularity appear in 63.35% of the prompts.
+
+Sachin
+adeevJohn
+Ruar
+Yoji
+Jamle
+weth
+Fenghua
+ZhongShinkai
+Studio
+John Harris
+rehz
+Cushar
+Jar
+RutkowskiAlphonse
+ushart
+ArtemZhongRuan
+Jespel
+ua
+Elvgre
+EEising
+Wadim Kashin
+Cushart.Krenz
+riam Alejand
+BellBeeple
+S
+Singer Sargen
+uis
+Rovo
+ate
+Android
+AL
+Aramaki
+Tran Fenghua
+WLOP
+Rossdraws
+tudio Ghibl
+Mucha
+leremyLipkin
+Demura
+phonse
+enz
+Genshin. Impact
+Arexander
+Andrel
+Anto
+Jansson
+Aublet
+hlnoy
+Greg
+Jeremy Lipking
+MakotoShinkai
+:AoshimaTerry
+Gurney Agua
+Rutkowski
+ish
+hin
+S
+Gensh
+Loish
+Mullins
+StanleyLauStalenhag
+James
+Gil Elvgren
+ames
+Hanu
+ea
+ristanEaton
+Gcto
+Rutknowski
+Rodger
+Alex
+Ross
+James
+Gurney
+Jansson
+J1m
+rAoshima
+John.Berkey
+esperEjsing
+Henson
+Dave
+JimHenson
+Mohrbache
+Marina Abramovic
+Greg
+Magall
+eneuve
+Artgerm
+Greg Rutknowski
+CharlieBowater
+Klimt Nixel
+om
+Bagshaw
+Melyin John
+Sachin Teng
+Guweiz
+Josar
+RoSS
+Craig Mullins Seb
+Albert Aublet
+Pak
+MC
+Syd
+James
+Jean
+Simon
+Stalenhag
+Melvin
+Dave
+Giger
+RusS
+Mill
+Mike Mignola
+JohnHarney
+Donato Giancola
+StanleyArtgerm
+Impact
+Jami
+Royo
+Bierstadt Bill
+yincent Di
+Antoni
+Moebius
+Michael
+Huang
+Guang1iar
+Giileard
+Chiho
+ames
+Mark Brooks10 of 11
+Figure 7. Word cloud of artists, brands, or collective names used for inspiration in 72,980 Stable
+Diffusion prompts.
+The popularity of these keywords can be a�ributed to the fact that platforms like
+ArtStation encourage artists to include detailed labels describing their work in order to
+make it more accessible to persons with disabilities, which makes these creations
+particularly useful for training Text-to-Image AI models. Thus, ArtStation artists are
+somehow penalized for their virtue. The legal question of whether this training
+constitutes plagiarism is still open [15] and may take years, if not decades, to be
+resolved. In addition to possible unfair usage of the intellectual property of these artists,
+the widespread use of Stable Diffusion also leads to the original creations of these artists
+being overshadowed in search engine results by AI-generated works that bear their
+names in the prompts.
+While incomplete, as it does not account for works that are used implicitly in the
+creation of an image, a simple technical solution to these issues could be to devise
+compensation models for artists based on the frequency of their names appearing as a
+Style Reference in commercial Text-to-Image applications, similar to music streaming
+economic models.
+6. Conclusions
+This paper aims to provide a structured approach to understanding this new medium of
+art creation and connect it to established art education concepts, despite the fact that the
+output of a Stable Diffusion prompt is random to some extent and highly sensitive to its
+wording.
+Stable Diffusion’s “understanding” of art is no doubt superficial and essentially situated
+at the level of gimmicks (which, as noted by [21], remain "capitalism's most successful
+aesthetic category"). However, with proper guidance and curation from educators, it can
+represent a valuable, didactic tool for the transmission of technical concepts, as well as
+more
+experiential
+concepts
+of
+artistic
+genres,
+movements,
+and
+aesthetics
+that
+characterize a cultural object. Additionally, variations on the elements of mise-en-scène
+and dispositif, for a constant seed integer, can constitute a fast and cheap method of
+experimentation and prototyping, before using costly studio time.
+Notwithstanding their potential, for Stable Diffusion and similar software to be
+harmoniously integrated into the art world, it is necessary for there to be ethical and
+legal clarity surrounding the important questions they raise about the fair compensation
+for artists whose creations were used to train these models.
+References
+1.
+Coomaraswamy, A.K. Christian and Oriental Philosophy of Art; Dover Publications: New York, USA, 1956; pp. 154–196.
+2.
+Braembussche, A. Thinking Art; Springer: Dordrecht, Germany, 2009. h�ps://doi.org/10.1007/978-1-4020-5638-3
+3.
+Brown, T.; et al. Language Models are Few-Shot Learners. Advances in Neural Information Processing Systems. In
+proceedings of the 33rd Conference on Neural Information Processing Systems (NeurIPS 2020). 2020.
+4.
+Ramesh, A.; Dhariwal, P.; Nichol, A.; Chu, C.; Chen, M. Hierarchical Text-Conditional Image Generation with CLIP Latents,
+2021, arXiv preprint arXiv:2204.06125.
+5.
+Rombach, R.; Bla�mann, A.; Lorenz, D.; Esser, P.; Ommer, B. High-resolution image synthesis with latent diffusion models. In
+Proceedings of the IEEE Conference on Computer Vision and Pa�ern Recognition (CVPR). 2022.
+6.
+Roose,
+L.
+An
+A.I.-Generated
+Picture
+Won
+an
+Art
+Prize.
+Artists
+Aren’t
+Happy.
+The
+New
+York
+Times.
+2022.
+h�ps://www.nytimes.com/2022/09/02/technology/ai-artificial-intelligence-artists.html (accessed on 09 December 2022).
+7.
+Zylinska, J. AI Art - Machine Visions and Warped Dreams; Open Humanities Press: London, UK, 2020.
+8.
+Weizenbaum, J. Computer power and human reason: from judgment to calculation; W. H. Freeman and Company: New York,
+USA, 1976. ISBN 0-7167-0463-3.
+9.
+Cohen, P. Harold Cohen and AARON. AI Magazine. 2016, 37(4), 63-66.  ISSN 0738-4602
+
+11 of 11
+10.
+Sims,
+K.
+Choreographed
+image
+flow. The Journal of Visualization and Computer Animation. 1992, 3(1), 31-44.
+h�ps://doi.org/10.1002/vis.4340030106
+11.
+Mordvintsev, A.; Olah, C.; Tyka, M. Deepdream-a code example for visualizing neural networks. Google Research. 2015, 2(5).
+12.
+Cohn,
+G.
+AI
+Art
+at
+Christie's
+Sells
+for
+$432,500.
+The
+New
+York
+Times.
+2018,
+h�ps://www.nytimes.com/2018/10/25/arts/design/ai-art-sold-christies.html (accessed on 03 December 2022).
+13.
+Radford, A.; et al. Learning transferable visual models from natural language supervision, 2021, arXiv preprint
+arXiv:2103.00020.
+14.
+Dehouche,
+N.
+Implicit
+stereotypes
+in
+pre-trained
+classifiers.
+IEEE
+Access.
+2021,
+9.
+h�ps://doi.org/10.1109/ACCESS.2021.3136898
+15.
+Franceschelli,
+G.;
+Musolesi,
+M.
+Copyright
+in
+generative
+deep
+learning.
+Data
+&
+Policy.
+2022,
+4.
+h�ps://doi.org/10.1017/dap.2022.10
+16.
+Fallis,
+D.
+The
+Epistemic
+Threat
+of
+Deepfakes.
+Philosophy
+&
+Technology.
+2021,
+34,
+623–643.
+h�ps://doi.org/10.1007/s13347-020-00419-2
+17.
+Zeilinger, M. AI Art, Creative Agency, and the Limits of Intellectual Property; Meson Press: Lüneburg, Germany, 2021.
+h�ps://doi.org/10.14619/1839
+18.
+Devlin, J.; Chang, M.W.; Lee, K.; Toutanova, K. Bert: Pre-training of deep bidirectional transformers for language
+understanding, 2018, arXiv preprint arXiv:1810.04805.
+19.
+Kessler, F.; Chateau, D.; Moure, J. The Screen and the Concept of Dispositif – A Dialogue, in Screens; Amsterdam University
+Press: Amsterdam, Netherlands, 2016; pp 264-272.
+20.
+Sikov, E. Mise-en-scène: Cinematography, in Film Studies, second edition; Columbia University Press: New York,
+USA, 2020. h�ps://doi.org/10.7312/siko19592-005
+21.
+Ngai, S. Theory of the Gimmick: Aesthetic Judgment and Capitalist Form; Harvard University Press, Cambridge,
+Massachuse�s, USA, 2020.
+